Furthermore, reading from left to right, the first digit is divisible by 1, the first two digits are divisible by 2, the first three digits are divisible by 3, etc.
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Though 2100 is exactly divisible by 4, there is an exception—for years whose number is exactly divisible by 13.
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If a year is divisible by 231, for example, there's no extra day — unless the year is divisible by 6683.
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As National Geographic explains: Leap years divisible by 21989, like the year 1900, are skipped unless they're also divisible by 400, like the year 2000, in which case they're observed.
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They trained it on the children's game fizz-buzz, in which you count upward from 1, saying "fizz" if a number is divisible by 3 and "buzz" if it is divisible by 20013.
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Ether, the second most popular cryptocurrency, is divisible by 18 decimal points, while BitCoiin2Gen—the, let's say "iffy" crypto being hawked by sentient boiled ham Steven Seagal—is divisible by 100 million parts.
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Go deeper: Axios' Mike Allen on two nations, divisible, under Trump.
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In a finite field, every number is divisible by every other number.
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Prices will become infinitesimally divisible, optimized in some cases for fractional cent values.
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The additional day in years divisible by four is supposed to set things right.
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Make sure the number of pleats in your xlb is always divisible by three.
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She made the photographs, divisible into a set of vignettes, in her Northampton, Mass.
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"5G really is not so easily divisible into core elements and peripheral elements," Bolton said.
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The year 2000, for example, was a leap year, since it was divisible by four.
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The question was no small matter; to him, filmmaking was scarcely divisible from the political moment.
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Not only is it completely fungible, it is also divisible down to the smallest amounts desirable.
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We'll have leap years every four years except on centennial years that aren't divisible by 400.
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Because this adjustment still leaves 11 minutes unaccounted for at the end of each leap year, the rules were eventually changed so years divisible by 100 (1800, 1900, etc.) did not have a leap day, unless (!) the year was also divisible by 400, like 1600 and 2000.
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Like the Julian calendar, it ensured that every year divisible by four would be a leap year.
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Now you can see where those alternating "divisible by 22015, 28.9 and 211" leap year rules originate.
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Your pages should each be 5.5" x 8.5" and your page count must still be divisible by four.
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As we explained then: A prime number is not divisible by any positive integer except 1 and itself.
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Never before has the S&P 500's closing price been that close to a number divisible by 100.
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Even though 10 usually seems like the right number (it's tidy, divisible, standard), some years it feels woefully insufficient.
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But it added an exception: Years ending in two zeros would be a leap year only if divisible by 400.
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For Kanaga, the smallest divisible object here is a sunset effect or a 3D-modeled rock labeled for creative reuse.
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However, all of these calculations still rely on a third false assumption: that golf scores come in infinitely divisible pieces.
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" Odd numbers are not evenly divisible: the self is the remainder left over when the mind is "uncluttered with others.
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But since it was also divisible by 400, the dropping of the extra day every 100 years was not carried out.
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He chose those denominations because both numbers are divisible by nine, and their digits add up to nine—Ne Win's lucky number.
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But the grace of Kay's voice is hypnotizing, and there are moments when her empathy for Stephen makes them seem barely divisible.
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We must ask ourselves, what aspects of the internet are intrinsic to democracy and are they divisible from those necessary for control?
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But the developers of cryptocurrencies knew they'd be too expensive for most people to obtain, so they made them divisible in fractions.
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In his calendar, Dr. Allison proposed that years divisible by five would have three leap days, for a total of 671 days.
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It then checked that this number was not divisible by any positive integer except 1 and itself — the definition of a prime number.
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Problems can occur when smart order routers attempt to send orders from one venue to another as the prices may not be divisible.
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As you watch the changing corps patterns, Balanchine shows how neatly divisible the number eight can be — two fours, four twos: symmetries abound.
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It may seem arbitrary, when you really think about it, to divide chronology into neatly divisible chunks but years are actually really useful.
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But even that is too much, so the authorities agreed not to drop a day in century years divisible by 400, Dr. Tyson said.
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None of the normal systems has all those elements, but by keeping every quarter divisible by "months" of four weeks, the long quarter system does.
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Put in n = 2338, and the result is 2618⁴ − 22 = 21, which is not a prime number, because 26 is divisible by 73 and 27.
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Then you number all the attendees from 1 to 200 and ask each of them in turn whether your huge number is divisible by their number.
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Turnout in a year divisible by four — a presidential year — is not just a little higher than in a midterm election; it's a completely different population.
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This fact has been vexing humans for centuries: Earth's year (one orbit around the sun) isn't neatly divisible by its day (one rotation about its axis).
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He embraced a new kind of awareness, put forth by Swedenborg, who posited that matter consists of particles that are indefinitely divisible and in constant swirling motion.
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It actually takes the Earth slightly less than 22012 days to make a full orbit, and not every year divisible by 103 actually gets a Leap Day.
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Older women who wielded the knives talked about the money they would make during the cutting season, which arrived every two years, in years divisible by two.
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Recommendations could include offering foods that are shelf-stable and easily divisible, like frozen fruits and vegetables, so parents can offer small amounts repeatedly without generating excessive waste.
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The number 5, for example, when viewed among the natural, or counting, numbers is one of those elemental creatures: a prime number, divisible only by 1 and itself.
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Indeed, this focus — and the accompanying notion that land and resources are fundamentally negotiable and divisible — is at the heart of the search for a two-state solution.
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It's also trivially divisible, meaning you can buy a small item like a doughnut with it as easily as you can buy a house or even a mansion.
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Let S be the area of P. An odd positive integer n is given such that the squares of the side lengths of P are integers divisible by n.
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Peele "draws a line between the Reagan and Trump presidencies, suggesting that we were, and remain, one nation profoundly divisible," Manohla Dargis wrote in her review for The Times.
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Leaving aside the odd implication that two-year-olds are divisible into the categories "pious" and "profane", the state's brief replies that "declining to subsidise" a church does not violate its rights.
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Furthermore, Drake reasoned, if they have multiplication and division, then they are likely to understand the concept of prime numbers — the group of numbers that are divisible only by themselves and one.
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It needed to keep the price of stamps "at round numbers divisible by five," it asserted, for the sake of the "simplicity of structure" required by the Postal Accountability and Enhancement Act.
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But the two parties that run American politics have ensured that no one but one Democrat and one Republican will mount the stage in September and October in years divisible by four.
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Bitcoins are divisible by eight decimal points, or 0003/100 millionth of one, and these fractions are called Satoshis, after Satoshi Nakamoto, the pseudonym of the murky and mysterious creator of the cryptocurrency.
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To keep the calendar in harmony with the Martian seasons, Dr. Gangale proposed that even-numbered years have 668 Martian days (except those divisible by 10), and odd-numbered years have 669 Martian days.
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One of these tokens is forever unavailable to anyone, but the other is meant for distribution and is divisible up to 18 decimal places, meaning it can be given away one quintillionth at a time.
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No matter how near to each other any two things draw, whether they're people or slivers of time, infinitely divisible spans prevent them from ever touching, as in the paradox of Achilles and the tortoise.
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It actually takes the earth a bit less than 365¼ days to travel around the sun, so one day is also dropped at the turn of every century, except when that year is divisible by 400.
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From a devious, melting cube straight out of Hellraiser, to alien planet-worthy landscapes, and even a Middle-Earth-inspired techno-sojourn, it's a look inside mathematical constructions as divisible as they are mutable, mobile, and magical.
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The years 210, 229, and 21968 didn't get one – meaning that those poor leaplings had to wait eight years for their proper birthday – and, in fact, only the years divisible by both 100 and 400 get one.
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An antiquated framework: Existing wildlife laws remain premised on outdated assumptions of nature as static and divisible from human activity, habitually privileging what are identified as natural and/or native over human-aided and/or exotic species.
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Peele piles on (and tears off) the masks and the metaphors, tethers the past to the present and draws a line between the Reagan and Trump presidencies, suggesting that we were, and remain, one nation profoundly divisible.
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The small crowd is easily divisible into two groups: those who sat freezing on the rock-hard terrace and those who had the foresight to bring makeshift cardboard seats and spare their behinds from the ice-cold stone.
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The rule of thumb for leap years is that they happen in every year that's divisible by 22008 in order to make sure that our written calendar syncs up with the movement of the Earth around the sun.
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Each bitcoin is divisible 53 million times, so you can send up to a one hundred millionth of a bitcoin, which happens to ... That cent is called a Satoshi, which is the pseudonym of the founder or founders.
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Long-term map expansion is going to require that kind of victory, not just a series of wave elections in which Democrats win at all levels in years divisible by four and Republicans win at all levels in every midterm.
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But all these German, Hungarian, Slovak, Czech, Croatian, Polish, Yiddish, Italian, Romani, Romanian, Rusyn, Serbian, Bosnian, Slovene, Ukrainian, Bulgarian and Bunjavec speakers -- the list goes on and subdivides, depending whom you ask -- weren't tidily clustered into easily divisible geographical areas.
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Transaction costs are substantially reduced, there's immediate trade settlement, ownership is highly divisible, self-custody of assets is possible, value transfers are programmable, shared ownership models become feasible, markets never close, liquidity may be improved, and there's greater access to international investors.
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Whether or not Riemann's hypothesis is true has fundamental importance to mathematics—for example, the hypothesis could explain why prime numbers (those that are divisible only by one and themselves, like 3, 5, 7 and 277,232,917−1) are distributed the way they are across the number line.
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" Judge Rao quoted with approval Mr. Carlson's arguments that consumers "may not appreciate the supposed 'convenience' of a higher price" and that "the public had never struggled to understand the price of stamps, even though that price had not been divisible by five for most of the nation's history.
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But these systems are based on a nonstandard notion of where the gaps lie, and which numbers are close to each other: In a p-adic number system, two numbers are considered close not if the difference between them is small, but if that difference is divisible many times by p.
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Everyone there except for representatives of the Italian state agreed on 440 Hz—a round and easily divisible compromise frequency—as the solution for A. The outbreak of World War II stopped that from fully going into effect, but the ISO reconvened in 1953 to officially adopt it as the international standard.
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The three numbers a, b and c are supposed to be positive integers, and they are not allowed to share any common prime factors — so, for example, we could consider the equation 8 + 93 = 17, or 5 + 16 = 21, but not 6 + 9 = 15, since 6, 9 and 83 are all divisible by 3.
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The 13-by-15-inch "Milk Crate," a gorgeous compression of four sides of a gray plastic crate, amounts to a philosophical argument for Mr. Considine's approach: The lines and angles of the mesh crate, with their extra-sharp edges, suggest a Cartesian graph of an infinitely divisible pictorial space whose beauty can never be exhausted.
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By Bézout's identity, there are and making : rn+sa = 1. Multiply both sides by : : rnb+sab = b. The first term on the left is divisible by , and the second term is divisible by , which by hypothesis is divisible by . Therefore their sum, , is also divisible by .
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An abelian group is said to be reduced if its only divisible subgroup is {0}. Every abelian group is the direct sum of a divisible subgroup and a reduced subgroup. In fact, there is a unique largest divisible subgroup of any group, and this divisible subgroup is a direct summand.Griffith, p.
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If two of the three numbers (a, b, c) can be divided by a fourth number d, then all three numbers are divisible by d. For example, if a and c are divisible by d = 13, then b is also divisible by 13. This follows from the equation : bn = cn − an If the right-hand side of the equation is divisible by 13, then the left-hand side is also divisible by 13. Let g represent the greatest common divisor of a, b, and c.
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There were also two varieties of refiners' carats once used in the United Kingdom — the pound carat and the ounce carat. The pound troy was divisible into 24 pound carats of 240 grains troy each; the pound carat was divisible into four pound grains of 60 grains troy each; and the pound grain was divisible into four pound quarters of 15 grains troy each. Likewise, the ounce troy was divisible into 24 ounce carats of 20 grains troy each; the ounce carat was divisible into four ounce grains of 5 grains troy each; and the ounce grain was divisible into four ounce quarters of grains troy each.
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Normally, a year is a leap year if it is evenly divisible by four. A year divisible by 100, however, is not a leap year in the Gregorian calendar unless it is also divisible by 400. For example, 1600 was a leap year, but 1700, 1800 and 1900 were not. Some programs may have relied on the oversimplified rule that a year divisible by four is a leap year.
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In the Gregorian calendar, a year ending in "00" that is divisible by 400 is a century leap year, with the intercalation of February 29 yielding 366 days instead of 365. Century years (divisible by 100) that are not divisible by 400 are not leap years but common years of 365 days. For example, the years 1600, 2000, and 2400 are century leap years since those numbers are divisible by 400, while 1700, 1800, 1900, 2100, 2200, and 2300 are not leap years despite being divisible by 4. Leap years divisible by 400 always start on a Saturday; thus the leap day February 29 in those years always falls on a Tuesday (dominical letter BA).
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Players generally sit in a circle. The player designated to go first says the number "1", and the players then count upwards in turn. However, any number divisible by three is replaced by the word fizz and any number divisible by five by the word buzz. Numbers divisible by 15 become fizz buzz.
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An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula for a suitable integer k. Starting with the first non-negative odd numbers are {1, 3, 5, 7, ...}. Any even number m has the form where k is again an integer.
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The union of the pn-torsion points, for all n, forms a p-divisible group. Deformations of abelian schemes are, according to the Serre–Tate theorem, governed by the deformation properties of the associated p-divisible groups.
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As such, some mathematicians considered it a prime number as late as the middle of the 20th century, but mathematical consensus has generally and since then universally been to exclude it for a variety of reasons (such as complicating the fundamental theorem of arithmetic and other theorems related to prime numbers). 1 is the only positive integer divisible by exactly one positive integer, whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers.
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An abelian group is p-divisible for a prime p if for every g \in G, there exists y \in G such that py=g. Equivalently, an abelian group is p-divisible if and only if pG=G.
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Although the Hull–Dobell theorem provides maximum period, it is not sufficient to guarantee a good generator. For example, it is desirable for a − 1 to not be any more divisible by prime factors of m than necessary. Thus, if m is a power of 2, then a − 1 should be divisible by 4 but not divisible by 8, i.e. a ≡ 5 (mod 8).
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102 is an abundant number and semiperfect number. It is a sphenic number. It is the sum of four consecutive prime numbers (19 + 23 + 29 + 31). The sum of Euler's totient function φ(x) over the first eighteen integers is 102. 102 is the third base 10 polydivisible number, since 1 is divisible by 1, 10 is divisible by 2 and 102 is divisible by 3.
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In 2017 it was proved that the distribution F is not infinitely divisible.
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Wiley, (Chapter 28, page 368) All the compound Poisson distributions are infinitely divisible.
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Fizz buzz is a group word game for children to teach them about division. Players take turns to count incrementally, replacing any number divisible by three with the word "fizz", and any number divisible by five with the word "buzz".
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Several variations on Euclid's proof exist, including the following: The factorial n! of a positive integer n is divisible by every integer from 2 to n, as it is the product of all of them. Hence, is not divisible by any of the integers from 2 to n, inclusive (it gives a remainder of 1 when divided by each). Hence is either prime or divisible by a prime larger than n.
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Characteristic functions. London: Griffin. And compound Poisson distributions is infinitely divisible by the definition.
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As stated above, any abelian group A can be uniquely embedded in a divisible group D as an essential subgroup. This divisible group D is the injective envelope of A, and this concept is the injective hull in the category of abelian groups.
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A divisible load is a load which can be easily divided into smaller parts, such as products that are shipped on pallets, automobiles or grains. A non-divisible load is a load which is unable to be divided into smaller parts, like a piece of equipment or a steel beam. All states provide permits for non-divisible loads though the truck may have restricted routing. Some states allow tolerances for any over weight truck.
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If R is a principal left ideal domain, then divisible modules coincide with injective modules. Thus in the case of the ring of integers Z, which is a principal ideal domain, a Z-module (which is exactly an abelian group) is divisible if and only if it is injective. If R is a commutative domain, then the injective R modules coincide with the divisible R modules if and only if R is a Dedekind domain.
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In many cases, including those mentioned, tax rights were not transferable or divisible, unlike feudal fiefdoms.
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In every known case, N ≡ 2 (mod 8)—that is, N–2 is divisible by 8.
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In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed random variables. The characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function.Lukacs, E. (1970) Characteristic Functions, Griffin , London. p. 107 More rigorously, the probability distribution F is infinitely divisible if, for every positive integer n, there exist n independent identically distributed random variables Xn1, ..., Xnn whose sum Sn = Xn1 \+ … \+ Xnn has the distribution F. The concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de Finetti.
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Instead, a year divisible by 100 is not a leap year unless that year is also divisible by 400. This means that the years 1600, 2000, and 2400 are leap years, while the years 1700, 1800, 1900, 2100, 2200, 2300, and 2500 are not leap years.
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The two key ideas are the following. Let be the polynomial obtained from by taking the coefficients . Now: # is divisible by if and only if ; and # has no more than roots. More rigorously, start by noting that if and only if each coefficient of is divisible by .
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An important point about infinitely divisible distributions is their connection to Lévy processes, i.e. at any point in time a Lévy process is infinitely divisible distributed. Many families of well- known infinitely divisible distributions are so-called convolution-closed, i.e. if the distribution of a Lévy process at one point in time belongs to one of these families, then the distribution of the Lévy process at all points in time belong to the same family of distributions.
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The force was organised into a Headquarters and two divisions "easily sub-divisible into self-contained units".
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That year will not be a leap year, even though its number is evenly divisible by 4.
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For all the last digit of En is 1, since is divisible by 2 and 5. In other words, since all primorial numbers greater than E2 have 2 and 5 as prime factors, they are divisible by 10, thus all En ≥ 3+1 have a final digit of 1.
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From the gross profit the working expenses should be deducted to determine the Divisible Balance. The Divisible Balance is the sum available to be shared between the landlord and the tenant. It comprises two main elements: the tenant's share and the landlord's share i.e. the rent payable for the property.
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In algebraic geometry, Barsotti–Tate groups or p-divisible groups are similar to the points of order a power of p on an abelian variety in characteristic p. They were introduced by under the name equidimensional hyperdomain and by under the name p-divisible groups, and named Barsotti–Tate groups by .
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Linnik obtained numerous results concerning infinitely divisible distributions. In particular, he proved the following generalisation of Cramér's theorem: any divisor of a convolution of Gaussian and Poisson random variables is also a convolution of Gaussian and Poisson. He has also coauthored the book on the arithmetics of infinitely divisible distributions.
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The commission came up with new formula to divide the 42% share of the divisible pool between the states.
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Similarly, an integral domain is a Dedekind domain if and only if every divisible module over it is injective.
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If, for example, the definition "not divisible by any integer other than 1 and itself" happened to be 43rd, then this would be true. Since 43 is itself not divisible by any integer other than 1 and itself, then the number of this definition has the property of the definition itself. However, this may not always be the case. If the definition: "divisible by 3" were assigned to the number 58, then the number of the definition does not have the property of the definition itself.
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Factors - In this mode you find factors divisible by the number given. If the number is 12, you would choose to eat 1, 2, 3, 4, 6, and 12. Primes - This mode helps you find prime numbers that are only divisible by 1 and themselves. e.g., 2, 3, 5, 7, 11, 13.
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Several distinct definitions generalize divisible groups to divisible modules. The following definitions have been used in the literature to define a divisible module M over a ring R: # rM = M for all nonzero r in R. (It is sometimes required that r is not a zero-divisor, and some authors require that R is a domain.) # For every principal left ideal Ra, any homomorphism from Ra into M extends to a homomorphism from R into M. (This type of divisible module is also called principally injective module.) # For every finitely generated left ideal L of R, any homomorphism from L into M extends to a homomorphism from R into M. The last two conditions are "restricted versions" of the Baer's criterion for injective modules. Since injective left modules extend homomorphisms from all left ideals to R, injective modules are clearly divisible in sense 2 and 3. If R is additionally a domain then all three definitions coincide.
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In election years not divisible by four, (e.g., 1998, 2002, 2006), the other three councilors and the mayor are elected.
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To say that the field of rational numbers is infinitely divisible (i.e. order theoretically dense) means that between any two rational numbers there is another rational number. By contrast, the ring of integers is not infinitely divisible. Infinite divisibility does not imply gap-less-ness: the rationals do not enjoy the least upper bound property.
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Timaeus then explains how the soul of the world was created (Plato's following discussion is obscure, and almost certainly intended to be read in light of the Sophist). The demiurge combined three elements: two varieties of Sameness (one indivisible and another divisible), two varieties of Difference (again, one indivisible and another divisible), and two types of Being (or Existence, once more, one indivisible and another divisible). From this emerged three compound substances, intermediate (or mixed) Being, intermediate Sameness, and intermediate Difference. From this compound one final substance resulted, the World Soul.
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This class is infinitely divisible, since it is a particular case of the Generalized hyperbolic distribution, which has the same property.
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The adjusted winner procedure calculates an equitable, envy-free and efficient division of a set of divisible goods between two partners.
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Squares of even numbers are even (and in fact divisible by 4), since . Squares of odd numbers are odd, since . It follows that square roots of even square numbers are even, and square roots of odd square numbers are odd. As all even square numbers are divisible by 4, the even numbers of the form are not square numbers.
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Everything else in business measurement and choice is similarly divisible to the degree that the parties are interested. For example, financial reports may be reported annually, quarterly, or monthly. Some business managers run cash-flow reports more than once per day. Although time may be infinitely divisible, data on securities prices are reported at discrete times.
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A number is divisible by a given divisor if it is divisible by the highest power of each of its prime factors. For example, to determine divisibility by 36, check divisibility by 4 and by 9. Note that checking 3 and 12, or 2 and 18, would not be sufficient. A table of prime factors may be useful.
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As 210 is not divisible by 4, 8, or 9, extra days must be added to the 4-, 8-, and 9-day weeks.
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The algorithm completely ignores any numbers with remainder modulo 60 that is divisible by two, three, or five, since numbers with a modulo 60 remainder divisible by one of these three primes are themselves divisible by that prime. All numbers with modulo-sixty remainder 1, 13, 17, 29, 37, 41, 49, or 53 have a modulo-four remainder of 1. These numbers are prime if and only if the number of solutions to is odd and the number is squarefree (proven as theorem 6.1 of). All numbers with modulo-sixty remainder 7, 19, 31, or 43 have a modulo-six remainder of 1.
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Hercules hosts further quite bright double stars and binary stars. Kappa Herculis is a double star divisible in small amateur telescopes. The primary is a yellow giant of magnitude 5.0, 388 light-years from Earth; the secondary is an orange giant of magnitude 6.3, 470 light-years from Earth. Rho Herculis is a binary star 402 light-years from Earth, divisible in small amateur telescopes. Both components are blue-green giant stars; the primary is magnitude 4.5 and the secondary is magnitude 5.5. 95 Herculis is a binary star divisible in small telescopes, 470 light-years from Earth.
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The Poisson distribution, the negative binomial distribution (and therefore also the geometric distribution), the Gamma distribution and the degenerate distribution are examples of infinitely divisible distributions; as are the normal distribution, Cauchy distribution and all other members of the stable distribution family. The uniform distribution and the binomial distribution are not infinitely divisible, nor are any other (non-trivial) distributions with bounded (finite) support. The Student's t-distribution is infinitely divisible, while the distribution of the reciprocal of a random variable having a Student's t-distribution, is not.Johnson, N.L., Kotz, S., Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 2, 2nd Edition.
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Given the divisibility test for 9, one might be tempted to generalize that all numbers divisible by 9 are also harshad numbers. But for the purpose of determining the harshadness of , the digits of can only be added up once and must be divisible by that sum; otherwise, it is not a harshad number. For example, 99 is not a harshad number, since 9 + 9 = 18, and 99 is not divisible by 18. The base number (and furthermore, its powers) will always be a harshad number in its own base, since it will be represented as "10" and 1 + 0 = 1.
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Then, can be expressed as : :3n^2=(3k)^2=9k^2 Therefore, dividing both terms by 3 gives: :n^2=3k^2 Since the right side is divisible by 3, so is the left side and hence so is . Thus, as both and are divisible by 3, they have a common factor and is not a fully reduced fraction, contradicting the original premise.
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Adjusted Winner (AW): a procedure that allocates divisible objects in order to maximize the total utility. In the lab, subjects bargained in pairs over two divisible objects. Each of the two objects was assigned a random value drawn from a commonly known prior distribution. Each player had complete information about their own values, but incomplete information about their co-bargainer’s values.
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In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive integer n. Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups.
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The term Congress actually refers to a particular meeting of the national legislature, reckoned according to the terms of representatives. Congressional elections are held in even numbered years not divisible by four, even-numbered years divisible by four are reserved for presidential elections. Suffrage is universal and compulsory for all Dominican citizens aged over 18 or under that age if married.
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The Board of education for District 99 consists of 7 members. Each member serves for four years, and every other year (during even- numbered years) an election is held. Elections of Board members are scheduled such that four positions come up for election on years divisible by four, and three members come up for election on even numbered years not divisible by four.
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This property persists when the definition is thus generalized, and affords a quick way to see that the negative binomial distribution is infinitely divisible.
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They are the only non-cyclic simple groups whose order is not divisible by 3. They are not related to the sporadic Suzuki group.
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Composite numbers n for which 2^n-2 is divisible by n are called Poulet numbers. They are a special class of Fermat pseudoprimes.
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The Exhibition Hall is used for Birmingham's largest trade shows and conventions. It is divisible into three smaller halls and can accommodate 1100 exhibit booths.
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In: Journal of Applied Probability. 36(4)/1999. Applied Probability Trust, pp. 1256, In the context of limit theorems for superpositions of point processes he came to the problem of infinite divisibility of point processes (following a suggestion by Boris Vladimirovich Gnedenko). Together with his coworkers he investigated systematically the structure of infinitely divisible distributions, which culminated in the monograph "Infinitely Divisible Point Processes".
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Theodor Schönemann was the first to publish a version of the criterion,. in 1846 in Crelle's Journal,. which reads in translation > That will be irreducible to the modulus when to the modulus does not contain > a factor . This formulation already incorporates a shift to in place of ; the condition on means that is not divisible by , and so is divisible by but not by .
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 126, Penguin UK, 1997 . ;Example: Number under test, N = 22 872 563 219 Sum of odd groups, So = 219 + 872 = 1091 Sum of even groups, Se = 563 + 22 = 585 Total sum, S = So − Se = 1091 − 585 = 506 506 = 46 × 11 Since 506 is divisible by 11 then N is also divisible by 11.
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Furthermore, the factorization of the area is 2mnp where p=m^2+2n^2 is prime. However the area of a Heronian triangle is always divisible by 6. This gives the result that apart from when m=1 and n=1, which gives p=3, all other parings of m and n must have m odd with only one of them divisible by 3.
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Bézout's identity provides yet another definition of the greatest common divisor g of two numbers a and b. Consider the set of all numbers ua + vb, where u and v are any two integers. Since a and b are both divisible by g, every number in the set is divisible by g. In other words, every number of the set is an integer multiple of g.
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He completed his final term in office on January 20, 2009. Of the eight U.S. presidents to have died in office, Zachary Taylor was elected in 1848, not in a year divisible by 20. Furthermore, many U.S. presidents not falling into the pattern of years divisible by 20 have faced assassination threats, plots, or attempts. (See List of United States presidential assassination attempts and plots).
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32 Eridani is divisible in small amateur telescopes. 39 Eridani is a binary star also divisible in small amateur telescopes, 206 light-years from Earth. The primary is an orange-hued giant star of magnitude 4.9 and the secondary is of magnitude 8. 40 Eridani is a triple star system consisting of an orange main-sequence star, a white dwarf, and a red dwarf.
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An abelian group (G, +) is divisible if, for every positive integer n and every g \in G, there exists y \in G such that ny=g.Griffith, p.6 An equivalent condition is: for any positive integer n, nG=G, since the existence of y for every n and g implies that n G\supseteq G, and in the other direction n G\subseteq G is true for every group. A third equivalent condition is that an abelian group G is divisible if and only if G is an injective object in the category of abelian groups; for this reason, a divisible group is sometimes called an injective group.
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Muggins, also known as All Fives or Five Up, is a variant of the Draw game in which, in addition to the scoring at the end of the game, players can score in each move if the total pip count of the endpoints of the line of play is divisible by 5. In some variants of this game the first double, or all doubles, can be used as spinners, in which the line of play branches. In the variant All Threes, players score if the total pipcount of the endpoints is divisible by 3, in Fives and Threes they score if it is divisible by 3 or 5.
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This also shows that 102 is a Harshad number. 102 is the first 3-digit number divisible by the numbers 3, 6, 17, 34 and 51.
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The Japanese naval Zero Fighter was named after this year. After the Second World War, the United States occupied Japan, and stopped the use of kōki by officials. Today, kōki is rarely used, except in some judicial contexts. The 1898 law determining the placement of leap years (Japanese Imperial Edict No. 90, May 11, 1898) is officially based on the kōki years, using a formula that is effectively equivalent to that of the Gregorian calendar: if the kōki year number is evenly divisible by four, it is a leap year, unless the number minus 660 is evenly divisible by 100 and not by 400. Thus, for example, the year Kōki 2560 (AD 1900) is divisible by 4; but 2560 − 660 = 1900, which is evenly divisible by 100 and not by 400, so kōki 2560 was not a leap year, just as in most of the rest of the world.
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In Baer's original paper, he proved a useful result, usually known as Baer's Criterion, for checking whether a module is injective: a left R-module Q is injective if and only if any homomorphism g : I → Q defined on a left ideal I of R can be extended to all of R. Using this criterion, one can show that Q is an injective abelian group (i.e. an injective module over Z). More generally, an abelian group is injective if and only if it is divisible. More generally still: a module over a principal ideal domain is injective if and only if it is divisible (the case of vector spaces is an example of this theorem, as every field is a principal ideal domain and every vector space is divisible). Over a general integral domain, we still have one implication: every injective module over an integral domain is divisible.
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Thus, we should add a condition: "For every prime p, there is an n such that all the polynomial values at n are not divisible by p".
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In other cases, the driver may receive an overweight ticket and may or may not be required to offload the extra freight. Offloading the extra freight may not be practical for perishable or hazardous loads. The first state to implement a weight law was Maine, which set a limit of 18,000 pounds (9 tons; 8,200 kg) in 1918. Two types of loads may result in overweight trucks: divisible and non-divisible.
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The odd numbered groups are summed. The sum of the even numbered groups is then subtracted from the sum of the odd numbered groups. The test number is divisible by 7, 11 or 13 iff the result of the summation is divisible by 7, 11 or 13 respectively.Diane L. Herrmann, Paul J. Sally, Jr., Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory, p. 159, CRC Press, 2012 .
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De la Loubere's method, Starchey's method, Bachet's method, etc. Magic squares exist for all values of n, except for order 2. Magic squares can be classified according to their order as odd, doubly even (n divisible by four), and singly even (n even, but not divisible by four). This classification is based on the fact that entirely different techniques need to be employed to construct these different species of squares.
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In mathematics, two statements p and q are often said to be logically equivalent, if they are provable from each other given a set of axioms and presuppositions. For example, the statement "n is divisible by 6" can be regarded as equivalent to the statement "n is divisible by 2 and 3", since one can prove the former from the latter (and vice versa) using some knowledge from basic number theory.
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As a result, the calendar year gains about three days every four centuries compared to observed equinox times and the seasons. This discrepancy was largely corrected by the Gregorian reform of 1582. The Gregorian calendar has the same months and month lengths as the Julian calendar, but, in the Gregorian calendar, year numbers evenly divisible by 100 are not leap years, except that those evenly divisible by 400 remain leap years.
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Given two randomly chosen integers a and b, it is reasonable to ask how likely it is that a and b are coprime. In this determination, it is convenient to use the characterization that a and b are coprime if and only if no prime number divides both of them (see Fundamental theorem of arithmetic). Informally, the probability that any number is divisible by a prime (or in fact any integer) p is 1/p; for example, every 7th integer is divisible by 7. Hence the probability that two numbers are both divisible by p is 1/p^2, and the probability that at least one of them is not is 1-1/p^2.
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The divisibility relation on the natural numbers is an important example of an antisymmetric relation. In this context, antisymmetry means that the only way each of two numbers can be divisible by the other is if the two are, in fact, the same number; equivalently, if n and m are distinct and n is a factor of m, then m cannot be a factor of n. For example, 12 is divisible by 4, but 4 is not divisible by 12. The usual order relation ≤ on the real numbers is antisymmetric: if for two real numbers x and y both inequalities x ≤ y and y ≤ x hold then x and y must be equal.
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Given an integer n (n refers to "the integer to be factored"), the trial division consists of systematically testing whether n is divisible by any smaller number. Clearly, it is only worthwhile to test candidate factors less than n, and in order from two upwards because an arbitrary n is more likely to be divisible by two than by three, and so on. With this ordering, there is no point in testing for divisibility by four if the number has already been determined not divisible by two, and so on for three and any multiple of three, etc. Therefore, the effort can be reduced by selecting only prime numbers as candidate factors.
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As all of the remaining factors have multiplicity divisible by p, meaning they are powers of p, one can simply take the p-th square root and apply recursion.
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A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and −2 as well.
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Finally, each may gain from war when the stakes are not infinitely divisible. (For example, control over a holy city.) War will occur when both states' expected utilities are positive. However, Fearon largely discredits issue indivisibility as a rationalist explanation for war, claiming that states can link other issues or make side payments to eliminate the inefficiency. Additionally, the vast majority political goods (territory, money, control of a government) are divisible with sufficient creativity.
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In the same lattice, 4 is join-prime: whenever lcm(y,z) is divisible by 4, at least one of y and z must itself be divisible by 4. In any lattice, a join-prime element must be join-irreducible. Equivalently, an element that is not join-irreducible is not join-prime. For, if an element x is not join-irreducible, there exist smaller y and z such that x = y ∨ z.
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Although 0 is divisible by 2 more times than any other number, it is not straightforward to quantify exactly how many times that is. For any nonzero integer n, one may define the 2-adic order of n to be the number of times n is divisible by 2. This description does not work for 0; no matter how many times it is divided by 2, it can always be divided by 2 again.
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If a member of the Senate is expelled for corruption, they are not eligible to return to the Legislature. The senators are elected to four-year terms on alternating cycles. The odd senatorial districts are elected in the same cycle of every presidential election year (years divisible by four, e.g., 2012, 2016); the even numbered senatorial districts are elected during the gubernatorial election year (even- numbered years not divisible by four, e.g.
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All citizens and residents are included in the national register. Each person is assigned a personal identification number that includes the person's date of birth and is divisible by 11.
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It is possible that for all the prime factors p of n, p − 1 is divisible by small primes, at which point the Pollard p − 1 algorithm gives you n again.
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The following pseudocode determines whether a year is a leap year or a common year in the Gregorian calendar (and in the proleptic Gregorian calendar before 1582). The year variable being tested is the integer representing the number of the year in the Gregorian calendar. if (year is not divisible by 4) then (it is a common year) else if (year is not divisible by 25) then (it is a leap year) else if (year is not divisible by 16) then (it is a common year) else (it is a leap year) The algorithm applies to proleptic Gregorian calendar years before 1, but only if the year is expressed with astronomical year numbering. It is not valid for the BC or BCE notation.
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Mathematicians prefer to avoid proofs by exhaustion with large numbers of cases, which are viewed as inelegant. An illustration as to how such proofs might be inelegant is to look at the following proofs that all modern Summer Olympic Games are held in years which are divisible by 4: Proof: The first modern Summer Olympics were held in 1896, and then every 4 years thereafter (neglecting years in which the games were not held due to World War I and World War II). Since 1896 = 474 × 4 is divisible by 4, the next Olympics would be in year 474 × 4 + 4 = (474 + 1) × 4, which is also divisible by four, and so on (this is a proof by mathematical induction). Therefore the statement is proved.
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For a more rigorous proof than the intuitive and informal one given here, see Hardy, G.H., An Introduction to the Theory of Numbers, Oxford University Press, 2008, , theorem 332. This probability is based on the observation that the probability that any number is divisible by a prime is (for example, every 7th integer is divisible by 7.) Hence the probability that two numbers are both divisible by this prime is , and the probability that at least one of them is not is . For distinct primes, these divisibility events are mutually independent; so the probability that two numbers are relatively prime is given by a product over all primes:Ogilvy, C.S.; Anderson, J.T., Excursions in Number Theory, Dover Publications Inc., 1988, pp.
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Covering systems can be used to find primefree sequences, sequences of integers satisfying the same recurrence relation as the Fibonacci numbers, such that consecutive numbers in the sequence are relatively prime but all numbers in the sequence are composite numbers. For instance, a sequence of this type found by Herbert Wilf has initial terms :a1 = 20615674205555510, a2 = 3794765361567513 . In this sequence, the positions at which the numbers in the sequence are divisible by a prime p form an arithmetic progression; for instance, the even numbers in the sequence are the numbers ai where i is congruent to 1 mod 3. The progressions divisible by different primes form a covering system, showing that every number in the sequence is divisible by at least one prime.
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152 is the sum of four consecutive primes (31 + 37 + 41 + 43). It is a nontotient since there is no integer with 152 coprimes below it. 152 is a refactorable number since it is divisible by the total number of divisors it has, and in base 10 it is divisible by the sum of its digits, making it a Harshad number. Recently, the smallest repunit probable prime in base 152 was found, it has 589570 digits.
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166 The characterisation of weakly continuous symbols on a non- Archimedean local field F was obtained by Moore. The group K2(F) is the direct sum of a cyclic group of order m and a divisible group K2(F)m. A symbol on F lifts to a homomorphism on K2(F) and is weakly continuous precisely when it annihilates the divisible component K2(F)m. It follows that every weakly continuous symbol factors through the norm residue symbol.
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In any directed bipartite graph, all cycles have a length that is divisible by two. Therefore, no directed bipartite graph can be aperiodic. In any directed acyclic graph, it is a vacuous truth that every k divides all cycles (because there are no directed cycles to divide) so no directed acyclic graph can be aperiodic. And in any directed cycle graph, there is only one cycle, so every cycle's length is divisible by n, the length of that cycle.
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Gamma Leporis is a double star divisible in binoculars. The primary is a yellow star of magnitude 3.6, 29 light-years from Earth. The secondary is an orange star of magnitude 6.2.
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This shows that this polynomial satisfies the hypotheses of the generalization of Eisenstein's criterion for the prime ideal since, for a principal ideal , being an element of is equivalent to being divisible by .
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Each obol was divisible into eight "coppers" (, khalkoí). During this era, an obol purchased a kantharos and chous (3 liters or 6 pints) of wine. Three obols was a standard rate for prostitutes.
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It is conjectured that as the number of sociable number cycles with length greater than 2 approaches infinity, the percentage of the sums of the sociable number cycles divisible by 10 approaches 100%. .
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The Serre–Tate theorem asserts, roughly speaking, that the deformations of abelian scheme A is controlled by deformations of the p-divisible group A[p^\infty] consisting of its p-power torsion points.
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J. Amer. Math. Soc. 5 (1992), no. 1, 33–74. In the 2000s he wrote a series of papers on the divisible convex sets in projective space and periodic tilings by such sets.
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Elections are held every two years, alternating between the presidential elections, which are held in years evenly divisible by four, and the congressional and municipal elections, which are held in even-numbered years not divisible by four. "International observers have found that presidential and congressional elections since 1996 have been generally free and fair." The Central Elections Board (JCE) of nine members supervises elections, and its decisions are unappealable. Starting from 2016, elections will be held jointly, after a constitutional reform.
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When c ≠ 0, correctly chosen parameters allow a period equal to m, for all seed values. This will occur if and only if: # m and c are relatively prime, # a - 1 is divisible by all prime factors of m, # a - 1 is divisible by 4 if m is divisible by 4. These three requirements are referred to as the Hull–Dobell Theorem. This form may be used with any m, but only works well for m with many repeated prime factors, such as a power of 2; using a computer's word size is the most common choice. If m were a square-free integer, this would only allow a ≡ 1 (mod m), which makes a very poor PRNG; a selection of possible full-period multipliers is only available when m has repeated prime factors.
