An 8K TV quadruples the number of pixels, just as 4K did with 1080p.
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That's expected to reach 16% by 2020, even as the amount of data nearly quadruples.
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But when that quadruples, all of a sudden there aren't enough hours in the day.
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And if it's cut with fentanyl, the profit quadruples along with the danger to the users.
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The United States remains the second-largest growth market for solar PV, followed by India, whose capacity quadruples .
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This can benefit the co-investor if the startup quadruples revenues by selling through the corporation's distribution channels.
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"Triples are hard," Chen said of his tumble, sparking laughter in the interview zone after all the chatter about quadruples.
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A mutation in one of those genes more than quadruples your risk of breast cancer to between 45 and 65 percent.
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Krieg: So when a political organization, especially one dedicated to democratic principles, quadruples in size it is effectively a different thing.
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The agreement reached Sunday also more than quadruples funds to fight opioid addiction, and preserved Planned Parenthood funding, at least for now.
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The Dutch PhD student quadruples his bit count with his latest retro project, an astrophotography videogame he developed for the Atari 2600.
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This model quadruples the amount of buttons, so it's now possible to customize this headset to your taste through HyperX's NGenuity software.
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Then with little warning, it quadruples in size and speed to create a hulking mountain of water with barrels that rarely have an exit.
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Research shows that in military units in which commanders initiate or even just tolerate sexual harassment, the likelihood of sexual assault triples or quadruples.
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The 22GB configuration qualifies for the bundle, too, but at $24, it's hard to recommend since $23000 more for the 2159.99GB model quadruples your storage.
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"I never dreamt as a youngster that we would ever see that many quadruples, it was all about triples then," the legendary skater tells PEOPLE.
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Given that the median household brings in about $60,000, this means the average family federal debt share quadruples their annual income – and that's before taxes.
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One-quarter of nursing home residents are hospitalized each year, and the daily cost of caring for them more than quadruples when they move to the hospital.
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In fact, according to the United States Trade Representative, TPP more than quadruples the number of people outside the United States who are protected by enforceable labor provisions.
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This is not just common sense, it's also a survival strategy for both lions and humans, especially as Africa's population quadruples in this century to four billion people.
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Her closet in her condo is like a survivalist's dream, triples and quadruples of toilet paper, kitchen gloves, Ziploc bags, because in her uncertain upbringing, nothing was permanent.
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This sum nearly quadruples the total U.S. economic assistance in 22018 to South Sudan, Syria, and the Democratic Republic of the Congo — all countries with severe humanitarian crises.
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And, having an unwanted child after being denied an abortion quadruples the odds a mother and her new child will be forced to live below the poverty line.
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"This acquisition will add three million metric tons of volume which quadruples our overall feeds production capacity," said Sabin Aboitiz, Aboitiz Equity's chief operating officer and Pilmico's president and CEO.
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New mining laws in Colorado require thousands of workers to wear a certain type of hardhat, and suddenly a plastics company in Norway quadruples its business to meet the increased demand.
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" Morgan Stanley estimated that scheduled changes "will result in a rate that nearly equals the prior code by 2023, and nearly quadruples today's rate by 2027 if Congress does not extend these policies.
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It more than quadruples the number of legible tablets previously known from London: of the 405 most recently studied tablets, researchers have deciphered over 7003; only 19 were readable before the Bloomberg excavations.
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I would call that our Plan A. If that happens you're going to suddenly see a lot more investment in this space, because if you can fly supersonic over land the market size quadruples.
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The most sensitive of the trade spats, a preliminary tariff from the Trump administration that quadruples the prices of Bombardier's new C Series airliner in the United States, took an unexpected turn this week.
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In fact, forcing women to carry an unwanted pregnancy to term quadruples their odds of living below the federal poverty line, and laws that restrict abortion access have proven to deteriorate economic outcomes for women.
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On Wednesday, it reported profits of $5.8 billion for the quarter, and its operating margin of 44% doubles that of IT firms in the S&P 500 and quadruples the margin of the entire index.
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However, a new study, published Wednesday in the British Medical Journal, has revealed that the condition in fact quadruples the risk of liver disease and doubles the risk of arthritis and frailty in older demographics.
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If the early-stage fund reaches a point where it quadruples returns for investors, the carry jumps to 30 percent, and for the growth fund, it needs to triple to see that increase, according to sources.