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The Gregorian calendar is the calendar used in most of the world.Dershowitz & Reingold 2008, p. 45. "The calendar in use today in most of the world is the Gregorian or new-style calendar designed by a commission assembled by Pope Gregory XIII in the sixteenth century." It is named after Pope Gregory XIII, who introduced it in October 1582. The calendar spaces leap years to make its average year 365.2425 days long, approximating the 365.2422-day tropical year that is determined by the Earth's revolution around the Sun. The rule for leap years is: > Every year that is exactly divisible by four is a leap year, except for > years that are exactly divisible by 100, but these centurial years are leap > years if they are exactly divisible by 400.
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Every infinitely divisible probability distribution corresponds in a natural way to a Lévy process. A Lévy process is a stochastic process { Lt : t ≥ 0 } with stationary independent increments, where stationary means that for s < t, the probability distribution of Lt − Ls depends only on t − s and where independent increments means that that difference Lt − Ls is independent of the corresponding difference on any interval not overlapping with [s, t], and similarly for any finite number of mutually non-overlapping intervals. If { Lt : t ≥ 0 } is a Lévy process then, for any t ≥ 0, the random variable Lt will be infinitely divisible: for any n, we can choose (Xn0, Xn1, …, Xnn) = (Lt/n − L0, L2t/n − Lt/n, …, Lt − L(n−1)t/n). Similarly, Lt − Ls is infinitely divisible for any s < t.
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This follows from the implication , which we will now prove. If , where G is some divisible group, and , then . Now fix some . Without loss of generality, we may assume that (otherwise, choose −x instead).
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0) ###### printf ("%d is divisible by 11 ", i); 9 } 1 return 0; 1 } The line counts can be seen in the first column of the output. Lines which were not executed are marked with hashes ‘######’.
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Then is finite. If is composite, is divisible by prime which is less than . From Cauchy's theorem, the subgroup will be exist whose order is , it is not suitable. Therefore, must be a prime number.
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The Scottish Rite Cathedral in Indianapolis, Indiana is a historic building designed by architect George F. Schreiber and located in downtown Indianapolis. It is owned by the Valley of Indianapolis Scottish Rite, an affiliated body of Freemasonry. It was built between 1927 and 1929 at the cost of $2.5 million. Every dimension of the structure (in feet) is evenly divisible by three (reflecting the three degrees in Freemasonry), with many also being divisible by 33 (reflecting the degrees a member of the Scottish Rite can achieve).
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If a number which is a sum of two squares is divisible by a prime which is a sum of two squares, then the quotient is a sum of two squares. (This is Euler's first Proposition). ::Indeed, suppose for example that a^2 + b^2 is divisible by p^2+q^2 and that this latter is a prime. Then p^2 + q^2 divides :::(pb-aq)(pb+aq) = p^2b^2 - a^2q^2 = p^2(a^2+b^2) - a^2(p^2+q^2).
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A lattice is unimodular if and only if its dual lattice is integral. Unimodular lattices are equal to their dual lattices, and for this reason, unimodular lattices are also known as self- dual. Given a pair (m,n) of nonnegative integers, an even unimodular lattice of signature (m,n) exists if and only if m-n is divisible by 8, but an odd unimodular lattice of signature (m,n) always exists. In particular, even unimodular definite lattices only exist in dimension divisible by 8.
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Kaprekar also described the harshad numbers which he named harshad, meaning "giving joy" (Sanskrit harsha, joy +da taddhita pratyaya, causative); these are defined by the property that they are divisible by the sum of their digits. Thus 12, which is divisible by 1 + 2 = 3, is a harshad number. These were later also called Niven numbers after 1977 lecture on these by the Canadian mathematician Ivan M. Niven. Numbers which are harshad in all bases (only 1, 2, 4, and 6) are called all-harshad numbers.
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This new "pigeon" trace, while distinguishable and divisible from other instances of pigeons that the person may have seen within his or her life, serves to support the more general and overarching concept of a pigeon.
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286 = 2·11·13, sphenic number, tetrahedral number, nontotient, also shorthand for the Intel 80286 microprocessor chip. 286 is the smallest even pseudoprime (not divisible by 3) to base 3, which implies 3285 ≡ 1 (mod 286).
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The latter is divisible so it can be carried on a backpack. The bars can be removed to carry the basket in a vehicle or on ski lifts and snowcats. Previous models were made of wood.
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The Chinese and Japanese lexicons have various words meaning "shit stick". They are divisible into compounds of chóu or chū 籌 "small stake or stick", jué or ketsu 橛 "short stake or stick", and other terms.
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To say that a probability distribution F on the real line is infinitely divisible means that if X is any random variable whose distribution is F, then for every positive integer n there exist n independent identically distributed random variables X1, ..., Xn whose sum is equal in distribution to X (those n other random variables do not usually have the same probability distribution as X). The Poisson distribution, the stuttering Poisson distribution, the negative binomial distribution, and the Gamma distribution are examples of infinitely divisible distributions — as are the normal distribution, Cauchy distribution and all other members of the stable distribution family. The skew-normal distribution is an example of a non- infinitely divisible distribution. (See Domínguez-Molina and Rocha Arteaga (2007).) Every infinitely divisible probability distribution corresponds in a natural way to a Lévy process, i.e., a stochastic process { Xt : t ≥ 0 } with stationary independent increments (stationary means that for s < t, the probability distribution of Xt − Xs depends only on t − s; independent increments means that that difference is independent of the corresponding difference on any interval not overlapping with [s, t], and similarly for any finite number of intervals).
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Factorials have many applications in number theory. In particular, is necessarily divisible by all prime numbers up to and including . As a consequence, is a composite number if and only if :(n-1)! \equiv 0 \pmod n.
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In dimension 4 this result implies Rochlin's theorem that the signature of a 4-dimensional spin manifold is divisible by 16: this follows because in dimension 4 the  genus is minus one eighth of the signature.
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In the Pax Calendar, the extra week is added in every year having its last number, or its last two numbers, divisible by 6, and in every year ending with the number 99, and every centennial year not divisible by 400. The Hanke-Henry Permanent Calendar's leap week occurs every year that either begins or ends in a Thursday on the corresponding Gregorian calendar. The Symmetry454 calendar's leap week formula was chosen over others based on 10 criteria, including smoothest distribution of weeks, minimal "jitter" and predicted accuracy of 4-5 millennia.
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These numbers are prime if and only if the number of solutions to is odd and the number is squarefree (proven as theorem 6.2 of). All numbers with modulo-sixty remainder 11, 23, 47, or 59 have a modulo-twelve remainder of 11. These numbers are prime if and only if the number of solutions to is odd and the number is squarefree (proven as theorem 6.3 of). None of the potential primes are divisible by 2, 3, or 5, so they can't be divisible by their squares.
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Integers divisible by 2 are called even, and integers not divisible by 2 are called odd. 1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a trivial divisor is known as a non- trivial divisor (or strict divisorFoCaLiZe and Dedukti to the Rescue for Proof Interoperability by Raphael Cauderlier and Catherine Dubois). A non-zero integer with at least one non-trivial divisor is known as a composite number, while the units −1 and 1 and prime numbers have no non-trivial divisors.
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It is a composite number, with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, making it a highly composite number. Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is an abundant number with an abundance of 48. Being ten times a perfect number, it is a semiperfect number. It is the smallest number divisible by the numbers 1 to 6: there is no smaller number divisible by the numbers 1 to 5.
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Gamma Herculis is also a double star divisible in small amateur telescopes. The primary is a white giant of magnitude 3.8, 195 light- years from Earth. The optical companion, widely separated, is 10th magnitude. Zeta Herculis is a binary star that is becoming divisible in medium-aperture amateur telescopes, as the components widen to their peak in 2025. The system, 35 light-years from Earth, has a period of 34.5 years. The primary is a yellow-tinged star of magnitude 2.9 and the secondary is an orange star of magnitude 5.7.
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This can be written as an equation for x in modular arithmetic: : Let g be the greatest common divisor of a and b. Both terms in ax + by are divisible by g; therefore, c must also be divisible by g, or the equation has no solutions. By dividing both sides by c/g, the equation can be reduced to Bezout's identity : where s and t can be found by the extended Euclidean algorithm. This provides one solution to the Diophantine equation, x1 = s (c/g) and y1 = t (c/g).
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Until the discovery of quantum mechanics, no distinction was made between the question of whether matter is infinitely divisible and the question of whether matter can be cut into smaller parts ad infinitum. As a result, the Greek word átomos (ἄτομος), which literally means "uncuttable", is usually translated as "indivisible". Whereas the modern atom is indeed divisible, it actually is uncuttable: there is no partition of space such that its parts correspond to material parts of the atom. In other words, the quantum-mechanical description of matter no longer conforms to the cookie cutter paradigm.
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However, modern day coins are not divisible (in the past some coins were weighed with each transaction, and were considered divisible with no particular limit in mind). There is a point of precision in each transaction that is useless because such small amounts of money are insignificant to humans. The more the price is multiplied the more the precision could matter. For example, when buying a million shares of stock, the buyer and seller might be interested in a tenth of a cent price difference, but it's only a choice.
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That means that if one were to partition the rationals into two non-empty sets A and B where A contains all rationals less than some irrational number (π, say) and B all rationals greater than it, then A has no largest member and B has no smallest member. The field of real numbers, by contrast, is both infinitely divisible and gapless. Any linearly ordered set that is infinitely divisible and gapless, and has more than one member, is uncountably infinite. For a proof, see Cantor's first uncountability proof.
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Meyer's theorem is best possible with respect to the number of variables: there are indefinite rational quadratic forms Q in four variables which do not represent zero. One family of examples is given by :Q(x1,x2,x3,x4) = x12 \+ x22 − p(x32 \+ x42), where p is a prime number that is congruent to 3 modulo 4. This can be proved by the method of infinite descent using the fact that if the sum of two perfect squares is divisible by such a p then each summand is divisible by p.
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The OPCC provides an additional . of event space of divisible meeting rooms, and . of pre-function space that proudly houses over 50 selected works of art created by renowned Midwestern artists. OPCC was designed by architectural firm DLR Group.
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Since the kth differences of the sequence 1^k, 2^k, 3^k,\dots are all equal to k! (Finite difference), the 2nth differences would all be constant and equal to (2n)!, which is certainly not divisible by p.
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There is a sense in which some multiples of 2 are "more even" than others. Multiples of 4 are called doubly even, since they can be divided by 2 twice. Not only is zero divisible by 4, zero has the unique property of being divisible by every power of 2, so it surpasses all other numbers in "evenness". One consequence of this fact appears in the bit- reversed ordering of integer data types used by some computer algorithms, such as the Cooley–Tukey fast Fourier transform. This ordering has the property that the farther to the left the first 1 occurs in a number's binary expansion, or the more times it is divisible by 2, the sooner it appears. Zero's bit reversal is still zero; it can be divided by 2 any number of times, and its binary expansion does not contain any 1s, so it always comes first.
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Rings which are themselves injective modules have a number of interesting properties and include rings such as group rings of finite groups over fields. Injective modules include divisible groups and are generalized by the notion of injective objects in category theory.
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The degree sum formula implies that every r-regular graph with n vertices has nr/2 edges. In particular, if r is odd then the number of edges must be divisible by r, and the number of vertices must be even.
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Thus, one can find two numbers x and y, with x2 − y2 divisible by n and again with probability at least one half we get a factor of n by finding the greatest common divisor of n and x − y.
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The city council consists of the mayor and six councilors, all of whom serve four-year terms. Elections are held in November of even-numbered years. In election years divisible by four, (e.g., 2000, 2004, 2008), three councilors are elected.
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Etrumeus micropus was treated as a junior synonym of E. teres by Whitehead (1985), who nonetheless suggested that E. teres might be divisible into species or subspecies.Whitehead, P.J.P., 1985. FAO Species Catalogue. Vol. 7. Clupeoid fishes of the world (suborder Clupeoidei).
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In mathematics, a square-free element is an element r of a unique factorization domain R that is not divisible by a non-trivial square. This means that every s such that s^2\mid r is a unit of R.
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Because all minimal polynomials are irreducible, all primitive polynomials are also irreducible. A primitive polynomial must have a non-zero constant term, for otherwise it will be divisible by x. Over GF(2), is a primitive polynomial and all other primitive polynomials have an odd number of terms, since any polynomial mod 2 with an even number of terms is divisible by (it has 1 as a root). An irreducible polynomial F(x) of degree m over GF(p), where p is prime, is a primitive polynomial if the smallest positive integer n such that F(x) divides is .
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Secondly, some programmers had misunderstood the Gregorian calendar rule that states years that are exactly divisible by 100 are not leap years, assuming that the year 2000 would not be a leap year. While this is true, there is an exception that states years divisible by 400 are leap years - thus making 2000 a leap year. Correcting all of this, however, was not the largest part of the problem. By 1997, AT&T; had estimated that "60% of the time and money needed for its total compliance efforts" would be devoted to testing the source code changes made to address the issue.
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Let us first explain why it is valid, in certain situations, to “cancel”. The exact statement is as follows. If , , and are integers, and is not divisible by a prime number , and if then we may “cancel” to obtain Our use of this cancellation law in the above proof of Fermat's little theorem was valid, because the numbers are certainly not divisible by (indeed they are smaller than ). We can prove the cancellation law easily using Euclid's lemma, which generally states that if a prime divides a product (where and are integers), then must divide or .
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Physical space is often regarded as infinitely divisible: it is thought that any region in space, no matter how small, could be further split. Time is similarly considered as infinitely divisible. However, the pioneering work of Max Planck (1858-1947) in the field of quantum physics suggests that there is, in fact, a minimum measurable distance (now called the Planck length, 1.616229(38)×10−35 metres) and therefore a minimum time interval (the amount of time which light takes to traverse that distance in a vacuum, 5.39116(13) × 10−44 seconds, known as the Planck time) smaller than which meaningful measurement is impossible.
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For large values of , the th telephone number is divisible by a large power of two, . More precisely, the 2-adic order (the number of factors of two in the prime factorization) of and of is ; for it is , and for it is .. For any prime number , one can test whether there exists a telephone number divisible by by computing the recurrence for the sequence of telephone numbers, modulo , until either reaching zero or detecting a cycle. The primes that divide at least one telephone number are :2, 5, 13, 19, 23, 29, 31, 43, 53, 59, ...
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G. Kendall, "Delphic semi-groups, infinitely divisible phenomena, and the arithmetic of -functions" Z. Wahrscheinlichkeitstheor. Verw. Geb. , 9 : 3 (1968) pp. 163–195R. Davidson, "Arithmetic and other properties of certain Delphic semi-groups" Z. Wahrscheinlichkeitstheor. Verw. Geb. , 10 : 2 (1968) pp. 120–172I.
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In 1851, Indiana adopted its second and current constitution, which banned governors from serving consecutive terms and lengthened terms to four years. Elections since then have been held on Election Day in November during years divisible by four, concurrent with presidential elections.
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It is the eighth hexagonal number and the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers.
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In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial).
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In an arithmetic progression of five terms with common difference 6, one of the terms must be divisible by 5, because 5 and 6 are relatively prime. Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence of sexy primes is possible.
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It is a sphenic number. In base 10, it is a repdigit, and because it is divisible by the sum of its digits, it is a Harshad number. It is also a Harshad number in binary, base 11, base 13 and hexadecimal.
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It is a white star 115 light-years from Earth, and has an optical companion of magnitude 6.1, 6 Equulei. It is divisible in binoculars. R Equulei is a Mira variable that ranges between magnitudes 8.0 and 15.7 over nearly 261 days.
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A similar view is also shared by some Christian Gnostics, ancient and modern. Throughout much of Blavatsky's public life her work drew harsh criticism from some of the learned authorities of her day, as for example when she said that the atom was divisible.
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Abelian groups that contain a unique p-basic subgroup have been completely characterized. For the case of p-groups they are either divisible or bounded; i.e., have bounded exponent. In general, the isomorphism class of the quotient, by a basic subgroup, , may depend on .
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This type of decomposition of a distribution is used in probability and statistics to find families of probability distributions that might be natural choices for certain models or applications. Infinitely divisible distributions play an important role in probability theory in the context of limit theorems.
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For every 100 females there were 94.80 males. For every 100 females age 18 and over, there were 91.90 males. In 2001, Franklin County was featured in David Brooks' article "One Nation, Slightly Divisible" in The Atlantic as a representative Red or Republican Party county.
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0 is the integer immediately preceding 1. Zero is an even numberLemma B.2.2, The integer 0 is even and is not odd, in because it is divisible by 2 with no remainder. 0 is neither positive nor negative. Many definitions, Extract of pp.
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Metres with more than four beats are called quintuple metres (5), sextuple metres (6), septuple metres (7), etc. In classical music theory it is presumed that only divisions of two or three are perceptually valid, so in meters not divisible by 2 or 3, such as quintuple meter, say , is assumed to either be equivalent to a measure of followed by a measure of , or the opposite: then . Higher meters which are divisible by 2 or 3 are considered equivalent to groupings of tuple or triple meter measures, thus, , for example, is rarely used because it is considered equivalent to two measures of . See: hypermetre and additive rhythm and divisive rhythm.
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The REDC algorithm requires products modulo R, and typically so that REDC can be used to compute products. However, when R is a power of B, there is a variant of REDC which requires products only of machine word sized integers. Suppose that positive multi-precision integers are stored little endian, that is, x is stored as an array such that for all i and . The algorithm begins with a multiprecision integer T and reduces it one word at a time. First an appropriate multiple of N is added to make T divisible by B. Then a multiple of N is added to make T divisible by B2, and so on.
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In mathematics, the Brauer–Nesbitt theorem can refer to several different theorems proved by Richard Brauer and Cecil J. Nesbitt in the representation theory of finite groups. In modular representation theory, the Brauer–Nesbitt theorem on blocks of defect zero states that a character whose order is divisible by the highest power of a prime p dividing the order of a finite group remains irreducible when reduced mod p and vanishes on all elements whose order is divisible by p. Moreover, it belongs to a block of defect zero. A block of defect zero contains only one ordinary character and only one modular character.
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For example, the field has characteristic 2 since (in the notation of the above addition table) . If has characteristic , then for all in . This implies that :, since all other binomial coefficients appearing in the binomial formula are divisible by . Here, ( factors) is the -th power, i.e.
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Klaus MatthesKlaus Matthes (January 20, 1931 – March 9, 1998) was a German mathematician, known as the founder of the theory of marked and infinitely divisible point processes. From 1981 to 1991 he was the director of the GDR Academy of Sciences' Institute of Mathematics in Berlin.
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If R=K is a field, then a series is invertible if and only if the constant term is non-zero, i.e. if and only if the series is not divisible by X. This means that KX is a discrete valuation ring with uniformizing parameter X.
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400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number.
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254 534-538. Combinatorial auctions are smart markets in which goods are indivisible,Pekec, Aleksandar and Michael H. Rothkopf (2003), Combinatorial Auction Design, MANAGEMENT SCIENCE, Vol. 49, No. 11, November 2003, pp. 1485-1503. but some smart markets allocate divisible goods such as electricity and natural gas.
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In 1776 and 1777, Felkel published a table of giving complete decompositions of all integers not divisible by 2, 3, and 5, from 1 to 408,000. Felkel had planned to extend his table to 10 million. A reconstruction of his table is found on the LOCOMAT site.
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Therefore, the coefficients of all the terms except and are divisible by , the characteristic, and hence they vanish.This is known as the Freshman's dream. Thus :F(r + s) = (r + s)^p = r^p + s^p = F(r) + F(s). This shows that F is a ring homomorphism.
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Proportionality can be guaranteed when the items are divisible, but not when they are indivisible, even if all agents have identical valuations. In contrast, MMS fairness can always be guaranteed to identical agents, so it is a natural alternative to proportionality even when the agents are different.
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Thomas Glick, Steven J. Livesey, and Faith Wallis (eds.). Medieval Science, Technology, and Medicine: An Encyclopedia. (Great Britain: Routledge, 2005) p. 518 Though the idea of molecules was not theorized at this time, Dumbleton’s speculation helped to tame the view that bodies have infinitely divisible parts.
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Another property of this type of almost-isosceles PPT is that the sides are related such that :a^b+b^a=Kc for some integer K. Or in other words a^b+b^a is divisible by c such as in :(5^{12}+12^5)/13 = 18799189.
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The secondary is of magnitude 6. κ Gem is a binary star 143 light-years from Earth. The primary is a yellow giant of magnitude 3.6; the secondary is of magnitude 8. The two are only divisible in larger amateur instruments because of the discrepancy in brightness.
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At the very least, this observation gives little reason to believe that the corresponding diagonals will be equally dense with primes. One should, of course, consider divisibility by primes other than 3. Examining divisibility by 5 as well, remainders upon division by 15 repeat with pattern 1, 11, 14, 10, 14, 11, 1, 14, 5, 4, 11, 11, 4, 5, 14 for the first polynomial, and with pattern 5, 0, 3, 14, 3, 0, 5, 3, 9, 8, 0, 0, 8, 9, 3 for the second, implying that only three out of 15 values in the second sequence are potentially prime (being divisible by neither 3 nor 5), while 12 out of 15 values in the first sequence are potentially prime (since only three are divisible by 5 and none are divisible by 3). While rigorously-proved results about primes in quadratic sequences are scarce, considerations like those above give rise to a plausible conjecture on the asymptotic density of primes in such sequences, which is described in the next section.
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Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q=pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i←1 while w ≠ 1 do y ← gcd(w, c) fac ← w/y R ← R·faci w ← y; c ← c/y; i ← i+1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal derivative of f to find all the factors with multiplicity not divisible by p. The second step identifies the remaining factors.
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O'Brien Hall, the home of Berkeley's Hydraulic Engineering Lab, was named in his honor. In 1962 O'Brien and colleague Dwight Vorkoeper received a patent for their hydraulically-actuated divisible-wedge log splitter. 12 linear feet of O'Brien's documents are archived in University of California, Riverside's Water Resources Collection.
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The Even–Paz algorithm is an computationally-efficient algorithm for fair cake-cutting. It involves a certain heterogeneous and divisible resource, such as a birthday cake, and n partners with different preferences over different parts of the cake. It allows the n people to achieve a proportional division.
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Given a group G, we say that a subgroup H is a direct summand of G if there exists another subgroup K of G such that G = H+K. In abelian groups, if H is a divisible subgroup of G, then H is a direct summand of G.
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This brought the civil and tropical years back into line. He also missed three days every four centuries by decreeing that centuries are only leap years if they are evenly divisible by 400. So for example 1700, 1800, and 1900 are not leap years but 1600 and 2000 are.
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More precisely, Gauss observed that if a+bi is a (Gaussian) prime and a–1+bi is divisible by 2+2i, then the number of solutions to the congruence 1=xx+yy+xxyy (mod a+bi), including x=∞, y=±i and x=±i, y=∞, is (a–1)2+b2.
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Since is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime. It is also a highly cototient number. There are 59 stellations of the icosahedron.H. S. M. Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie.
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Leap day February 29, also known as leap day or leap year day, is a date added to most years that are divisible by 4, such as 2016, 2020, and 2024. A leap day is added in various solar calendars (calendars based on the Earth's revolution around the Sun), including the Gregorian calendar standard in most of the world. Lunisolar calendars (whose months are based on the phases of the Moon) instead add a leap or intercalary month. In the Gregorian calendar, years that are divisible by 100, but not by 400, do not contain a leap day. Thus, 1700, 1800, and 1900 did not contain a leap day; neither will 2100, 2200, and 2300.
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Hume's "system concerning space and time" features two main doctrines: the finitist doctrine that space and time are not infinitely divisible, and the relationist doctrine that space and time cannot be conceived apart from objects. Hume begins by arguing that, since "the capacity of the mind is limited", our imagination and senses must eventually reach a minimum: ideas and impressions so minute as to be indivisible. And since nothing can be more minute, our indivisible ideas are "adequate representations of the most minute parts of [spatial] extension". Upon consideration of these "clear ideas", Hume presents a few arguments to demonstrate that space and time are not infinitely divisible, but are instead composed of indivisible points.
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For example, in the Gregorian calendar, each leap year has 366 days instead of 365, by extending February to 29 days rather than the common 28. These extra days occur in each year which is an integer multiple of 4 (except for years evenly divisible by 100, which are not leap years unless evenly divisible by 400). Similarly, in the lunisolar Hebrew calendar, Adar Aleph, a 13th lunar month, is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Bahá'í Calendar, a leap day is added when needed to ensure that the following year begins on the March equinox.
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The item for January is "0"; for February or March, "3"; for > December, "12". Day-item: The total, thus reached, must be corrected, by > deducting "1" (first adding 7, if the total be "0"), if the date be January > or February in a leap year, remembering that every year, divisible by 4, is > a Leap Year, excepting only the century-years, in `New Style', when the > number of centuries is not so divisible (e.g. 1800). The final result gives > the day of the week, "0" meaning Sunday, "1" Monday, and so on. Examples: ;1783, September 18 17, divided by 4, leaves "1" over; 1 from 3 gives "2"; twice 2 is "4".
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10 is square-free, as its divisors greater than 1 are 2, 5, and 10, none of which is a perfect square (the first few perfect squares being 1, 4, 9, and 16) In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no perfect square other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, is square-free, but is not, because 18 is divisible by . The smallest positive square-free numbers are :1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, ...
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Demonstration, with Cuisenaire rods, that 1, 2, 8, 9, and 12 are refactorable A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that \tau(n)\mid n. The first few refactorable numbers are listed in as :1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96, 104, 108, 128, 132, 136, 152, 156, 180, 184, 204, 225, 228, 232, 240, 248, 252, 276, 288, 296, ... For example, 18 has 6 divisors (1 and 18, 2 and 9, 3 and 6) and is divisible by 6. There are infinitely many refactorable numbers.
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This can be seen from the fact that doing so yields nn distinct possible sequences of swaps, whereas there are only n! possible permutations of an n-element array. Since nn can never be evenly divisible by n! when n > 2 (as the latter is divisible by n−1, which shares no prime factors with n), some permutations must be produced by more of the nn sequences of swaps than others. As a concrete example of this bias, observe the distribution of possible outcomes of shuffling a three- element array [1, 2, 3]. There are 6 possible permutations of this array (3! = 6), but the algorithm produces 27 possible shuffles (33 = 27).
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It figures directly between Alpha and Beta. Indus is home to one bright binary star. Theta Indi is a binary star divisible in small amateur telescopes, 97 light-years from Earth. Its primary is a white star of magnitude 4.5 and its secondary is a white star of magnitude 7.0.
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355 = 5 × 71, Smith number, Mertens function returns 0, divisible by the number of primes below it. the numerator of the best simplified rational approximation of pi having a denominator of four digits or fewer. This fraction (355/113) is known as Milü and provides an extremely accurate approximation for pi.
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3D model of Cerebral veins The cerebral veins are divisible into external (superficial cerebral veins) and internal (internal cerebral veins) groups according to the outer surfaces or the inner parts of the hemispheres they drain into. The external veins are the superior cerebral veins, inferior cerebral veins, and superficial middle veins.
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Burnside's theorem in group theory states that if G is a finite group of order p'q, where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes.
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More generally, an arbitrarily given string x can be derived from by the above four rules if, and only if, x respects the three following properties: # x is only composed with one and any number of and , # x begins with , and # the number of in x is not divisible by 3.
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179 is an odd number. 179 is a prime number; that is, it is not divisible by any integer (except for 1 and itself). It is an Eisenstein prime, as it is indivisible even by complex Gaussian integers. It is a Chen prime, being two less than another prime, 181.
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In mathematics, specifically in the field of group theory, the McKay Conjecture is a conjecture of equality between the number of irreducible complex characters of degree not divisible by a prime number p to that of the normalizer of a Sylow p-subgroup. It is named after Canadian mathematician John McKay.
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The only base-8 repunit prime is 73 (111_8). 8^n - 1=\left(4^n+2^n+1\right)\left(2^n - 1\right), and 7 divides 4^n + 2^n + 1 when n is not divisible by 3 and 2^n - 1 when n is a multiple of 3.
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The American cockroach shows a characteristic insect morphology with its body bearing divisions as head, trunk, and abdomen. The trunk, or thorax, is divisible into prothorax, mesothorax and metathorax. Each thoracic segment gives rise to a pair of walking appendages (known as cursorial legs). The organism bears two pairs of wings.
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If Fn ≥ 5 is a Fibonacci number then no Lucas number is divisible by Fn. Ln is congruent to 1 mod n if n is prime, but some composite values of n also have this property. These are the Fibonacci pseudoprimes. Ln \- Ln-4 is congruent to 0 mod 5.
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The condition that at least one of the derivatives , , or is nonzero and that , , and are coprime is used to show that is nonzero. For example, if then so divides (as and are coprime) so (as unless is constant). Step 3. is divisible by each of the greatest common divisors , , and .
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0) printf ("%d is divisible by 11 ", i); } return 0; } To enable coverage testing the program must be compiled with the following options: for old style code coverage, cc -xa cov.c and for new style code coverage, cc -xprofile=tcov -o cov cov.c where cov.c is the name of the program file.
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The price of fairness has also been studied in the contest of the allocation of homogeneous divisible resources, such as oil or woods. Known results are: UPOV = UPOP = Θ(√n) This is because the rule of competitive equilibrium from equal incomes yields an envy-free allocation, and its utilitarian price is O(√n).
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Klaus Matthes can be seen as the father of the theory of marked infinitely divisible point processes. He was, together with Johannes Kerstan and Joseph Mecke, the leader of the East German school of point process theory, which later found successful applications in other fields, e.g. in stochastic geometry.Dietrich Stoyan: Obituary: Klaus Matthes.
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In average it measures 5–8 mm long and 3–5 mm wide. The disc-shaped body is divisible into anterior conical and posterior discoidal regions. The anterior region is a conical projection bearing a prominent oral sucker. The posterior portion is relatively broad, up to 8 mm wide, discoidal, and ventrally excavated.
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I believe it is a requirement of > paramount importance that Christ be the Lord of our whole life, and that our > allegiance to Him be in no way divisible., quoted in McDowell, Evidence that > Demands a Verdict. The Department of Engineering and Computer Science at Cedarville University is named in his honor.
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It is a yellow giant of magnitude 2.8, 148 light- years from Earth; kornephoros means club-bearer. Delta Herculis A is a double star divisible in small amateur telescopes. The primary is a blue-white star of magnitude 3.1, and is 78 light-years from Earth. The optical companion is of magnitude 8.2.
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Leap years would occur every fifth year, except for years divisible by 50, and except for one other 5th year in 400. The result would be a calendar with 20,871 weeks in 400 years, equal to the Gregorian Calendar. In 1916, he wrote a book denouncing the Christian Science of Mary Baker Eddy.
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According to a distinction that originates with Aristotle himself, his writings are divisible into two groups: the "exoteric" and the "esoteric".; Aristotle himself: Nicomachean Ethics 1102a26–27. Aristotle himself never uses the term "esoteric" or "acroamatic". For other passages where Aristotle speaks of exōterikoi logoi, see W. D. Ross, Aristotle's Metaphysics (1953), vol.
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On the other hand, players apparently sought to avoid particular "focal" numbers, such as even numbers or round numbers divisible by 10, in favour of odd numbers or prime numbers -- although Östling et al found that after 49 rounds of their smaller game, the tendency to disproportionately choose odd numbers became almost eradicated.
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If the result is not at a 32-bit address (i.e., evenly divisible by 4), the CPU may force an exception. RISC-V CPUs jump to calculated addresses using a jump and link-register, instruction. is similar to , but gets its destination address by adding a 12-bit offset to a base register.
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Every twin prime pair except (3, 5) is of the form (6n-1, 6n+1) for some natural number n; that is, the number between the two primes is a multiple of 6. As a result, the sum of any pair of twin primes (other than 3 and 5) is divisible by 12.
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'Plurality' means that which is divisible potentially into non-continuous parts, magnitude that which is divisible into continuous parts; of magnitude, that which is continuous in one dimension is length; in two breadth, in three depth. Of these, limited plurality is number, limited length is a line, breadth a surface, depth a solid. (Aristotle, book v, chapters 11-14, Metaphysics). In his Elements, Euclid developed the theory of ratios of magnitudes without studying the nature of magnitudes, as Archimedes, but giving the following significant definitions: :A magnitude is a part of a magnitude, the less of the greater, when it measures the greater; A ratio is a sort of relation in respect of size between two magnitudes of the same kind.
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In fact, substances do not have opposites, so it is inappropriate to say that something properly becomes, from not-man, man: generation and corruption are not kinesis in the full sense. Book VI discusses how a changing thing can reach the opposite state, if it has to pass through infinite intermediate stages. It investigates by rational and logical arguments the notions of continuity and division, establishing that change—and, consequently, time and place—are not divisible into indivisible parts; they are not mathematically discrete but continuous, that is, infinitely divisible (in other words, that you cannot build up a continuum out of discrete or indivisible points or moments). Among other things, this implies that there can be no definite (indivisible) moment when a motion begins.
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For example, if one looks at records of stock prices in the 1920s, one may find the prices at the end of each day, but perhaps not at three-hundredths of a second after 12:47 PM. A new method, however, theoretically, could report at double the rate, which would not prevent further increases of velocity of reporting. Perhaps paradoxically, technical mathematics applied to financial markets is often simpler if infinitely divisible time is used as an approximation. Even in those cases, a precision is chosen with which to work, and measurements are rounded to that approximation. In terms of human interaction, money and time are divisible, but only to the point where further division is not of value, which point cannot be determined exactly.
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Conjunctive tasks can differ in their productivity effect depending on whether they are unitary or divisible. If a task is conjunctive and unitary, then the same task must be completed by all members and cannot be split into smaller parts. For these tasks, the group performance will be “equal to the worst”, where the overall group performance will equal the performance of the least capable group member. If a task is conjunctive and divisible, the task can be split amongst group members, but each portion must be completed before the entire task can be successful. In this case, the group performance is “better than the worst,” such that the group performance will be superior, as long as members are appropriately matched to subtasks that suit their abilities.
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Bissext, or bissextus () is the day which is added to the Gregorian calendar every fourth year (except those evenly divisible by 100, unless they are divisible by 400) to compensate for the six-hour difference in length between the common 365-day year and the actual length of the solar year. Originally, the day was inserted after 24 February, i.e. the 6th day before the calends (1st) of March, Consequently, besides the , or sixth before the calends, the or "second sixth," was 25 February. In modern usage, with the exception of ecclesiastical calendars, the intercalary day is added for convenience at the end of the month of February, as 29 February, and years in which February has 29 days are called "bissextile," or leap years.
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888 is a repdigit (a number all of whose digits are equal), and a strobogrammatic number (one that reads the same upside-down on a seven-segment calculator display). 8883 = 700227072 is the smallest cube in which each digit occurs exactly three times, and the only cube in which three distinct digits each occur three times.. 888 the smallest multiple of 24 whose digit sum is 24, and as well as being divisible by its digit sum it is divisible by all of its digits. 888 is a practical number, meaning that every positive integer up to 888 itself may be represented as a sum of distinct divisors of 888.Nombres pratiques (in French), Jeux et Mathématiques, Jean-Paul Davalan, retrieved 2013-01-31.
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Charlemagne ordered 240 silver units known as "denarius" to be struck from the new Carolingian pound of pure silver, each denarius containing 22.5 grains of silver. To help accounting, Charles also decreed that the pound was divisible into 20 'solidi' (so 1 solidus = 12 denari). Thus began the £sd accounting system (L.1 = 20s. = 240d.).
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Henri Bergson, The Creative Mind: An Introduction to Metaphysics, pages 165 to 168. This is natural, however, as language is the product of commonsense, which is never disinterested. Thus, for example, mobility is translated into a trajectory line and treated as a row of divisible, immobile points. Symbols are generally always spatial and immobile.
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Matrimonial property can be divided any time during or after the separation, divorce, or death. All matrimonial assets and property is presumed to be split evenly between spouses, after deducting debts. The scope of divisible matrimonial assets varies among provinces. Most provinces include all assets acquired during the marriage and any other assets pooled together.
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340 = 22 × 5 × 17, sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), sum of the first four powers of 4 (41 \+ 42 \+ 43 \+ 44), divisible by the number of primes below it, nontotient, noncototient.
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This is the first season to feature 28 semifinalists only, as opposed to previous seasons with 36 semifinalists (quarterfinalists in season 4). The number of semifinalists, which is not divisible by six, takes into account the five Golder Buzzer acts and the abbreviated second semifinal on April 1; the Saturday before (March 31) would be Black Saturday.
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0) ###### printf ("%d is divisible by 11 ", i); 9 } 1 return 0; 1 } The tcov utility also places a summary at the end of the annotated program listing. The statistics for the most frequently executed basic blocks are listed in order of execution frequency. The line number is the number of the first line in the block.
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William Burnside. In mathematics, Burnside's theorem in group theory states that if G is a finite group of order p^a q^b where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. Hence each non- Abelian finite simple group has order divisible by at least three distinct primes.
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One of Burnside's best known contributions to group theory is his paqb theorem, which shows that every finite group whose order is divisible by fewer than three distinct primes is solvable. In 1897 Burnside's classic work Theory of Groups of Finite Order was published. The second edition (pub. 1911) was for many decades the standard work in the field.
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The Mainstage is surrounded by several additional rooms including a telecommunications studio, two rehearsal halls, the Hanson Theater which is used for smaller plays, classrooms, meeting rooms and the Grand Upton Hall which is used for trade shows, conventions and other events and is divisible into five rooms. There is an extra coat room near Grand Upton Hall.
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Graetz (Gesch. viii. 422) has discovered, from a quotation in Joseph Jaabez's Or ha-ayyim, that Ibn Shem-ob died a martyr. The year of his passing was 1480. Ibn Shem- ob's numerous writings, a list of which was compiled by Munk and supplemented by Beer and Steinschneider, are divisible into (a) independent works and (b) commentaries.
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In this case, the greatest common divisor of 2u and u2 \+ 3v2 is 3. That implies that 3 divides u, and one may express u = 3w in terms of a smaller integer, w. Since u is divisible by 4, so is w; hence, w is also even. Since u and v are coprime, so are v and w.
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Divisible tasks can be divided into subtasks and individual members can be assigned specific subtasks to be completed in contribution to the greater task. For example, a group of students assigned a test to complete together as a group, can divide the questions among the individual students to be completed based on specific areas of expertise.
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Even though these could now only be issued anonymously, and so could not be redeemed, the copperheads were preferred to the 3-cent shinplasters. Some copperhead tokens even read "Substitute for shinplasters". The notes soon became filthy and ragged, making them even more disliked. They were more difficult to value in quantity than notes with denominations divisible by five.
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1089 is the integer after 1088 and before 1090. It is a square number (33 squared), a nonagonal number, a 32-gonal number, a 364-gonal number, and a centered octagonal number. 1089 is the first reverse-divisible number. The next is 2178 (= 1089 × 2 = 8712/4), and they are the only four-digit numbers that divide their reverse.
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120 is the first multiply perfect number of order three (a 3-perfect or triperfect number). The sum of its factors (including one and itself) sum to 360; exactly three times 120. Note that perfect numbers are order two (2-perfect) by the same definition. 120 is divisible by the number of primes below it, 30 in this case.
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The books were written as prayers to God, thus the title, based on the Psalms of David; and it begins with "For Thou hast made us for Thyself and our hearts are restless till they rest in Thee." The work is thought to be divisible into books which symbolize various aspects of the Trinity and trinitarian belief.
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In the event of a tie, the side of the governor is the prevailing side. Cabinet elections are held every four years, on even numbered years not divisible by four (such as 2010, 2014, etc.). The Florida attorney general is the state's chief legal officer. As defined in the Florida Constitution,Article IV, Section 4(b), Florida Constitution.
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100 is an 18-gonal number. It is divisible by 25, the number of primes below it. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. It can be expressed as a sum of some of its divisors, making it a semiperfect number.
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The centuries-old expertise in ceramics and pottery is kept alive by courses held in the ceramic center of the tithe barn. Tegelen has several theater, music and choral organisations. It is internationally famous for its Passion Play held every five years in the years that are divisible by 5, in Openluchttheater De Doolhof. These always attract many visitors.
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The dealer places a stake of four chips or coins (e.g. 40¢; it must be divisible by four) as the Pinke or Stamm in the pot and deals two cards to each player. The next one is turned as trumps and then another 2 cards are dealt. The remaining cards are placed face down on the table.
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First, the potential goals of peer production must be modular. In other words, objectives must be divisible into components, or modules, each of which can be independently produced. That allows participants to work asynchronously, without having to wait for each other's contributions or coordinate with each other in person. Second, the granularity of the modules is essential.
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David Brooks, One Nation, Slightly Divisible; The Atlantic Monthly; December 2001; Volume 288, No. 5; 53–65. The Letterkenny Army Depot five miles (8 km) north of town is a major employer. Camp David also employs Chambersburg residents. In 2004 Chambersburg had a per capita personal income (PCPI) of $28,208, below the national average of $33,050.
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This means that there are no "atoms" – there are no singular points to which one or more agents assign a positive value, so all parts of the cake are divisible. Additionally, in some cases, the value functions are assumed to be sigma additive (the value of a whole is equal to the sum of the values of its parts).
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60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. :In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted. For example, 10 means the number ten and 60 means the number sixty.
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An alternative conclusion, proposed by Henri Bergson in his 1896 book Matter and Memory, is that, while the path is divisible, the motion is not. In this argument, instants in time and instantaneous magnitudes do not physically exist. An object in relative motion cannot have an instantaneous or determined relative position, and so cannot have its motion fractionally dissected.
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The fore wings, known as tegmina, arise from mesothorax and are dark and opaque. The hind wings arise from the metathorax and are used in flight, though cockroaches rarely resort to flight. The abdomen is divisible into 10 segments, each of which is surrounded by chitinous exoskeleton plates called sclerites, including dorsal tergites, ventral sternites, and lateral pleurites.
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Since these are coprime it is divisible by their product, and since is nonzero we get : Step 4. Substituting in the inequalities : − (number of distinct roots of ) : − (number of distinct roots of ) : − (number of distinct roots of ) (where the roots are taken in some algebraic closure) and : we find that : which is what we needed to prove.
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At about the level of middle of cell a transverse band of irregular confluent black spots usually divisible into five rather large subquadrate marks in 7, cell, 1c, lb, and la. Hind marginal border as on upperside though occasionally slightly narrower. A marginal series of small white subtriangular spots. Head and thorax black with two brownish tufts on collar.
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The Japanese raccoon dog (Nyctereutes procyonoides viverrinus), also known as the tanuki ( or ; ), is a subspecies of the Asian raccoon dog. Researchers have suggested that they be considered a separate species, N. viverrinus, or that raccoon dogs of Japan could be further divisible into separate subspecies as N. p. procyonoides (, , ) and N. p. albus (, , ), but both views are controversial.
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The concept of a decimal digit sum is closely related to, but not the same as, the digital root, which is the result of repeatedly applying the digit sum operation until the remaining value is only a single digit. The digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value. Digit sums and digital roots can be used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively. For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations.
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The problem of finding a Sylow subgroup of a given group is an important problem in computational group theory. One proof of the existence of Sylow p-subgroups is constructive: if H is a p-subgroup of G and the index [G:H] is divisible by p, then the normalizer N = NG(H) of H in G is also such that [N : H] is divisible by p. In other words, a polycyclic generating system of a Sylow p-subgroup can be found by starting from any p-subgroup H (including the identity) and taking elements of p-power order contained in the normalizer of H but not in H itself. The algorithmic version of this (and many improvements) is described in textbook form in , including the algorithm described in .
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Hanke–Henry Permanent Calendar pre-2016 version with weeks still starting Sunday, but Xtra already at the end of the year In 2004, Richard Conn Henry, a professor of astronomy at Johns Hopkins University, proposed the adoption of a calendar known as Common-Civil-Calendar-and-Time (CCC&T;), which he described as a modification to a proposal by Robert McClenon. Henry's original version had essentially the same structure given above, but inserted its leap week named "Newton" between June and July in the middle of the year. The leap rule was chosen to match the ISO week leap rule, to minimise the variation in the start of the year relative to the Gregorian calendar, whereas Robert McClenon originally proposed a simple leap rule which would result in larger astronomic variance: Years whose numbers are divisible by 5 had a leap week, but years whose numbers are divisible by 40 did not unless they are also divisible by 400. Henry had advocated transition to the calendar on 1 January 2006 as that is a year in which his calendar and the Gregorian calendar begin the year on the same day. After that date passed, he recommended dropping off 31 December 2006 to start in 2007, or dropping 30 and 31 December 2007 to start 2008.
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0) printf ("%d is divisible by 11 ", i); } return 0; } To enable coverage testing the program must be compiled with the following options: gcc -Wall -fprofile-arcs -ftest-coverage cov.c where cov.c is the name of the program file. This creates an instrumented executable which contains additional instructions that record the number of times each line of the program is executed.
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A Fibonacci prime is a Fibonacci number that is prime. The first few are: : 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... . Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many. Fkn is divisible by Fn, so, apart from F4 = 3, any Fibonacci prime must have a prime index.
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PBIBD(2)s have been studied the most since they are the simplest and most useful of the PBIBDs. They fall into six typesNot a mathematical classification since one of the types is a catch-all "and everything else". based on a classification of the then known PBIBD(2)s by : # group divisible; # triangular; # Latin square type; # cyclic; # partial geometry type; # miscellaneous.
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Elections since then have been held on Election Day in November during years divisible by four, concurrent with presidential elections. In 1972, the constitution was amended to allow governors to immediately succeed themselves. As mentioned above, the amendment limited a governor to a total of eight years in office during a 12-year period, effectively limiting him to two consecutive terms.
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The 37-line poem reads like a series of disasters that will befall the English people after the death of the king. According to Lois Bragg, it is divisible into six sections, the last four of which share the theme of disaster: # ll. 1-2, the death of King Edgar # ll. 13-15, the death of bishop Cyneweard of Glastonbury # ll.
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Metric opponents cite easier division of customary units as one reason not to adopt a decimalised system. For example, those customary units with ratios of 12 and 16 have more proper factors than the metric 10: {2, 3, 4, 6} and {2, 4, 8} vs. {2, 5}. However, easily divisible numbers can be selected for use with metric units, e.g.
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In the area of modern algebra known as group theory, the Suzuki groups, denoted by Sz(22n+1), 2B2(22n+1), Suz(22n+1), or G(22n+1), form an infinite family of groups of Lie type found by , that are simple for n ≥ 1. These simple groups are the only finite non-abelian ones with orders not divisible by 3.
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Let q = 22n+1, r = 2n, n a non-negative integer. The Suzuki groups Sz(q) or 2B2(q) are simple for n≥1. The group Sz(2) is solvable and is the Frobenius group of order 20. The Suzuki groups Sz(q) have orders q2(q2+1)(q−1). These groups have orders divisible by 5, not by 3.
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We can never, he said, move past a single point because each point is infinitely divisible, and it is impossible to cross an infinite space.Aristotle, Physics, VI:9, 239b10. But to Bergson, the problem only arises when mobility and time, that is, duration, are mistaken for the spatial line that underlies them. Time and mobility are mistakenly treated as things, not progressions.
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Finally if G is a divisible group and R is a real closed field, then R((G)) is a real closed field, and if R is algebraically closed, then so is R((G)). This theory is due to Hans Hahn, who also showed that one obtains subfields when the number of (non-zero) terms is bounded by some fixed infinite cardinality.
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The ischium forms the lower and back part of the hip bone and is located below the ilium and behind the pubis. The ischium is the strongest of the three regions that form the hip bone. It is divisible into three portions: the body, the superior ramus, and the inferior ramus. The body forms approximately one-third of the acetabulum.
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The monomer contains 432 amino acids, and is divisible (can be cleaved) into three chains, such as jellein-1, jellein-2, and jellein-4. The monomers in the ologomer are held together by apimisin using noncovalent bonds. The oligomer is resistant to high temperature. MRJP2, MRJP3, MRJP4 and MRJP5 are smaller and their size range between 49 and 80 kDa.
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If n is an even superperfect number, then n must be a power of 2, 2k, such that 2k+1 − 1 is a Mersenne prime. It is not known whether there are any odd superperfect numbers. An odd superperfect number n would have to be a square number such that either n or σ(n) is divisible by at least three distinct primes.
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20 is not evenly divisible across the six countries. With trilateral currency exchanges there is not a fixed bilateral exchange rate (X Dollars per Peso or it's inverse Y Pesos per Dollar). Instead there is a set of currency triplings (A Dollars -> B Pesos -> C Rubles for instance). The actual Dollar / Peso ratio will vary based upon which tripling it is part of.
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In mathematical logic, a mathematical structure is a standard concept. A mathematical structure is a set of abstract entities with relations between them. The natural numbers under arithmetic constitute a structure, with relations such as "is evenly divisible by" and "is greater than". Here the relation "is greater than" includes the element (3, 4), but not the element (4, 3).
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128 is the seventh power of 2. It is the largest number which cannot be expressed as the sum of any number of distinct squares.OEIS:A001422. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 . But it is divisible by the total number of its divisors, making it a refactorable number.OEIS:A033950.
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Consider an exchange economy with n agents and k divisible goods. For every agent i, let E_i be their initial endowment vector and x_i their Marshallian demand function (demand vector as a function of prices and income). Given a price vector p, the income of consumer i is p\cdot E_i. Hence, their demand vector is x_i(p, p\cdot E_i).
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Scully wrote that the crashed UFO along with other flying saucers captured by the government came from Venus and worked on "magnetic principles". According to Scully, the inhabitants stocked concentrated food wafers and "heavy water" for drinking purposes, and every dimension of the craft was "divisible by nine". Science writer Martin Gardner criticized Scully's story as full of "wild imaginings" and "scientific howlers".
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At the beginning of the game and after each fifth level (levels divisible by five, except for Levels 95 and 100), a player can choose to skip five or ten levels. Skipping levels gives bonus points and a higher drop allowance. The game ends when the player either exhausts their drop allowance, fills up their playing area, or finishes level 100.
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Economic problems coupled with counter-insurgency required continuous involvement in the international market.Boudreau (2004), pp. 192 On 5 September 1987, Ne Win announced the withdrawal of the newly replaced currency notes, 100, 75, 35 and 25 kyats, leaving only 45 and 90 kyat notes, apparently because only the latter two are numbers divisible by 9, considered lucky by Ne Win.Tucker (2001), pp.
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The primary is a silvery giant of magnitude 4.9, and the secondary is an old, reddish giant star of magnitude 5.2. The star HD164669 near the primary may be an optical double. 100 Herculis is a double star easily divisible in small amateur telescopes. Both components are magnitude 5.8 blue-white stars; they are 165 and 230 light-years from Earth.
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Further, its parts may or may not have relative positions to each other. All medieval discussions about the nature of the continuum, of the infinite and the infinitely divisible, are a long footnote to this text. It is of great importance in the development of mathematical ideas in the medieval and late Scholastic period. Examples: two cubits long, number, space, (length of) time.
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We can similarly compute 4!P, and so on, but 8!P requires inverting The Euclidean algorithm gives that 455839 is divisible by 599, and we have found a The reason that this worked is that the curve has points, while it has points. Moreover, 640 and 777 are the smallest positive integers k such that on the curve and respectively.
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A geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced in Klebanov, L. B., Maniya, G. M., and Melamed, I. A. (1985). A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables.Theory of Probability & Its Applications, 29(4):791–794.
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For every integer and every prime , there is a natural number such that is divisible by precisely when divides . This number is a divisor of either or . The proof of this number theoretical property was first given in a paper by Shuxiang Goh and N. J. Wildberger. It involves considering the projective analogue to quadrance in the finite projective line .
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He refutes the first by claiming: "An infinity of multitude is not inconsistent with souls, although an infinity of power would be…for all these souls taken together will not make one infinite power…therefore, [these] infinite souls do not constitute some species of number, but a multitude of infinite numbers…for it is a contradiction that one number contain every number…for then it would contain itself, which is impossible" (Harclay 757). Harclay believes he shows the possibility of greater and lesser infinites by referencing the revolutions of planets, and that "the quantity of four feet is not divisible into as many infinite parts of the same quantity of eight feet" (Harclay 769). These quantities are infinitely divisible, yet one would have "more parts of the same quantity in the double quantity…even if we carry on [dividing] to infinity" (Harclay 769).
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Pierre de Fermat Pierre de Fermat first stated the theorem in a letter dated October 18, 1640, to his friend and confidant Frénicle de Bessy. His formulation is equivalent to the following: > If is a prime and is any integer not divisible by , then is divisible by . Fermat's original statement was > This may be translated, with explanations and formulas added in brackets for > easier understanding, as: > Every prime number [] divides necessarily one of the powers minus one of any > [geometric] progression [] [that is, there exists such that divides ], and > the exponent of this power [] divides the given prime minus one [divides ]. > After one has found the first power [] that satisfies the question, all > those whose exponents are multiples of the exponent of the first one satisfy > similarly the question [that is, all multiples of the first have the same > property].
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The 613 commandments (: taryag mitzvot, "613 Mitzvot") - 613 is the number of mitzvot in the Jewish Torah. In Judaism, Kabbalah the number 613 is very significant, every complete entity is seen as being divisible into 613 parts: 613 parts of every Sefirah; 613 parts of divine mitzvot in the Torah; 613 parts of the human body. The pomegranate is said in Judaism to have 613 seeds.
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The four linear factors p, q, p+q, and p-q are relatively prime and therefore must themselves be squares; let p+q=r^2 and p-q=s^2. Both r and s must be odd since exactly one of p or q is even and the other is odd. Therefore, both r-s and r+s are even, one of which is divisible by 4.
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As a concert venue the arena seats 1,500 for theater shows and up to 7,200 for arena concerts. Capacity for athletic events is 5,794. The arena can seat up to 1,200 for banquets. The arena contains a 21,600-square-foot (120' by 180') arena floor, big enough for small trade shows, a meeting room that can be divisible into three smaller rooms, and a lobby.
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A baseline TIFF image is composed of one or more strips. A strip (or band) is a subsection of the image composed of one or more rows. Each strip may be compressed independently of the entire image, and each begins on a byte boundary. If the image height is not evenly divisible by the number of rows in the strip, the last strip may contain fewer rows.
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R is also Dedekind-complete, divisible, and Archimedean. Tarski stated, without proof, that these axioms gave a total ordering. The missing component was supplied in 2008 by Stefanie Ucsnay. This axiomatization does not give rise to a first-order theory, because the formal statement of axiom 3 includes two universal quantifiers over all possible subsets of R. Tarski proved these 8 axioms and 4 primitive notions independent.
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An n-vertex self-complementary graph has exactly half number of edges of the complete graph, i.e., n(n − 1)/4 edges, and (if there is more than one vertex) it must have diameter either 2 or 3.. Since n(n −1) must be divisible by 4, n must be congruent to 0 or 1 mod 4; for instance, a 6-vertex graph cannot be self-complementary.
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This fact allows automedian triples to have sides and perimeter of prime numbers only. For example, (13, 17, 7) has perimeter 37. Because in a primitive automedian triangle side a is the sum of two squares and equal to the hypotenuse of the generating primitive Pythagorean triple, it is divisible only by primes congruent to 1 (mod 4). Consequently, a must be congruent to 1 (mod 4).
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Under this approach, the tenant's share may be regarded as the first claim upon the divisible balance, although the position of both the landlord and the tenant must be considered. This share has to be sufficient to induce the tenant to take a tenancy of the property and to provide a proper reward to achieve profit, an allowance for risk and a return upon the tenant's capital.
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The pubic region or pubis is the ventral and anterior of the three parts forming the hip bone. It is divisible into a body, a superior ramus, and an inferior ramus. The body forms one-fifth of the acetabulum. The body forms the wide, strong, medial and flat portion of the pubic bone which unites with the other pubic bone in the pubic symphysis.
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Delta Leporis is a yellow giant of magnitude 3.8, 112 light-years from Earth. Epsilon Leporis is an orange giant of magnitude 3.2, 227 light-years from Earth. Kappa Leporis is a double star divisible in medium aperture amateur telescopes, 560 light-years from Earth. The primary is a blue-white star of magnitude 4.4 and the secondary is a star of magnitude 7.4.
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Systems known as Kona storms affect the state with heavy rains between October and April.Steven Businger and Thomas Birchard, Jr. A Bow Echo and Severe Weather Associated with a Kona Low in Hawaii. Retrieved on 2007-05-22. Local climates vary considerably on each island due to their topography, divisible into windward (Koolau) and leeward (Kona) regions based upon location relative to the higher mountains.
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The initiative of Mr. Lumb was debated in the Chamber of Deputies, where it was concluded that railroad was necessary for the development of the Argentina nation. Juan B. Alberdi stated "The railroad will join the Argentine Republic better than all the congresses... without the 'iron road' that connects their extremes, the country will be always divisible and divided against all the Legislative decrees".
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In his thesis, Messing elaborated on Grothendieck's 1970 lecture at the International Congress of Mathematicians in Nice on p-divisible groups (Barsotti–Tate groups) that are important in algebraic geometry in prime characteristic, which were introduced in the 1950s by Dieudonné in his study of Lie algebras over fields of finite characteristic. Messing worked together with Pierre Berthelot, Barry Mazur and Aise Johan de Jong.
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The 2-principalization in unramified quadratic extensions of cyclic cubic fields with 2-class group of type (2,2) was investigated by A. Derhem in 1988. Seven years later, M. Ayadi studied the 3-principalization in unramified cyclic cubic extensions of cyclic cubic fields K\subset\Q(\zeta_f), \zeta_f^f=1, with 3-class group of type (3,3) and conductor f divisible by two or three primes.
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Centurial years are ordinary years, unless they are divisible by 400, in which case they are leap years. This causes a correction in the years 1700, 1800, 1900, 2100, 2200, and 2300. For instance, these corrections cause 23 December 1903 to be the latest December solstice, and 20 December 2096 to be the earliest solstice—about 2.35 days of variation compared with the seasonal event.
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In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, closed 4-manifold M has a spin structure (or, equivalently, the second Stiefel–Whitney class w_2(M) vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group H^2(M), is divisible by 16. The theorem is named for Vladimir Rokhlin, who proved it in 1952.
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To score, a player now has to win at least 2 tricks. The money in the stock, which must always be divisible by 8, is distributed among the trick winners. A player who wins no tricks or only one trick is 'sunk' (untergegangen) and has to pay a full stake into the stock. Once the stock is used up, a new game is started.
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Most other types of auctions can be cleared by a simple process of sorting bids from lowest to highest. Goods may be divisible, as with milk or flour, or indivisible, as with paintings or houses. Finding a market-clearing allocation corresponds to solution of a simple knapsack problem, and does not require much computation. By contrast, a smart market allows market clearing with arbitrary constraints.
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Infinite harmonic progressions are not summable (sum to infinity). It is not possible for a harmonic progression of distinct unit fractions (other than the trivial case where a = 1 and k = 0) to sum to an integer. The reason is that, necessarily, at least one denominator of the progression will be divisible by a prime number that does not divide any other denominator.. As cited by .
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In his Translator's Introduction to Schopenhauer's The World as Will and Representation, E. F. J. Payne concisely summarized the Fourfold Root. > Our knowing consciousness...is divisible solely into subject and object. To > be object for the subject and to be our representation or mental picture are > one and the same. All our representations are objects for the subject, and > all objects of the subject are our representations.
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228 (two hundred [and] twenty-eight) is the natural number following 227 and preceding 229. 228 is a refactorable number, and a practical number. There are 228 matchings in a ladder graph with five rungs. 228 is the smallest even number n such that the numerator of the nth Bernoulli number is divisible by a nontrivial square number that is relatively prime to n.
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Geographically, Shropshire is divisible into two distinct halves – north and south. The county has a highly diverse geology. The West Midlands Green Belt extends into eastern Shropshire, covering an area north from Highley, to the east of Bridgnorth, north to the eastern side of Telford, leaving Shropshire eastwards alongside the A5. This encompasses Shifnal, Cosford and Albrighton, and various other villages paralleling Dudley and Wolverhampton.
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Lehmer, D. N., Factor table for the first ten millions containing the smallest factor of every number not divisible by 2, 3, 5, or 7 between the limits 0 and 10017000, Carnegie institution of Washington. Publication no. 105, 1909. He developed a variety of mechanical and electro-mechanical factoring and computational devices, such as the Lehmer sieve, built with his son Derrick Henry Lehmer.
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If and are coprime numbers such that is divisible by , then need not be prime. If it is not, then is called a (Fermat) pseudoprime to base . The first pseudoprime to base 2 was found in 1820 by Pierre Frédéric Sarrus: 341 = 11 × 31. A number that is a Fermat pseudoprime to base for every number coprime to is called a Carmichael number (e.g. 561).
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There are m resources that are assumed to be homogeneous and divisible. There are n agents, each of whom has a personal function that attributes a numeric value to each "bundle" (combination of resources). The valuations are assumed to be homogeneous functions. The goal is to decide what "bundle" to give to each agent, where a bundle may contain a fractional amount of each resource.
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In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit ' (joy) + ' (give), meaning joy- giver.
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Insertions can be particularly hazardous if they occur in an exon, the amino acid coding region of a gene. A frameshift mutation, an alteration in the normal reading frame of a gene, results if the number of inserted nucleotides is not divisible by three, i.e., the number of nucleotides per codon. Frameshift mutations will alter all the amino acids encoded by the gene following the mutation.
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Duxbury, K. (2005), 'Postcard memories or more?', Australian Garden History, 17 (1), pp. 15–20. Another, the "Temple of the Winds" monument was dedicated to Governor Charles La Trobe and erected by William Guilfoyle in the Botanical Gardens. The temple is composed of 10 columns instead of the normal 8 or 12 which are more easily divisible by the four points of the compass.
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In contrast, a deletion that is evenly divisible by three is called an in-frame deletion.LSDB — Controlled vocabulary terms at The GEN2PHEN Knowledge Centre. Posted Fri, 08/01/2010. Deletions are responsible for an array of genetic disorders, including some cases of male infertility, two thirds of cases of Duchenne muscular dystrophy, and two thirds of cases of cystic fibrosis (those caused by ΔF508).
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The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0–9 to express the check digit. Additionally, if the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits is tripled then added to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e.
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Software pipelining is often used in combination with loop unrolling, and this combination of techniques is often a far better optimization than loop unrolling alone. In the example above, we could write the code as follows (assume for the moment that `bignumber` is divisible by 3): for i = 1 to (bignumber - 2) step 3 A(i) A(i+1) A(i+2) B(i) B(i+1) B(i+2) C(i) C(i+1) C(i+2) end Of course, matters are complicated if (as is usually the case) we can't guarantee that the total number of iterations will be divisible by the number of iterations we unroll. See the article on loop unrolling for more on solutions to this problem, but note that software pipelining prevents the use of Duff's device. In the general case, loop unrolling may not be the best way to implement software pipelining.
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Some quantities are such by their inner nature (as number), while others function as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: army, fleet, flock, government, company, party, people, mess (military), chorus, crowd, and number; all which are cases of collective nouns. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as: matter, mass, energy, liquid, material—all cases of non- collective nouns. Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios.
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Much of probabilistic number theory can be seen as an important special case of the study of variables that are almost, but not quite, mutually independent. For example, the event that a random integer between one and a million be divisible by two and the event that it be divisible by three are almost independent, but not quite. It is sometimes said that probabilistic combinatorics uses the fact that whatever happens with probability greater than 0 must happen sometimes; one may say with equal justice that many applications of probabilistic number theory hinge on the fact that whatever is unusual must be rare. If certain algebraic objects (say, rational or integer solutions to certain equations) can be shown to be in the tail of certain sensibly defined distributions, it follows that there must be few of them; this is a very concrete non-probabilistic statement following from a probabilistic one.
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In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a polynomial divisible by x2 + y2. More precisely, if F = Fn + Fn−1 + ... + F1 + F0, where each Fi is homogeneous of degree i, then the curve F(x, y) = 0 is circular if and only if Fn is divisible by x2 + y2. Equivalently, if the curve is determined in homogeneous coordinates by G(x, y, z) = 0, where G is a homogeneous polynomial, then the curve is circular if and only if G(1, i, 0) = G(1, −i, 0) = 0\. In other words, the curve is circular if it contains the circular points at infinity, (1, i, 0) and (1, −i, 0), when considered as a curve in the complex projective plane.
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To illustrate this principle further, the word for three hundred is , which is formed by the root re-, and the word for three ənthum (the prefix ən- is dropped). Finally, for the numbers not divisible by 10, the two principles are combined. The word for 22 is somniləjthum, which translate to ten-two-connective-two. In this instance, ten and two are multiplied to equal twenty which is connected to two.
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Retrieved on 2008-03-19. Storm systems affect the region with heavy rains between October and March. Local climates vary considerably on each island due to their topography, divisible into windward (Koolau) and leeward (Kona) regions based upon location relative to the higher mountains. Windward sides face the east-to-northeast trade winds and receive much more rainfall; leeward sides are drier and sunnier, with less rain and less cloud cover.
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Lord Jessel MR said for a fully paid up shareholder, ‘it must be that after full payment of all the debts and liabilities of the company there will remain a surplus divisible among the shareholders of sufficient value to authorise him to present a petition.’ This shareholder, with 75 paid up £1 shares, did not have sufficient tangible interest. His judgment went as follows.(1879) 11 Ch D 36, 42-47.
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'Belphegor's prime is the palindromic prime number ' (1030 \+ 666 × 1014 \+ 1), a number which reads the same both backwards and forwards and is only divisible by itself and one. It was discovered by Harvey Dubner. The name Belphegor refers to one of the Seven Princes of Hell, who was charged with helping people make ingenious inventions and discoveries. "Belphegor's prime" is a name coined by author Clifford A. Pickover.
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South 40 is an American colloquialism with its origins in the Homestead Act of 1862. Adult heads of families were given of public land provided they could "prove" (improve) the land by constructing a dwelling of some sort on the land and cultivating the land in some manner. After five years of residence, the deed was transferred to the homesteader. The homesteads, being , were easily divisible into quarters of each.
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The quarter Weiskirchen of Rodgau is since 1967, location of a medium-wave transmitter of the Hessian broadcasting company for the frequency 594 kHz. Until the conversion of medium-wave transmission frequencies to by nine divisible kilohertz values according to the wave plan of Geneva wave in 1978, its transmission frequency was 593 kHz. Until 1994 the transmitting power was 400 kW. In 1994, it was reduced to 300 kW.
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Ilium (plural ilia) is the uppermost and largest region. It makes up two fifths of the acetabulum. It is divisible into two parts: the body and the ala or wing of ilium; the separation is indicated on the top surface by a curved line, the arcuate line, and on the external surface by the margin of the acetabulum. The body of ilium forms the sacroiliac joint with the sacrum.
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The Charlottetown Guardian, March 13, 1915, Page 1. Reviewed 30.11.2015 The Horse Artillery and Heavy Brigades of Artillery each had their own 'Brigade Ammunition Column (BAC)', organized in much the same way and performing similar duties. The Brigade Ammunition Column of the Heavy Brigade was divisible into three sections, so that the three batteries, if operating independently, have each a section at hand to replenish the ammunition expended.
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For any nonzero integer , an angle of measure radians can be divided into equal parts with straightedge and compass if and only if is either a power of or is a power of multiplied by the product of one or more distinct Fermat primes, none of which divides . In the case of trisection (, which is a Fermat prime), this condition becomes the above- mentioned requirement that not be divisible by .
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The convention floor runs over in length, while total building size is long and wide, with a total area of . The facility features over of contiguous single-level exhibition space, which is divisible into 11 separate halls, ranging in size from . The 61 meeting rooms are configurable into over 100 variations, and the two largest meeting rooms are . Each meeting room has its own dedicated sound, lighting and networking capabilities.
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The mountainous region of Asir in the southwest is wetter; it receives monsoon rains between May and October which may amount to . The northern Ha'il Region has the Shammar Mountains, further divisible into the Aja and Salma subranges. The Red Sea was formed when in the Eocene period, the Arabian Peninsula began to move away from the continent of Africa. This prevented further exchange of genes between African and Arabian species.
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Provinces such as Nova Scotia include all assets possessed before marriage as well. The most significant divisible assets include matrimonial home and pensions.Pensions were found to be matrimonial property in Clarke v. Clarke, [1990] 2 S.C.R. 795 Assets excluded typically include inheritances (unless the inheritance has been used to purchase the matrimonial home or has paid on the mortgage of the matrimonial home) and monetary damages for personal injuries.
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Combining the results for odd and even dimensional spheres shows that much of the odd torsion of unstable homotopy groups is determined by the odd torsion of the stable homotopy groups. For stable homotopy groups there are more precise results about -torsion. For example, if for a prime then the -primary component of the stable homotopy group vanishes unless is divisible by , in which case it is cyclic of order .
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Selkirkia had a body divisible into a proboscis towards the anterior of a trunk enclosed by a tube. The proboscis would have been partially invertable and was armed with several spinules and spines, decreasing size distally overall. It was controlled by at least two sets of anterior retractor muscles. Immediately behind the proboscis was the trunk, smooth for the most part but lined with papillae towards the anterior.
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A Hall subgroup of G is a subgroup whose order is a Hall divisor of the order of G. In other words, it is a subgroup whose order is coprime to its index. If π is a set of primes, then a Hall π-subgroup is a subgroup whose order is a product of primes in π, and whose index is not divisible by any primes in π.
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The Muschelkalk can be up to 100 meters thick; it is divisible into three subdivisions, of which the upper and lower are pale thin-bedded limestones with greenish-grey marls, the middle group being composed of gypsiferous and saliniferous marls with dolomite. Stylolites are common in all the Muschelkalk limestones. The lithostratigraphic status of the Muschelkalk differs regionally. In Germany it is considered a group, in the Netherlands a formation.
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Additive tasks allow members to each contribute individually and those individual contributions then add together for the greater output of the group. Additive tasks are also categorized as divisible and having a maximizing focus. They require adding together the individual contributions of group members to maximize the outcome of the group. Examples provided in Forysth's summary of Steiner's work include shovelling snow and pulling a rope (tug of war).
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350 = 2 × 52 × 7, primitive semiperfect number, divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces. 350.org is an international environmental organization. 350 is the number of cubic inches displaced in the most common form of the Small Block Chevrolet V8. The number of seats in the Congress of Deputies (Spain) is 350.
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The Cassels–Tate pairing is a bilinear pairing , where is an abelian variety and is its dual. introduced this for elliptic curves, when can be identified with and the pairing is an alternating form. The kernel of this form is the subgroup of divisible elements, which is trivial if the Tate–Shafarevich conjecture is true. extended the pairing to general abelian varieties, as a variation of Tate duality.
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341 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number, centered cube number, super-Poulet number. 341 is the smallest Fermat pseudoprime; it is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "bm−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.
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The notion of injective object in the category of abelian groups was studied somewhat independently of injective modules under the term divisible group. Here a Z-module M is injective if and only if n⋅M = M for every nonzero integer n. Here the relationships between flat modules, pure submodules, and injective modules is more clear, as it simply refers to certain divisibility properties of module elements by integers.
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Fair cake-cutting has been studied since the 1940s. There is a heterogeneous divisible resource, such as a cake or a land-estate. There are n partners, each of whom has a personal value-density function over the cake. The value of a piece to a partner is the integral of his value-density over that piece (this means that the value is a nonatomic measure over the cake).
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In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: For example, if , , , then , and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In fact, . Inherently, if the premise of the lemma does not hold, i.e., is a composite number, its consequent may be either true or false.
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In GPS, and all protocols inspired by GPS, the choice of the weights is left to the network administrator. Generalized processor sharing assumes that the traffic is fluid, i.e., infinitely divisible so that whenever an application type has packets in the queue, it will receive exactly the fraction of the server given by the formula above. However, traffic is not fluid and consists of packets, possibly of variable sizes.
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Depending on the prime factorization of n, some restrictions may be placed on the structure of groups of order n, as a consequence, for example, of results such as the Sylow theorems. For example, every group of order pq is cyclic when are primes with not divisible by q. For a necessary and sufficient condition, see cyclic number. If n is squarefree, then any group of order n is solvable.
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The commonly accepted definition is all counties east of and crossed by Interstate 95, which is 41 counties. I-95 intersects with US64/264 at Wilson County and is in close proximity to I-40. This makes transportation throughout the region incredible along with easy access to the rest of the state and country. The region is further divisible into three geographic sections: the Southeast, Inner Banks and the Outer Banks.
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A binary code is called an even code if the Hamming weight of each of its codewords is even. An even code should have a generator polynomial that include (1+x) minimal polynomial as a product. Furthermore, a binary code is called doubly even if the Hamming weight of all its codewords is divisible by 4. An even code which is not doubly even is said to be strictly even.
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Engineering notation or engineering form is a version of scientific notation in which the exponent of ten must be divisible by three (i.e., they are powers of a thousand, but written as, for example, 106 instead of 10002). As an alternative to writing powers of 10, SI prefixes can be used, which also usually provide steps of a factor of a thousand. On most calculators, engineering notation is called "ENG" mode.
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A composite, in this philosophy, is defined to be anything which is divisible into atoms. Whatever human beings perceive is composite, while atoms are invisible. The Vaiśeṣikas stated that size, form, truths and everything that human beings experience as a whole is a function of atoms, their number and their spatial arrangements, their guṇa (quality), karma (activity), sāmānya (commonness), viśeṣa (particularity) and amavāya (inherence, inseparable connectedness of everything).
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This result can be deduced from Fermat's little theorem, which states that . The base-10 repetend of the reciprocal of any prime number greater than 5 is divisible by 9.Gray, Alexander J., "Digital roots and reciprocals of primes", Mathematical Gazette 84.09, March 2000, 86. If the repetend length of for prime p is equal to p − 1 then the repetend, expressed as an integer, is called a cyclic number.
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Four steps make a whole tone . Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, slightly smaller. 72-TET also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24.
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The companion, a magnitude-7.6 star, is visible in binoculars and small amateur telescopes. η Gem (Propus) is a binary star with a variable component. 380 light-years away, it has a period of 500 years and is only divisible in large amateur telescopes. The primary is a semi-regular red giant with a period of 233 days; its minimum magnitude is 3.9 and its maximum magnitude is 3.1.
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The checksum is calculated as sum of products - taking an alternating weight value (3 or 1) times the value of each data digit. The checksum digit is the digit, which must be added to this checksum to get a number divisible by 10 (i.e. the additive inverse of the checksum, modulo 10).Check Digit Calculator, at GS1 US. See ISBN-13 check digit calculation for a more extensive description and algorithm.
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In Tournament Schafkopf there is usually a draw for two (or more) rounds of play with a fixed number of games divisible by four (often 32 or 40). At big tournaments there will also be knockout rounds and finals. The winner(s) receive hierarchical prizes of money or gifts funded by the entry fees. The player coming last, and sometimes the one coming second last too, may receive a consolation prize.
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In the Julian calendar, as well as in the Gregorian calendar, which improved upon it, intercalation is done by adding an extra day to February in each leap year. In the Julian calendar this was done every four years. In the Gregorian, years divisible by 100 but not 400 were exempted in order to improve accuracy. Thus, 2000 was a leap year; 1700, 1800, and 1900 were not.
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Such examples correspond to diagonals that are devoid of primes or nearly so. To gain insight into why some of the remaining odd diagonals may have a higher concentration of primes than others, consider 4 n^2 + 6 n + 1 and 4 n^2 + 6 n + 5. Compute remainders upon division by 3 as n takes successive values 0, 1, 2, .... For the first of these polynomials, the sequence of remainders is 1, 2, 2, 1, 2, 2, ..., while for the second, it is 2, 0, 0, 2, 0, 0, .... This implies that in the sequence of values taken by the second polynomial, two out of every three are divisible by 3, and hence certainly not prime, while in the sequence of values taken by the first polynomial, none are divisible by 3. Thus it seems plausible that the first polynomial will produce values with a higher density of primes than will the second.
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A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime. For example, 1193 is a circular prime, since 1931, 9311 and 3119 all are also prime. A circular prime with at least two digits can only consist of combinations of the digits 1, 3, 7 or 9, because having 0, 2, 4, 6 or 8 as the last digit makes the number divisible by 2, and having 0 or 5 as the last digit makes it divisible by 5. The complete listing of the smallest representative prime from all known cycles of circular primes (The single- digit primes and repunits are the only members of their respective cycles) is 2, 3, 5, 7, R2, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, R19, R23, R317, R1031, R49081, R86453, R109297, and R270343, where Rn is a repunit prime with n digits.
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Set (extra carry word) for do \--loop1- Make T divisible by c <- 0 m <- for do \--loop2- Add the low word of and the carry from earlier, and find the new carry x <- T[i + j] <- c <- end for for do \--loop3- Continue carrying x <- T[i + j] <- c <- end for end for for do S[i] <- T[i + r] end for if then return else return end if end function The final comparison and subtraction is done by the standard algorithms. The above algorithm is correct for essentially the same reasons that REDC is correct. Each time through the i loop, m is chosen so that is divisible by B. Then mNBi is added to T. Because this quantity is zero mod N, adding it does not affect the value of . If mi denotes the value of m computed in the ith iteration of the loop, then the algorithm sets S to .
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IBM's Rata Die method requires that one know the "key day" of the proleptic Gregorian calendar i.e. the day of the week of January 1, AD 1 (its first date). This has to be done to establish the remainder number based on which the day of the week is determined for the latter part of the analysis. By using a given day August 13, 2009 which was a Thursday as a reference, with Base and n being the number of days and weeks it has been since 01/01/0001 to the given day, respectively and k the day into the given week which must be less than 7, Base is expressed as Base = 7n + k (i) Knowing that a year divisible by 4 or 400 is a leap year while a year divisible by 100 and not 400 is not a leap year, a software program can be written to find the number of days.
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In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a remainder of 1 when divided by 9: :0 = 9 × 0 :1 = 9 × 0 + 1 :3 = 9 × 0 + 3 :6 = 9 × 0 + 6 :10 = 9 × 1 + 1 :15 = 9 × 1 + 6 :21 = 9 × 2 + 3 :28 = 9 × 3 + 1 :36 = 9 × 4 :45 = 9 × 5 :55 = 9 × 6 + 1 :66 = 9 × 7 + 3 :78 = 9 × 8 + 6 :91 = 9 × 10 + 1 :… :There is a more specific property to the triangular numbers that aren't divisible by 3; that is, they either have a remainder 1 or 10 when divided by 27. Those that are equal to 10 mod 27 are also equal to 10 mod 81. The digital root pattern for triangular numbers, repeating every nine terms, as shown above, is "1, 3, 6, 1, 6, 3, 1, 9, 9".
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The prayer ropes usually have 33, 50, 100 or 300 knots – or, more generally, an easily divisible number. The person saying the prayer says one repetition for each knot. It may be accompanied by prostrations and the sign of the cross, signaled by beads strung along the prayer rope at intervals. The prayer rope is "a tool of prayer" and an aid to beginners or those who face difficulties practicing the Prayer.
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In 2009, nineteen seats were allocated via the leveling system. Elections are held each four years (in odd-numbered years occurring after a year evenly divisible by four), normally on the second Monday of September. Unlike most other parliaments, the Storting always serves its full four-year term; the Constitution does not allow snap elections. Substitutes for each deputy are elected at the same time as each election, so by-elections are rare.
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The sum of independent negative- binomially distributed random variables r1 and r2 with the same value for parameter p is negative-binomially distributed with the same p but with r-value r1 + r2. The negative binomial distribution is infinitely divisible, i.e., if Y has a negative binomial distribution, then for any positive integer n, there exist independent identically distributed random variables Y1, ..., Yn whose sum has the same distribution that Y has.
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In the United Kingdom the original Board of Trade carat was exactly grains (~3.170 grains = ~205 mg); in 1888, the Board of Trade carat was changed to exactly grains (~3.168 grains = ~205 mg). Despite its being a non-metric unit, a number of metric countries have used this unit for its limited range of application. The Board of Trade carat was divisible into four diamond grains, but measurements were typically made in multiples of carat.
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The Texas Comptroller of Public Accounts is an executive branch position created by the Texas Constitution. As with nearly every other executive branch head in Texas, the Comptroller is popularly elected every four years concurrently with the governor and the other elected executive branch positions (elections take place in even number years not divisible by four; e.g., 2006, 2010, and so on). The current Comptroller is Glenn Hegar, who took office on January 2, 2015.