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The 12003GB model currently costs $999 bundled with the tablet, though if you need more space for music, movies, and games, paying an extra $50 is a tiny premium that quadruples the amount of storage that you'll get.
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Now look what happens in the two weeks after Tax Day, on average: The average gain quadruples for the S&P 500, and the Russell 2000 and Nasdaq go from average losses to increases greater than 1 percent.
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Mattson and the drummer, Amir Oosman, who also quadruples as the tour manager, driver, and production assistant, put on similar outfits, inspired by their leader's signature style, the mishmashed attire of his childhood, the nostalgic commodities we'd rather just forget.
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Go deeper: Iran quadruples production rate of low-enriched uranium Editor's note: This story has been updated to include new developments reported by AP. The UN watchdog is now raising questions about whether Iran is complying with key provisions to limit the nation's use of advanced centrifuges.
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Throughout its 350-year development, this town of 2,400 full-time residents (in the summer, the population quadruples) has been accessible only from the towns of Greenport or North Haven via a 10-minute ferry ride to the island's north or south points; this has kept its deciduous-thick nature reserves and private, permit-only beaches quiet and rustic.
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Shellnutt, Kate. "Megachurches getting bigger; Lakewood quadruples in size since 2000" (). Houston Chronicle. March 21, 2011.
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Harris, Chris. "Super Tuesday Youth Voter Turnout Triples, Quadruples in Some States." MTV News. retrieved 6 Feb 2008.
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"Megachurches getting bigger; Lakewood quadruples in size since 2000." Houston Chronicle. March 21, 2011. Retrieved on May 3, 2014.
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The workforce employed at the campus annually quadruples in the weeks around Halloween to account for increased seasonal demand.
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Ghana: Cfao Almost Quadruples Profit. allafrica.com (AllAfrica.com). It was formed in 1909 and is currently headed by Thomas Pelletier.
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He decides to report on the happenings during his broadcasts (which quadruples his audience size) and then bandies the locals into a collective search for the alien.
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Apartments are leased fully furnished, and are available in 15 different layouts, including: singles, doubles, triples, quadruples, and quintuples. Prices vary from $600 to $1,200 per room per month.
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A n-dimensional simplex has the minimum n+1 vertices, with all pairs of vertices connected by edges, all triples of vertices defining faces, all quadruples of points defining tetrahedral cells, etc.
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During the months of April through to October, Skala becomes a popular tourist resort. With award-winning beaches, a plentiful amount of hotels and many restaurants, the town’s population quadruples during the summer months.
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All four primitive Pythagorean quadruples with only single-digit values A Pythagorean quadruple is a tuple of integers , , and , such that . They are solutions of a Diophantine equation and often only positive integer values are considered.R. Spira, The diophantine equation , Amer. Math. Monthly Vol.
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The gun layout of the Hatsuharus was retained but Type C gun houses were used and the torpedo mountings were quadruples, for the first time. The four added ships were further developed, showing an evolution into the succeeding Asashios. All ten were lost during the war.
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If the declarer decides to make any announcements before the pickup, he announces the game and then the bonuses e.g. "Dreiblatt with Pagat ultimo!" or "Zweiblatt with Absolute". The defenders may contra either; at this point it quadruples the score. The declarer may "recontra" which multiplies the game value or bonus by 16.
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This method generates all Pythagorean quadruples exactly once each when and run through all pairs of natural numbers and runs through all permissible values for each pair. No such method exists if both and are odd, in which case no solutions exist as can be seen by the parametrization in the previous section.
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All Pythagorean quadruples (including non-primitives, and with repetition, though , and do not appear in all possible orders) can be generated from two positive integers and as follows: If and have different parity, let be any factor of such that . Then and . Note that . A similar method existsSierpiński, Wacław, Pythagorean Triangles, Dover, 2003 (orig.
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If a player during a Power Play or in the Power Zone, their points penalty doubles, and if the foul shot originated in a Power Zone and during a Power Play, the penalty quadruples. The most recent version of the Power Ball. The Power Ball looks similar to the 11-ball in pocket billiards but without the number designation.
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15,16 A spacial perspectivity of a projective configuration in one plane yields such a configuration in another, and this applies to the configuration of the complete quadrangle. Thus harmonic quadruples are preserved by perspectivity. If one perspectivity follows another the configurations follow along. The composition of two perspectivities is no longer a perspectivity, but a projectivity.