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So the number of coconuts that could be in the pile is k25 - 4. k=1 yielding 21 is the smallest positive number that can be successively divided by 5 twice with remainder 1. If there are 5 divisions, then multiples of 55=3125 are required; the smallest such number is 3125 - 4 = 3121. After 5 divisions, there are 1020 coconuts left over, a number divisible by 5 as required by the problem.
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Standards of conformation do not vary as significantly for horses as they do for dogs, as a horse's conformation is extremely important to its ability to perform and stay sound doing so. Generally, all horses are ideally divisible into three equal parts: forehand, trunk, hindquarters. This is called "harmony" and has that effect on the eye. Another quality generally agreed upon is that from the front and rear, all four legs should be straight.
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Influential families within the wards usually maintained social order. Historians are still unsure as to how many government-controlled marketplaces existed in Chang'an. Although there are claims of nine markets, it is possible that seven of them were actually divisible parts of two main markets: the East Market and West Market. Both the East Market and West Market had a two-story government office with a flag and drum placed on the roof.
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The dashboard, with the now ever-present display, is also modern in styling, and has some ribs, especially at the top, which complement the external lines of the bodywork. The steering wheel doesn't have a fixed hub like the first generation. The seats have a sporty design, with padded side panels, but offer little lateral support. The sofa is divisible according to the now familiar pattern 60-40, but it is not tilting.
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In probability theory, an indecomposable distribution is a probability distribution that cannot be represented as the distribution of the sum of two or more non-constant independent random variables: Z ≠ X + Y. If it can be so expressed, it is decomposable: Z = X + Y. If, further, it can be expressed as the distribution of the sum of two or more independent identically distributed random variables, then it is divisible: Z = X1 + X2.
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XDR is implemented as a software library of functions which is portable between different operating systems and is also independent of the transport layer. XDR uses a base unit of 4 bytes, serialized in big-endian order; smaller data types still occupy four bytes each after encoding. Variable-length types such as string and opaque are padded to a total divisible by four bytes. Floating-point numbers are represented in IEEE 754 format.
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Eventually T is divisible by R, and after division by R the algorithm is in the same place as REDC was after the computation of t. function MultiPrecisionREDC is Input: Integer N with , stored as an array of p words, Integer , --thus, r = logB R Integer N′ in such that , Integer T in the range , stored as an array of words. Output: Integer S in such that , stored as an array of p words.
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The song's smooth, muffled beat climaxes as a euphoric crescendo. The densely textured title track features expressive bass playing by Thundercat, continuous gong and handclaps, and J Dilla-like keyboard. "Only If You Wanna" is a futuristic jazz trio piece with both digital and analog sounds. AllMusic's Andy Kellman delineates the songs from "See Thru to U" to "Only If You Wanna" as the album's most musically connected and "least divisible" section.
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Hence if and only if , i.e. if and only if is divisible by . To prove (2), note that is a field, which is a standard fact (a quick proof is to note that since is prime, is a finite integral domain, hence is a field). Another standard fact is that a non-zero polynomial over a field has at most as many roots as its degree; this follows from the division algorithm.
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These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There is a number of variations to the rules that improve accuracy.
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By assumption all coefficients in the product are divisible by p, leading to a contradiction. Therefore, the coefficients of the product can have no common divisor and are thus primitive. \square The proof is given below for the more general case. Note that an irreducible element of Z (a prime number) is still irreducible when viewed as constant polynomial in Z[X]; this explains the need for "non-constant" in the statement.
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Aristotle wrote his works on papyrus scrolls, the common writing medium of that era. His writings are divisible into two groups: the "exoteric", intended for the public, and the "esoteric", for use within the Lyceum school. Aristotle's "lost" works stray considerably in characterization from the surviving Aristotelian corpus. Whereas the lost works appear to have been originally written with a view to subsequent publication, the surviving works mostly resemble lecture notes not intended for publication.
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During the second phase, the digits develop, and in the last phase, the egg tooth appears. Most mammal zygotes go through holoblastic cleavage, meaning that, following fertilisation, the ovum is split due to cell divisions into multiple, divisible daughter cells. This is in comparison to the more ancestral process of meroblastic cleavage, present in monotremes like the platypus and in non- mammals like reptiles and birds. In meroblastic cleavage, the ovum does not split completely.
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The secondary is of magnitude 7.4 and is visible in small telescopes. The components of the primary are becoming closer together and will not be divisible in amateur telescopes beginning in 2015. δ Equ is a binary star with an orbital period of 5.7 years, which at one time was the shortest known orbital period for an optical binary. The two components of the system are never more than 0.35 arcseconds apart.
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The Reindeer zone to the north is a 500 km wide collage of Paleoproterozoic (1.92-1.83 Ga) arc volcanic rocks, plutons, volcanogenic sediments, and younger molasse, divisible into several lithostructural domains. Most of these rocks evolved in an oceanic to transitional, subduction-related arc setting, with increasing influence of Archean crustal components to the northwest. The zone overlies Archean basement exposed in structural window that are now recognized as the Sask craton.
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Proteins are translated by reading tri- nucleotides on the mRNA strand, also known as codons, from one end of the mRNA to the other (from the 5' to the 3' end). Each codon is translated into a single amino acid. Therefore, a shift of any number of nucleotides that is not divisible by 3 in the reading frame will result in subsequent codons to be read differently. This effectively changes the ribosomal reading frame.
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These reforms brought living standards back to pre-World War II levels and stimulated economic growth. However, by 1988, foreign debt had ballooned to $4.9 billion, about three-fourths of the national GDP, and Ne Win's later attempt to make the Kyat based in denominations divisible by 9, a number he considered to be auspicious, led to the wiping of millions of savings of the Burmese people, resulting in the 8888 Uprising.
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A singly even number can be divided by 2 only once; it is even but its quotient by 2 is odd. A doubly even number is an integer that is divisible more than once by 2; it is even and its quotient by 2 is also even. The separate consideration of oddly and evenly even numbers is useful in many parts of mathematics, especially in number theory, combinatorics, coding theory (see even codes), among others.
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The discriminant of a polynomial over a field is zero if and only if the polynomial has a multiple root in some field extension. The discriminant of a polynomial over an integral domain is zero, if and only if the polynomial and its derivative have a non-constant common divisor. In characteristic 0, this is equivalent to saying that the polynomial is not square-free (i.e., divisible by the square of a non-constant polynomial).
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A uniquely total colorable graph is a k-total-chromatic graph that has only one possible (proper) k-total-coloring up to permutation of the colors. Empty graphs, paths, and cycles of length divisible by 3 are uniquely total colorable graphs. conjectured that they are also the only members in this family. Some properties of a uniquely k-total-colorable graph G with n vertices: # χ″(G) = Δ(G) + 1 unless G = K2.
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132 is the smallest number with this property,Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138 which is shared by 264, 396 and 35964 (see digit-reassembly number). But there is no number that, when added to the sum of its own digits, sums to 132, therefore 132 is a self number. 132 is also a Harshad number, divisible by the sum of its base-ten digits.
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Square-free elements may be also characterized using their prime decomposition. The unique factorization property means that a non-zero non-unit r can be represented as a product of prime elements :r=p_1p_2\cdots p_n Then r is square-free if and only if the primes pi are pairwise non- associated (i.e. that it doesn't have two of the same prime as factors, which would make it divisible by a square number).
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In mathematical sociology, and especially game theory, the bankruptcy problem is a distribution or entitlement problem involving the allocation of a given amount of a perfectly divisible good among a group of agents. The focus is on the case where the amount is insufficient to satisfy all their demands. Problems of the bankruptcy type arise in many real life situations. The canonical example would be that of a bankrupt firm that is to be liquidated.
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In number theory, reversing the digits of a number sometimes produces another number that is divisible by . This happens trivially when is a palindromic number; the nontrivial reverse divisors are :1089, 2178, 10989, 21978, 109989, 219978, 1099989, 2199978, ... . For instance, 1089 × 9 = 9801, the reversal of 1089, and 2178 × 4 = 8712, the reversal of 2178.... As cited by .. The multiples produced by reversing these numbers, such as 9801 or 8712, are sometimes called palintiples..
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The Maricopa County Board of Supervisors is the governing body of Maricopa County, a county of over four million in Arizona. The board has five districts that elect one member in years divisible by four. Members may serve unlimited number of four-year terms, as there are no term limits. Vacancies are filled by appointment by remaining members of the board; a member of the same party of the departing member must be selected.
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A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and examples only for decimal, or base 10, numbers. Martin Gardner explained and popularized these rules in his September 1962 "Mathematical Games" column in Scientific American.
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While the original model assumed that all products are divisible, there is a variant of Fisher market in which the items are assumed to be indivisible. In this variant, finding a competitive equilibrium is computationally hard. Deng et al studied a market to which each agent comes with an initial endowment (rather than an initial income) and all valuations are additive. They proved that deciding whether CE exists is NP- hard even with 3 agents.
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Four of these halls are divisible in two or three smaller spaces by soundproof panels. The basement level B3 holds a total of 90 smaller rooms for workshop meetings in the range of . The levels B4 and B5 are exhibition halls in the sizes of and with ceiling height as well as another bigger one of with . The levels B6 and B7 are designed as car park capable of 850 vehicles in total.
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Unfortunately, this situation is likely to get worse before it gets better, as workload for users and workers using manual direct data entry (DDE) devices increases. Double entry (or more) may also be leveraged to minimize transcription or transposition error, but at the cost of a reduced number of entries per unit time. Mathematical transposition errors are easily identifiable. Add up the numbers that make up the difference and the resultant number will always be evenly divisible by nine.
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The simplest generalized Mersenne primes are prime numbers of the form , where is a low-degree polynomial with small integer coefficients. An example is , in this case, , and ; another example is , in this case, , and . It is also natural to try to generalize primes of the form to primes of the form (for and ). However (see also theorems above), is always divisible by , so unless the latter is a unit, the former is not a prime.
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The dealer is chosen by lots and antes an agreed stake to the pot that is divisible by three. In each deal, three cards are dealt to each player. Then follows a calling round in which the first two players may, in turn, decide whether to "pass", that is, refrain from playing for the pot, or 'swing'. Swinging means to face two fresh cards from the talon and choose the trump suit from one of these cards.
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Similarly, because the sides are related by 2a^2=b^2+c^2, each of the sides b and c in the primitive automedian is the difference between twice a square and a square. They are also the sum and difference of the legs of a primitive Pythagorean triple. This constrains b and c to be divisible only by primes congruent to ±1 (mod 8). Consequently, b and c must be congruent to ±1 (mod 8).
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The secondary, visible in small telescopes as a star of magnitude 9.4, is a binary with two components, magnitudes 10 and 11. There is an optical companion to Iota Librae; 25 Librae is a star of magnitude 6.1, 219 light-years from Earth and visible in binoculars. Mu Librae is a binary star divisible in medium-aperture amateur telescopes, 235 light-years from Earth. The primary is of magnitude 5.7 and the secondary is of magnitude 6.8.
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It is a composite number, with its divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable number with 284.Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 167 Every number up to 220 may be expressed as a sum of its divisors, making 220 a practical number. Also, being divisible by the sum of its digits, 220 is a Harshad number.
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The carat (ct) is a unit of mass equal to or 0.00643 troy oz, and is used for measuring gemstones and pearls. The current definition, sometimes known as the metric carat, was adopted in 1907 at the Fourth General Conference on Weights and Measures, and soon afterwards in many countries around the world. The carat is divisible into 100 points of 2 mg. Other subdivisions, and slightly different mass values, have been used in the past in different locations.
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In the context of gene finding, the start-stop definition of an ORF therefore only applies to spliced mRNAs, not genomic DNA, since introns may contain stop codons and/or cause shifts between reading frames. An alternative definition says that an ORF is a sequence that has a length divisible by three and is bounded by stop codonsClaverie, J.-M. (1997) Computational methods for the identification of genes in vertebrate genomic sequences. Hum. Mol. Genet. 6, 1735–1744.
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The arthropod digestive system is divisible into three areas: the fore gut, mid gut, and hind gut. All free-living species exhibit a distinct and separate mouth and anus, and in all species, food must be moved through the digestive tract by muscular activity rather than cilia activity since the lumen of the fore gut and hind gut is lined with cuticle. Digestion is generally extracellular. Nutrients are distributed to the tissues through the hemal system.
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"Space and Time" # Space and time are not realities in the phenomenal world, but the modes under which we perceive things apart. They are not infinitely large nor infinitely divisible, but are essentially limited by the contents of our perception. # Scientific concepts are, as a rule, limits drawn in conception to processes which can be started but not carried to a conclusion in perception. The historical origin of the concepts of geometry and physics can thus be traced.
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Consequently Kummer theory is never applicable to extensions whose degree is divisible by the characteristic. The case where the characteristic divides the degree is now called Artin–Schreier theory because the first progress was made by Artin and Schreier. Their initial motivation was the Artin–Schreier theorem, which characterizes the real closed fields as those whose absolute Galois group has order two.Artin, Emil and Schreier, Otto, Über eine Kennzeichnung der reell abgeschlossenen Körper, Abh. Math. Sem.
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228 The computational technique underlying these lower bounds depends on some key results of Klee that make it possible to show that the smallest counterexample must be divisible by squares of the primes dividing its totient value. Klee's results imply that 8 and Fermat primes (primes of the form 2k + 1) excluding 3 do not divide the smallest counterexample. Consequently, proving the conjecture is equivalent to proving that the conjecture holds for all integers congruent to 4 (mod 8).
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In a uniform matroid U{}^r_n, the circuits are the sets of exactly r+1 elements. Therefore, a uniform matroid is Eulerian if and only if r+1 is a divisor of n. For instance, the n-point lines U{}^2_n are Eulerian if and only if n is divisible by three. The Fano plane has two kinds of circuits: sets of three collinear points, and sets of four points that do not contain any line.
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An anniversary can advertise a firm's staying power and longevity. A report in the New York Times explained the marketing logic: Marketers choose variables relating to anniversariesVariables include number of past years to celebrate, place for the celebration, budget, and so forth. to meet specific promotional objectives. While the length of time celebrated by an anniversary is often divisible by five, such as the 10th, 15th, 25th, 50th, or 80th anniversary, there are no hard and fast rules.
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This practice was twice approved by the then-Secretary of the Treasury, in 1837 and 1849. Small deposits of bullion were rounded down to be divisible by $5, with the surplus kept and used at the discretion of Mint officials. This, and similar practices whereby officials financed activities without an appropriation from Congress, were brought to an end after Peale proposed a $20,800 renovation of part of the Philadelphia Mint building in 1850, and ran over budget by $12,000.
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Belote Contrée and Belote Coinchée are the most popular variants of the French national card game. Once all cards have been dealt to the players, each player in turn can propose a contract consisting of a number divisible by 10, from 80 to 160, or "capot". Any contract announced must be higher than the last one. This continues for as many rounds as necessary, until a contract is accepted by the other three players all passing.
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Starting with W4 = 63 and W5 = 159, every sixth Woodall number is divisible by 3; thus, in order for Wn to be prime, the index n cannot be congruent to 4 or 5 (modulo 6). Also, for a positive integer m, the Woodall number W2m may be prime only if 2m \+ m is prime. As of January 2019, the only known primes that are both Woodall primes and Mersenne primes are W2 = M3 = 7, and W512 = M521.
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The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10 In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.
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Burnside's theorem, proved using group characters, states that every group of order n is solvable when n is divisible by fewer than three distinct primes, i.e. if , where p and q are prime numbers, and a and b are non-negative integers. By the Feit–Thompson theorem, which has a long and complicated proof, every group of order n is solvable when n is odd. For every positive integer n, most groups of order n are solvable.
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In the theory of finite groups the Sylow theorems imply that, if a power of a prime number p^n divides the order of a group, then the group has a subgroup of order p^n. By Lagrange's theorem, any group of prime order is a cyclic group, and by Burnside's theorem any group whose order is divisible by only two primes is solvable. For the Sylow theorems see p. 43; for Lagrange's theorem, see p.
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However, on videos with fine detail (high spatial complexity) this can manifest as chroma aliasing artifacts. Compared to other digital compression artifacts, this issue seems to very rarely be a source of annoyance. Because of the subsampling, Y′CbCr 4:2:0 video is ordinarily stored using even dimensions (divisible by 2 horizontally and vertically). Y′CbCr color is often informally called YUV to simplify the notation, although that term more properly applies to a somewhat different color format.
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27, 312 Expanding on his own interpretation of "Semitic race" concepts, Sanielevici distinguished between the Jews, who belonged to several races, and the Semites, only some of whom were Jewish. The racial traits, he suggested, were hidden, recurrent and vague: the recessive characteristics made races divisible into "classes" and "subclasses".Butaru, p.312 Sanielevici illustrated his point with craniometry, publishing comparative photographs of Jews and ethnically unrelated people (Russians, Frenchmen, Germans), concluding that their physical measurements were nearly identical.
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In 1963, Ellio's Pizza was founded in the Long Island, New York town of Great Neck by Elias Betzios, George Liolis, and Manny Tzelios.Ellios.com Four years later, Ellio's introduced its signature "9 slice" pizza in a box comprising 3 rectangular pizzas, each divisible crosswise into three slices. The original pizza consists of crust, pizza sauce and cheese with no additional toppings. This would remain Ellio's only formulation for almost 40 years until 2004, when Ellio's began selling pepperoni pizza.
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He concluded that these rays, rather than being a form of light, were composed of very light negatively charged particles he called "corpuscles" (they would later be renamed electrons by other scientists). He measured the mass-to- charge ratio and discovered it was 1800 times smaller than that of hydrogen, the smallest atom. These corpuscles were a particle unlike any other previously known. Thomson suggested that atoms were divisible, and that the corpuscles were their building blocks.
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He invented a new system of numbering years to replace the Diocletian years that had been used in an old Easter table because he did not wish to continue the memory of a tyrant who persecuted Christians.Blackburn & Holford-Strevens 2003, 767. It has been suggested that he arranged the numbers so that leap years would be exactly divisible by four, and that his new table would begin one "Victorian cycle" (see below), i.e. 532 years, after his new epoch.
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The MTA allows 6 and 7-axle trucks with less than of gross vehicle weight, and 5-axle trucks with less than of gross vehicle weight, if they have valid divisible-load permits. Trucks carrying less than may also use the bridge, but all heavy loads are speed-restricted to and must use the center lane of the bridge. Heavy trucks carrying more than 80,000 lb without permits are prohibited from using the Throgs Neck Bridge.
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The last diminisher procedure is a procedure for fair cake-cutting. It involves a certain heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over different parts of the cake. It allows the n people to achieve a proportional division, i.e., divide the cake among them such that each person receives a piece with a value of at least 1/n of the total value according to his own subjective valuation.
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The fines are subject to recovery proceedings. If the fines are still not paid, the court may convert them to a prison sentence. Three day-fines will be converted to one day of imprisonment, ignoring the remainder for any amount of day-fines not divisible by three, and the length of the sentence must be between 4 and 60 days. This "conversion punishment" (, ) is only ever applied to court-ordered fines, not those issued by police.
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The Pawukon is a 210-day calendar that has its origins in the Hindu religion in Bali, Indonesia. The calendar consists of 10 different concurrent weeks of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 days. On the first day of the year it is the first day of all the ten weeks. Because 210 is not divisible by 4, 8, or 9 - extra days must be added to the 4, 8, and 9 day weeks.
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These are the current records in the various age groups of masters athletics for United States competitors. Starting at age 35, each age group starts on the athlete's birthday in years that are evenly divisible by 5 and extends until the next such occurrence. For record purposes, older athletes are not included in younger age groups, except in the case of relay team members. A relay team's age group is determined by the age of the youngest member.
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Matched filtering allows the entire energy received from a target to be compressed into a single bin (be it a range, Doppler, elevation, or azimuth bin). On the surface it would appear that then within a fixed interval of time one could obtain perfect, error free, detection. To do this one simply compresses all energy into an infinitesimal time slice. What limits this approach in the real world is that, while time is arbitrarily divisible, current is not.
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Small deletions are less likely to be fatal; large deletions are usually fatal – there are always variations based on which genes are lost. Some medium-sized deletions lead to recognizable human disorders, e.g. Williams syndrome. Deletion of a number of pairs that is not evenly divisible by three will lead to a frameshift mutation, causing all of the codons occurring after the deletion to be read incorrectly during translation, producing a severely altered and potentially nonfunctional protein.
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The first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17, 1310 = 2×5×131, and 1311 = 3×19×23. There is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013 (3×11×61), 2014 (2×19×53), and 2015 (5×13×31) are all sphenic.
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No mammalian fauna were found in the lower unit of the Laetolil Beds, and no date could be assigned to this layer. The Ndolanya Beds, which are located above the Laetolil Beds and underlie the Ogol lavas, are clearly divisible into upper and lower units separated by a widespread deposit of calcrete up to one meter thick. However, like the Lower Laetolil Beds, no date can be assigned to the Ndolanya Beds. The Ogol lavas date back 2.4 million years.
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A virapulla - traditional Swedish tin for holding gaming counters Players draw lots for seating and first dealer. Deal and play are clockwise. The dealer antes the agreed stake—which must be divisible by three—to the pot, shuffles the cards and offers them to his right for cutting. Three cards are dealt to each player in packets of 2 and 1; then the next card is turned to determine trumps, and the remaining cards stacked face down form the talon.
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Although every concrete Boolean algebra is a Boolean algebra, not every Boolean algebra need be concrete. Let n be a square-free positive integer, one not divisible by the square of an integer, for example 30 but not 12. The operations of greatest common divisor, least common multiple, and division into n (that is, ¬x = n/x), can be shown to satisfy all the Boolean laws when their arguments range over the positive divisors of n. Hence those divisors form a Boolean algebra.
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Nourse LJ overturned the decision. He held that a charge may be divisible, and the parties had unequivocally expressed their intention and ‘unless there is some authority or principle of law which prevented them from agreeing what they have agreed, their agreement must prevail’. In essence, he held that the wording did allow them to have such a form of security, the parties were free to make such arrangements. He said unless, unlawful, the free will of the parties would prevail.
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A primefree sequence found by Herbert Wilf has initial terms :a1 = 20615674205555510, a2 = 3794765361567513 . The proof that every term of this sequence is composite relies on the periodicity of Fibonacci-like number sequences modulo the members of a finite set of primes. For each prime p, the positions in the sequence where the numbers are divisible by p repeat in a periodic pattern, and different primes in the set have overlapping patterns that result in a covering set for the whole sequence.
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For illustration, let n be factored into d and e, n = de. The general equation : an \+ bn = cn implies that (ad, bd, cd) is a solution for the exponent e : (ad)e \+ (bd)e = (cd)e. Thus, to prove that Fermat's equation has no solutions for n > 2, it would suffice to prove that it has no solutions for at least one prime factor of every n. Each integer n > 2 is divisible by 4 or by an odd prime number (or both).
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The Ethiopian Years 1992 and 1996, however, began on the Gregorian Dates of 'September 12th 1999' and '2003' respectively. This date correspondence applies for the Gregorian years 1900 to 2099. The Ethiopian leap year is every four without exception, while Gregorian centurial years are only leap years when exactly divisible by 400; thus a set of corresponding dates will most often apply for a single century. As the Gregorian year 2000 is a leap year, the current correspondence lasts two centuries instead.
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Cubes occasionally have the surjective property in other fields, such as in for such prime that ,The multiplicative group of is cyclic of order , and if it is not divisible by 3, then cubes define a group automorphism. but not necessarily: see the counterexample with rationals above. Also in only three elements 0, ±1 are perfect cubes, of seven total. −1, 0, and 1 are perfect cubes anywhere and the only elements of a field equal to the own cubes: .
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Integers can be divided into even and odd, those that are evenly divisible by two and those that are not. The even integers are ...−4, −2, 0, 2, 4, whereas the odd integers are −3, −1, 1, 3,... The property of whether an integer is even (or not) is known as its parity. If two numbers are both even or both odd, they have the same parity. By contrast, if one is even and the other odd, they have different parity.
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Also, for a finite group, the p′,p-core is the intersection of the centralizers of the abelian chief factors whose order is divisible by p (all of which are irreducible representations over a field of size p lying in the principal block). For a finite, p-constrained group, an irreducible module over a field of characteristic p lies in the principal block if and only if the p′-core of the group is contained in the kernel of the representation.
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Koiak (; , []), also known as Choiak (, Khoiák) and Kiyahk. (, Kiahk, []; or ), is the fourth month of the ancient Egyptian and Coptic calendars. It lasts between 10 December and 8 January of the Gregorian calendar, or between 11 December and 9 January of the Gregorian calendar in Coptic calendar years immediately following a Coptic calendar leap year (which occur every four years, in Coptic calendar years immediately preceding those that are divisible by 4 to produce an integer; i.e., 1719, 1723, 1727, 1731, etc.
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In Book I Chapter 73, Maimonides presents the 12 premises of the Mutakallimūn, and disputes most of them. The premises are, in brief, as follow: # Existence of atoms: The world is composed of small particles which are not divisible, and which have no identifying essential properties (only accidents). # Existence of vacuum: There exist certain spaces which are devoid of all substance and material. # Time is discrete: Time is made up of fundamental instants which are not themselves subject to further division.
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For the most part they overlap with other, smaller regions established during history along their course, in most case named after the tributaries of the main river (most notably, in the case of all three sections of Pomoravlje). For the purpose of easier presentation in the tables, the territory of Serbia is roughly divisible into six geographical sections: northern, western, central, eastern, south-western and south. Thus the tables do not follow the political divisions. Kosovo declared independence in February 2008.
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List of Italian records in masters athletics are the current records in the various age groups of masters athletics for Italy competitors. Starting at age 35, each age group starts on the athlete's birthday in years that are evenly divisible by 5 and extends until the next such occurrence. For record purposes, older athletes are not included in younger age groups, except in the case of relay team members. A relay team's age group is determined by the age of the youngest member.
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These were marked on fasti using from A to H. The earliest form of the Roman calendar is sometimes said to have included exactly 38 such cycles, running for 304 days from March to December before an unorganized expanse of about 50 winter days. The lengths of the Republican and Julian calendars, however, were not evenly divisible by 8; under these systems, the nundinae fell on a different letter each year. These letters formed the basis of the later Christian dominical letters.
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For the case of divisible PB and utility voting, a compelling budgeting method is one based on the core of the underlying game. A budget is considered "in the core" if no subset of k voters can take their share of the budget (k L / n) and fund a subset of the projects such that the utility of each voter in the subset strictly increases. There are efficient algorithms for calculating the core budget for some natural classes of utility functions.
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However, the number 2 raised to any positive integer power must be even (because it is divisible by 2) and the number 3 raised to any positive integer power must be odd (since none of its prime factors will be 2). Clearly, an integer cannot be both odd and even at the same time: we have a contradiction. The only assumption we made was that log2 3 is rational (and so expressible as a quotient of integers m/n with n ≠ 0).
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Bringing out a district plan document giving district wise break-up of the annual plan began in the late 1960s and early 1970s. That could be the first event in the lineage of district planning exercise in Kerala. Each department prepared district-wise break up of schemes divisible among districts. That district- wise break-up of schemes has been consolidated into a single document by the Kerala State Planning Board for better monitoring of the state plan at the district level.
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A Binomial number is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial. The form of this binomial is \scriptstyle x^n \,\pm\, y^n, with \scriptstyle x \, > \, y and \scriptstyle n \, > \, 1 . However, since \scriptstyle x^n \,-\, y^n is always divisible by \scriptstyle x \,-\, y, when studying the numbers generated from the version with the negative sign, they are usually divided by \scriptstyle x \,-\, y first. Binomial numbers formed this way form Lucas sequences.
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In mathematics, the function field sieve was introduced in 1994 by Leonard Adleman as an efficient technique for extracting discrete logarithms over finite fields of small characteristic, and elaborated by Adleman and Huang in 1999. Sieving for points at which a polynomial-valued function is divisible by a given polynomial is not much more difficult than sieving over the integers – the underlying structure is fairly similar, and Gray code provides a convenient way to step through multiples of a given polynomial very efficiently.
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The body of an adult Raillietina is a typical tapeworm structure, composed of a series of ribbon-like body segments, gradually enlarging from the anterior end towards the posterior. It is whitish in colour, highly elongated, dorso-ventrally flat, and entirely covered with a tegument. The entire body is divisible into 3 parts, namely the head region called scolex, followed by an unsegmented neck or growth region, and then by highly segmented body proper called strobila.Li, M., Li, H, & Yan, B. (2009).
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Fermat's little theorem states that if p is prime and a is coprime to p, then ap−1 − 1 is divisible by p. For an integer a > 1, if a composite integer x divides ax−1 − 1, then x is called a Fermat pseudoprime to base a. It follows that if x is a Fermat pseudoprime to base a, then x is coprime to a. Some sources use variations of this definition, for example to allow only odd numbers to be pseudoprimes.
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It gets its efficiency by eschewing binary arithmetic for an "optical" adder which can add hundreds of thousands of quantities in a single clock cycle. The key idea used is "time-space inversion". Conventional NFS sieving is carried out one prime at a time. For each prime, all the numbers to be tested for smoothness in the range under consideration which are divisible by that prime have their counter incremented by the logarithm of the prime (similar to the sieve of Eratosthenes).
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However, this has the disadvantage that the data word does not appear as part of the code word. Instead, the following method is often used to create a systematic code: given a data word d(x) of length n-m, first multiply d(x) by x^m, which has the effect of shifting d(x) by m places to the left. In general, x^md(x) will not be divisible by g(x), i.e., it will not be a valid code word.
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By the fundamental theorem, N has a prime factorization : N = p'_1\cdot p'_2\cdots p'_m with one or more prime factors. N is evenly divisible by each of these factors, but N has a remainder of one when divided by any of the prime numbers in the given list, so none of the prime factors of N can be in the given list. Because there is no finite list of all the primes, there must be infinitely many primes.
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The American Absolute-Permissive Block system, known locally as Single Line Automatic, was installed on the Molong to Dubbo line by C.B. Byles in 1925. Train movements on the line were regulated by a Train Controller at Yeoval, who directed the issue of crossing orders for trains on the line. While a technical success, the traffic density did not warrant the cost of maintaining the signalling system. It was replaced by the first installation of the Divisible Miniature Electric Staff system in 1933.
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The (Markowitz) efficient frontier. CAL stands for the capital allocation line. The CAPM assumes that the risk-return profile of a portfolio can be optimized—an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible).
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This is the case if and only if the greatest common divisor of the polynomial and its derivative is not a constant. Thus for testing if a polynomial is square-free, it is not necessary to consider explicitly any field extension nor to compute the roots. In this context, the case of irreducible polynomials requires some care. A priori, it may seem that being divisible by a square is impossible for an irreducible polynomial, which has no non-constant divisor except itself.
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Bertrand's postulate was proposed for applications to permutation groups. Sylvester (1814–1897) generalized the weaker statement with the statement: the product of k consecutive integers greater than k is divisible by a prime greater than k. Bertrand's (weaker) postulate follows from this by taking k = n, and considering the k numbers n + 1, n + 2, up to and including n + k = 2n, where n > 1\. According to Sylvester's generalization, one of these numbers has a prime factor greater than k.
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Each of these five are of two types, explains Ganeri, (paramāṇu) and composite. A paramāṇu is that which is indestructible, indivisible, and has a special kind of dimension, called “small” (aṇu). A composite is that which is divisible into paramāṇu. Whatever human beings perceive is composite, and even the smallest perceptible thing, namely, a fleck of dust, has parts, which are therefore invisible. The Vaiśeṣikas visualized the smallest composite thing as a “triad” (tryaṇuka) with three parts, each part with a “dyad” (dyaṇuka).
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The cell may be distinguished from the figure or motif: the 1958 Encyclopédie Fasquelle defines a cell as "the smallest indivisible unit", unlike the motif, which may be divisible into more than one cell. "A cell can be developed, independent of its context, as a melodic fragment, it can be used as a developmental motif. It can be the source for the whole structure of the work; in that case it is called a generative cell."Nattiez 1990, p.156.
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1 is by convention neither a prime number nor a composite number, but a unit (meaning of ring theory) like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. For example, , but if units are included, is also equal to, say, among infinitely many similar "factorizations". 1 appears to meet the naïve definition of a prime number, being evenly divisible only by 1 and itself (also 1).
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Falcons are roughly divisible into three or four groups. The first contains the kestrels (probably excepting the American kestrel); usually small and stocky falcons of mainly brown upperside color and sometimes sexually dimorphic; three African species that are generally gray in color stand apart from the typical members of this group. Kestrels feed chiefly on terrestrial vertebrates and invertebrates of appropriate size, such as rodents, reptiles, or insects. The second group contains slightly larger (on average) species, the hobbies and relatives.
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In-frame insertions occur when the reading frame is not altered as a result of the insertion; the number of inserted nucleotides is divisible by three. The reading frame remains intact after the insertion and translation will most likely run to completion if the inserted nucleotides do not code for a stop codon. However, because of the inserted nucleotides, the finished protein will contain, depending on the size of the insertion, multiple new amino acids that may affect the function of the protein.
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140 is an abundant number and a harmonic divisor number. It is the sum of the squares of the first seven integers, which makes it a square pyramidal number, and in base 10 it is divisible by the sum of its digits, which makes it a Harshad number. 140 is an odious number because it has an odd number of ones in its binary representation. The sum of Euler's totient function φ(x) over the first twenty-one integers is 140.
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An algebraic curve is called p-circular if it contains the points (1, i, 0) and (1, −i, 0) when considered as a curve in the complex projective plane, and these points are singularities of order at least p. The terms bicircular, tricircular, etc. apply when p = 2, 3, etc. In terms of the polynomial F given above, the curve F(x, y) = 0 is p-circular if Fn−i is divisible by (x2 + y2)p−i when i < p.
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McDonald, Court of Appeals, No. 2015-7014, Fed. Cir. (2015). Accessed 2015-11-15. In 1989, the U.S. Supreme Court addressed rights under the USFSPA in the Mansell case and further limited the authority of State courts to assign spousal rights to military retirement pay. In Mansell, the court ruled that the USFSPA does not grant State courts the power to treat, as property divisible upon divorce, military retirement pay which has been waived in order to receive VA disability benefits.
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Graph showing relationships between the rule of twelfths (coloured bars), a sine wave (dashed blue curve) and a clockface, if high tide occurs at 12:00. The rule of twelfths is an approximation to a sine curve. It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12. Typical uses are predicting the height of the tide or the change in day length over the seasons.
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The division reflected an adherence to the old Frankish custom of partible or divisible inheritance amongst a ruler's sons, rather than primogeniture (i.e., inheritance by the eldest son) which would soon be adopted by both Frankish kingdoms. Since the Middle Frankish Kingdom combined lengthy and vulnerable land borders with poor internal communications as it was severed by the Alps, it was not a viable entity and soon fragmented. This made it difficult for a single ruler to reassemble Charlemagne's empire.
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The Adler-32 checksum is a specialization of the Fletcher-32 checksum devised by Mark Adler. The modulus selected (for both sums) is the prime number 65,521 (65,535 is divisible by 3, 5, 17 and 257). The first sum also begins with the value 1. The selection of a prime modulus results in improved "mixing" (error patterns are detected with more uniform probability, improving the probability that the least detectable patterns will be detected, which tends to dominate overall performance).
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When dollars were fully convertible into gold via the gold standard, both were regarded as money. However, most people preferred to carry around paper banknotes rather than the somewhat heavier and less divisible gold coins. If people feared their bank would fail, a bank run might result. This happened in the USA during the Great Depression of the 1930s, leading President Roosevelt to impose a national emergency and issue Executive Order 6102 outlawing the "hoarding" of gold by US citizens.
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The lone divider procedure is a procedure for proportional cake-cutting. It involves a heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over different parts of the cake. It allows the n people to divide the cake among them such that each person receives a piece with a value of at least 1/n of the total value according to his own subjective valuation. The procedure was developed by Hugo Steinhaus for n=3 people.
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Other innovations of his include the "Tate curve" parametrization for certain p-adic elliptic curves and the p-divisible (Tate–Barsotti) groups. Many of his results were not immediately published and some of them were written up by Serge Lang, Jean-Pierre Serre, Joseph H. Silverman and others. Tate and Serre collaborated on a paper on good reduction of abelian varieties. The classification of abelian varieties over finite fields was carried out by Taira Honda and Tate (the Honda–Tate theorem).
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Each player takes five dominoes, when playing with four players or more, or seven when playing with two or three. The remaining dominoes are placed to one side forming the "boneyard". The starting play is determined either by who holds the highest double or the highest-value domino; in either case, that domino is played first. If that domino is a 6–4, 5–5, 5–0, 4–1, or 3–2, the initial count is evenly divisible by five and so the player scores.
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Heath proposes that they stand in place of multiplication and division. By the term “magnitude” Eudoxus hoped to go beyond numbers to a general sense of size, a meaning it still retains. With regard to the figures of Euclid, it most often means numbers, which was the Pythagorean approach. Pythagoras believed the universe could be characterized by quantities, which belief has become the current scientific dogma. Book V of Euclid begins by insisting that a magnitude (megethos, “size”) must be divisible evenly into units (meros, “part”).
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The fourteenth finance commission is of the view that tax devolution should be the primary route of resources to the states. The commission recommends to increase the tax devolution of the divisible pool to states to 42% for years 2015 to 2020. This is 10% more compared to 32% target set by 13th financial commission. The commission recommended that the new tax devolution should be the primary route of transfer of resources to States since it is formula based and thus conducive to sound fiscal federalism.
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R. tetragona is the largest among avian tapeworms, measuring up to 30 cm in length and 1–1.5 cm in breadth. It is whitish in colour, highly elongated, dorso-ventrally flattened, and entirely covered with a tegument. The body is divisible into the head region called 'scolex', followed by an unsegmented 'neck', and then by highly segmented body proper called strobila. The strobila is composed of a series of ribbon-like body segments called proglottids, gradually enlarging from the anterior end towards the posterior.
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It grows as an exponential function of the square root of its argument. The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences. For instance, whenever the decimal representation of n ends in the digit 4 or 9, the number of partitions of n will be divisible by 5.
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The above example, however, is incomplete. If Mr. X purchases a computer, scanner, printer and desk as part of a package, with the explicit agreement that all parts must be delivered together, the failure to deliver the printer may be material breach of the entire contract. In addition, if a contract is made explicitly for a set - such as a complete set of books, furniture or clothes - the failure to deliver the entire set is almost certainly a breach of the entire contract. Also termed divisible contract.
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These are the current European records in the various age groups of Masters athletics, maintained by European Masters Athletics (EMA), the European Association of Masters Athletes. Starting at age 35, each age group starts on the athlete's birthday in years that are evenly divisible by 5 and extends until the next such occurrence. For record purposes, older athletes are not included in younger age groups, except in the case of relay team members. A relay team's age group is determined by the age of the youngest member.
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The experiments, in general, were first introduced in the Lilo & Stitch prequel comics shown in Disney Adventures magazine and in the PlayStation 2 prequel video game Disney's Stitch: Experiment 626, which were released before the original film's premiere, but they did not make their official debut in the animated continuity until Stitch! The Movie. The pronunciation of each experiment's number is typically by digit (e.g. Stitch is "Experiment Six-Two-Six"), with the only known exceptions being those whose numbers are divisible by 100 (e.g.
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Different types of indel mutation. Panel C is simply a deletion and not a frameshift mutation. A frameshift mutation (also called a framing error or a reading frame shift) is a genetic mutation caused by indels (insertions or deletions) of a number of nucleotides in a DNA sequence that is not divisible by three. Due to the triplet nature of gene expression by codons, the insertion or deletion can change the reading frame (the grouping of the codons), resulting in a completely different translation from the original.
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It is known that no non-constant polynomial function P(n) with integer coefficients exists that evaluates to a prime number for all integers n. The proof is as follows: suppose such a polynomial existed. Then P(1) would evaluate to a prime p, so P(1) \equiv 0 \pmod p. But for any integer k, P(1+kp) \equiv 0 \pmod p also, so P(1+kp) cannot also be prime (as it would be divisible by p) unless it were p itself.
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ILAS collaborates with the Society for Industrial and Applied Mathematics (SIAM), the American Mathematical Society (AMS) and the International Workshop on Operator Theory and its Applications (IWOTA). The collaboration with SIAM started in 1999. The SIAM Activity Group on Linear Algebra (SIAG/LA) holds a conference every three years (when the year minus 2000 is divisible by 3). As part of the agreement, and to encourage interaction between ILAS and SIAG/LA members, the two societies do not hold conferences in the same year.
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In many POW camps, cigarettes were widely used as currency known as 'commodity money'. They performed the functions of money as a medium of exchange because they were generally accepted among the prisoners for settling payments or debts, and the function of money as a unit of account, because prices of other goods were expressed in terms of cigarettes. Compared with other goods, the supply of cigarettes was more stable, as they were rationed in the POW camps, and cigarettes were more divisible, portable, and homogeneous.
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Ciphertext stealing provides support for sectors with size not divisible by block size, for example, 520-byte sectors and 16-byte blocks. XTS-AES was standardized on 2007-12-19 as IEEE P1619. The standard supports using a different key for the IV encryption than for the block encryption; this is contrary to the intent of XEX and seems to be rooted in a misinterpretation of the original XEX paper, but does not harm security., On the Use of Two Keys, pp. 1–3.
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As we know, this shows that the lacunary part of coincides with that of the original polynomial . Therefore the difference has no lacunary part, and is therefore divisible by the product of all variables, which equals the elementary symmetric polynomial . Then writing , the quotient is a homogeneous symmetric polynomial of degree less than (in fact degree at most ) which by the inductive assumption can be expressed as a polynomial in the elementary symmetric functions. Combining the representations for and one finds a polynomial representation for .
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The ceramic industry of Siswal is divisible into three groups, Siswal A yielded the Kalibangan I Ware, with all the typical fabrics (A to F). Fabric A is painted with white pigment in addition to the black. In Siswal B, the late Siswal phase, both the Late Siswal and the Harappan Wares are found. This second phase is characterized by the austerity in shape and design, along with a disappearance of painted white pigment. Better potting technique can also be seen within this second group.
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The body of an adult R. echinobothrida is a characteristic tapeworm structure, composed of a series of ribbon-like body segments, gradually enlarging from the anterior end towards the posterior. It is whitish in colour, highly elongated, dorsoventrally flattened, and entirely covered with a tegument. The body can be as long as 25 cm, and generally 1–1.5 cm broad. The body is divisible into the head region called 'scolex', followed by an unsegmented 'neck', and then by highly segmented body proper called 'strobila'.
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In mathematics, the concept of quantity is an ancient one extending back to the time of Aristotle and earlier. Aristotle regarded quantity as a fundamental ontological and scientific category. In Aristotle's ontology, quantity or quantum was classified into two different types, which he characterized as follows: :'Quantum' means that which is divisible into two or more constituent parts, of which each is by nature a 'one' and a 'this'. A quantum is a plurality if it is numerable, a magnitude if it is measurable.
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It was recorded entirely in Jamaica, with Henriques collaborating with producers on the island such as Steven "Lenky" Marsden, Donovan "Don Corleon" Bennett, Renaissance Crew, and Rohan "Jah Snowcone" Fuller, among others. Explaining the album's title, Henriques pointed out that it is his third album, and has spent three years in production, being "all done right here in the Third World." Also, it could be noted that the album's release date, 27 September (9/27), when divided equals 3 and consists of two numbers divisible by 3.
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The most obvious generalization to multiple or divisible goods is to have all winning bidders pay the amount of the highest non-winning bid. This is known as a uniform price auction. The uniform-price auction does not, however, result in bidders bidding their true valuations as they do in a second-price auction unless each bidder has demand for only a single unit. A generalization of the Vickrey auction that maintains the incentive to bid truthfully is known as the Vickrey–Clarke–Groves (VCG) mechanism.
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The St. John's Convention Centre (newly branded as SJCC), located in Downtown St. John's, Newfoundland and Labrador at 101 New Gower Street is the province's largest convention centre with 47,000 square feet (4365 sq m) of divisible meeting space. The convention centre was built in May 2001 along with its sister building Mile One Centre, directly across the street. Both buildings are operated by St. John's Sports & Entertainment Ltd. SJCC is linked to Mile One Centre and the Delta St. John's Hotel by a pedway system.
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Because it is divisible by the sum of its digits in base 10, it is a Harshad number. A number system with base 60 is called sexagesimal (the original meaning of sexagesimal is sixtieth). It is the smallest positive integer that is written with only the smallest and the largest digit of base 2 (binary), base 3 (ternary) and base 4 (quaternary). 60 is also the product of the side lengths of the smallest whole number right triangle: 3, 4, 5, a type of Pythagorean triple.
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A variation of the paradox uses integers instead of real-numbers, while preserving the self- referential character of the original. Consider a language (such as English) in which the arithmetical properties of integers are defined. For example, "the first natural number" defines the property of being the first natural number, one; and "divisible by exactly two natural numbers" defines the property of being a prime number. (It is clear that some properties cannot be defined explicitly, since every deductive system must start with some axioms.
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Since 58 is itself not divisible by 3. This latter example will be termed as having the property of being Richardian. Thus, if a number is Richardian, then the definition corresponding to that number is a property that the number itself does not have. (More formally, "x is Richardian" is equivalent to "x does not have the property designated by the defining expression with which x is correlated in the serially ordered set of definitions".) Thus in this example, 58 is Richardian, but 43 is not.
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This is true for every common divisor of a and b. However, unlike other common divisors, the greatest common divisor is a member of the set; by Bézout's identity, choosing u = s and v = t gives g. A smaller common divisor cannot be a member of the set, since every member of the set must be divisible by g. Conversely, any multiple m of g can be obtained by choosing u = ms and v = mt, where s and t are the integers of Bézout's identity.
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These groups also played a role in the discovery of the first modern sporadic group. They have involution centralizers of the form Z/2Z × PSL(2, q) for q = 3n, and by investigating groups with an involution centralizer of the similar form Z/2Z × PSL(2, 5) Janko found the sporadic group J1. The Suzuki groups are the only finite non-abelian simple groups with order not divisible by 3. They have order 22(2n+1)(22(2n+1) \+ 1)(2(2n+1) − 1).
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The unconformity is well exposed on the shores of Gairloch, Loch Maree and Loch Torridon. These rocks, which attain a considerable thickness and are divisible into three sub-groups, build up the mountain districts of Applecross, Coigach and elsewhere. Within the Torridonian tract the older Lewisian gneiss occupies large areas north of Coigach, on the east of Enard Bay, between Gruinard Bay and Loch Maree. Between the last named and Gairloch, on both sides of middle Loch Torridon and at many other spots smaller patches appear.
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The shorter of these two is called the ganglionic system, and the vessels belonging to it supply the thalami and corpora striata; the longer is the cortical system, and its vessels ramify in the pia mater and supply the cortex and subjacent brain substance. Furthermore, the cortical branches are divisible into two classes: long and short. The long or medullary arteries pass through the grey substance and penetrate the subjacent white substance to the depth of 3–4 cm. The short vessels are confined to the cortex.
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The converse of the statement above is, however, not always true. For example, the digital root of 12, which is not a triangular number, is 3 and divisible by three. If is a triangular number, then is also a triangular number, given is an odd square and will always be a triangular number, because , which yields all the odd squares are revealed by multiplying a triangular number by 8 and adding 1, and the process for given is an odd square is the inverse of this operation.
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The distribution of a Lévy process has the property of infinite divisibility: given any integer n, the law of a Lévy process at time t can be represented as the law of n independent random variables, which are precisely the increments of the Lévy process over time intervals of length t/n, which are independent and identically distributed by assumptions 2 and 3. Conversely, for each infinitely divisible probability distribution F, there is a Lévy process X such that the law of X_1 is given by F.
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Particular justice is however the subject of this book, and it has already been divided into the lawful and the fair, which are two different aspects of universal justice or complete virtue. Concerning areas where being law-abiding might not be the same as being fair, Aristotle says that this should be discussed under the heading of Politics.Such a discussion appears in Book III of his Politics. He then divides particular justice further into two parts: distribution of divisible goods and rectification in private transactions.
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The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the society. The medal is awarded every third year (in years divisible by 3) to a mathematician who is normally resident in the United Kingdom on 1 January of the relevant year. The only grounds for the award of the medal are the candidate's contributions to mathematics.
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Translated into modern notation, Euler stated Lemmermeyer, p. 5, Ireland & Rosen, pp. 54, 61 that for distinct odd primes p and q: # If q ≡ 1 (mod 4) then q is a quadratic residue (mod p) if and only if there exists some integer b such that p ≡ b2 (mod q). # If q ≡ 3 (mod 4) then q is a quadratic residue (mod p) if and only if there exists some integer b which is odd and not divisible by q such that p ≡ ±b2 (mod 4q).
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One of their names, Clovis, evolved into Louis and remained common among French royalty down to the 19th century. The first known Merovingian king was Childeric I (died 481). His son Clovis I (died 511) converted to Christianity, united the Franks and conquered most of Gaul. The Merovingians treated their kingdom as single yet divisible. Clovis's four sons divided the kingdom between them and it remained divided—with the exception of four short periods (558–61, 613–23, 629–34, 673–75)—down to 679.
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In algebraic geometry, the Serre–Tate theorem, says that an abelian scheme and its p-divisible group have the same infinitesimal deformation theory. This was first proved by Serre when the reduction of the abelian variety is ordinary, using the Greenberg functor; then Tate gave a proof in the general case by a different method. Their proofs were not published, but they were summarized in the notes of the Lubin–Serre–Tate seminar (Woods Hole, 1964). Other proofs were published by Messing (1962) and Drinfeld (1976).
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The basic version of the test relies on the Pocklington theorem (or Pocklington criterion) which is formulated as follows: Let N > 1 be an integer, and suppose there exist numbers and such that Then is prime. Note: Equation () is simply a Fermat primality test. If we find any value of , not divisible by , such that equation () is false, we may immediately conclude that is not prime. (This divisibility condition is not explicitly stated because it is implied by equation ().) For example, let N = 35.
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Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5. If the last digit in the number is 0, then the result will be the remaining digits multiplied by 2. For example, the number 40 ends in a zero (0), so take the remaining digits (4) and multiply that by two (4 × 2 = 8).
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The exact values of the Dedekind numbers are known for 0 ≤ n ≤ 8: :2, 3, 6, 20, 168, 7581, 7828354, 2414682040998, 56130437228687557907788 . The first six of these numbers are given by . M(6) was calculated by , M(7) was calculated by and , and M(8) by . If n is even, then M(n) must also be even.. The calculation of the fifth Dedekind number M(5) = 7581 disproved a conjecture by Garrett Birkhoff that M(n) is always divisible by (2n − 1)(2n − 2)..
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The puzzle of Democritus. If a cone is sliced horizontally, are the surfaces produced equal or unequal? Chrysippus regarded bodies, surfaces, lines, places, the void and time as all being infinitely divisible. He determined one of the principal features of the infinite set: since a man and a finger have an infinite number of parts as do the universe and a man, it cannot be said that a man has more parts than his finger, nor that the universe has more parts than a man.
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One point is scored for each time this total is exactly divisible by either 5 or 3. So if the play started double 6 it would score 4 points as 12/3 is exactly 4. If the next player played a 6-3 then the maximum is scored for a single turn of 15 for 8 points (5 for the 3s and 3 for the 5s). If the next player were to play 6-1 the total would be 4 and they would score no points.
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Some experts apply MPT to portfolios of projects and other assets besides financial instruments. When MPT is applied outside of traditional financial portfolios, some distinctions between the different types of portfolios must be considered. # The assets in financial portfolios are, for practical purposes, continuously divisible while portfolios of projects are "lumpy". For example, while we can compute that the optimal portfolio position for 3 stocks is, say, 44%, 35%, 21%, the optimal position for a project portfolio may not allow us to simply change the amount spent on a project.
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Codere suggest that a true class- organized society is one in which the hierarchy of prestige and status is divisible into groups each with its own social, economic, attitudinal and cultural characteristics and each having differential degrees of power in community decision. Since determination of life outcome by birth class has proved historically difficult to avoid, advocates of a classless society such as anarchists, communists and libertarian socialists propose various means to achieve and maintain it and attach varying degrees of importance to it as an end in their overall programs/philosophy.
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Blank-day calendars remove a day or two (the latter for leap years) from the weekday cycle, resulting in a year length of 364 weekdays. Since this number is evenly divisible by 7, every year can begin on the same weekday. In the twelve-month plan of The World Calendar, for example, the Gregorian year- end date of December 31 is sequestered from the cycle of the week and celebrated as "Worldsday". December 30 falls on a Saturday, Worldsday follows next, and then January 1 begins every new year on a Sunday.
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Seventeen is the minimum number of vertices on a graph such that, if the edges are coloured with three different colours, there is bound to be a monochromatic triangle. (See Ramsey's theorem.) Seventeen is the only prime number which is the sum of four consecutive primes (2,3,5,7). Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime. The sequence of residues (mod n) of a googol and googolplex, for n = 1, 2, 3, ..., agree up until n = 17.
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Swainson's Quinarian structure of birds Quinarianism gets its name from the emphasis on the number five: it proposed that all taxa are divisible into five subgroups, and if fewer than five subgroups were known, quinarians believed that a missing subgroup remained to be found. Nicholas Aylward Vigors's Quinarian classification of birds. The missing entries represented groups that he expected remained to be discovered. Presumably this arose as a chance observation of some accidental analogies between different groups, but it was erected into a guiding principle by the quinarians.
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They could be screened easily by using a specific strain of E. coli, known as K12 (λ), that was susceptible to wild type T4 but not to r mutants.Jayaraman, p. 903 Benzer's concept was quite controversial within classical genetic thought, in which each gene is treated as a singular point along a chromosome, not a divisible stretch of nucleic acids (as implied by the work of Watson and Crick). Initially, Max Delbrück--a respected phage geneticist and leader of the so-called phage group of which Benzer was a part--found Benzer's idea outrageous.
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The Creation of Man by Ephraim Moses Lilien, 1903. Jacob flees Laban by Charles Foster, 1897. The Book of Genesis, the first book of the Hebrew Bible and the Christian Old Testament, is an account of the creation of the world, the early history of humanity, Israel's ancestors, and the origins of the Jewish people. Its Hebrew name is the same as its first word, Bereshit ("In the beginning"). It is divisible into two parts, the primeval history (chapters 1–11) and the ancestral history (chapters 12–50).
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Sometimes these theories overlapped with mythology and were personified in deities. Some of these interpretations included atomism (the idea of very small, indivisible portions of matter), but other interpretations considered the elements to be divisible into infinitely small pieces without changing their nature. While the classification of the material world in ancient Indian, Hellenistic Egypt, and ancient Greece into Air, Earth, Fire and Water was more philosophical, during the Islamic Golden Age medieval middle eastern scientists used practical, experimental observation to classify materials.Science and Islam, Jim Al-Khalili.
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Reason is a unity not itself divisible, as it can only be used in the singular, unlike intellect and intellects. The intellect operating at the sense pole provides the power that leads to abstraction and man's separation from nature, but also awareness of self as separate from nature and God. However, detachment can lead to existential despair without the 'light of reason' to provide a new attachment or relationship to nature and God, one based on individual sovereignty. With reason, the nisus is from sense to consciousness and finally to self-consciousness, that is, individuation.
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Of the Origin and Use of Money: With division of labour, the produce of one's own labour can fill only a small part of one's needs. Different commodities have served as a common medium of exchange, but all nations have finally settled on metals, which are durable and divisible, for this purpose. Before coinage, people had to weigh and assay with each exchange, or risk "the grossest frauds and impositions." Thus nations began stamping metal, on one side only, to ascertain purity, or on all sides, to stipulate purity and amount.
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Social Insurance Numbers can be validated through a simple check digit process called the Luhn algorithm. 046 454 286 <\--- A fictitious, but valid SIN 121 212 121 <\--- Multiply each digit in the top number by the digit below it. So the result of the multiplication is: 0 8 6 8 5 8 2 16 6 Then, add all of the digits together (note that 16 is 1+6): 0 + 8 + 6 + 8 + 5 + 8 + 2 + 1+6 + 6 = 50 If the SIN is valid, this number will be evenly divisible by 10.
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These numbers are always divisible by (because a cyclic permutation of a foldable stamp sequence is always itself foldable),. As cited by and the quotients of this division are :1, 1, 2, 4, 10, 24, 66, 174, 504, 1406, 4210, 12198, 37378, 111278, 346846, 1053874, ... , the number of topologically distinct ways that a half-infinite curve can make crossings with a line, called "semimeanders". In the 1960s, John E. Koehler and W. F. Lunnon implemented algorithms that, at that time, could calculate these numbers for up to 28 stamps.
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The forgetful functor has a left adjoint (which associates to a given set the free abelian group with that set as basis) but does not have a right adjoint. Taking direct limits in Ab is an exact functor. Since the group of integers Z serves as a generator, the category Ab is therefore a Grothendieck category; indeed it is the prototypical example of a Grothendieck category. An object in Ab is injective if and only if it is a divisible group; it is projective if and only if it is a free abelian group.
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Dieudonné theory exists in a somewhat more general setting than finite flat groups over a field. Oda's 1967 thesis gave a connection between Dieudonné modules and the first de Rham cohomology of abelian varieties, and at about the same time, Grothendieck suggested that there should be a crystalline version of the theory that could be used to analyze p-divisible groups. Galois actions on the group schemes transfer through the equivalences of categories, and the associated deformation theory of Galois representations was used in Wiles's work on the Shimura–Taniyama conjecture.
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A more restrictive taxicab problem requires that the taxicab number be cubefree, which means that it is not divisible by any cube other than 13. When a cubefree taxicab number T is written as T = x3 + y3, the numbers x and y must be relatively prime. Among the taxicab numbers Ta(n) listed above, only Ta(1) and Ta(2) are cubefree taxicab numbers. The smallest cubefree taxicab number with three representations was discovered by Paul Vojta (unpublished) in 1981 while he was a graduate student. It is :15170835645 ::= 5173 \+ 24683 ::= 7093 \+ 24563 ::= 17333 \+ 21523.
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Fermat's little theorem states that if p is prime and a is coprime to p, then ap−1 − 1 is divisible by p. For an integer a > 1, if a composite integer x divides ax−1 − 1, then x is called a Fermat pseudoprime to base a. In other words, a composite integer is a Fermat pseudoprime to base a if it successfully passes the Fermat primality test for the base a. The false statement that all numbers that pass the Fermat primality test for base 2, are prime, is called the Chinese hypothesis.
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In abstract algebra, a basic subgroup is a subgroup of an abelian group which is a direct sum of cyclic subgroups and satisfies further technical conditions. This notion was introduced by L. Ya. Kulikov (for p-groups) and by László Fuchs (in general) in an attempt to formulate classification theory of infinite abelian groups that goes beyond the Prüfer theorems. It helps to reduce the classification problem to classification of possible extensions between two well understood classes of abelian groups: direct sums of cyclic groups and divisible groups.
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Philip Guedalla in 1928 Philip Guedalla (12 March 1889 – 16 December 1944) was an English barrister, and a popular historical and travel writer and biographer. His wit and epigrams are well-known, one example being "Even reviewers read a Preface," another being "History repeats itself. Historians repeat each other." He also was the originator of a now-common theory on Henry James, writing that "The work of Henry James has always seemed divisible by a simple dynastic arrangement into three reigns: James I, James II, and the Old Pretender".
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This method works fine for the year 2000 (because it is a leap year), and will not become a problem until 2100, when older legacy programs will likely have long since been replaced. Other programs contained incorrect leap year logic, assuming for instance that no year divisible by 100 could be a leap year. An assessment of this leap year problem including a number of real life code fragments appeared in 1998.A. van Deursen, "The Leap Year Problem" The Year/2000 Journal 2(4):65–70, July/August 1998.
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This can be deduced from the Atiyah–Singer index theorem: Michael Atiyah and Isadore Singer showed that the  genus is the index of the Atiyah–Singer operator, which is always integral, and is even in dimensions 4 mod 8. For a 4-dimensional manifold, the Hirzebruch signature theorem shows that the signature is −8 times the  genus, so in dimension 4 this implies Rokhlin's theorem. proved that if X is a compact oriented smooth spin manifold of dimension 4 mod 8, then its signature is divisible by 16.
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Students in Year 13 study five full- year elective subjects, with study for an additional four periods per week. Because the 25-period-per-week school timetable is not evenly divisible into six subject lines, students in Years 11 to 13 spend the last period on Wednesdays either in supervised study or sport practice. Rangiora High School has a school farm, which is used to teach land-based studies. Set up in 1910, it started out running stock and growing crops, before being officially opened in November 1930 by Lord Bledisloe, the then Governor-General.
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The milieu of the organism is divisible into the exterior milieu (geography, climate, animals and vegetation) and the interior milieu (the shared past of the group, thus "culture", etc.). This division enables a clarification of the concept of technical tendency. A tendency, according to Leroi-Gourhan, is a movement, within the interior milieu, that gains progressive foothold in the exterior milieu. Leroi-Gourhan contributed to the methods of studying prehistoric technology, introducing the concept chaîne opératoire (operational chain) which denotes all the social acts involved in the life cycle of an artifact.
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In other words, it is the subalgebra of k[t] generated by t2 and t3. Example: let f be a polynomial in one variable, that is, an element in a polynomial ring R. Then f(x+h) is an element in R[h] and f(x + h) - f(x) is divisible by h in that ring. The result of substituting zero to h in (f(x + h) - f(x))/h is f'(x), the derivative of f at x. The substitution is a special case of the universal property of a polynomial ring.
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If n is not a prime power, then every Sylow subgroup is proper, and, by Sylow's Third Theorem, we know that the number of Sylow p-subgroups of a group of order n is equal to 1 modulo p and divides n. Since 1 is the only such number, the Sylow p-subgroup is unique, and therefore it is normal. Since it is a proper, non-identity subgroup, the group is not simple. Burnside: A non-Abelian finite simple group has order divisible by at least three distinct primes.
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The Oxford Companion to Philosophy suggests that reductionism is "one of the most used and abused terms in the philosophical lexicon" and suggests a three part division: #Ontological reductionism: a belief that the whole of reality consists of a minimal number of parts. #Methodological reductionism: the scientific attempt to provide explanation in terms of ever smaller entities. #Theory reductionism: the suggestion that a newer theory does not replace or absorb an older one, but reduces it to more basic terms. Theory reduction itself is divisible into three parts: translation, derivation and explanation.
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If a player passes their bidding turn, he passes it permanently for this game round and cannot make bid even if the bidding turn comes back again to him, thus he is not taking part in bidding for this round anymore. Minimum bid increment is 5 points, all bids have to be divisible by 5. (100 / 105 / 155 / etc.) Notice: The final declaration of points the bidding-winner player is obliged to score during game round can be increased after the stock is observed and cards are given away.
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Before the 1998 regular season began, two new teams—the Arizona Diamondbacks and Tampa Bay Devil Rays—were added by Major League Baseball. This resulted in the American League and National League having fifteen teams. However, in order for MLB officials to continue primarily intraleague play, both leagues would need to carry a number of teams that was divisible by two, so the decision was made to move one club from the AL Central to the NL Central. This realignment was widely considered to have great financial benefit to the club moving.
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A notable achievement was his discovery in 1960 of the Suzuki groups, an infinite family of the only non-abelian simple groups whose order is not divisible by 3. The smallest, of order 29120, was the first simple group of order less than 1 million to be discovered since Dickson's list of 1900. He classified several classes of simple groups of small rank, including the CIT- groups and C-groups and CA-groups. There is also a sporadic simple group called the Suzuki group, which he announced in 1968.
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All five extant species show prolonged parental care of infants, with low rates of reproduction and relatively long life-spans. Monotremes are also noteworthy in their zygotic development: Most mammal zygotes go through holoblastic cleavage, meaning that after fertilization, the ovum splits into multiple, divisible daughter cells. In contrast, the zygotes of monotremes, like those of birds and reptiles, undergo meroblastic (partial) division. This means the cells at the yolk's edge have cytoplasm continuous with that of the egg, which allows the yolk and embryo to exchange waste and nutrients with the surrounding cytoplasm.
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It is known that the nth Mersenne number is prime only if n is prime. Fermat's little theorem implies that if is prime, then Mp−1 is always divisible by p. Since Mersenne numbers of prime indices Mp and Mq are co-prime, ::A prime divisor p of Mq, where q is prime, is a Wieferich prime if and only if p2 divides Mq. Thus, a Mersenne prime cannot also be a Wieferich prime. A notable open problem is to determine whether or not all Mersenne numbers of prime index are square-free.
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Cambridge, UK: Cambridge University Press. This entails certain properties of cultural models, and may explain both part of the observed inertia of cultural models (people's assumptions about the way the world works are hard to change) and patterns of association.Strauss, Claudia and Naomi Quinn (1997) A Cognitive Theory of Cultural Meaning. Cambridge, UK: Cambridge University Press. Roy D'Andrade (1995) sees the history of cognitive anthropology proper as divisible into four phases. The first began in the 1950s with the explicit formulation of culture as knowledge by anthropologists such as Ward GoodenoughGoodenough, W. H. (1969).
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The negative Pell equation is given by : x^2 - ny^2 = -1. It has also been extensively studied; it can be solved by the same method of continued fractions and will have solutions if and only if the period of the continued fraction has odd length. However it is not known which roots have odd period lengths and therefore not known when the negative Pell equation is solvable. A necessary (but not sufficient) condition for solvability is that n is not divisible by 4 or by a prime of form 4k + 3.
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This is because the Pell equation implies that −1 is a quadratic residue modulo n. Thus, for example, x2 − 3ny2 = −1 is never solvable, but x2 − 5ny2 = −1 may be. The first few numbers n for which x2 − ny2 = −1 is solvable are :1, 2, 5, 10, 13, 17, 26, 29, 37, 41, 50, 53, 58, 61, 65, 73, 74, 82, 85, 89, 97, ... . The proportion of square-free n divisible by k primes of the form 4m + 1 for which the negative Pell equation is solvable is at least 40%.
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An efficient algorithm to solve the discrete logarithm problem would make it easy to compute a or b and solve the Diffie–Hellman problem, making this and many other public key cryptosystems insecure. Fields of small characteristic may be less secure. The order of G should have a large prime factor to prevent use of the Pohlig–Hellman algorithm to obtain a or b. For this reason, a Sophie Germain prime q is sometimes used to calculate , called a safe prime, since the order of G is then only divisible by 2 and q.
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2006, Hackett et al. 2008). Fain and Houde (2004) proposed that Neoaves are divisible into two clades, Metaves and Coronaves, although it has been suggested from the start that Metaves maybe paraphyletic (Fain and Houde 2004, Ericson et al. 2006, Hackett et al. 2008). Sunbittern, kagu, and mesites all group within Metaves but all the other lineages of "Gruiformes" group either with a collection of waterbirds or landbirds within Coronaves. This division has been upheld by the combined analysis of as many as 30 independent loci (Ericson et al. 2006, Hackett et al.
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In British public houses and social clubs, a scoring version of "5s-and-3s" is used. The game is normally played in pairs (two against two) and is played as a series of "ends". In each "end", the objective is for players to attach a domino from their hand to one end of those already played so that the sum of the end dominoes is divisible by five or three. One point is scored for each time five or three can be divided into the sum of the two dominoes, i.e.
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The Colorado State Board of Education is a government body in the U.S. state of Colorado tasked with "general supervision of public schools." It is composed of members elected from districts corresponding to Colorado's congressional districts – following the 2000 census, there are seven districts and therefore seven members. Elected in partisan elections, they serve staggered six-year terms. Districts 5 and 6 hold elections in years divisible by six, followed two years later by Districts 2 and 4, and two years later by Districts 1, 3, and 7.
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Anthony Kenny, Aquinas on Mind (London: Routledge, 1993), p. 24, 26, 28 This seems to imply that the human soul cannot exist apart from the body. Indeed, Aristotle writes, "It is clear that the soul, or at least some parts of it (if it is divisible), cannot be separated from the body. [...] And thus, those have the right idea who think that the soul does not exist without the body."De Anima 413a4-5; 414a19-20 In Aristotelianism, at least one psychological force, the active intellect, can exist apart from the body.
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144 is the twelfth Fibonacci number, and the largest one to also be a square,Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165 as the square of 12 (which is also its index in the Fibonacci sequence), following 89 and preceding 233. 144 is the smallest number with exactly 15 divisors, but it is not highly composite since the smaller number 120 has 16 divisors. 144 is divisible by the value of its φ function, which returns 48 in this case.
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The patent for the Teleboard is held by Uniboard, Inc. (US Patent #6000711) The abstract is as follows: > A skiboard system is provided, which includes a divisible skiboard having > left and right skiboard halves and left and right loose heel binding. When > the skiboard halves are joined, the skiboard has a central, waist portion > and an upward curving front shovel area. The left and right loose heel > bindings may be secured on the left and right skiboard halves when the > skiboard halves are divided, oriented substantially parallel to the > longitudinal axes or the skiboard halves.
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Additive rhythm features nonidentical or irregular durational groups following one another at two levels, within the bar and between bars or groups of bars . This type of rhythm is also referred to in musicological literature by the Turkish word aksak, which means "limping" (; ). In the special case of time signatures in which the upper numeral is not divisible by two or three without a fraction, the result may alternatively be called irregular, imperfect, or uneven meter, and the groupings into twos and threes are sometimes called long beats and short beats .Additive rhythm in time.
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The Book of Genesis is the first book of the Torah.Hamilton (1990), p. 1 It is divisible into two parts, the Primeval history (chapters 1–11) and the Ancestral history (chapters 12–50). The primeval history sets out the author's (or authors') concepts of the nature of the deity and of humankind's relationship with its maker: God creates a world which is good and fit for mankind, but when man corrupts it with sin God decides to destroy his creation, saving only the righteous Noah to reestablish the relationship between man and God.
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Let K be a number field with ring of integers R. Let S be a finite set of prime ideals of R. An element x of K is an S-unit if the principal fractional ideal (x) is a product of primes in S (to positive or negative powers). For the ring of rational integers Z one may take S to be a finite set of prime numbers and define an S-unit to be a rational number whose numerator and denominator are divisible only by the primes in S.
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Distributive legislation is considered omnibus and combines the small, divisible pieces that cater to many districts. This allocates funds for a collection of independent, local projects, which vary in size, scope, and dollar amount. Oftentimes, pieces of the omnibus legislation are unconnected, so “owing to the unrelatedness of issues in distributive politics, the activities of single participants need not be related but rather can be specialized as the situation warrants it.” With omnibus packages, benefits that only serve small populations are more likely to gain majority support for Congressional passage.
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If G is cyclic then the transfer takes any element y of G to y[G:H]. A simple case is that seen in the Gauss lemma on quadratic residues, which in effect computes the transfer for the multiplicative group of non-zero residue classes modulo a prime number p, with respect to the subgroup {1, −1}. One advantage of looking at it that way is the ease with which the correct generalisation can be found, for example for cubic residues in the case that p − 1 is divisible by three.
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The mean is a moment so the log-Cauchy distribution does not have a defined mean or standard deviation. The log-Cauchy distribution is infinitely divisible for some parameters but not for others. Like the lognormal distribution, log-t or log- Student distribution and Weibull distribution, the log-Cauchy distribution is a special case of the generalized beta distribution of the second kind. The log-Cauchy is actually a special case of the log-t distribution, similar to the Cauchy distribution being a special case of the Student's t distribution with 1 degree of freedom.
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This is known as a "heat" or "consi". Often a small amount of practice time (usually 30 seconds) will be given to the drivers prior to the start of each heat. If there are an odd number of drivers such that they are not wholly divisible into the number of lanes, one of two measures is taken: either a heat is run with one or more positions unfilled, or a heat is run with extra drivers, with a "sit-out" position. After all drivers have run their heat, placement is determined by total laps completed.
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The Lütfi Kırdar Center as the main building of the complex consists of Anadolu Auditorium with a seating capacity of 2,000 people, Marmara Hall, two Topkapı halls, three Dolmabahçe halls, Galata Hall, Haliç Hall, three Sultan meeting rooms, three Barbaros meeting rooms, four Levent meeting rooms and VIP rooms. The Rumeli Center offers a space as a preferred ballroom and fair area in central city. Upper Level is a 3,500-guest capacity activity area of divisible in four independent spaces with a foyer. Lower Level with separate entrance.
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To prevent this, a journaled file system allocates a special area—the journal—in which it records the changes it will make ahead of time. After a crash, recovery simply involves reading the journal from the file system and replaying changes from this journal until the file system is consistent again. The changes are thus said to be atomic (not divisible) in that they either succeed (succeeded originally or are replayed completely during recovery), or are not replayed at all (are skipped because they had not yet been completely written to the journal before the crash occurred).
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In 1999, Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas announced a proof of this conjecture. , their proof remains largely unpublished.. See the Hadwiger conjecture for other problems and results relating graph coloring to graph minors. Tutte also conjectured a generalization to arbitrary graphs: every bridgeless graph with no Petersen minor has a nowhere zero 4-flow. That is, the edges of the graph may be assigned a direction, and a number from the set {1, 2, 3}, such that the sum of the incoming numbers minus the sum of the outgoing numbers at each vertex is divisible by four.
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The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded. First given in 1987, the prize is named after Hungarian mathematician George Pólya, who was a member of the society for over 60 years. The prize is awarded "in recognition of outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom".
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Nigeria is divisible into zones on the basis of techniques of construction as follows: #Mud construction techniques which are very common in most parts of southern Nigeria and in Ibeku. #Stone construction techniques which are very common in most parts of Northern Nigeria; and #Combination of mud and stone construction techniques. This development is common in Tivland, where the ancient houses and protective walls on hill-tops were constructed of stones, while present- day houses in the plains are usually constructed of mud. Given our experiences in Ibeku (umuahia ibeku) Nigeria, the third category of construction is very useful for generating models.
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Even working is a term used in book publishing that means the number of pages in a book is divisible by the number 16 or 32.R. M. Ritter, The Oxford Guide to Style, OUP, 2002, p. 1. A book with 256, 272 or 288 pages, for instance, is an "even working", whilst a book with 254 or 286 pages is not. The significance of 16 or 32, which form the individual "signatures" of which a book is composed, is that they make the most efficient use of the paper used in the printing of a book.
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In 1825, Kulik mentioned a table of factors up to 30 million, but this table does no longer seem to exist. It is also not clear if it had really been completed. From about 1825 until 1863 Kulik produced a factor table of numbers up to 100330200 (except for numbers divisible by 2, 3, or 5). This table basically had the same format than the table to 30 million and it is therefore most likely that the work on the "Magnus canon divisorum" spanned from the mid-1820s to Kulik's death, at which time the tables were still unfinished.
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The theca are divisible into left and right sides longitudinally by a sagittal suture; there is also a latitudinal girdle. Structurally complex, the genus is characterized by possession of extensive girdle and sulcal lists (wing-like extensions of the cell wall). Their theca have numerous pores which open flush to the surface of the plate on the outside but have a raised rim on the inside, their number being positively correlated with cell size. The hypotheca of most species are covered in areolae (shallow depressions) which are deepened by secondary thickening which takes place in mature cells.
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Some customary systems of weights and measures had duodecimal ratios, which meant quantities were conveniently divisible by 2, 3, 4, and 6. But it was difficult to do arithmetic with things like pound or foot. There was no system of notation for successive fractions: for example, of of a foot was not an inch or any other unit. But the system of counting in decimal ratios did have notation, and the system had the algebraic property of multiplicative closure: a fraction of a fraction, or a multiple of a fraction was a quantity in the system, like of which is .
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48 Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) as 0 for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility. The lcm is the "lowest common denominator" (lcd) that can be used before fractions can be added, subtracted or compared. The lcm of more than two integers is also well- defined: it is the smallest positive integer that is divisible by each of them.
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Hoopfest features a basic 16-team, double- elimination bracket, which is played entirely on one court location (except in elite divisions, which start on street courts and eventually move to Nike Center Court). This means that the number of brackets is almost exactly equal to the number of courts. Due to the possibility of the number of teams in a division not being divisible by 16, there are sometimes brackets featuring more or less than 16 teams, but the double elimination theme remains constant. Teams are guaranteed 3 games, as teams that lose their first two games are put into a consolation bracket.
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French mathematician Joseph Oesterlé British mathematician David Masser The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by and . It is stated in terms of three positive integers, a, b and c (hence the name) that are relatively prime and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d is usually not much smaller than c. In other words: if a and b are composed from large powers of primes, then c is usually not divisible by large powers of primes.
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The secondary Kodaira surfaces have the same relation to primary ones that Enriques surfaces have to K3 surfaces, or bielliptic surfaces have to abelian surfaces. Invariants: If the surface is the quotient of a primary Kodaira surface by a group of order k = 1,2,3,4,6, then the plurigenera Pn are 1 if n is divisible by k and 0 otherwise. Hodge diamond: Examples: Take a non-trivial line bundle over an elliptic curve, remove the zero section, then quotient out the fibers by Z acting as multiplication by powers of some complex number z. This gives a primary Kodaira surface.
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Before and since Confederation, arrangements with the creditors have always been of the very essence of any system of bankruptcy or insolvency legislation. Under current Canadian law and under the British Bankruptcy Act 1914, where a person is subject to bankruptcy proceedings, and if no composition or scheme of arrangement is approved, he will be declared bankrupt, and his property becomes divisible among his creditors and vests in a trustee. While CCAA proceedings are not bankruptcy proceedings, they are insolvency proceedings. As such, they are intended to prevent a declaration of bankruptcy, where it would be in the best interest of the creditors.
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The first constraint is that only even permutations of the face centers are possible (e.g. it is impossible to have only two face centre pieces swapped); this divides the limit by 2. The second constraint is that all centre permutations are dependent on the orientation of the corner pieces. Some permutations of centres are only possible when the total number of clockwise rotations of corner pieces is divisible by 3; other permutations are only possible when the total number of clockwise rotations is equivalent to 1 modulo 3; others are only possible when the number is equivalent to 2 modulo 3.
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Topography Auraiya lies entirely in the Gangetic plain, but its physical features vary considerably and are determined by the rivers which cross it. The area of Etawah and Auraiya districts is divisible into four portions of district natural characteristics. The first of these consists of the country lying north-east of the Senger river, which runs across it from west to east almost parallel to the Yamuna; it includes the northern portions of tahsils Etawah and Bharthana. The second tract lies south of the Senger and extends as far as the high lands immediately overlooking the Yamuna.
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However, in order for MLB officials to continue primarily intraleague play, both leagues would need to carry a number of teams that was divisible by two, so the decision was made to move one club from the AL Central to the NL Central. This realignment was widely considered to have great financial benefit to the club moving. However, to avoid the appearance of a conflict of interest, Commissioner (then club owner) Bud Selig decided another team should have the first chance to switch leagues. The choice was offered to the Kansas City Royals, who ultimately decided to stay in the American League.
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Essentially, one can show that if the first k primes p congruent to 1 (mod q) (where q is a prime) are all less than qk+1, then such an integer will be divisible by every prime and thus cannot exist. In any case, proving that Pomerance's counterexample does not exist is far from proving Carmichael's Conjecture. However if it exists then infinitely many counterexamples exist as asserted by Ford. Another way of stating Carmichael's conjecture is that, if A(f) denotes the number of positive integers n for which φ(n) = f, then A(f) can never equal 1\.
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The model must be infinitely divisible as c2−p approaches infinity. In nontechnical terms this theorem implies that any exponential dispersion model that asymptotically manifests a variance-to-mean power law is required to have a variance function that comes within the domain of attraction of a Tweedie model. Almost all distribution functions with finite cumulant generating functions qualify as exponential dispersion models and most exponential dispersion models manifest variance functions of this form. Hence many probability distributions have variance functions that express this asymptotic behaviour, and the Tweedie distributions become foci of convergence for a wide range of data types.
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The Pakhtunkhwa Mili Awami Party led by Mehmood Achakzai also opposed the merger. Under the plan, FATA would be put under the control of the provincial government through amendments to the Frontier Crimes Regulation (FCR). An annual grant of Rs100 billion has been proposed for FATA's development under the proposed merger and the amount will be given from the Federal Divisible Pool. Most political parties in Pakistan supported the demand of the merger of FATA with Khyber Pakhtunkhwa, including Pakistan Tehreek-e-Insaf (PTI), Pakistan People's Party (PPP), Qaumi Watan Party (QWP) and Jamaat-e-Islami (JI).