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Morphological functions (e.g., morphological complement, modifier, and nucleus) are comparable to grammatical functions in syntax in taking 'morphological quadruples' as their arguments and assigning relations among morphological constituents as values. They figure, via their semantic content, in morphosemantic meaning composition. The lexicon of an idiolect system is construed as a pair consisting of the lexeme lexicon and the word lexicon.
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AT&T; conducted trials in 2017 for business use of 400-gigabit Ethernet. Researchers Robert Maher, Alex Alvarado, Domaniç Lavery, and Polina Bayvel of University College London were able to increase networking speeds to 1.125 terabits per second. Christos Santis, graduate student Scott Steger, Amnon Yariv, Martin and Eileen Summerfield developed a new laser that potentially quadruples transfer speeds with fiber optics.
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The size of the storm also affects the surge height; this is due to the storm’s area not being proportional to its perimeter. If a storm doubles in diameter, its perimeter also doubles, but its area quadruples. As there is proportionally less perimeter for the surge to dissipate to, the surge height ends up being higher. Hurricane Ike storm surge damage in Gilchrist, Texas in 2008.
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Mid-summer is celebrated by tubing (floating the creek on inner tubes). Annual celebrations include a two-day rodeo and parade, hinging on the 4th of July celebration of Independence Day (United States). The town's population temporarily quadruples over this period, as tourists and area residents gather to celebrate. The main street is also closed to through traffic to accommodate live music that lasts into the wee hours of the morning.
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Hammamet ( ') is a town in Tunisia. Thanks to its beaches, it is a popular destination for swimming and water sports and is one of the primary tourist destinations in Tunisia. It is located in the south-eastern section of Cap Bon and is part of the Nabeul Governorate. The reported number of inhabitants varies from 100,000 to 400,000 and the population quadruples due to tourists' arrival in the summer.
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In 1984, brothers John and Peter Borwein produced an iterative algorithm that quadruples the number of digits in each step; and in 1987, one that increases the number of digits five times in each step. Iterative methods were used by Japanese mathematician Yasumasa Kanada to set several records for computing between 1995 and 2002. This rapid convergence comes at a price: the iterative algorithms require significantly more memory than infinite series.
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Finally, the intonation structure is a sequence of modified intonation structures of the syntactic base forms occurring in the syntactic unit. The syntactic intonation structure is crucial for syntactic accents and for the distinction of sentence types (as far as this is based on intonation patterns). Traditional grammatical relations such as subject, object, attribute, etc. are reconstructed in Integrational Syntax as functions ('grammatical functions') taking 'syntactic quadruples' as their arguments.
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Simplicial complexes can be seen to have the same geometric structure as the contact graph of a sphere packing (a graph where vertices are the centers of spheres and edges exist if the corresponding packing elements touch each other) and as such can be used to determine the combinatorics of sphere packings, such as the number of touching pairs (1-simplices), touching triplets (2-simplices), and touching quadruples (3-simplices) in a sphere packing.
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The London-based newspaper The Independent, published an article on Kragerø stating that "When Norwegians want to get away from it all they head for Kragero. Forests, fjords and islands await them at the place where Edvard Munch found peace and relaxation." The population of Kragerø quadruples during its summer months due to high tourism. Edvard Munch fell in love with Kragerø in his time, and called it "The Pearl of the Coastal Towns" (Perlen blandt kystbyene).
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69 (1962), No. 5, 360–365. However, to provide a more complete geometric interpretation, the integer values can be allowed to be negative and zero (thus allowing Pythagorean triples to be included) with the only condition being that . In this setting, a Pythagorean quadruple defines a cuboid with integer side lengths , , and , whose space diagonal has integer length ; with this interpretation, Pythagorean quadruples are thus also called Pythagorean boxes.R. A. Beauregard and E. R. Suryanarayan, Pythagorean boxes, Math.
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A set of four positive integers a, b, c and d such that is called a Pythagorean quadruple. The simplest example is (1, 2, 2, 3), since 12 \+ 22 \+ 22 = 32. The next simplest (primitive) example is (2, 3, 6, 7), since 22 \+ 32 \+ 62 = 72. All quadruples are given by the formula :(m^2+n^2-p^2-q^2)^2+(2mq+2np)^2+(2nq-2mp)^2=(m^2+n^2+p^2+q^2)^2.