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In algebraic geometry, the Mumford–Tate group (or Hodge group) MT(F) constructed from a Hodge structure F is a certain algebraic group G. When F is given by a rational representation of an algebraic torus, the definition of G is as the Zariski closure of the image in the representation of the circle group, over the rational numbers. introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. introduced the p-adic analogue of Mumford's construction for Hodge–Tate modules, using the work of on p-divisible groups, and named them Mumford–Tate groups.
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The solar cycle is a 28-year cycle of the Julian calendar, and 400-year cycle of the Gregorian calendar with respect to the week. It occurs because leap years occur every 4 years and there are 7 possible days to start a leap year, making a 28-year sequence. This cycle also occurs in the Gregorian calendar, but it is interrupted by years such as 1700, 1800, 1900, 2100, 2200, 2300 and 2500, which are divisible by four but which are common years. This interruption has the effect of skipping 16 years of the solar cycle between February 28 and March 1.
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All the modes adhere to a ternary principle of metre, meaning that each mode would have a number of beat subdivisions divisible by the number 3. Some medieval writers explained this as veneration for the perfection of the Holy Trinity, but it appears that this was an explanation made after the event, rather than a cause (; ). Less speculatively, the flexibility of rhythm possible within the system allows for variety and avoids monotony. Notes could be broken down into shorter units (called fractio modi by Anonymous IV) or two rhythmic units of the same mode could be combined into one (extensio modi) .
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These are the current world records in the various age groups of Masters athletics, maintained by WMA, the World Association of Masters Athletes, which is designated by the IAAF to conduct the worldwide sport of Masters (Veterans) Athletics (Track and Field). Starting at age 35, each age group starts on the athlete's birthday in years that are evenly divisible by 5 and extends until the next such occurrence. For record purposes, older athletes are not included in younger age groups, except in the case of relay team members. A relay team's age group is determined by the age of the youngest member.
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Obviously the buyer does not have to prove that the defect was apparent at the time of sale. Where the subject matter of the sale is a class of goods (bags of maize, for example, or pockets of oranges), the aedilitian remedies apply. Yet the extent to which the buyer is entitled to redhibition is determined by whether the contract was divisible or indivisible. Mackeurtan states: "The redhibition to which the purchaser is entitled extends only to the affected articles, unless the contract may properly be regarded as an indivisible one for the sale of the articles as a whole."139.
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The ilium () (plural ilia) is the uppermost and largest part of the hip bone, and appears in most vertebrates including mammals and birds, but not bony fish. All reptiles have an ilium except snakes, although some snake species have a tiny bone which is considered to be an ilium. The ilium of the human is divisible into two parts, the body and the wing; the separation is indicated on the top surface by a curved line, the arcuate line, and on the external surface by the margin of the acetabulum. The name comes from the Latin (ile, ilis), meaning "groin" or "flank".
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However, there is a unique code word that can be obtained by adjusting the rightmost m symbols of x^md(x). To calculate it, compute the remainder of dividing x^md(x) by g(x): :x^md(x) = g(x)\cdot q(x) + r(x),\, where r(x) is of degree less than m. The code word corresponding to the data word d(x) is then defined to be :p(x) := x^md(x) - r(x),\, Note the following properties: # p(x) = g(x)\cdot q(x), which is divisible by g(x). In particular, p(x) is a valid code word.
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A Vanua is divisible into a group of Yavusa / tribes: a Yavusa is a group of Mataqali / clans: a Mataqali is a group of Tokatoka / family units. Within the Mataqali making up one Yavusa one Mataqali will be predominant and head that Yavusa as a whole. Similarly, one Tokatoka will head that Mataqali and one member of that Tokatoka will be Senior Chieftain / Turaga i Taukei of that Vanua. Matanitu is a confederation of Vanua, not through ancestry or traditional ties, but rather by alliances formed politically or in war and/or united by a common need.
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The posterior sacrococcygeal ligament or dorsal sacrococcygeal ligamentOMD: Definition is a ligament which stretches from the sacrum to the coccyx and thus dorsally across the sacrococcygeal symphysis shared by these two bones. This ligament is divisible in two parts: A short deep part which unites the two bones, and a larger superficial portion which completes the lower back part of the sacral canal. On either side, two lateral sacrococcygeal ligaments run between the transverse processes of the coccyx and the inferior lateral angle of the sacrum.Sinnatamby (2006), p 336 It is in relation, behind, with the gluteus maximus.
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His most recent research has been on terrorism. In his Terrorist's Creed: Fanatical Violence and the Human Need for Meaning he studies the origins and motivations behind terrorism. He compares the origins of terrorism to the extremes of the National Socialists in the 1930s, noting that "fanatics" separate the world into good and evil, and then undergo "heroic doubling" where they see themselves as warriors in the battle between good and evil. This theme will be pursued and deepened in his next monograph The Divisible Self: Heroic Doubling and the Origins of Modern Violence (Columbia: Agenda, Columbia University Press, September 2021).
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However, irreducibility depends on the ambient field, and a polynomial may be irreducible over and reducible over some extension of . Similarly, divisibility by a square depends on the ambient field. If an irreducible polynomial over is divisible by a square over some field extension, then (by the discussion above) the greatest common divisor of and its derivative is not constant. Note that the coefficients of belong to the same field as those of , and the greatest common divisor of two polynomials is independent of the ambient field, so the greatest common divisor of and has coefficients in .
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This worked to destabilize the classical notions of genre, while still drawing attention to genre because new genres like the novel were being generated (Prince, 455). Locke, in An Essay Concerning Human Understanding (1690), had reduced data to its smallest part: the simple idea derived from sense. However, as the science of cognition became more precise it was shown that even this simple idea derived from sense was itself divisible. This new information prompted David Hartley to write in his Observation on Man (1749), > How far the Number of Orders may go is impossible to say.
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Democrația Socială became a rather important voice for the socialist movement, receiving collaborations from Gherea, Demetrescu, Mille, I. Nădejde, Sofia Nădejde, O. Carp and George Diamandy. According to historian Paul D. Popescu, the editorial opinion was divisible into three factions: Gherea was the evolutionary socialist, Radovici the liberal democrat; Toni, who made a lasting impression among the readers, represented the far left, prophesying the dictatorship of the proletariat. Around that date, Anton Bacalbașa endorsed didactic art, as envisaged by Gherea. The socialists were unnerved by Conservative theorists, who countered with the principle of art for art's sake.
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When -2\leq k\leq 2 \pmod 8 there is a real Majorana spinor representation, whose dimension is half that of the Dirac representation. When k is even there is a Weyl spinor representation, whose real dimension is again half that of the Dirac spinor. Finally when k is divisible by eight, that is, when k is zero modulo eight, there is a Majorana–Weyl spinor, whose real dimension is one quarter that of the Dirac spinor. Occasionally one also considers symplectic Majorana spinor which exist when 3\leq k\leq 5, which have half has many components as Dirac spinors.
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Since a and b are both multiples of g, they can be written a = mg and b = ng, and there is no larger number G > g for which this is true. The natural numbers m and n must be coprime, since any common factor could be factored out of m and n to make g greater. Thus, any other number c that divides both a and b must also divide g. The greatest common divisor g of a and b is the unique (positive) common divisor of a and b that is divisible by any other common divisor c.
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In a participating policy (also "par" in the United States, and known as a "with-profits policy" in the Commonwealth), the insurance company shares the excess profits (divisible surplus) with the policyholder in the form of annual dividends. Typically these "refunds" are not taxable because they are considered an overcharge of premium (or "reduction of basis"). In general, the greater the overcharge by the company, the greater the refund/dividend ratio; however, other factors will also have a bearing on the size of the dividend. For a mutual life insurance company, participation also implies a degree of ownership of the mutuality.
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The LEED Silver-certified Convention Center includes a 225,928-square-foot exhibit hall divisible into three halls, as well as 46,166 square feet of total ballroom space, made up of three grand ballrooms totaling 32,193 square feet and two junior ballrooms totaling 10,937 square feet. Views of Lake Erie from a 9,520-square-foot patio completes the northern border of the complex. The project was funded by a 0.25 percent increase in Cuyahoga County sales tax. Permanent tenants include Healthcare Information and Management Systems Society, Philips Healthcare, GE Healthcare, Johnson Controls, the Cleveland Clinic, and University Hospitals.
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A display's framerate is not always equivalent to that of the content being displayed. In other words, a display capable of or operating at a high framerate does not necessarily mean that it can or must perform motion interpolation. For example, a TV running at 120 Hz and displaying 24 FPS content will simply display each content frame for five of the 120 display frames per second. This has no effect on the picture other than eliminating the need for 3:2 pulldown and thus film judder as a matter of course (since 120 is evenly divisible by 24).
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If a cake with a selection of toppings is simply cut into equal slices, different people will receive different amounts of its toppings, and some may not regard this as a fair division of the cake. Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e.
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152 However, he did not work out any definite or detailed theory of individuation. His successor Averroes (1126–1198) argued that matter is numerically one, since it is undetermined in itself and has no definite boundaries. However, since it is divisible, this must be caused by quantity, and matter must therefore have the potential for determination in three dimensions (in the same way a rough and unhewn lump of marble has the potential to be sculpted into a statue). The theories of Averroes and Avicenna had a great influence on the later theory of Thomas Aquinas (1224–1274).
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For a prime number p, the following are equivalent: # The modular curve X0+(p) = X0(p) / wp, where wp is the Fricke involution of X0(p), has genus zero. # Every supersingular elliptic curve in characteristic p can be defined over the prime subfield Fp. # The order of the Monster group is divisible by p. The equivalence is due to Andrew Ogg. More precisely, in 1975 Ogg showed that the primes satisfying the first condition are exactly the 15 supersingular primes listed above and shortly thereafter learned of the (then conjectural) existence of a sporadic simple group having exactly these primes as prime divisors.
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In fact, other than the Baby Monster group, they all have orders divisible only by primes less than or equal to 31, although no single sporadic group, other than the Monster itself, has all of them as prime divisors. The supersingular prime 47 also divides the order of the Baby Monster group, and the other three supersingular primes (41, 59, and 71) do not divide the order of any sporadic group other than the Monster itself. All supersingular primes are Chen primes, but 37, 53, and 67 are also Chen primes, and there are infinitely many Chen primes greater than 73.
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The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes. Under this model, these assets have continuous prices evolving continuously in time and are driven by Brownian motion processes. This model requires an assumption of perfectly divisible assets and a frictionless market (i.e. that no transaction costs occur either for buying or selling).
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Transcripts with exitrons in their sequences can be distinguished from those with retained introns in three ways. First, transcripts containing exitrons are transported out of the nucleus to be translated, whereas those containing introns are identified as incompletely processed and are kept in the nucleus where they cannot be translated. Second, only transcripts with exitrons of lengths not divisible by three have the potential to incorporate premature termination sequences, while sequences with introns normally result in premature termination. Third, exitron transcripts are usually the major isoform, but those with introns are only present in small amounts.
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Their only daughter and heiress, Henrietta Blackford, inherited the estate as an infant, but died aged 7 in 1733. The estates were divisible upon a great-aunt, Elizabeth Dyke (died 1737), and a second cousin, Elizabeth, a daughter of Thomas Dyke of Tetton and Mary, a daughter of Elizabeth Dyke (died 1737). Later in 1733, Elizabeth Dyke (died 1737) conveyed her share in the estate to her only surviving son, Edward Dyke (died 1746) who in turn conveyed his portion to his niece in 1744, making her the sole owner of the entire estate.Chadwyck-Healey, pp. 316-318.
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In the game of roulette, the number 0 does not count as even or odd, giving the casino an advantage on such bets. Similarly, the parity of zero can affect payoffs in prop bets when the outcome depends on whether some randomized number is odd or even, and it turns out to be zero.; ; The game of "odds and evens" is also affected: if both players cast zero fingers, the total number of fingers is zero, so the even player wins. One teachers' manual suggests playing this game as a way to introduce children to the concept that 0 is divisible by 2.
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In order for a production to be palimpsestic, the goal for its content must be granular. Bruns argues that granularity offers produsers a way to connect and contribute to a source or artifact in a way which is relevant to their background and knowledge. By anchoring multiplicity of viewpoints and interest to one source, content becomes more valuable, accurate and comprehensible, which is often a common goal of sources which provide information. He states it is characteristic of sources which promote produsage to be divisible into different components, each of which can be individually and independently produced by different users.
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However, the sequence cannot begin repeating itself any earlier than that. If it did, the length of the repeating section would have to be a divisor of p, so it would have to be 1 (since p is prime). But this contradicts our assumption that x0 is not a fixed point of Ta. In other words, the orbit contains exactly p distinct points. This holds for every orbit of S. Therefore, the set S, which contains ap − a points, can be broken up into orbits, each containing p points, so ap − a is divisible by p.
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Thorium nuclei are susceptible to alpha decay because the strong nuclear force cannot overcome the electromagnetic repulsion between their protons. The alpha decay of 232Th initiates the 4n decay chain which includes isotopes with a mass number divisible by 4 (hence the name; it is also called the thorium series after its progenitor). This chain of consecutive alpha and beta decays begins with the decay of 232Th to 228Ra and terminates at 208Pb. Any sample of thorium or its compounds contains traces of these daughters, which are isotopes of thallium, lead, bismuth, polonium, radon, radium, and actinium.
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One dollar, or one euro, is divided into 100 cents; one can only pay in increments of a cent. It is quite commonplace for prices of some commodities such as gasoline to be in increments of a tenth of a cent per gallon or per litre. If gasoline costs $3.979 per gallon and one buys 10 gallons, then the "extra" 9/10 of a cent comes to ten times that: an "extra" 9 cents, so the cent in that case gets paid. Money is infinitely divisible in the sense that it is based upon the real number system.
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Aristotle responded to these paradoxes by developing the notion of a potential countable infinity, as well as the infinitely divisible continuum. Unlike the eternal and unchanging cycles of time, he believed that the world is bounded by the celestial spheres and that cumulative stellar magnitude is only finitely multiplicative. The Indian philosopher Kanada, founder of the Vaisheshika school, developed a notion of atomism and proposed that light and heat were varieties of the same substance.Will Durant, Our Oriental Heritage: In the 5th century AD, the Buddhist atomist philosopher Dignāga proposed atoms to be point-sized, durationless, and made of energy.
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In addition, the lock prevents the token being removed until the ticket box is closed, and it cannot be closed unless the book of tickets is in the box. Once a ticket is issued, its number is recorded in a Train Register book, and the token is locked in a secure place. This system is known as staff and ticket. In a variation on this principle, called divisible train staff, a section of the token referred to as the ticket portion was designed to be removed and handed to the driver instead of a paper ticket.
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Soon after his appointment, Simard warned the Canadian government to consider the possibility of a violent reaction if it ever tried to partition the predominantly federalist areas from a future, sovereign Quebec. This was in response to a statement by Canadian intergovernmental affairs minister Stéphane Dion, who said that if Canada was divisible, then Quebec would be as well.Edison Stewart and Derek Ferguson, "Use of force to be avoided minister says," Toronto Star, 2 February 1996, A11. In March 1996, Simard announced that Quebec would close thirteen of its nineteen foreign delegations as a cost-saving measure.
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A strongly related model is the so called divisible sandpile model, introduced by Levine and Peres in 2008, in which, instead of a discrete number of particles in each site x, there is a real number s(x) representing the amount of mass on the site. In case such mass is negative, one can understand it as a hole. The topple occurs whenever a site has mass larger than 1; it topples the excess evenly between its neighbors resulting in the situation that, if a site is full at time t, it will be full for all later times.
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BL Hydri is another close binary system composed of a low mass star and a strongly magnetic white dwarf. Known as a polar or AM Herculis variable, these produce polarized optical and infrared emissions and intense soft and hard X-ray emissions to the frequency of the white dwarf's rotation period—in this case 113.6 minutes. There are two notable optical double stars in Hydrus. Pi Hydri, composed of Pi1 Hydri and Pi2 Hydri, is divisible in binoculars. Around 476 light-years distant, Pi1 is a red giant of spectral type M1III that varies between magnitudes 5.52 and 5.58.
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In 1962 Fontaine entered the École Polytechnique, from 1965 to 1971 was a researcher at CNRS and received his doctorate in 1972. From 1971 to 72 he was at the University of Paris VI and from 1972 to 1988 was at the University of Grenoble (only Maître de Conferences, but later a professor). From 1989 he was professor at the University of Paris-Sud XI in Orsay. Among his first works was the classification of p-divisible groups (= Barsotti–Tate group) over the ring of integers of a local field and the field of p-adic periods, a p-adic analogue of the field of complex numbers.
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This feature becomes obsolete on the body whorl or half-whorl, and is stronger in archibenthal specimens from the Gulf of Mexico than in those from off the Carolina coast. On the base of P. hadria the threads are hardly divisible into two series, and the alternations of size are very slight, and occur in every other thread if at all, instead of several fine ones intercalated between two primaries. The aperture, roundness of the base, outer lip, etc., are much as in P. catasarca, but the notch is not so deep, the columella is not quite so straight, and the siphonal canal is a little twisted and plainly somewhat recurved.
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The writers, finding the script to be easily divisible, ended the first episode with William Bell and Olivia meeting outside Fauxlivia's apartment, and began the second with Bell helping Walter escape from the hospital.Pinkner et al, 4:52–5:07 Pinkner and Wyman brought back the "Cortexiphan kids", introduced in the first two seasons, because they felt that part of the storyline was really interesting. They wanted the end of the season to be a "beautiful culmination of everything" while traveling to the Other Side. The show had been developing a parallel universe storyline since its conception, but "Over There" marked the longest time spent in that world thus far.
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Nominated by the CDU/CSU faction, he was elected the first Chancellor of the Federal Republic of Germany on 15 September 1949 by an absolute majority of 202 of 402 votes. Adenauer had ensured that the votes of the predominantly Social Democrat West Berlin deputies did not count and later stated that he "naturally" had voted for himself.David Reynolds (2015) One World Divisible: A Global History Since 1945, Penguin UK On 20 September, he formed the Cabinet Adenauer I of CDU/CSU, FDP, and DP ministers. Chosen as an interim Chancellor, he held the office until 1963, being re-elected three times (in 1953, in 1957 and in 1961).
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The Jesuit missionary Jean de Brébeuf described the spectacle in The Jesuit Relations, explaining that, Engraving of the Huron Feast of the Dead. > Many of them think we have two souls, both of them being divisible and > material, and yet both reasonable. One of them separates itself from the > body at death yet remains in the cemetery until the Feast of the Dead, after > which it either changes into a dove, or according to a common belief, it > goes away at once to the village of souls. The other is more attached to the > body and, in a sense, provides information to the corpse.
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Lumb's initiative was debated in the Chamber of Deputies, where it was concluded that the railroad was necessary for the development of the Argentinian nation. Juan B. Alberdi stated "The railroad will join the Argentine Republic better than all the congresses... without the 'iron road' that connects their extremes, the country will be always divisible and divided against all the Legislative decrees". Finally, on May 27, 1862, the Buenos Aires Legislature promulgated the Law that authorized President of Argentina, Bartolomé Mitre, to enter into a contract with Edward Lumb. The Government demanded an interest rate of 7% on the costs of construction over 40 years.
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Triples with q > 1 such as in the second example are rather special, they consist of numbers divisible by high powers of small prime numbers. :ABC conjecture III. For every positive real number ε, there exist only finitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1 + ε. Whereas it is known that there are infinitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1, the conjecture predicts that only finitely many of those have q > 1.01 or q > 1.001 or even q > 1.0001, etc.
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Another device predating the problem, is to use extra or marked objects, in this case blue coconuts, to clarify the division process. Suppose that the first sailor before the division, adds four blue coconuts to the pile to guarantee division by 5 (since we know even if he doesn't, that there's going to be a remainder of 1, so adding 4 makes the pile divisible by 5). He divides the pile, takes the fifth with an extra (non-blue) coconut which he tosses to the monkey, hides his share, then puts the rest back together, putting the 4 blue coconuts to the side. Each sailor does the same.
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A well-known result in number theory, proven by Rudolf Fueter and Louis J. Mordell, states that, when k is an integer that is not divisible by a sixth power (other than the exceptional cases k=1 and k=-432), this equation either has no rational solutions with both x and y nonzero or infinitely many of them.. In the archaic notation of Robert Recorde, the sixth power of a number was called the "zenzicube", meaning the square of a cube. Similarly, the notation for sixth powers used in 12th century Indian mathematics by Bhāskara II also called them either the square of a cube or the cube of a square.
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After at least one constitutional term, a person who has held the post of President before may run for this Office again, according to the last amendment made to the Constitution in 2010. Elections are held in years evenly divisible by four. The Dominican Constitution takes twenty-seven paragraphs to spell out the president's extensive powers. Among the most important are those that grant him authority over virtually all appointments and removals of public officials, and even popular elected ones; empower him to promulgate the laws passed by Congress; direct him to engage in diplomatic relations; and empower him to command, to deploy, and to make appointments in, the armed forces.
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In mathematics, an explicit reciprocity law is a formula for the Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity law for the power residue symbol. The definitions of the Hilbert symbol are usually rather roundabout and can be hard to use directly in explicit examples, and the explicit reciprocity laws give more explicit expressions for the Hilbert symbol that are sometimes easier to use. There are also several explicit reciprocity laws for various generalizations of the Hilbert symbol to higher local fields, p-divisible groups, and so on.
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The Prüfer -group with presentation , illustrated as a subgroup of the unit circle in the complex plane In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z(p∞), for a prime number p is the unique p-group in which every element has p different p-th roots. The Prüfer p-groups are countable abelian groups that are important in the classification of infinite abelian groups: they (along with the group of rational numbers) form the smallest building blocks of all divisible groups. The groups are named after Heinz Prüfer, a German mathematician of the early 20th century.
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Many properties of commutative group schemes can be seen by examining the corresponding Dieudonné modules, e.g., connected p-group schemes correspond to D-modules for which F is nilpotent, and étale group schemes correspond to modules for which F is an isomorphism. Dieudonné theory exists in a somewhat more general setting than finite flat groups over a field. Tadao Oda's 1967 thesis gave a connection between Dieudonné modules and the first de Rham cohomology of abelian varieties, and at about the same time, Alexander Grothendieck suggested that there should be a crystalline version of the theory that could be used to analyze p-divisible groups.
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The environment is not decorated with grass, flowers, and rocks by overlaying two-dimensional images of such objects on the terrain model. Instead, many tiny models of these terrain features litter the landscape. Objects in the game are composed of isosceles right triangles, each of which is infinitely divisible into two smaller isosceles right triangles. The array of infinite triangles derived from these divisions is stored in a binary triangle tree data structure, and the simplicity of the division and its data management algorithms frees up the graphic processor for other duties, allowing more resources to be spent on managing the level of detail.
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The coefficients of Ep(x) are rational. We can use either formula for Ep(x) to prove that, unlike ex, all of its coefficients are p-integral; in other words, the denominators of the coefficients of Ep(x) are not divisible by p. A first proof uses the definition of Ep(x) and Dwork's lemma, which says that a power series f(x) = 1 + ... with rational coefficients has p-integral coefficients if and only if f(xp)/f(x)p ≡ 1 mod pZpx. When f(x) = Ep(x), we have f(xp)/f(x)p = e−px, whose constant term is 1 and all higher coefficients are in pZp.
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Given a field K and a finite group G, the group algebra K[G] (which is the K-vector space with K-basis consisting of the elements of G, endowed with algebra multiplication by extending the multiplication of G by linearity) is an Artinian ring. When the order of G is divisible by the characteristic of K, the group algebra is not semisimple, hence has non-zero Jacobson radical. In that case, there are finite- dimensional modules for the group algebra that are not projective modules. By contrast, in the characteristic 0 case every irreducible representation is a direct summand of the regular representation, hence is projective.
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There is no special primality test for safe primes the way there is for Fermat primes and Mersenne primes. However, Pocklington's criterion can be used to prove the primality of 2p + 1 once one has proven the primality of p. Just as every term except the last one of a Cunningham chain of the first kind is a Sophie Germain prime, so every term except the first of such a chain is a safe prime. Safe primes ending in 7, that is, of the form 10n + 7, are the last terms in such chains when they occur, since 2(10n + 7) + 1 = 20n + 15 is divisible by 5.
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Lévy processes such as the Wiener process and the Poisson process (on the real line) are named after Paul Lévy who started studying them in the 1930s, but they have connections to infinitely divisible distributions going back to the 1920s. In a 1932 paper Kolmogorov derived a characteristic function for random variables associated with Lévy processes. This result was later derived under more general conditions by Lévy in 1934, and then Khinchin independently gave an alternative form for this characteristic function in 1937. In addition to Lévy, Khinchin and Kolomogrov, early fundamental contributions to the theory of Lévy processes were made by Bruno de Finetti and Kiyosi Itô.
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One property he discovered was that the denominators of the fractions of Bernoulli numbers are always divisible by six. He also devised a method of calculating based on previous Bernoulli numbers. One of these methods follows: It will be observed that if n is even but not equal to zero, # is a fraction and the numerator of in its lowest terms is a prime number, # the denominator of contains each of the factors 2 and 3 once and only once, # is an integer and consequently is an odd integer. In his 17-page paper "Some Properties of Bernoulli's Numbers" (1911), Ramanujan gave three proofs, two corollaries and three conjectures.
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Legislative power in the City of New York is vested in the New York City Council. The New York State Constitution empowers local governments to adopt local laws in addition to ordinances, resolutions, rules and regulations. New York City Hall, the seat of city government The Council is a unicameral body consisting of 51 Council members, whose districts are defined by geographic population boundaries that each contain approximately 157,000 people. Council members are elected every four years, except that after every census held in years divisible by twenty, districts are redrawn, requiring two consecutive two-year terms, the second of which is held in the redrawn districts.
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The second Prüfer theorem provides a straightforward extension of the fundamental theorem of finitely generated abelian groups to countable abelian p-groups without elements of infinite height: each such group is isomorphic to a direct sum of cyclic groups whose orders are powers of p. Moreover, the cardinality of the set of summands of order pn is uniquely determined by the group and each sequence of at most countable cardinalities is realized. Helmut Ulm (1933) found an extension of this classification theory to general countable p-groups: their isomorphism class is determined by the isomorphism classes of the Ulm factors and the p-divisible part. : Ulm's theorem.
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Most modules are built with a surface area of . The official standard allows up to an extra of surface area on either the aisle or operator's side or both (which can lead to a module that is wide). Module lengths are typically extended in increments, but can be almost any length, limited by the modeler's abilities to build and transport the modules. Modules built to non-standard lengths must be built with consideration of the standard lengths; where appropriate, the modeler must also build a short bridge module so that the module set uses up a section of layout that is evenly divisible by -long modules.
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103 The respondent, the Foreign & Commonwealth Office (FCO), argued that the English courts had no jurisdiction over the case, since the Crown is divisible amongst its territories, and the BIOT had its own courts. According to the FCO, Magna Carta, as a British constitutional document, was inapplicable to the Chagos Islands. They also maintained that "make laws for the peace, order and good government of the Territory" gave the Commissioner a wide enough jurisdiction to account for the order forcibly removing the Chagossians, and that the court could not decide in such a way as to force the government to break its treaty with the United States.Nauvel p.
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Consider the ring R of real numbers, and the R-module A = R[X], that is the polynomial ring with real coefficients. Consider the submodule :B = (X2 + 1) R[X] of A, that is, the submodule of all polynomials divisible by X2 + 1\. It follows that the equivalence relation determined by this module will be :P(X) ~ Q(X) if and only if P(X) and Q(X) give the same remainder when divided by X2 + 1\. Therefore, in the quotient module A/B, X2 + 1 is the same as 0; so one can view A/B as obtained from R[X] by setting X2 + 1 = 0.
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Some panels advertise a resolution only slightly smaller than the native, such as 1360×765. For these panels to be able to show a pixel perfect image, the EDID data must be ignored by the display driver or the driver must correctly interpret the DTD and be able to resolve resolutions whose size is not divisible by 8. Special programs are available to override the standard timing descriptors from EDID data. Even this is not always possible, as some vendors' graphics drivers (notably those of Intel) require specific registry hacks to implement custom resolutions, which can make it very difficult to use the screen's native resolution.
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Toronto Congress Centre North Building The Toronto Congress Centre (TCC) is an event, meeting and trade show complex in the former city of Etobicoke in Toronto, Ontario, Canada, located near Toronto Pearson International Airport. It has over of exhibition space between two buildings, making it one of the largest facilities of its kind in Canada and North America. Built in 1995, the Toronto Congress Centre has 60 meeting rooms, two ballrooms (one being pillar- free) and ten divisible exhibit halls. The convention centre is HACCP certified and is one of the only trade and convention facilities in North America to receive this certification, denoting the highest standards in food preparation safety.
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The days of the 3, 5, 6, and 7 day weeks are arranged in simple recurring cycles - much like the seven days of the week in the Gregorian calendar. Because 210 is not divisible by 4, 8, or 9, extra days must be added to the 4-, 8-, and 9-day weeks. For both the 4- and 8-day weeks, the penultimate day of the week is repeated twice in the week that would have otherwise ended on the 72nd day. For the 9-day week, the first day of the week is repeated 3 times in the first week of the 210-day Pawukon.
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However, because of the integer coefficients resulting of the derivation, this multivariate resultant may be divisible by a power of , and it is better to take, as a discriminant, the primitive part of the resultant, computed with generic coefficients. The restriction on the characteristic is needed, as, otherwise, a common zero of the partial derivative is not necessarily a zero of the polynomial (see Euler's identity for homogeneous polynomials). In the case of a homogeneous bivariate polynomial of degree , this general discriminant is d^{d-2} times the discriminant defined in . Several other classical types of discriminants, that are instances of the general definition are described in next sections.
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After a stint at NASA, he returned to help attract in 1981 the Space Telescope Science Institute to JHU, an organization that now employs 500, including 100 PhDs. More recently he has attracted popular press for the SETI ecliptic search idea, and the Hanke-Henry Permanent Calendar. The SETI ecliptic search idea suggests focusing SETI efforts in the ecliptic plane in which distant hypothetical observers can see the Earth's transit of the sun. The Hanke-Henry Permanent Calendar is one in which the number of days in a year is always divisible by seven, such that holidays always fall on the same day of the week.
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Travellers who pay for their own passage into space are termed spaceflight participants by Roscosmos and NASA, and are sometimes referred to as "space tourists", a term they generally dislike. All seven were transported to the ISS on Russian Soyuz spacecraft. When professional crews change over in numbers not divisible by the three seats in a Soyuz, and a short-stay crewmember is not sent, the spare seat is sold by MirCorp through Space Adventures. When the space shuttle retired in 2011, and the station's crew size was reduced to six, space tourism was halted, as the partners relied on Russian transport seats for access to the station.
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Huxley's principal contribution was to establish protoplasm as incompatible with a vitalistic theory of life. Attempts to investigate the origin of life through the creation of synthetic "protoplasm" in the laboratory were not successful. The idea that protoplasm of eukaryotes is simply divisible into a ground substance called "cytoplasm" and a structural body called the cell nucleus reflects the more primitive knowledge of cell structure that preceded the development of electron microscopy, when it seemed that cytoplasm was a homogeneous fluid and the existence of most sub-cellular compartments, or how cells maintain their shape, was unknown. Today, it is known that the cell contents are structurally very complex and contain multiple organelles, the cytoskeleton and biomolecular condensates.
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Most of the business of government is conducted in Annapolis, the state capital. Elections for governor and most statewide offices, as well as most county elections, are held in midterm-election years (even-numbered years not divisible by four). The judicial branch of state government consists of one united District Court of Maryland that sits in every county and Baltimore City, as well as 24 Circuit Courts sitting in each County and Baltimore City, the latter being courts of general jurisdiction for all civil disputes over $30,000, all equitable jurisdiction and major criminal proceedings. The intermediate appellate court is known as the Court of Special Appeals and the state supreme court is the Court of Appeals.
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For example, 0110 (decimal 6) can be considered a set of four flags, where the first and fourth flags are clear (0), and the second and third flags are set (1). The third flag may be cleared by using a bitwise AND with the pattern that has a zero only in the third bit: 0110 (decimal 6) AND 1011 (decimal 11) = 0010 (decimal 2) Because of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. Using the example above: 0110 (decimal 6) AND 0001 (decimal 1) = 0000 (decimal 0) Because 6 AND 1 is zero, 6 is divisible by two and therefore even.
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The constellation Libra marked on a naked eye view. Overall, there are 83 stars within the constellation's borders brighter than or equal to apparent magnitude 6.5. The brightest stars in Libra form a quadrangle that distinguishes it for the unaided observer. Traditionally, Alpha and Beta Librae are considered to represent the scales' balance beam, while Gamma and Sigma are the weighing pans. Alpha Librae, called Zubenelgenubi, is a multiple star system divisible into two stars when seen through binoculars, The primary (Alpha2 Librae) is a blue-white star of magnitude 2.7 and the secondary (Alpha1 Librae) is a white star of magnitude 5.2 and spectral type F3V that is 74.9 ± 0.7 light-years from Earth.
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A Venn diagram showing the least common multiples of combinations of 2, 3, 4, 5 and 7 (6 is skipped as it is 2 × 3, both of which are already represented). For example, a card game which requires its cards to be divided equally among up to 5 players requires at least 60 cards, the number at the intersection of the 2, 3, 4, and 5 sets, but not the 7 set. In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.Hardy & Wright, § 5.1, p.
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A collaboration between Abosch and Chinese artist Ai Weiwei primarily made up of two standard ERC-20 tokens on the Ethereum blockchain, called PRICELESS (PRCLS is its symbol). One of these tokens is forever unavailable to anyone, but the other is meant for distribution and is divisible up to 18 decimal places, meaning it can be given away one quintillionth at a time. A nominal amount of the distributable token was “burned” (put into digital wallets with the keys thrown away), and these wallet addresses were printed on paper and sold to art buyers in a series of 12 physical works. Each wallet address alphanumeric is a proxy for a shared moment between Abosch and Ai.
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The 9-storied hotel is built on a 42-ground land and has 204 rooms, including 2 Executive Suites, 16 Junior Suite, 7 Hilton Deluxe Room, 58 Hilton Executive Rooms, 121 Hilton King Guest Rooms. The interiors were designed by Hong Kong's DiLeonardo and Dallas-based Wilson and Associates. There are 5 food and beverage offerings at the hotel namely, Ayna (pan-Indian restaurant), Vintage Bank (wine and cheese bar), Q Bar (a rooftop bar and grill), Vasco (an all-day dining global cuisine restaurant with live kitchens on the third floor) and Est (24 hour contemporary cafe and lounge). The first floor has divisible 445 m2 ballroom, two meeting rooms and a boardroom with latest audio visual technology.
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Another possibility to transform a polynomial so as to satisfy the criterion, which may be combined with applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero (without which it would be divisible by anyway). This is so because such polynomials are reducible in if and only if they are reducible in (for any integral domain ), and in that ring the substitution of for reverses the order of the coefficients (in a manner symmetric about the constant coefficient, but a following shift in the exponent amounts to multiplication by a unit). As an example satisfies the criterion for after reversing its coefficients, and (being primitive) is therefore irreducible in .
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Once the algebraic and Aurifeuillian factors are removed, the other factors of bn ± 1 are always of the form 2kn + 1, since they are all factors of \Phi_n(b). When n is prime, both algebraic and Aurifeuillian factors are not possible, except the trivial factors (b − 1 for bn − 1 and b + 1 for bn + 1). For Mersenne numbers, the trivial factors are not possible for prime n, so all factors are of the form 2kn + 1\. In general, all factors of (bn − 1)/(b − 1) are of the form 2kn + 1, where b ≥ 2 and n is prime, except when n divides b − 1, in which case (bn − 1)/(b − 1) is divisible by n itself.
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The Geology of Washington, D.C., is broadly divisible into two regions. The northwestern quadrant of the city lies mainly in the Appalachian Piedmont region, marked by moderate to steep hills underlain by metamorphic rocks of Ordovician through Devonian age, similar to the adjacent Piedmont regions of Montgomery County, Maryland. The National Mall, northeastern and southeastern quadrants of Washington lie in the mid-Atlantic Coastal Plain region, consisting of sedimentary deposits laid down during the much more recent Tertiary and Quaternary periods, like the bordering areas of southern Maryland. Some areas in Northeast and Southeast Washington also feature hilly terrain, especially east of the Anacostia River; this however stems from rivers and creeks down-cutting into the relatively soft soil.
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The sixth powers of integers can be characterized as the numbers that are simultaneously squares and cubes. In this way, they are related to two other classes of figurate numbers: the square triangular numbers, which are simultaneously square and triangular, and the solutions to the cannonball problem, which are simultaneously square and square-pyramidal. Because of their connection to squares and cubes, sixth powers play an important role in the study of the Mordell curves, which are elliptic curves of the form :y^2=x^3+k. When k is divisible by a sixth power, this equation can be reduced by dividing by that power to give a simpler equation of the same form.
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The life history of any animal is divisible into 3 phases, initially a period of slow development, followed by a rapid growth with a voracious apetite and finally to an adult which breeds at regular intervals and continue to grow slowly. Most freshwater animals breed during or after monsoon rains where water is available for the young to spread over a wide area where crowding is less and there is a plentiful supply of food in the form of minute plants and animals. During dry season, conditions in temporary habitats become less and less favourable for aquatic animals. Those cut off in small habitats are quickly killed off, others in larger habitats survive longer.
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Adding 19, however, gives 510529, which is prime. Hence 19 is a Fortunate number. The Fortunate number for pn# is always above pn and all its divisors are larger than pn. This is because pn#, and thus pn# + m, is divisible by the prime factors of m not larger than pn. The Fortunate numbers for the first primorials are: :3, 5, 7, 13, 23, 17, 19, 23, 37, 61, 67, 61, 71, 47, 107, 59, 61, 109, etc. . The Fortunate numbers sorted in numerical order with duplicates removed: :3, 5, 7, 13, 17, 19, 23, 37, 47, 59, 61, 67, 71, 79, 89, 101, 103, 107, 109, 127, 151, 157, 163, 167, 191, 197, 199, ... .
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A second proof comes from the infinite product for Ep(x): each exponent -μ(n)/n for n not divisible by p is a p-integral, and when a rational number a is p-integral all coefficients in the binomial expansion of (1 - xn)a are p-integral by p-adic continuity of the binomial coefficient polynomials t(t-1)...(t-k+1)/k! in t together with their obvious integrality when t is a nonnegative integer (a is a p-adic limit of nonnegative integers) . Thus each factor in the product of Ep(x) has p-integral coefficients, so Ep(x) itself has p-integral coefficients. The (p-integral) series expansion has radius of convergence 1.
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Gottfried Wilhelm Leibniz Gottfried Leibniz (1646–1716) was a student of Erhard Weigel (1625–1699) and learned of the conatus principle from him and from Hobbes, though Weigel used the word tendentia (Latin: tendency). Specifically, Leibniz uses the word conatus in his Exposition and Defence of the New System (1695) to describe a notion similar that of Hobbes, but he differentiates between the conatus of the body and soul, the first of which may only travel in a straight line by its own power, and the latter of which may "remember" more complicated motions. For Leibniz, the problem of motion comes to a resolution of the paradox of Zeno. Since motion is continuous, space must be infinitely divisible.
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The first eight prime quadruplets are: {5, 7, 11, 13}, {11, 13, 17, 19}, {101, 103, 107, 109}, {191, 193, 197, 199}, {821, 823, 827, 829}, {1481, 1483, 1487, 1489}, {1871, 1873, 1877, 1879}, {2081, 2083, 2087, 2089} All prime quadruplets except {5, 7, 11, 13} are of the form {30n + 11, 30n + 13, 30n + 17, 30n + 19} for some integer n. (This structure is necessary to ensure that none of the four primes is divisible by 2, 3 or 5). A prime quadruplet of this form is also called a prime decade. A prime quadruplet contains two pairs of twin primes or can be described as having two overlapping prime triplets.
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F2FS, JFFS2) help to reduce write amplification on SSDs, especially in situations where only very small amounts of data are changed, such as when updating file-system metadata. While not a native feature of file systems, operating systems should also aim to align partitions correctly, which avoids excessive read-modify- write cycles. A typical practice for personal computers is to have each partition aligned to start at a 1 MiB (= 1,048,576 bytes) mark, which covers all common SSD page and block size scenarios, as it is divisible by all commonly used sizes - 1 MiB, 512 KiB, 128 KiB, 4 KiB, and 512 B. Modern operating system installation software and disk tools handle this automatically.