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Attribute values can be ordered sets of composite components, character large objects (CLOB's), binary large objects (BLOB's), or unlimited sparse arrays. Other higher-level structures built of multiple Items include key/value associations like ordered maps, ordered sets, Entity- Attribute-Value nets of quadruples, trees, DAG's, taxonomies, or full-text indexes. Mixtures of these can occur along with other custom client-defined structures. Any ItemSpace may be represented as an extended JSON document, and JSON printers and parsers are provided.
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L.E. Dickson, Some relations between the theory of numbers and other branches of mathematics, in Villat (Henri), ed., Conférence générale, Comptes rendus du Congrès international des mathématiciens, Strasbourg, Toulouse, 1921, pp. 41–56; reprint Nendeln/Liechtenstein: Kraus Reprint Limited, 1967; Collected Works 2, pp. 579–594. Thus, all primitive Pythagorean quadruples are characterized by Lebesgue's identity :(m^2 + n^2 + p^2 + q^2)^2 = (2mq + 2np)^2 + (2nq - 2mp)^2 + (m^2 + n^2 - p^2 - q^2)^2.
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Neykova has been involved in rowing since 1985, when she began training at CSKA Sofia coached Verka Aleksieva. In 1989, she was vice- world junior champion, winning that title in 1990. After several unsuccessful attempts with women's doubles and quadruples, she switched to Single Sculls and won her first medal at the 1999 world championships in Canada. She has two world titles in that discipline, at Sevilla 2002 and Milan 2003, as well as being world second in 2007 in Gifu.
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The Luce Foundation Center for American Art on the third floor of the Smithsonian American Art Museum. The Luce Foundation Center, which opened in July 2000, is the first visible art storage and study center in Washington, D.C. and the fourth center to bear the Luce Family name. It has 20,400 square feet on the third and fourth floors of American Art Museum. It presents more than 3,300 objects in 64 secure glass cases, which quadruples the number of artworks from the permanent collection on public view.
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A Kathak performance can be solo, duo or team. In a technical performance, the speed and energy the dancers exchange with the audience increases in multiples, that is the tempo doubles or quadruples. During the performance, one or more of the Kathak artists may come to the microphone, interact with the audience, explain something, tell an anecdote in a particular language, or rhythmically recite a song. The costumes of the dancer and the facial cosmetics between a Hindu or Muslim Kathak dance troupe varies.
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In actual case, the blockchain essentially has no querying abilities when compared to traditional database and with a doubling of nodes, network traffic quadruples with no improvement in throughput, latency, or capacity. To overcome these shortcomings, taking a traditional database and adding blockchain features to it sounds more feasible. That's how the concept of Blockchain-based database came into existence which consists of multiple member clouds riding on two primary layers, the first one is Database Interface and the second one is the Blockchain Anchoring.
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Location of Mercês within Minas Gerais Mercês is a Brazilian municipality located in the state of Minas Gerais. The city belongs to the mesoregion of Zona da Mata and to the microregion of Ubá. Mercês is notable for its disproportionately large populations of Scientologists as opposed to other districts; this statistic more than quadruples any municipality which it borders. This abnormality may be attributed to the presence of a church centre for the religion located in a region, although few attend it on a strictly regulated basis.
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The contact graph of an arbitrary finite packing of unit balls is the graph whose vertices correspond to the packing elements and whose two vertices are connected by an edge if the corresponding two packing elements touch each other. The cardinality of the edge set of the contact graph gives the number of touching pairs, the number of 3-cycles in the contact graph gives the number of touching triplets, and the number of tetrahedrons in the contact graph gives the number of touching quadruples (in general for a contact graph associated with a sphere packing in n dimensions that the cardinality of the set of n-simplices in the contact graph gives the number of touching (n + 1)-tuples in the sphere packing). In the case of 3-dimensional Euclidean space, non-trivial upper bounds on the number of touching pairs, triplets, and quadruples were proved by Karoly Bezdek and Samuel Reid at the University of Calgary. The problem of finding the arrangement of n identical spheres that maximizes the number of contact points between the spheres is known as the "sticky-sphere problem".
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Chapman had challenged this earlier (1775), but Beaufoy's work was taken up by Isambard Kingdom Brunel as the "square-cube" law. Simply put, if a vessel is doubled in size the resistance to motion quadruples, but the size of engines and the carrying capacity (fuel, cargo) increase eight-fold. He married his cousin Margaretta Beaufoy (died 1800) in a 1784 "runaway" marriage, after which they had a "long sojurn" in Switzerland. They had three sons (Henry, Mark and George) and a daughter; Margaretta took the infant girl Henriette to watch Mark ascend Mont Blanc.