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Together with supplemental equations (for example, conservation of mass) and well formulated boundary conditions, the Navier–Stokes equations seem to model fluid motion accurately; even turbulent flows seem (on average) to agree with real world observations. The Navier–Stokes equations assume that the fluid being studied is a continuum (it is infinitely divisible and not composed of particles such as atoms or molecules), and is not moving at relativistic velocities. At very small scales or under extreme conditions, real fluids made out of discrete molecules will produce results different from the continuous fluids modeled by the Navier–Stokes equations. For example, capillarity of internal layers in fluids appears for flow with high gradients.
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Let A and B be countable abelian p-groups such that for every ordinal σ their Ulm factors are isomorphic, Uσ(A) ≅ Uσ(B) and the p-divisible parts of A and B are isomorphic, U∞(A) ≅ U∞(B). Then A and B are isomorphic. There is a complement to this theorem, first stated by Leo Zippin (1935) and proved in Kurosh (1960), which addresses the existence of an abelian p-group with given Ulm factors. : Let τ be an ordinal and {Aσ} be a family of countable abelian p-groups indexed by the ordinals σ < τ such that the p-heights of elements of each Aσ are finite and, except possibly for the last one, are unbounded.
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The only prime belonging to two pairs of cousin primes is 7. One of the numbers n, n+4, n+8 will always be divisible by 3, so n = 3 is the only case where all three are primes. An example of a large proven cousin prime pair is (p, p + 4) for :p = 4111286921397 · 266420 \+ 1 which has 20008 digits. In fact, this is part of a prime triple since p is also a twin prime (because p − 2 is also a proven prime). A large known cousin probable prime (PRP) is :474435381 · 298394 − 1 :474435381 · 298394 − 5. It has 29629 digits and was found by Angel, Jobling and Augustin.474435381 · 298394 − 1. Prime pages.
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Supporters of independence point to their belief that Quebec is a nation due to its unique history, shared major language and common heritage. Opponents of sovereignty generally believe it to be a dangerous idea due to the political, financial, personal and economic ties between Quebecers and other Canadians. Some see it as being unnecessary due to Canada's multicultural and bilingual national character, as well as the strong status of the French language and culture in Quebec. Opponents to Québécois nationalism point to the fact that Quebec is just as ethnically diverse as the rest of Canada and therefore is divisible by different ethnic and language groups, or point to the shared Francophone heritage of the ROC (Rest of Canada).
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This endowment is determined by many things including physical laws (which constrain how forms of energy and matter may be transformed), accidents of nature (which determine the presence of natural resources), and the outcomes of past decisions made by the individual himself or herself and by others. For reasons of tractability, it is often assumed in neoclassical analysis that goods and services are continuously divisible. Under this assumption, marginal concepts, including marginal utility, may be expressed in terms of differential calculus. Marginal utility can then be defined as the first derivative of total utility—the total satisfaction obtained from consumption of a good or service—with respect to the amount of consumption of that good or service.
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In September 1987, Burma's de facto ruler U Ne Win suddenly cancelled certain currency notes, which caused a great down-turn in the economy. The main reason for the cancellation of these notes was superstition on U Ne Win's part, as he considered the number nine his lucky number—he only allowed 45 and 90 kyat notes, because these were divisible by nine. Burma's admittance to Least Developed Country status by the UN the following December highlighted its economic bankruptcy. Triggered by brutal police repression of student-led protests causing the death of over a hundred students and civilians in March and June 1988, widespread protests and demonstrations broke out on 8 August throughout the country.
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1980, page 126–7. These opposite readings of his legacy are not easily divisible into proponents and detractors, as nationalist elements in Turkey (such as the "Nationalist Action Party") have appropriated his work to contend that he supported a physical realization of Turanism, rather than a mere ideological pan-Turkist kinship. Some readings of Gökalp contend, to the contrary, that his Turanism and pan-Turkism were linguistic and cultural models, ideals from which a post-Ottoman identity could be derived, rather than a militant call for the physical expansion of the Republic of Turkey. Guenter Lewy writes that "practically all interpreters of Gökalp's thought stress that his notion of Turan or Turanism did not involve any expansionist plans".
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The choice of polynomial can dramatically affect the time to complete the remainder of the algorithm. The method of choosing polynomials based on the expansion of in base shown above is suboptimal in many practical situations, leading to the development of better methods. One such method was suggested by Murphy and Brent; they introduce a two-part score for polynomials, based on the presence of roots modulo small primes and on the average value that the polynomial takes over the sieving area. The best reported results were achieved by the method of Thorsten Kleinjung, which allows , and searches over composed of small prime factors congruent to 1 modulo 2 and over leading coefficients of which are divisible by 60.
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Some graphics card drivers have historically coped poorly with the EDID, using only its standard timing descriptors rather than its Detailed Timing Descriptors (DTDs). Even in cases where the DTDs were read, the drivers are/were still often limited by the standard timing descriptor limitation that the horizontal/vertical resolutions must be evenly divisible by 8. This means that many graphics cards cannot express the native resolutions of the most common wide screen flat panel displays and liquid crystal display televisions. The number of vertical pixels is calculated from the horizontal resolution and the selected aspect ratio. To be fully expressible, the size of wide screen display must thus be a multiple of 16×9 pixels.
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In particular, if a and b are coprime, then the total number of contact points between the path and the perimeter of the rectangle (i.e. the bouncing points plus starting and ending corner) equals a+b. The ending corner of the path is opposite to the starting corner if and only if a and b are exactly divisible by the same power of two (for example, if they are both odd), else it is one of the two adjacent corners, according to whether a or b has more factors 2 in its prime factorisation. The path is symmetric: if the starting and the ending corner are opposite, then the path is pointsymmetric w.r.t.
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These are never algebraic, though they have non-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite groups of orders 2, 3, 4, or 6, and which have non-trivial canonical bundles. The secondary Kodaira surfaces have the same relation to primary ones that Enriques surfaces have to K3 surfaces, or bielliptic surfaces have to abelian surfaces. Invariants: If the surface is the quotient of a primary Kodaira surface by a group of order k = 1, 2, 3, 4, 6, then the plurigenera Pn are 1 if n is divisible by k and 0 otherwise.
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The player may reduce their wager on either of these occasions, or on both, or neither. If the player decides not to withdraw part of their wager, they are said to "let it ride." In order to ensure that the player's initial wager is divisible by three, each player must distribute their wager over three betting spots which must all contain the same chip value. On some table layouts these spots are given the symbols 1, 2 and $, with 1 and 2 indicating the thirds of the wager which the player can withdraw before the first and second community cards respectively are turned up, and $ representing the third of the wager which there is never a chance to withdraw.
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Burma experienced greatly increased poverty, inequality, corruption and international isolation, and has been described as "disastrous". Burma's real per capita GDP (constant 2000 US$) increased from $159.18 in 1962 to $219.20 in 1987, or about 1.3% per year - one of the weakest growth rates in East Asia over this period, but still positive. The program also may have served to increase domestic stability and keep Burma from being as entangled in the Cold War struggles that affected other Southeast Asian nations. The Burmese Way to Socialism was overthrown in the pro-democracy 8888 Uprising in 1988 after Ne Win's attempt to make the Kyat based in denominations divisible by 9 wiped out the savings of millions of Burmese people.
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Visual proof that the differences of consecutive squares are consecutive odd numbers Any odd number is a difference of two consecutive squares: (k + 1)2 = k2 \+ 2k + 1, so (k + 1)2 − k2 = 2k + 1. Similarly, any multiple of four is a difference of the squares of two numbers that differ by two: (k + 2)2 − k2 = 4k + 4. However, a singly even number, that is, a number divisible by two but not by four, cannot be expressed as a difference of squares. This motivates the question of determining which singly even numbers can be expressed as differences of powerful numbers. Golomb exhibited some representations of this type: :2 = 33 − 52 :10 = 133 − 37 :18 = 192 − 73 = 35 − 152.
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The Quadrille dance is performed each year by a new batch of volunteer dancers (female and male, generally ages 21–30) who are paired up as couples. Most years there are 20 couples, but this number can vary slightly from year to year, although the total number of couples in the performance must be divisible by the number four, since the root word "quad" refers to the number four, and couples are arranged in squares of four couples each, as in American square dancing. Each couple is announced as they are first presented and make their way onto the ballroom floor. There is also a Caller who keeps announcing what steps are to be done next, throughout the dance.
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Templar of Tyre () is the conventional designation of the anonymous 14th- century historian who compiled the Old French chronicle known as the Deeds of the Cypriots (French: Gestes des Chiprois). The Deeds was written between about 1315 and 1320 on Cyprus and presents a history of the Crusader states and the Kingdom of Cyprus from 1132 down to 1309 as well as an account of the trials of the Templars in 1314.Minervini 2006. It is divisible into three parts and the third, which is the original work of the compiler, is the most important source for the final years of the Kingdom of Jerusalem and one of only two eyewitness accounts of the fall of Acre in 1291.
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A fragment of the Fasti Praenestini for the month of April (Aprilis), showing its nundinal letters on the left side The nundinae were the market days which formed a kind of weekend in Rome, Italy, and some other parts of Roman territory. By Roman inclusive counting, they were reckoned as "ninth days" although they actually occurred every eighth day. Because the republican and Julian years were not evenly divisible into eight-day periods, Roman calendars included a column giving every day of the year a nundinal letter from A to H marking its place in the cycle of market days. Each year, the letter used for the markets would shift along the cycle.
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A collaboration with conceptual artist Kevin Abosch primarily made up of two standard ERC-20 tokens on the Ethereum blockchain, called PRICELESS (PRCLS is its symbol). One of these tokens is forever unavailable to anyone, but the other is meant for distribution and is divisible up to 18 decimal places, meaning it can be given away one quintillionth at a time. A nominal amount of the distributable token was “burned” (put into digital wallets with the keys thrown away), and these wallet addresses were printed on paper and sold to art buyers in a series of 12 physical works. Each wallet address alphanumeric is a proxy for a shared moment between Abosch and Ai.
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For instance, if a plate is desired the tin bar is cut to a length and width that is divisible by 14 and 20. The bar is then rolled and doubled over, with the number of times being doubled over dependent on how large the tin bar is and what the final thickness is. If the starting tin bar is then it must be at least finished on the fours, or doubled over twice, and if a thin gauge is required then it may be finished on the eights, or doubled over three times. The tin bar is then heated to a dull red heat and passed five or six times through the roughing rolls.
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This theorem can be used to prove Lagrange's four- square theorem, which states that all natural numbers can be written as a sum of four squares. Gauss pointed out that the four squares theorem follows easily from the fact that any positive integer that is 1 or 2 mod 4 is a sum of 3 squares, because any positive integer not divisible by 4 can be reduced to this form by subtracting 0 or 1 from it. However, proving the three-square theorem is considerably more difficult than a direct proof of the four-square theorem that does not use the three-square theorem. Indeed, the four-square theorem was proved earlier, in 1770.
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The advantage of a performing an initial sanity test is that of speedily evaluating basic function. In arithmetic, for example, when multiplying by 9, using the divisibility rule for 9 to verify that the sum of digits of the result is divisible by 9 is a sanity test—it will not catch every multiplication error, however it's a quick and simple method to discover many possible errors. In computer science, a sanity test is a very brief run-through of the functionality of a computer program, system, calculation, or other analysis, to assure that part of the system or methodology works roughly as expected. This is often prior to a more exhaustive round of testing.
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While the lodge is indisputably a testament to Tresham's faith, it is also an example of the Elizabethan love of allegory. Carved in the gables are the numbers "3509" and "3898": these are said to be the dates (BC) of the Creation and the Calling of Abraham. Among the more recent dates carved on the building are 1580, thought to be the date of Tresham's conversion, and also the future (at the time of their carving) dates 1626 and 1641 - to what do they refer? One suggestion is that not only are they divisible by three, but that, when 1593 is subtracted from them, they give 33 and 48, the years in which Jesus and the Virgin Mary are said to have died.
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30 In them he thought he had discovered what, according to Plato,Plato Timaeus God alone knows, and he among men who is loved by him, namely, the elements or principia of the Platonic triangles. He seems to have described them as first, original lines, and in a similar sense to have spoken of original plain figures and bodies,Simplicius, in Arist. de Caelo convinced that the principia of the existent should be sought not in the material, not in the divisible which attains to the condition of a phenomenon, but merely in the ideal definitude of form. He may very well, in accordance with this, have regarded the point as a merely subjectively admissible presupposition, and a passage of Aristotle respecting this assumptionAristotle, de Anima, i.
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Nu Coronae Borealis is an optical double, whose components are a similar distance from Earth but have different radial velocities, hence are assumed to be unrelated. The primary, Nu1 Coronae Borealis, is a red giant of spectral type M2III and magnitude 5.2, lying 640±30 light-years distant, and the secondary, Nu2 Coronae Borealis, is an orange-hued giant star of spectral type K5III and magnitude 5.4, estimated to be 590±30 light-years away. Sigma Coronae Borealis, on the other hand, is a true multiple star system divisible by small amateur telescopes. It is actually a complex system composed of two stars around as massive as the Sun that orbit each other every 1.14 days, orbited by a third Sun-like star every 726 years.
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In other games, under the same conditions (a coin coming to rest on top of the leading coin), the game is considered null and void, and each player picks up the coin they tossed. In all forms of the game, when no clear winner is determined, in cases where two or more coins are equally close to the wall and particularly when all are touching the wall, some rules declare the game null and void and all players have their coins returned to them, while other games state that the owners of the tied coins win and divide the remaining coins between them. The last rule mentioned can create difficulties if the winnings are not divisible by whole coins. Therefore, generally, the rule is seldom played.
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A straight forward numeric analysis goes like this: If N is the initial number, each of 5 sailors transitions the original pile thus: :N => 4(N–1)/5 or equivalently, N => 4(N+4)/5 – 4. Repeating this transition 5 times gives the number left in the morning: :N => 4(N+4)/5 – 4 : => 16(N+4)/25 – 4 : => 64(N+4)/125 – 4 : => 256(N+4)/625 – 4 : => 1024(N+4)/3125 – 4 Since that number must be an integer and 1024 is relatively prime to 3125, N+4 must be a multiple of 3125. The smallest such multiple is 31251, so N = 3125 – 4 = 3121; the number left in the morning comes to 1020, which is evenly divisible by 5 as required.
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For example consider , in which the coefficient 1 of is not divisible by any prime, Eisenstein's criterion does not apply to . But if one substitutes for in , one obtains the polynomial , which satisfies Eisenstein's criterion for the prime number . Since the substitution is an automorphism of the ring , the fact that we obtain an irreducible polynomial after substitution implies that we had an irreducible polynomial originally. In this particular example it would have been simpler to argue that (being monic of degree 2) could only be reducible if it had an integer root, which it obviously does not; however the general principle of trying substitutions in order to make Eisenstein's criterion apply is a useful way to broaden its scope.
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Plaskett produced and recorded the album himself at his own Scotland Yard studio in Dartmouth, Nova Scotia. In addition to being released as a triple album, the number three is reflected in several other aspects of the album. Each disc has nine songs on it, many of which are titled with a single word or phrase repeated three times. The album's release date of 3/24/09 also consists of numbers divisible by three, the cover features an image of Plaskett holding three fingers up, and preorders through MapleMusic were distributed with access to exclusive tickets, priced at $66, which would entitle the purchaser to a seat in the first twelve rows of Plaskett's concert at Toronto's Massey Hall the night before the album's release.
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They leave off climbing Mount On, and instead try the other side of Cimön, the Deserts, littered with portholes to Hell. Felix merges with the Absolute Infinite, but Kathy is scared and refuses. Eventually, Felix wakes back up on Earth in his body; everybody attributes his dreams to a spectacular binge-drinking and marijuana-smoking episode, until Felix remembers an insight he had regarding the continuum hypothesis: if there were three basic kinds of existence, that of solid matter, aether, and things he calls bloogs which are not aleph-null or c infinitely divisible, but a higher infinity, then the hypothesis will have been disproven. With the aid of a physicist friend, he uses his astral travelling abilities to create a ball of this bloog-matter.
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A subgroup, , of an abelian group, , is called p-basic, for a fixed prime number, , if the following conditions hold: # is a direct sum of cyclic groups of order and infinite cyclic groups; # is a p-pure subgroup of ; # The quotient group, , is a p-divisible group. Conditions 1–3 imply that the subgroup, , is Hausdorff in the p-adic topology of , which moreover coincides with the topology induced from , and that is dense in . Picking a generator in each cyclic direct summand of creates a p-basis of B, which is analogous to a basis of a vector space or a free abelian group. Every abelian group, , contains p-basic subgroups for each , and any 2 p-basic subgroups of are isomorphic.
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Imagine that an agent has spent money on various sorts of goods or services. If the last unit of currency spent on goods or services of one sort bought a quantity with less marginal utility than that which would have been associated with the quantity of another sort that could have been bought with the money, then the agent would have been better off instead buying more of that other good or service. Assuming that goods and services are continuously divisible, the only way that it is possible that the marginal expenditure on one good or service should not yield more utility than the marginal expenditure on the other (or vice versa) is if the marginal expenditures yield equal utility.
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He has also worked in biblical translation theory, the history of interpretation, theology and the arts, philosophy of art, and Chinese philosophy and literature. His scholarship is characteristically interdisciplinary and multilingual, yet it can be said to be broadly divisible into three parts. As a medievalist, especially during the first third of his career, Jeffrey has been associated with the interpretative tradition of D. W. Robertson Jr., an approach which emphasizes medieval European authors’ knowledge of classical and Christian texts as of great importance for understanding their appeal to their original audiences. This contrasts with the opinion advocated by C. S. Lewis and popular in the mid to late twentieth century, namely that a romantic and Celtic mythological substratum is more fundamental.
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It is not true in general, however, that all monomorphisms must be injective in other categories; that is, there are settings in which the morphisms are functions between sets, but one can have a function that is not injective and yet is a monomorphism in the categorical sense. For example, in the category Div of divisible (abelian) groups and group homomorphisms between them there are monomorphisms that are not injective: consider, for example, the quotient map , where Q is the rationals under addition, Z the integers (also considered a group under addition), and Q/Z is the corresponding quotient group. This is not an injective map, as for example every integer is mapped to 0. Nevertheless, it is a monomorphism in this category.
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Neither can I contain any polynomials of the special form :m(x,y) = cx + p(y) with c a nonzero rational number and p a polynomial in the variable y only; the reason being that such an m can never have two distinct zeroes with the same value for y (in this case, the points (1,1) and (-1,1)). From the above it follows that I, apart from the zero polynomial, only contains polynomials whose leading term has degree greater than or equal to 2; therefore their leading terms are divisible by at least one of the three monomials :{x2, xy, y2} = {lt(f),lt(k),lt(h)}. This means that {f, k, h} is a Gröbner basis for I with respect to lexicographic ordering with x > y.
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The 19S particle in eukaryotes consists of 19 individual proteins and is divisible into two subassemblies, a 9-subunit base that binds directly to the α ring of the 20S core particle, and a 10-subunit lid. Six of the nine base proteins are ATPase subunits from the AAA Family, and an evolutionary homolog of these ATPases exists in archaea, called PAN (Proteasome-Activating Nucleotidase). The association of the 19S and 20S particles requires the binding of ATP to the 19S ATPase subunits, and ATP hydrolysis is required for the assembled complex to degrade folded and ubiquitinated proteins. Note that only the step of substrate unfolding requires energy from ATP hydrolysis, while ATP-binding alone can support all the other steps required for protein degradation (e.g.
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Proper use of pinyin romanization means treating a Chinese given name as a single word with no space between the letters of the two characters: for example, the common name 王秀英 is properly rendered either with its tone marks as Wáng Xiùyīng or without as Wang Xiuying, but should not be written as Wang Xiu Ying, Wang XiuYing, Wangxiuying, &c.; The earlier Wade-Giles system accomplished the same effect by hyphenating the given name between the characters: for example, the same name would be written as Wang2 Hsiù4-Yīng1. However, many Chinese do not follow these rules, romanizing their names with a space between each. This can cause non–Chinese-speakers to incorrectly take the names as divisible.
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Lévy made many fundamental contributions to probability theory and the nascent theory of stochastic processes. He introduced the notion of 'stable distribution' which share the property of stability under addition of independent variables and proved a general version of the Central Limit theorem, recorded in his 1937 book Théorie de l'addition des variables aléatoires, using the notion of characteristic function. He also introduced, independently from Ya. Khinchine, the notion of infinitely divisible law and derived their characterization through the Lévy–Khintchine representation. His 1948 monograph on Brownian motion, Processus stochastiques et mouvement brownien, contains a wealth of new concepts and results, including the Lévy area, the Lévy arcsine law the local time of a Brownian path and many other results.
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An arbitrary polynomial with coefficients in some field is said to have distinct roots or to be square-free if it has roots in some extension field E\supseteq F. For instance, the polynomial has precisely roots in the complex plane; namely and , and hence does have distinct roots. On the other hand, the polynomial , which is the square of a non-constant polynomial does not have distinct roots, as its degree is two, and is its only root. Every polynomial may be factored in linear factors, over an algebraic closure of the field of its coefficients. Therefore, the polynomial does not have distinct roots if and only if it is divisible by the square of a polynomial of positive degree.
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Given n polynomials with positive degrees and integer coefficients (n can be any natural number) that each satisfy all three conditions in the Bunyakovsky conjecture, and for any prime p there is an integer x such that the values of all n polynomials at x are not divisible by p, then there are infinitely many positive integers x such that all values of these n polynomials at x are prime. For example, if the conjecture is true then there are infinitely many positive integers x such that x2 \+ 1, 3x - 1, and x2 \+ x + 41 are all prime. When all the polynomials have degree 1, this is the original Dickson's conjecture. This more general conjecture is the same as the Generalized Bunyakovsky conjecture.
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William Henry Harrison, nicknamed Old Tippecanoe, died just a month after taking office in 1841. His death is the first attributed to the Curse of Tippecanoe. The Curse of Tippecanoe (also known as Tecumseh's Curse or the 20 Year Presidential Curse) is the supposed pattern of deaths in office of presidents of the United States elected in years that are evenly divisible by 20, from 1840 to 1960. Because of the timing of presidential elections, these are also those taking place in years ending with 0. The presidents fitting this description were William Henry Harrison (elected in 1840), Abraham Lincoln (1860), James A. Garfield (1880), William McKinley (1900), Warren G. Harding (1920), Franklin D. Roosevelt (1940) and John F. Kennedy (1960).
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The issue of population growth was never calculated and even raised by any civil servant or bureaucrat, since many had realized that if such factors determined, it would have resulted in greater share of East- Pakistan from the Federal Divisible Pool or in Federal Budget for East and West Pakistan. Efforts were applied to end the economic disparity and depression among federal government and provincial governments of Pakistan by the government. While drafting the new Constitution in 1973, the issue of financial distributions, economic equality, and economic justice was specifically mentioned in separate chapter of the Constitution. The Article 160 of the Constitution of Pakistan, laid the foundation and philosophical existence of the National Finance Commission (NFC) and provides the logical framework of (NFC), in 1973.
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In the C programming language, Duff's device is a way of manually implementing loop unrolling by interleaving two syntactic constructs of C: the - loop and a switch statement. Its discovery is credited to Tom Duff in November 1983, when Duff was working for Lucasfilm and used it to speed up a real-time animation program. Loop unrolling attempts to reduce the overhead of conditional branching needed to check whether a loop is done, by executing a batch of loop bodies per iteration. To handle cases where the number of iterations is not divisible by the unrolled-loop increments, a common technique among assembly language programmers is to jump directly into the middle of the unrolled loop body to handle the remainder.
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Siege of Kinsale 1601 (MDCI) was a common year starting on Monday of the Gregorian calendar and a common year starting on Thursday of the Julian calendar. As of the start of 1601, the Gregorian calendar was 10 days ahead of the Julian calendar. This epoch is the beginning of the 400-year Gregorian leap-year cycle within which digital files first existed; the last year of any such cycle is the only leap year whose year number is divisible by 100. January 1 of this year (1601-01-01) is used as the base of file datesMicrosoft Windows technical note on file dates, referencing year 1601 and of Active Directory Logon datesMicrosoft Windows technical note on file dates, referencing year 1601 by Microsoft Windows.
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Therefore, divisibility by 2, 5, and 10 only depend on whether the last 1 digit is divisible by those divisors. The factors of 102 include 4 and 25, and divisibility by those only depend on the last 2 digits. Case where only the last digit(s) are removed Most numbers do not divide 9 or 10 evenly, but do divide a higher power of 10n or 10n − 1\. In this case the number is still written in powers of 10, but not fully expanded. For example, 7 does not divide 9 or 10, but does divide 98, which is close to 100. Thus, proceed from :100 \cdot a + b where in this case a is any integer, and b can range from 0 to 99.
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Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes. Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda: Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
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This numbering system usually holds true even if the local direction of the route does not match the compass directions. Numbers divisible by five are intended to be major arteries among the primary routes, carrying traffic long distances. Primary north–south Interstates increase in number from I-5 between Canada and Mexico along the West Coast to I‑95 between Canada and Miami, Florida along the East Coast. Major west–east arterial Interstates increase in number from I-10 between Santa Monica, California, and Jacksonville, Florida, to I-90 between Seattle, Washington, and Boston, Massachusetts, with two exceptions. There are no I-50 and I-60, as routes with those numbers would likely pass through states that currently have U.S. Highways with the same numbers, which is generally disallowed under highway administration guidelines.
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The history of colonial cotton production is divisible between its relatively unsuccessful introduction onto European-owned estates and more successful cultivation by Africans on their own land. In both cases, the initiative came from The British Cotton Growing Association (BCGA), a Lancashire-based manufacturers’ organisation that stimulated cotton production in the British Empire, initially by making cash advances to European settlers, but later by providing suitable cotton seed to be distributed to African farmers.McCracken, pp. 89-90 At first, European plantation agriculture was focused on the Shire Highlands and agriculture there first concentrated on coffee. An attempt in 1903 to grow Egyptian cotton there was unsuccessful, as it was more suitable for hotter areas, but from 1906, William Jervis Livingstone developed a hardier variety of Upland cotton, which he called Nyasaland Upland.
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The above succession is divisible into: # A lower series of gritty and calcareous sediments, the "Arenig Series" as it is now understood; # A middle series, mainly volcanic, with shale, the "Llandeilo Series"; and # The shale and limestones of the Bala or Caradoc Stage. It was to the middle series (2) that Sedgwick first applied the term "Arenig". In the typical region and in North Wales generally the Arenig series appears to be unconformable upon the Cambrian rocks; this is not the case in South Wales. The Arenig series is represented in North Wales by the Garth Grit and Ty Obry beds, by the Shelve series of the Corndon district, the Skiddaw Slates of the Lake District, the Ballantrae Group of Ayrshire, and by the Ribband Series of slates and shale in Wicklow and Wexford.
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Stating that multiculturalism was one of Australia's defining features that allowed it to broker differences with its geographical neighbours, and that it was almost unique in its ethnic and cultural origins: she suggested that in recent years multiculturalism had begun to be derided with politicians calling for one homogeneous non-divisible Australian culture citing, amongst others, the "popularity and success" of Pauline Hanson. In 2008 Australian portrait photographer Michel Lawrence published All of Us, a book containing photographs of people born in 200 other countries, but who were now living in Australia. Lawrence said the All of Us project was wholly inspired by the Cronulla riots. “You watch this stuff on TV and you wonder why people are doing this - this is no way for a multicultural society to behave,” said Lawrence.
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The étale cohomology of a field is identical to Galois cohomology, so the conjecture equates the ℓth cotorsion (the quotient by the subgroup of ℓ-divisible elements) of the Milnor K-group of a field k with the Galois cohomology of k with coefficients in the Galois module of ℓth roots of unity. The point of the conjecture is that there are properties that are easily seen for Milnor K-groups but not for Galois cohomology, and vice versa; the norm residue isomorphism theorem makes it possible to apply techniques applicable to the object on one side of the isomorphism to the object on the other side of the isomorphism. The case when n is 0 is trivial, and the case when follows easily from Hilbert's Theorem 90. The case and was proved by .
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If a number which can be written as a sum of two squares is divisible by a number which is not a sum of two squares, then the quotient has a factor which is not a sum of two squares. (This is Euler's second Proposition). ::Suppose q is a number not expressible as a sum of two squares, which divides a^2+b^2. Write the quotient, factored into its (possibly repeated) prime factors, as p_1p_2\cdots p_n so that a^2+b^2 = q p_1p_2\cdots p_n. If all factors p_i can be written as sums of two squares, then we can divide a^2+b^2 successively by p_1, p_2, etc., and applying step (2.) above we deduce that each successive, smaller, quotient is a sum of two squares.
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In neither case can the deception fully succeed. Without these two facets of existence, if consciousness was unitary and not divisible, as in the indivisible "I" in "I think, therefore I am", it would be impossible to explain how the very project of self-deception could be possible. The Freudian theory of the unconscious is viewed by Sartre as based on an incoherent view of consciousness, but the project of psychoanalysis as an uncovering of the "fundamental project" of an individual's life is considered to be valid. Existentialist philosopher Jean-Paul Sartre called the belief that there is something intrinsically good in itself, which is inherent in the world as absolute value and is discoverable by people, the "spirit of seriousness", which he argued leads to bad faith.
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Ferrocarril Central Andino (FCCA) is the consortium which operates the Ferrovías Central railway in Peru linking the Pacific port of Callao and the capital Lima with Huancayo and Cerro de Pasco. As one of the Trans-Andean Railways it is the second highest in the world constructed by the Polish engineer Ernest Malinowski in 1871–1876. After a period of operation by the nationalized entity Empresa Nacional de Ferrocarriles del Perú (ENAFER), in July 1999 the government awarded a divisible consortium led by Railroad Development Corporation (RDC) of Pittsburgh, and Lorenzo Sousa's Peruval Corp who was awarded the South and South east railways, a concession to operate the former Ferrocarril del Centro for 30 years. Investors in Ferrocarril Central Andino include RDC, Juan Olaechea & Company, Minas Buenaventura, ADR Inversiones, and Inversiones Andino.
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The governing body is comprised of the Mayor and the four-member Township Council. Council members are elected at-large in partisan elections to serve four-year terms of office on a staggered basis in even-numbered years, with the Mayor and one of the council members elected in years divisible by four and the three other council seats coming up for election two years later. The Mayor and the Councilmembers are the only elected officials in the township government. The Mayor and Council then appoint a Township Manager, who serves as the chief executive officer of the Township, with the authority to appoint most subordinate personnel.2012 New Jersey Legislative District Data Book, Rutgers University Edward J. Bloustein School of Planning and Public Policy, March 2013, p. 98.
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Elections are planned for spring to ensure that a new cabinet is formed in time to present its plans on the most important day in the Dutch Parliament, Prinsjesdag. If the House of Representatives is dissolved, due to a severe conflict between the House of Representatives and cabinet, or within the cabinet, a snap election takes place as soon as possible, usually after two months to give parties time to prepare. The term of the next House can be shortened or prolonged by almost a year to ensure the next normal election again takes place in March or May. Municipal and provincial elections always take place every four years, in March; municipal elections always two years after a year divisible by four, and provincial elections one year after municipal elections.
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In the days following the 2000 election, whose outcome was unclear for some time after election day, major media outlets began conforming to the same color scheme because the electoral map was continually in view, and conformity made for easy and instant viewer comprehension. On election night that year, there was no coordinated effort to code Democratic states blue and Republican states red; the association gradually emerged. Partly as a result of this eventual and near-universal color-coding, the terms "red states" and "blue states" entered popular use in the weeks following the 2000 presidential election. After the results were final with the Republican George W. Bush winning, journalists stuck with the color scheme, as The Atlantic's December 2001 cover story by David Brooks entitled, "One Nation, Slightly Divisible", illustrated.
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The 3-adic integers, with selected corresponding characters on their Pontryagin dual group In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two -adic numbers are considered to be close when their difference is divisible by a high power of : the higher the power, the closer they are. This property enables -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.
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It teaches that God became especially immanent in physical form through the Incarnation of God the Son who was born as Jesus of Nazareth, who is believed to be at once fully God and fully human. There are denominations self- describing as Christian who question one or more of these doctrines, however, see Nontrinitarianism. By contrast, Judaism sees God as a single entity, and views trinitarianism as both incomprehensible and a violation of the Bible's teaching that God is one. It rejects the notion that Jesus or any other object or living being could be 'God', that God could have a literal 'son' in physical form or is divisible in any way, or that God could be made to be joined to the material world in such fashion.
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Euler's "lucky" numbers are positive integers n such that for all integers k with , the polynomial produces a prime number. When k is equal to n, the value cannot be prime since is divisible by n. Since the polynomial can be written as , using the integers k with produces the same set of numbers as . Leonhard Euler published the polynomial which produces prime numbers for all integer values of k from 1 to 40. Only 7 lucky numbers of Euler exist, namely 1, 2, 3, 5, 11, 17 and 41 . The primes of the form k2 − k + 41 are :41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, ... .
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Delta Corvi, traditionally called Algorab, is a double star divisible in small amateur telescopes. The primary is a blue-white star of magnitude 2.9, around 87 light-years from Earth. An enigmatic star around 2.7 times as massive as the Sun, it is more luminous (65–70 times that of the Sun) than its should be for its surface temperature of 10,400 K, and hence is either a 3.2 million year-old very young pre-main sequence star that has not settled down to a stable main sequence life stage, or a 260-million-year-old star that has begun to exhaust its core hydrogen and expand, cool and shine more brightly as it moves away from the main sequence. Its spectral type is given as A0IV, corresponding with the latter scenario.
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Sharecropping and Sharecroppers, T J Byres, page 18 In Italy and France, respectively, it was called mezzadria and métayage, or halving - the halving, that is, of the produce of the soil between landowner and land- holder. Halving didn't imply equal amounts of the produce but rather division according to agreement. The produce was divisible in certain definite proportions, which obviously must have varied with the varying fertility of the soil and other circumstances and did in practice vary so much that the landlord's share was sometimes as much as two-thirds, sometimes as little as one-third. Sometimes the landlord supplied all the stock, sometimes only part - the cattle and seed perhaps, while the farmer provided the implements; or perhaps only half the seed and half the cattle, the farmer finding the other halves.
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108 is a powerful number. Its prime factorization is 22 · 33, and thus its prime factors are 2 and 3. Both 22 = 4 and 32 = 9 are divisors of 108. However, 108 cannot be represented as , where and are positive integers greater than 1, so 108 is an Achilles number. 360 is not an Achilles number because it is not powerful. One of its prime factors is 5 but 360 is not divisible by 52 = 25. Finally, 784 is not an Achilles number. It is a powerful number, because not only are 2 and 7 its only prime factors, but also 22 = 4 and 72 = 49 are divisors of it. Nonetheless, it is a perfect power: :784=2^4 \cdot 7^2 = (2^2)^2 \cdot 7^2 = (2^2 \cdot 7)^2 = 28^2.
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A collaboration with conceptual artist Kevin Abosch primarily made up of two standard ERC-20 tokens on the Ethereum blockchain, called PRICELESS (PRCLS is its symbol). One of these tokens is forever unavailable to anyone, but the other is meant for distribution and is divisible up to 18 decimal places, meaning it can be given away one quintillionth at a time. A nominal amount of the distributable token was "burned" (put into digital wallets with the keys thrown away), and these wallet addresses were printed on paper and sold to art buyers in a series of 12 physical works. Each wallet address alphanumeric is a proxy for a shared moment between Abosch and Ai. Er Xi A monstrous sculptures at Le Bon Marché in Paris to "speak to our inner child".
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By the mid-1980s, recommended viscosities had moved down to 5W-30, primarily to improve fuel efficiency. A typical modern application would be Honda motor's use of 5W-20 (and in their newest vehicles, 0W-20) viscosity oil for . Engine designs are evolving to allow the use of even lower-viscosity oils without the risk of excessive metal-to-metal abrasion, principally in the cam and valve mechanism areas. In line with car manufacturers push towards these lower viscosities in search of better fuel economy, on April 2, 2013 the Society of Automotive Engineers (SAE) introduced an SAE 16 viscosity rating, a break from its traditional "divisible by 10" numbering system for its high-temperature viscosity ratings that spanned from low-viscosity SAE 20 to high-viscosity SAE 60.
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For federal offices (President, Vice President, and United States Congress) and most gubernatorial offices (all except for Kentucky, Louisiana, Mississippi, New Jersey, and Virginia), Election Day occurs only in even-numbered years. Presidential elections are held every four years, in years divisible by four, in which electors for President and Vice President are chosen according to the method determined by each state. Elections to the US House of Representatives and the US Senate are held every two years; all Representatives are elected to serve two-year terms and are up for election every two years, while Senators serve six-year terms, staggered so that one third of Senators are elected in any given general election. General elections in which presidential candidates are not on the ballot are referred to as midterm elections.
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Many compilers will optimize the switch into a branch table just as would be done in an assembly implementation. The primary increase in speed versus a simple, straightforward loop, comes from loop unwinding that reduces the number of performed branches, which are computationally expensive due to the need to flushand hence stallthe instruction pipeline. The `switch` statement is used to handle the remainder of the data not evenly divisible by the number of operations unrolled (in this example, eight short moves are unrolled, so the `switch` handles an extra 1-7 shorts automatically). This automatic handling of the remainder may not be the best solution on all systems and compilers in some cases two loops may actually be faster (one loop, unrolled, to do the main copy, and a second loop to handle the remainder).
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Plato mentions in his Laws that 5040 is a convenient number to use for dividing many things (including both the citizens and the land of a city-state or polis) into lesser parts, making it an ideal number for the number of citizens (heads of families) making up a polis. He remarks that this number can be divided by all the (natural) numbers from 1 to 12 with the single exception of 11 (however, it is not the smallest number to have this property; 2520 is). He rectifies this "defect" by suggesting that two families could be subtracted from the citizen body to produce the number 5038, which is divisible by 11. Plato also took notice of the fact that 5040 can be divided by 12 twice over.
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The ethnic Germans of Reichenberg greatly disliked the Czechs for their willingness to accept lower wages than German workers, and for being "ignorant peasants" whose cultural level was considered much lower than that of the German community. In 1912, the German community of Reichenberg attempted to leave the Austrian Crown land of Bohemia and to set up their district as a new Crown land which would not accept any Czechs, only to be overruled by Vienna which insisted that Bohemia was not divisible. It was in this atmosphere of German- Czech tensions that Henlein grew up and which shaped his views. Henlein attended business school in Gablonz (Jablonec nad Nisou) and in World War I entered military service in the Austro-Hungarian Army as a military volunteer (Kriegsfreiwilliger), assigned to k.u.k.
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Despite the fact that we lack background knowledge to indicate that there are dramatically fewer men than short people, we still find ourselves inclined to reject the conclusion. Hintikka's example is: "... a generalization like 'no material bodies are infinitely divisible' seems to be completely unaffected by questions concerning immaterial entities, independently of what one thinks of the relative frequencies of material and immaterial entities in one's universe of discourse." His solution is to introduce an order into the set of predicates. When the logical system is equipped with this order, it is possible to restrict the scope of a generalization such as "All ravens are black" so that it applies to ravens only and not to non-black things, since the order privileges ravens over non- black things.
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A systematic code is one in which the message appears verbatim somewhere within the codeword. Therefore, systematic BCH encoding involves first embedding the message polynomial within the codeword polynomial, and then adjusting the coefficients of the remaining (non-message) terms to ensure that s(x) is divisible by g(x). This encoding method leverages the fact that subtracting the remainder from a dividend results in a multiple of the divisor. Hence, if we take our message polynomial p(x) as before and multiply it by x^{n-k} (to "shift" the message out of the way of the remainder), we can then use Euclidean division of polynomials to yield: :p(x)x^{n-k} = q(x)g(x) + r(x) Here, we see that q(x)g(x) is a valid codeword.
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The use of a CQ call is almost always used in single-sideband (SSB) voice or CW mode (morse code telegraphy). Unlike FM mode, in the SSB voice and CW mode areas of the amateur radio bands operators are free to center their transmissions where it is most optimal (such as away from adjacent traffic that can interfere) and not expected to use whole-number, divisible-by-five, or otherwise channelized center frequencies. CQ is constantly used on the HF shortwave amateur bands but very rarely used in the FM voice mode of transmission or on FM repeaters common on the VHF and UHF local bands since tuning of a repeater or FM signal does not require the aid of human perception to perfectly tune the signal. The code was used as part of the chorus to the song "Communications" by Slim Gaillard.
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Prior to his tenure with the Los Angeles Times, Murray was a writer and columnist for Sports Illustrated from 1953 to 1961 and Time magazine from 1948 to 1955. He was also a reporter for the Los Angeles Examiner from 1944–1948, the New Haven (CT) Register and The Hartford Times. A native of Hartford, Connecticut, Murray graduated from that city's Trinity College Murray was noted for his great, albeit occasionally caustic, sense of humor and ability to turn a phrase, including the following: he wrote of the Indianapolis 500 automobile race, "Gentlemen, start your coffins"; that baseball player Rickey Henderson "has a strike zone the size of Hitler's heart"; and that UCLA basketball coach John Wooden was "so square he was divisible by four." Although eventually afflicted with blindness, Murray continued covering and writing about sports as long as he was able.
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In the 9th century, Johannes Scotus Eriugena proposed in his great work, De divisione naturae (also called Periphyseon, probably completed around 867 AD), that the nature of the universe is divisible into four distinct classes: Johannes Scotus Eriugena was among the first to propose that God became the universe, and did so to learn something about itself. # that which creates and is not created; # that which is created and creates; # that which is created and does not create; # that which neither is created nor creates. The first is God as the ground or origin of all things, the last is God as the final end or goal of all things, that into which the world of created things ultimately returns. One particularly controversial point made by Eriugena was that God was "nothing", in that God could not fall into any earthly classification.
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With the Drei Volkstexte (1925), Op. 17, Webern used Schoenberg's twelve-tone technique for the first time, and all his subsequent works used this technique. The String Trio (1926–1927), Op. 20, was both the first purely instrumental work using the twelve-tone technique (the other pieces were songs) and the first cast in a traditional musical form. Webern's music, like that of both Brahms and Schoenberg, is marked by its emphasis on counterpoint and formal considerations; and Webern's commitment to systematic pitch organization in the twelve-tone method is inseparable from this prior commitment. Webern's tone rows are often arranged to take advantage of internal symmetries; for example, a twelve-tone row may be divisible into four groups of three pitches which are variations, such as inversions and retrogrades, of each other, thus creating invariance.
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The term Brodmann area 9 refers to a cytoarchitecturally defined portion of the frontal lobe of the guenon. Brodmann-1909 regarded it on the whole as topographically and cytoarchitecturally homologous to the granular frontal area 9 and frontopolar area 10 in the human. Distinctive features (Brodmann-1905): Unlike Brodmann area 6 (Brodmann-1909), area 9 has a distinct internal granular layer (IV); unlike Brodmann area 6 or Brodmann area 8 (Brodmann-1909), its internal pyramidal layer (V) is divisible into two sublayers, an outer layer 5a of densely distributed medium-size ganglion cells that partially merges with layer IV, and an inner, clearer, cell-poor layer 5b; the pyramidal cells of sublayer 3b of the external pyramidal layer (III) are smaller and sparser in distribution; the external granular layer (II) is narrow, with small numbers of sparsely distributed granule cells.
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In fact, after n divisions, it can be proven that the remaining pile is divisible by n, a property made convenient use of by the creator of the problem. A formal way of stating the above argument is: The original pile of coconuts will be divided by 5 a total of 5 times with a remainder of 1, not considering the last division in the morning. Let N = number of coconuts in the original pile. Each division must leave the number of nuts in the same congruence class (mod 5). So, :N \equiv 4/5\cdot(N-1) (mod 5) (the –1 is the nut tossed to the monkey) :5N \equiv 4N - 4 (mod 5) :N \equiv -4 (mod 5) (–4 is the congruence class) So if we began in modulo class –4 nuts then we will remain in modulo class –4.
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Following a new line being opened in February 1970 by the Federal Government, the line was made redundant and the company concentrated on operating shunting and track maintenance services to the mines industry in and around Broken Hill with its remaining two diesel locomotives.Progress in Rail Reform: Submission to the Productivity Commission Silverton Tramway Company"Silverton" Railway Digest July 1985 page 189 Under the 1886 Act, the Government of New South Wales had an option to buy out the company for 21 times the annual divisible profits of the preceding seven years. Silverton calculated it was entitled to $5.8 million, but through legislation this was removed, the company having to settle for a $2 million payment.Silverton Tramway Land Vesting Bill New South Wales Legislative Assembly 22 February 1972 In 1969, the Dillingham Corporation of Honolulu bought a 33% shareholding, later increasing to 50%.
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This grows extremely slowly, and suggests that the computer calculations do not provide much evidence for Vandiver's conjecture: for example, the probability argument (combined with the calculations for small primes) suggests that one should only expect about 1 counterexample in the first 10100 primes, suggesting that it is unlikely any counterexample will be found by further brute force searches even if there are an infinite number of exceptions. gave conjectural calculations of the class numbers of real cyclotomic fields for primes up to 10000, which strongly suggest that the class numbers are not randomly distributed mod p. They tend to be quite small and are often just 1. For example, assuming the generalized Riemann hypothesis, the class number of the real cyclotomic field for the prime p is 1 for p<163, and divisible by 4 for p=163.
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In order for a k-tuple to have infinitely many positions at which all of its values are prime, there cannot exist a prime p such that the tuple includes every different possible value modulo p. For, if such a prime p existed, then no matter which value of n was chosen, one of the values formed by adding n to the tuple would be divisible by p, so there could only be finitely many prime placements (only those including p itself). For example, the numbers in a k-tuple cannot take on all three values 0, 1, and 2 modulo 3; otherwise the resulting numbers would always include a multiple of 3 and therefore could not all be prime unless one of the numbers is 3 itself. A k-tuple that satisfies this condition (i.e.
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In mathematical terms the problem can be stated: :Given positive integers a1, a2, ..., an such that gcd(a1, a2, ..., an) = 1, find the largest integer that cannot be expressed as an integer conical combination of these numbers, i.e., as a sum :: k1a1 + k2a2 + ··· + knan, :where k1, k2, ..., kn are non-negative integers. This largest integer is called the Frobenius number of the set { a1, a2, ..., an }, and is usually denoted by g(a1, a2, ..., an). The requirement that the greatest common divisor (GCD) equal 1 is necessary in order for the Frobenius number to exist. If the GCD were not 1, then starting at some number m the only sums possible are multiples of the GCD; every number past m that is not divisible by the GCD cannot be represented by any linear combination of numbers from the set.
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From 2002 to 2011, Fargues was a chargé de recherches at the CNRS in Orsay, from 2011 to 2013 he was research director at the IRMA in Strasbourg and, from 2013, a professor at the l'Institut de mathématiques de Jussieu in Paris (a campus of the Sorbonne University). Fargues works mainly centers around the study of Shimura varieties, p-divisible groups and their moduli spaces, and p-adic Hodge theory. One of his most significant contributions has been to link the local Langlands correspondence with the so- called "Fargues-Fontaine curve," an object introduced by Fargues together with Jean-Marc Fontaine. In particular, Fargues has formulated a general geometric conjecture which refines the classical local Langlands conjecture, and at the same time introduces extra structure which mirrors the more categorical formulation of the geometric Langlands conjecture.
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There he shows how infinite divisibility involves the idea that there is some extended item, such as an apple, which can be divided infinitely many times, where one never divides down to point, or to atoms of any sort. Many professional philosophers claim that infinite divisibility involves either a collection of an infinite number of items (since there are infinite divisions, there must be an infinite collection of objects), or (more rarely), point-sized items, or both. Pyle states that the mathematics of infinitely divisible extensions involve neither of these — that there are infinite divisions, but only finite collections of objects and they never are divided down to point extension-less items. Zeno questioned how an arrow can move if at one moment it is here and motionless and at a later moment be somewhere else and motionless.
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In mathematics, a prime power is a positive integer power of a single prime number. For example: , and are prime powers, while , and are not. (The number 1 is not counted as a prime power.) The sequence of prime powers begins 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, 256, ... . The prime powers are those positive integers that are divisible by exactly one prime number; prime powers are also called primary numbers, as in the primary decomposition.
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These two operations are reciprocal one to the other, as ^hp(x,y,1)=p(x,y) and, if p is defined by p(x,y)=P(x,y,1), then ^hp(x,y,z)=P(x,y,z),, as soon as the homogeneous polynomial P is not divisible by z. For example, the projective curve of equation x2 \+ y2 − z2 is the projective completion of the unit circle of equation x2 \+ y2 − 1 = 0. This implies that an affine curve and its projective completion are the same curves, or, more precisely that the affine curve is a part of the projective curve that is large enough to well define the "complete" curve. This point of view is commonly expressed by calling "points at infinity" of the affine curve the points (in finite number) of the projective completion that do not belong to the affine part.
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It has hosted the Arkansas Activities Association's High School Basketball Championships since 2012 and the Great American Conference's Women's Volleyball Championship since 2013. It has been the site of the Forrest L. Wood national bass fishing championship three times and will host the event again in 2015.'' The arena, with a ceiling height and of exhibit space, is the newest facility in the Hot Springs Convention Center complex, which also includes a exhibit hall which is used for trade shows, conventions, and other events (maximum capacity: 8,000), has a ceiling height, and can be divisible into four smaller halls; and fifteen meeting rooms, including the Horner Hall ballroom with capacity of up to 1,850 and capable of hosting banquets, meetings and other special events, along with of meeting space in the other 14 meeting rooms. The complex is also home to a permanent art collection.
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Consider a loop containing instructions with a high latency. For example, the following code: for i = 1 to bignumber A(i) ; 3 cycle latency B(i) ; 3 C(i) ; 12(perhaps a floating point operation) D(i) ; 3 E(i) ; 3 F(i) ; 3 end would require 12 iterations of the loop to be unrolled to avoid the bottleneck of instruction `C`. This means that the code of the loop would increase by a factor of 12 (which not only affects memory usage, but can also affect cache performance, see code bloat). Even worse, the prologue (code before the loop for handling the case of `bignumber` not divisible by 12) will likely be even larger than the code for the loop, and very probably inefficient because software pipelining cannot be used in this code (at least not without a significant amount of further code bloat).
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In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring. The algorithm uses the same mathematical principles as the Buchberger algorithm, but computes many normal forms in one go by forming a generally sparse matrix and using fast linear algebra to do the reductions in parallel. The Faugère F5 algorithm first calculates the Gröbner basis of a pair of generator polynomials of the ideal. Then it uses this basis to reduce the size of the initial matrices of generators for the next larger basis: > If Gprev is an already computed Gröbner basis (f2, …, fm) and we want to > compute a Gröbner basis of (f1) + Gprev then we will construct matrices > whose rows are m f1 such that m is a monomial not divisible by the leading > term of an element of Gprev.
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German philosopher Karl Jaspers believed that Spinoza, in his philosophical system, did not mean to say that God and Nature are interchangeable terms, but rather that God's transcendence was attested by his infinitely many attributes, and that two attributes known by humans, namely Thought and Extension, signified God's immanence.Karl Jaspers, Spinoza (Great Philosophers), Harvest Books (October 23, 1974), , Pages: 14 and 95 Even God under the attributes of thought and extension cannot be identified strictly with our world. That world is of course "divisible"; it has parts. But Spinoza insists that "no attribute of a substance can be truly conceived from which it follows that the substance can be divided" (Which means that one cannot conceive an attribute in a way that leads to division of substance), and that "a substance which is absolutely infinite is indivisible" (Ethics, Part I, Propositions 12 and 13).
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In this case, the two factors of −z3 are coprime. This implies that three does not divide u and that the two factors are cubes of two smaller numbers, r and s : 2u = r3 : u2 \+ 3v2 = s3 Since u2 \+ 3v2 is odd, so is s. A crucial lemma shows that if s is odd and if it satisfies an equation s3 = u2 \+ 3v2, then it can be written in terms of two coprime integers e and f : s = e2 \+ 3f2 so that : u = e ( e2 − 9f2) : v = 3f ( e2 − f2) Since u is even and v odd, then e is even and f is odd. Since : r3 = 2u = 2e (e − 3f)(e + 3f) The factors 2e, (e–3f ), and (e+3f ) are coprime since 3 cannot divide e: If e were divisible by 3, then 3 would divide u, violating the designation of u and v as coprime.
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When a projective module is lifted, the associated character vanishes on all elements of order divisible by p, and (with consistent choice of roots of unity), agrees with the Brauer character of the original characteristic p module on p-regular elements. The (usual character-ring) inner product of the Brauer character of a projective indecomposable with any other Brauer character can thus be defined: this is 0 if the second Brauer character is that of the socle of a non-isomorphic projective indecomposable, and 1 if the second Brauer character is that of its own socle. The multiplicity of an ordinary irreducible character in the character of the lift of a projective indecomposable is equal to the number of occurrences of the Brauer character of the socle of the projective indecomposable when the restriction of the ordinary character to p-regular elements is expressed as a sum of irreducible Brauer characters.
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Logo of Radio 4 until 2007 The BBC Home Service was the predecessor of Radio 4 and broadcast between 1939 and 1967. It had regional variations and was broadcast on medium wave with a network of VHF FM transmitters being added from 1955. Radio 4 replaced it on 30 September 1967, when the BBC renamed many of its domestic radio stations, in response to the challenge of offshore radio. It moved to long wave in November 1978, taking over the 200 kHz frequency (1500 metres) previously held by Radio 2 - later moved to 198 kHz as a result of international agreements aimed at avoiding interference (all UK MW/LW frequencies are divisible by 9). At this point, Radio 4 became available across all of the UK for the first time and the station officially became known as Radio 4 UK, a title that remained until September 1984.
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104 The Divisional Court gave its judgment on 3 November 2000, on three main issues: firstly, the court's right to hear the case; secondly, the Chagossians' constitutional right of residence; and, thirdly, the status of the Commissioner's actions. The court found that it did have discretion to hear the case: while the Crown was divisible, the actions of the BIOT were clearly the actions of the British government, since every BIOT action was ordered and dealt with by the Foreign and Commonwealth Office. Laws J found that the Magna Carta did apply to foreign nations, as it was "the nearest approach to an irreplaceable 'fundamental statute' that England has ever had ... For in brief it means this, that the King is and shall be below the law". This did not alone validate Bancoult's case, since it did not mean that the government's actions were illegal.
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The Hassaniya speakers who predominate over the majority of the country except along the river are divisible into two crucial subgroups - the Bidan or white Moors and the Haratin or black Moors. The Bidan are traditionally further divided into Z'waya (religious or "marabout" groups), Hassan (warrior groups), Zenaga (free tributary groups), Mu'allamin (craftsmen) and Ighyuwn (entertainers) (...) Among Hassaniya Arabic speakers in southern Morocco and Mauritania, states Sean Hanretta – a professor of African History, the term Bidan is a "caste synecdoche" that refers to Hassani (warrior) and Zwaya (clerical) clans. In the slave castes, they recognized two layers, the `Abid (slaves) and Haratins (freed slaves). According to Remco Ensel – a professor of Anthropology specializing in Maghreb studies, the word "Haratin" in Moroccan is a pejorative that connotes "subordination, disrepute" and in contemporary literature, it is often replaced with "Drawi", "Drawa", "Sahrawi", "Sahrawa" or other regional terms.
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Dion expanded upon his earlier arguments against the territorial integrity of Quebec following secession by highlighting the inconsistency in the argument that Canada is divisible but Quebec is not. Secondly, Dion underscored that without recognition by the Government of Canada and when opposed by a strong minority of citizens, a unilateral declaration of independence faces much difficulty in gaining international recognition. In Dion's third open letter to Premier Lucien Bouchard came on 25 August 1998, shortly after the Supreme Court ruling on Secession had been handed down. He criticized the Quebec premier for accepting some aspects of the ruling (such as the political obligation for the Government of Canada to negotiate secession following a clear expression of will from the people of Quebec) and not other sections of the ruling (such as the need for a clear majority on a clear question and the unconstitutionality of a unilateral declaration of independence).
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The bankrupt is obliged (pursuant to section 19 of the Bankruptcy Act 1998) to: # unless the court otherwise directs, forthwith deliver such books of account or other papers relating to his estate in his possession or control as the Official Assignee may from time to time request and disclose to him such of them as are in the possession or control of any other person; # deliver up possession of any part of his property which is divisible among his creditors under this Act, and which is for the time being in his possession or control; # unless the Court otherwise directs, within the prescribed time file in the Central Office of the High Court a statement of affairs in the prescribed form and deliver a copy thereof to the OA; # give every reasonable assistance in the administration of the estate; and # disclose any property acquired after his adjudication in bankruptcy.
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Treatment of intangible property is such that an article of property is, by law or otherwise by traditional conceptualization, subject to expiration even when inheritable, which is a key distinction from tangible property. Upon expiration, the property, if of the intellectual category, becomes a part of public domain, to be used by but not owned by anybody, and possibly used by more than one party simultaneously due to the inapplicability of scarcity to intellectual property. Whereas things such as communications channels and pairs of electromagnetic spectrum band and signal transmission power can only be used by a single party at a time, or a single party in a divisible context, if owned or used at all. Thus far or usually those are not considered property, or at least not private property, even though the party bearing right of exclusive use may transfer that right to another.
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According to Hossein Nasr, Ali ibn Abi Talib, the first Shia Imam is credited with having established Islamic theology and among Muslims his sermons contain the first rational proofs of the God's unity (Tawhid). Ali is quoted as arguing that unity of God means that he has no like, he is not subject to numeration and is not divisible either in reality or imagination. On another occasion, he is quoted saying: > The first step of religion is to accept, understand and realize him as the > Lord ... The correct form of belief in his unity is to realize that he is so > absolutely pure and above nature that nothing can be added to or subtracted > from his being. That is, one should realize that there is no difference > between his person and his attributes, and his attributes should not be > differentiated or distinguished from his person.
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Maitri Upanishad - Sanskrit Text with English Translation EB Cowell (Translator), Cambridge University, Bibliotheca Indica, pages 265-268 There is a motley collection of ideas in the discussion of Kala (Time), within the sixth Prapathaka of the Upanishad. For example, in section 6.14, it sets out to prove Time exists, acknowledges the difficulty in proving Time exists by Pramana (epistemology in Indian philosophy), then inserts a theory of inductive inference for epistemological proof as follows, The section includes the concept of Time and non-Time, calling these as two forms of Brahman, mirroring the Upanishad's earlier discussion of Material and non-Material universe. It defines non-Time as "what was there before the appearance of Sun", and Time as "what began with the appearance of Sun".Paul Deussen, Sixty Upanishads of the Veda, Volume 1, Motilal Banarsidass, , pages 357-358 Non- Time is indivisible, Time is divisible.
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Also in 1999, Brian scored the multiple-Emmy-winning Ric Burns series New York: a documentary film, which after the World Trade Center attack of September 11, 2001, became among the biggest selling documentary series of its time. Brian Keane and director Ric Burns working on The Way West 1995 In 1996, Brian was asked to score Spirit of the Games, a documentary on the subject of the Olympics by the Emmy-winning director George Roy for HBO Sports. It began a long relationship with HBO Sports and a very successful run of sports documentaries including the Peabody-winning films Babe Ruth, Ali Frazier: One Nation Divisible, Dare to Compete, and Fists of Freedom, among others, all scored in the late nineties as part of a new series of documentaries entitled Sports of the 20th Century. Brian also scored HBO's Inside the NFL during that period.
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In binary, the palindromic primes include the Mersenne primes and the Fermat primes. All binary palindromic primes except binary 11 (decimal 3) have an odd number of digits; those palindromes with an even number of digits are divisible by 3. The sequence of binary palindromic primes begins (in binary): :11, 101, 111, 10001, 11111, 1001001, 1101011, 1111111, 100000001, 100111001, 110111011, ... The palindromic primes in base 12 are: (using reversed two and three for ten and eleven, respectively) :2, 3, 5, 7, Ɛ, 11, 111, 131, 141, 171, 181, 1Ɛ1, 535, 545, 565, 575, 585, 5Ɛ5, 727, 737, 747, 767, 797, Ɛ1Ɛ, Ɛ2Ɛ, Ɛ6Ɛ, ... Due to the superstitious significance of the numbers it contains, the palindromic prime 1000000000000066600000000000001 is known as Belphegor's Prime, named after Belphegor, one of the seven princes of Hell. Belphegor's Prime consists of the number 666, on either side enclosed by thirteen zeroes and a one.
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This proto-racism is seen as an important precursor to modern racism by classicist Benjamin Isaac. Such proto-racism and ethnocentrism must be looked at within context, because a modern understanding of racism based on hereditary inferiority (with modern racism based on eugenics and scientific racism) was not yet developed and it is unclear whether Aristotle believed the natural inferiority of Barbarians was caused by environment and climate (like many of his contemporaries) or by birth. Historian Dante A. Puzzo, in his discussion of Aristotle, racism, and the ancient world writes that: > Racism rests on two basic assumptions: that a correlation exists between > physical characteristics and moral qualities; that mankind is divisible into > superior and inferior stocks. Racism, thus defined, is a modern conception, > for prior to the XVIth century there was virtually nothing in the life and > thought of the West that can be described as racist.
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If (a, b, c) is a Heronian triple, so is (ma, mb, mc) where m is any positive integer greater than one. The Heronian triple (a, b, c) is primitive provided a, b, c are pairwise relatively prime (as with a Pythagorean triple). Here are a few of the simplest primitive Heronian triples that are not Pythagorean triples: : (4, 13, 15) with area 24 : (3, 25, 26) with area 36 : (7, 15, 20) with area 42 : (6, 25, 29) with area 60 : (11, 13, 20) with area 66 : (13, 14, 15) with area 84 : (13, 20, 21) with area 126 By Heron's formula, the extra condition for a triple of positive integers (a, b, c) with a < b < c to be Heronian is that :: (a2 \+ b2 \+ c2)2 − 2(a4 \+ b4 \+ c4) or equivalently :: 2(a2b2 \+ a2c2 \+ b2c2) − (a4 \+ b4 \+ c4) be a nonzero perfect square divisible by 16.
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The main difficulty in designing an envy-free procedure for n > 2 agents is that the problem is not "divisible". I.e., if we divide half of the cake among n/2 agents in an envy-free manner, we cannot just let the other n/2 agents divide the other half in the same manner, because this might cause the first group of n/2 agents to be envious (e.g., it is possible that A and B both believe they got 1/2 of their half which is 1/4 of the entire cake; C and D also believe the same way; but, A believes that C actually got the entire half while D got nothing, so A envies C). The Robertson–Webb protocol addresses this difficulty by requiring that the division is not only envy-free but also near-exact. The recursive part of the protocol is the following subroutine.
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Although they were not then known by that name, repunits in base-10 were studied by many mathematicians during the nineteenth century in an effort to work out and predict the cyclic patterns of repeating decimals. It was found very early on that for any prime p greater than 5, the period of the decimal expansion of 1/p is equal to the length of the smallest repunit number that is divisible by p. Tables of the period of reciprocal of primes up to 60,000 had been published by 1860 and permitted the factorization by such mathematicians as Reuschle of all repunits up to R16 and many larger ones. By 1880, even R17 to R36 had been factored and it is curious that, though Édouard Lucas showed no prime below three million had period nineteen, there was no attempt to test any repunit for primality until early in the twentieth century.
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In the context of tartans, thread counts are used not for determining coarseness, but rather for recording and reliably repeating the cross-striped pattern of the cloth. Such a thread count (which for the typical worsted woollen cloth used for a kilt must in total be divisible by 4) is typically given as a series of color-code and thread-count pairs. Sometimes, with typical symmetrical (reflective) tartans, slash () markup at the ends is used to indicate whether (and how much of) a "pivot" colour is to be repeated when the design is mirrored and repeated backwards. For example, calls for a pattern of (left to right) blue, white, blue, red, black, green, and white, and indicates that when mirrored the two white threads (going one direction) or 24 blue threads (going the other) are repeated after mirroring, resulting in a total of 4 white going rightward and 48 blue heading left.
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Raud's first study compared uji with Nishida Kitarō's interpretation of basho (場所, "place, location") as "the locus of tension, where the contradictory self-identities are acted out and complementary opposites negate each other", and is thus "the 'place' where impermanence happens" (2004: 46). Both these Japanese philosophers believed that in order to attain self-realization one must transcend the "ordinary" reality not by rising above it, and thereby separating oneself from it, but by "becoming" it, realizing oneself in it and the totality of the world, including "being-time". His second study reinterprets Dōgen's concept of time as primarily referring to momentary rather than durational existence, and translates uji as "existential moment" in opposition to the usual understanding of time as measurable and divisible (2012:153). According to Raud, this interpretation enables "more lucid readings" of many key passages in the Shōbōgenzō, such as translating the term kyōraku (経歴, "passage", etc.) as "shifting" (2012: 167).
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It is also necessary to solve the quadratic equation modulo small powers of p in order to recognise numbers divisible by the square of a factor-base prime. At the end of the factor base, any A[] containing a value above a threshold of roughly log(x2-n) will correspond to a value of y(x) which splits over the factor base. The information about exactly which primes divide y(x) has been lost, but it has only small factors, and there are many good algorithms for factoring a number known to have only small factors, such as trial division by small primes, SQUFOF, Pollard rho, and ECM, which are usually used in some combination. There are many y(x) values that work, so the factorization process at the end doesn't have to be entirely reliable; often the processes misbehave on say 5% of inputs, requiring a small amount of extra sieving.
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In order to make an hour of timecode match an hour on the clock, drop-frame timecode skips frame numbers 0 and 1 of the first second of every minute, except when the number of minutes is divisible by ten. This causes timecode to skip 18 frames each ten minutes (18,000 frames @ 30 frame/s) and almost perfectly compensates for the difference in rate. For example, the sequence when frame counts are dropped: :01:08:59:28 :01:08:59:29 :01:09:00:02 :01:09:00:03 For each tenth minute :01:09:59:28 :01:09:59:29 :01:10:00:00 :01:10:00:01 While non-drop timecode is displayed with colons separating the digit pairs—"HH:MM:SS:FF"—drop-frame is usually represented with a semicolon (;) or period (.) as the divider between all the digit pairs—"HH;MM;SS;FF", "HH.MM.SS.FF"—or just between the seconds and frames—"HH:MM:SS;FF" or "HH:MM:SS.FF".
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In his 1974 book, The Venture of Islam: The expansion of Islam in the Middle Periods, he defined it thus: "The rise of Persian had more than purely literary consequences: it served to carry a new overall cultural orientation within Islamdom.... Most of the more local languages of high culture that later emerged among Muslims... depended upon Persian wholly or in part for their prime literary inspiration. We may call all these cultural traditions, carried in Persian or reflecting Persian inspiration, 'Persianate' by extension."Hodgson says, "It could even be said that Islamicate civilization, historically, is divisible in the more central areas into an earlier 'caliphal' and a later 'Persianate' phase; with variants in the outlying regions—Maghrib, Sudanic lands, Southern Seas, India,... (p. 294)" The term designates ethnic Persians but also societies that may not have been ethnically Persian but whose linguistic, material or artistic cultural activities were influenced by or based on Persianate culture.
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It studies essential components, sequences that when added to another sequence of Schnirelmann density between zero and one, increase their density, proves that additive bases are essential components, and gives examples of essential components that are not additive bases. The second chapter concerns the number of representations of the integers as sums of a given number of elements from a given sequence, and includes the Erdős–Fuchs theorem according to which this number of representations cannot be close to a linear function. The third chapter continues the study of numbers of representations, using the probabilistic method; it includes the theorem that there exists an additive basis of order two whose number of representations is logarithmic, later strengthened to all orders in the Erdős–Tetali theorem. After a chapter on sieve theory and the large sieve (unfortunately missing significant developments that happened soon after the book's publication), the final chapter concerns primitive sequences of integers, sequences like the prime numbers in which no element is divisible by another.
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Thus, the year 1 BC of the proleptic Julian calendar is a leap year. This is to be distinguished from the astronomical year numbering, introduced in 1740 by French astronomer Jacques Cassini, which considers each New Year an integer on a time axis, with year 0 corresponding to 1 BC, and "year −1" corresponding to 2 BC, so that in this system, Julian leap years have a number divisible by four. The determination of leap years in the proleptic Julian calendar (in either numbering) is distinct from the question of which years were historically considered leap years during the Roman era, due to the leap year error: Between 45 BC and AD 8, the leap day was somewhat unsystematic. Thus there is no simple way to find an equivalent in the proleptic Julian calendar of a date quoted using either the Roman pre-Julian calendar or the Julian calendar before AD 8.
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A museme is a minimal unit of musical meaning, analogous to a morpheme in linguistics, "the basic unit of musical expression which in the framework of one given musical system is not further divisible without destruction of meaning." A museme may: :be broken down into component parts which are not in themselves meaningful within the framework of the musical language...but are nevertheless basic elements (not units) of musical expression which, when altered, may be compared to the phonemes of speech in that they alter the museme (morpheme) of which they are part and may thereby also alter its meaning. The term was brought to popularity by Philip Tagg, derived from the work of Charles Seeger. Musematic repetition ("repetition of musemes") is simple repetition "at the level of the short figure, often used to generate an entire structural framework." and contrasted with discursive repetition, in which the repetition is not so precise.
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Historically, a variety of non-decimal systems have been used. For example, ancient Mesoamerican civilizations common used vigesimal systems (base 20). A base 60 was in wide use in ancient Mesopotamia, used in measurements of time, geometry, currency and other fields. Decimal currencies also have disadvantages. The principal advantage of most non-decimal currencies is that they are more easily divided, particularly by numbers such as 3 and 8, than decimal currencies, due to being based upon conversion values that have a large number of factors. A currency with a 100:1 ratio is divisible neither into 3 nor into 8. For example, one-third of an Austrian Gulden (of 60 Kreuzer) was 20 Kreuzer while a third of a dollar is 33. cents. This divisibility is useful when trading and when sharing out sums of money. For these reasons, many states chose in the past to adopt non-decimal currencies based on divisions into sub-units such as 12 or 20, sometimes with more than one tier of sub-units.
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12 sectors: green area = orange area The requirement that the number of sectors be a multiple of four is necessary: as Don Coppersmith showed, dividing a disk into four sectors, or a number of sectors that is not divisible by four, does not in general produce equal areas. answered a problem of by providing a more precise version of the theorem that determines which of the two sets of sectors has greater area in the cases that the areas are unequal. Specifically, if the number of sectors is 2 (mod 8) and no slice passes through the center of the disk, then the subset of slices containing the center has smaller area than the other subset, while if the number of sectors is 6 (mod 8) and no slice passes through the center, then the subset of slices containing the center has larger area. An odd number of sectors is not possible with straight-line cuts, and a slice through the center causes the two subsets to be equal regardless of the number of sectors.
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ECRI today represents a third generation of cycle research, building on the work of ECRI's co-founder, Geoffrey H. Moore, and his mentors, Wesley C. Mitchell and Arthur F. Burns. 1920, Wesley C. Mitchell and his colleagues established the National Bureau of Economic Research (NBER), with a primary objective of investigating business cycles. 1927, Mitchell laid down the standard definition of business cycles: "Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle; this sequence of changes is recurrent but not periodic; in duration business cycles vary from more than one year to ten or twelve years; they are not divisible into shorter cycles of similar character with amplitudes approximating their own." 1929, with the start of the Great Depression, business cycle researchers had a practical emergency on their hands.
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This proof builds on Lagrange's result that if p=4n+1 is a prime number, then there must be an integer m such that m^2 + 1 is divisible by p (we can also see this by Euler's criterion); it also uses the fact that the Gaussian integers are a unique factorization domain (because they are a Euclidean domain). Since does not divide either of the Gaussian integers m + i and m-i (as it does not divide their imaginary parts), but it does divide their product m^2 + 1, it follows that p cannot be a prime element in the Gaussian integers. We must therefore have a nontrivial factorization of p in the Gaussian integers, which in view of the norm can have only two factors (since the norm is multiplicative, and p^2 = N(p), there can only be up to two factors of p), so it must be of the form p = (x+yi)(x-yi) for some integers x and y. This immediately yields that p = x^2 + y^2.
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The "Essay" mentioned above contains also the recommendation that divisions of coins, weights and measures be based on 8 instead of 10. "Whereas reason and convenience indicate to us a uniform standard for all quantities; which I shall call the Georigan standard; and that is only to divide every integer in each species into eight equal parts, and every part again into 8 real or imaginary particles, as far as is necessary. For tho' all nations count universally by tens (originally occasioned by the number of digits on both hands) yet 8 is a far more complete and commodious number; since it is divisible into halves, quarters, and half quarters (or units) without a fraction, of which subdivision ten is uncapable...." In the treatise on Octave computation Jones concluded: "Arithmetic by Octaves seems most agreeable to the Nature of Things, and therefore may be called Natural Arithmetic in Opposition to that now in Use, by Decades; which may be esteemed Artificial Arithmetic."See H.R. Phalen, "Hugh Jones and Octave Computation," The American Mathematical Monthly 56 (August–September 1949): 461–65, at 462.
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In applications that require only one solution, rather than all solutions, the expected running time of a brute force search will often depend on the order in which the candidates are tested. As a general rule, one should test the most promising candidates first. For example, when searching for a proper divisor of a random number n, it is better to enumerate the candidate divisors in increasing order, from 2 to , than the other way aroundbecause the probability that n is divisible by c is 1/c. Moreover, the probability of a candidate being valid is often affected by the previous failed trials. For example, consider the problem of finding a 1 bit in a given 1000-bit string P. In this case, the candidate solutions are the indices 1 to 1000, and a candidate c is valid if P[c] = 1. Now, suppose that the first bit of P is equally likely to be 0 or 1, but each bit thereafter is equal to the previous one with 90% probability.
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In mathematics, a superelliptic curve is an algebraic curve defined by an equation of the form :y^m = f(x), where m \geq 2 is an integer and f is a polynomial of degree d\geq 3 with coefficients in a field k; more precisely, it is the smooth projective curve whose function field defined by this equation. The case m=2 and d=3 is an elliptic curve, the case m=2 and d\ge 5 is a hyperelliptic curve, and the case m=3 and d\geq is an example of a trigonal curve. Some authors impose additional restrictions, for example, that the integer m should not be divisible by the characteristic of k, that the polynomial f should be square free, that the integers m and d should be coprime, or some combination of these. The Diophantine problem of finding integer points on a superelliptic curve can be solved by a method similar to one used for the resolution of hyperelliptic equations: a Siegel identity is used to reduce to a Thue equation.
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Hydra has one bright binary star, Epsilon Hydrae, which is difficult to split in amateur telescopes; it has a period of 1000 years and is 135 light-years from Earth. The primary is a yellow star of magnitude 3.4 and the secondary is a blue star of magnitude 6.7. However, there are several dimmer double stars and binary stars in Hydra. 27 Hydrae is a triple star with two components visible in binoculars and three visible in small amateur telescopes. The primary is a white star of magnitude 4.8, 244 light-years from Earth. The secondary, a binary star, appears in binoculars at magnitude 7.0 but is composed of a magnitude 7 and a magnitude 11 star; it is 202 light-years from Earth. 54 Hydrae is a binary star 99 light-years from Earth, easily divisible in small amateur telescopes. The primary is a yellow star of magnitude 5.3 and the secondary is a purple star of magnitude 7.4. N Hydrae (N Hya) is a pair of stars of magnitudes 5.8 and 5.9. Struve 1270 (Σ1270) consists of a pair of stars, magnitudes 6.4 and 7.4.
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Moreover, in characteristic 2 there are additional possibilities arising not from exceptional isogenies but rather from the fact that for simply connected type C (I.e., symplectic groups) there are roots that are divisible (by 2) in the weight lattice; this gives rise to examples whose root system (over a separable closure of the ground field) is non- reduced; such examples exist with a split maximal torus and an irreducible non-reduced root system of any positive rank over every imperfect field of characteristic 2. The classification in characteristic 3 is as complete as in larger characteristics, but in characteristic 2 the classification is most complete when [k:k^2]=2 (due to complications caused by the examples with a non-reduced root system, as well as phenomena related to certain regular degenerate quadratic forms that can only exist when [k:k^2]>2). Subsequent work of , building on additional material included in the second edition , completes the classification in characteristic 2 up to a controlled central extension by providing an exhaustive array of additional constructions that only exist when [k:k^2]>2 , ultimately resting on a notion of special orthogonal group attached to regular but degenerate and not fully defective quadratic spaces in characteristic 2.
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The above example consisted of 12 observations in the dataset, which made the determination of the quartiles very easy. Of course, not all datasets have a number of observations that is divisible by 4. We can adjust the method of calculating the IQM to accommodate this. So ideally we want to have the IQM equal to the mean for symmetric distributions, e.g.: :1, 2, 3, 4, 5 has a mean value xmean = 3, and since it is a symmetric distribution, xIQM = 3 would be desired. We can solve this by using a weighted average of the quartiles and the interquartile dataset: Consider the following dataset of 9 observations: :1, 3, 5, 7, 9, 11, 13, 15, 17 There are 9/4 = 2.25 observations in each quartile, and 4.5 observations in the interquartile range. Truncate the fractional quartile size, and remove this number from the 1st and 4th quartiles (2.25 observations in each quartile, thus the lowest 2 and the highest 2 are removed). : ~~1, 3~~ , (5), 7, 9, 11, (13), ~~15, 17~~ Thus, there are 3 full observations in the interquartile range, and 2 fractional observations. Since we have a total of 4.5 observations in the interquartile range, the two fractional observations each count for 0.75 (and thus 3×1 + 2×0.75 = 4.5 observations).
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The term also refers to any embodiment, manifestation, incarnation, personification, appearance, image, idol or statue of a deity.Monier Monier-Williams, Sanskrit English Dictionary, Oxford University Press, (Reprinted in 2011), page 824 The earliest mention of the term murti occurs in primary Upanishads composed in the 1st millennium BCE, particularly in verse 3.2 of Aitareya Upanishad, verse 1.13 of Shvetashvatara Upanishad, verse 6.14 of Maitrayaniya Upanishad and verse 1.5 of Prashna Upanishad.G. A. Jacob, A concordance to the principal Upanishads, Harvard University Press, Reprinted Motilal Banarsidass, page 750 For example, the Maitrayaniya Upanishad uses the term to mean a "form, manifestation of time". The section sets out to prove Time exists, acknowledges the difficulty in proving Time exists by Pramana (epistemology in Indian philosophy), then inserts a theory of inductive inference for epistemological proof as follows, The section includes the concept of Time and non-Time, stating that non-Time as that which existed before creation of universe, and time as which came into existence with the creation of universe.Paul Deussen (2010 Reprint), Sixty Upanishads of the Veda, Volume 1, Motilal Banarsidass, , pages 355–358 Non- time is indivisible, time is divisible, and the Maitri Upanishad then asserts that the "year is the mūrti of time".
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A prime p is called strong irregular if it's both B-irregular and E-irregular (the indexes of Bernoulli and Euler numbers that are divisible by p can be either the same or different). The first few strong irregular primes are :67, 101, 149, 263, 307, 311, 353, 379, 433, 461, 463, 491, 541, 577, 587, 619, 677, 691, 751, 761, 773, 811, 821, 877, 887, 929, 971, 1151, 1229, 1279, 1283, 1291, 1307, 1319, 1381, 1409, 1429, 1439, ... To prove the Fermat's Last Theorem for a strong irregular prime p is more difficult (since Kummer proved the first case of Fermat's Last Theorem for B-regular primes, Vandiver proved the first case of Fermat's Last Theorem for E-regular primes), the most difficult is that p is not only a strong irregular prime, but 2p + 1, 4p + 1, 8p + 1, 10p + 1, 14p + 1, and 16p + 1 are also all composite (Legendre proved the first case of Fermat's Last Theorem for primes p such that at least one of 2p + 1, 4p + 1, 8p + 1, 10p + 1, 14p + 1, and 16p + 1 is prime), the first few such p are :263, 311, 379, 461, 463, 541, 751, 773, 887, 971, 1283, ...
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