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Piantoni began his career at the age of 19 with FC Nancy during 1950–1951 season. In the first match of the championships, against RC Lens on 27 August 1950, he scored two goals. In his first season, he managed to become the top scorer of the championship with 27 goals. He scored five goals on the 28th day against Le Havre AC (6–1) and two quadruples (four goals) during the return match against RC Lens (4–2) and RC Strasbourg on the final day (5–1).
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This proved a serious problem in the construction of the accelerator. A second problem in the construction period was the machines behavior at an energy called "transition energy". At this point the relative increase in particle velocity changes from being greater to being smaller, causing the amplitude of the betatron oscillation to go to zero and loss of stability in the beam. This was solved by a jump, or a sudden shift in the acceleration, in which pulsed quadruples made the protons transverse the transition energy level much faster.
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Some therapies for other forms of cancer increase the lifetime risk of endometrial cancer, which is a baseline 2–3%. Tamoxifen, a drug used to treat estrogen-positive breast cancers, has been associated with endometrial cancer in approximately 0.1% of users, particularly older women, but the benefits for survival from tamoxifen generally outweigh the risk of endometrial cancer. A one to two-year course of tamoxifen approximately doubles the risk of endometrial cancer, and a five-year course of therapy quadruples that risk. Raloxifene, a similar drug, did not raise the risk of endometrial cancer.
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120 for completing toe loop jumps was the ability to increase rotational velocity while in the air. They discovered that skaters do not have to skate faster into quadruple jumps. Most skaters "actually tended to skate slower into their quads as compared to their triples", although the differences in the speed in which they approached triples and quadruples were small. King conjectured that slowing their approach into the jumps were due to skaters' "confidence and a feeling of control and timing for the jump", rather than any difference in how they executed them.
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Trusova made her international senior debut at the 2019 CS Ondrej Nepela Memorial where she won the gold medal and set several new world records. In free skating she became the first lady ever to land three quadruples when she landed a quad Lutz and two quad toe loops, the second in combination. She set the new free skating record of 163.78 points and also the new combined total record of 238.69 points. Her technical element score (TES) of 98.34 points in free skating was also the new world record.
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Panoramic view of the beach of San Benedetto del Tronto The tourism represents the most important item of the city income. San Benedetto has established itself, since the early decades of the twentieth century, as a popular seaside resort. Since the second half of the sixties, it has also established itself as the first tourist destination of Marche in terms of number of presences. During the summer San Benedetto, triples and sometimes quadruples its inhabitants, can reach a daily population of between 150,000 and 200,000 inhabitants among tourists housed in accommodation and commuters.
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Hornby Island of British Columbia, Canada, is one of the two northernmost Gulf Islands, located near Vancouver Island's Comox Valley, the other being Denman Island. A small community of 958 residents (as of the 2011 census), Hornby is home to many artists, retired professionals, small business owners, remote workers, and young families who share a love of rural island life. Over the past 30 years, the island has become a coveted destination and its population easily quadruples in size during the summer months. The shoulder seasons are a preferred time for hiking, mountain biking, marine activities, weddings, and retreats.
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" Peter Hartlaub of the San Francisco Chronicle gave the film two out of four stars, saying "Cloudy With a Chance of Meatballs 2 is a humorous yet unfocused romp, so unwilling to settle on a single theme that hyperactivity medication should be handed out with the 3-D glasses." Matt Patches of Film.com gave the film 7.1 out of 10, saying "The 2009 original separated itself from the Pixar and Dreamworks competition with a joke-first approach. The sequel quadruples the recipe, with gags on top of gags on top of gags in a way only animation could achieve.
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According to John Aubrey, cribbage was created by the English poet Sir John Suckling in the early 17th century, as a derivation of the game "noddy". While noddy has become a historical, rarely-played game, cribbage has continued unchanged as a popular game in the English-speaking world. The objective of the game is to be the first player to score a target number of points, typically 61 or 121. Points are scored for showing certain jacks, playing the last card, for card combinations adding up to 15 or 31, and for pairs, triples, quadruples, runs and flushes.
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Common sources of damaging noise levels include car stereos, children's toys, motor vehicles, crowds, lawn and maintenance equipment, power tools, gun use, musical instruments, and even hair dryers. Noise damage is cumulative; all sources of damage must be considered to assess risk. If one is exposed to loud sound (including music) at high levels or for extended durations (85 dB A or greater), then hearing loss will occur. Sound intensity (sound energy, or propensity to cause damage to the ears) increases dramatically with proximity according to an inverse square law: halving the distance to the sound quadruples the sound intensity.
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A curious feature of this book on projective geometry is the opening on abstract algebra including laws of composition, group theory, ring theory, fields, finite fields, vector spaces and linear mapping. These seven introductory sections on algebraic structures provide an enhanced vocabulary for the treatment of 15 classical topics of projective geometry. Furthermore, sections (14) projectivities with non-commutative fields, (22) quadrics over non-commutative fields, and (26) finite geometries embellish the classical study. The usual topics are covered such as (4) Fundamental theorem of projective geometry, (11) projective plane, (12) cross-ratio, (13) harmonic quadruples, (18) pole and polar, (21) Klein model of non-Euclidean geometry, (22-4) quadrics.
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The classification of traditional coupled-cluster methods rests on the highest number of excitations allowed in the definition of T. The abbreviations for coupled-cluster methods usually begin with the letters "CC" (for "coupled cluster") followed by # S – for single excitations (shortened to singles in coupled-cluster terminology), # D – for double excitations (doubles), # T – for triple excitations (triples), # Q – for quadruple excitations (quadruples). Thus, the T operator in CCSDT has the form : T = T_1 + T_2 + T_3. Terms in round brackets indicate that these terms are calculated based on perturbation theory. For example, the CCSD(T) method means: # Coupled cluster with a full treatment singles and doubles.
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Fuel economy-maximizing behaviors also help reduce fuel consumption. Among the most effective are moderate (as opposed to aggressive) driving, driving at lower speeds, using cruise control, and turning off a vehicle's engine at stops rather than idling. A vehicle's gas mileage decreases rapidly with increasing highway speeds, normally above 55 miles per hour (though the exact number varies by vehicle), because aerodynamic forces are proportionally related to the square of an object's speed (when the speed is doubled, drag quadruples). According to the U.S. Department of Energy (DOE), as a rule of thumb, each one drives over is similar to paying an additional $0.30 per gallon for gas.
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For any pair of quadruples from a commutative ring, the following expressions are equal: ::(a_1^2+a_2^2+a_3^2+a_4^2)(b_1^2+b_2^2+b_3^2+b_4^2)= ::(a_1 b_1 - a_2 b_2 - a_3 b_3 - a_4 b_4)^2 + ::(a_1 b_2 + a_2 b_1 + a_3 b_4 - a_4 b_3)^2 + ::(a_1 b_3 - a_2 b_4 + a_3 b_1 + a_4 b_2)^2 + ::(a_1 b_4 + a_2 b_3 - a_3 b_2 + a_4 b_1)^2. Euler wrote about this identity in a letter dated May 4, 1748 to GoldbachLeonhard Euler: Life, Work and Legacy, R.E. Bradley and C.E. Sandifer (eds), Elsevier, 2007, p. 193Mathematical Evolutions, A. Shenitzer and J. Stillwell (eds), Math. Assoc. America, 2002, p. 174 (but he used a different sign convention from the above).
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These reference tones are chosen such that all chord tones have integer relations to these reference tones. For each chord there exists a lower and an upper reference tone, with all chord tones being integer multiples of the frequency of the lower reference tone and integer fractions of the frequency of the upper reference tone. In quadruple notation there are only positive (or zero) values if the chord is related to the lower reference tone, and only negative (or zero) values if the chord is related to the higher reference tone. To get a single numerical value describing the complexity of a chord, Vogel builds a weighted sum of the quadruples describing the notes of the chord. He suggests the weights 1, 3, 5, and 7 for the prime numbers 2, 3, 5, and 7.
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This reconstruction of traditional conceptions, which distinguishes between (universal) syntactic functions on the one hand and their values for individual syntactic quadruples on the other, again allows to formulate general definitions for the names of syntactic functions in the Integrational Theory of Language and to identify their occurrences in the syntactic units of specific idiolect systems by statements in a grammar. Such identification, relative to the syntactic structure and lexical interpretation contained in a given syntactic quadruple, typically depends on the marking structure more than on other components of the syntactic structure, or the lexical interpretation. In particular, government categories, given through classifications in the Lexical Word Ordering and contained in the marking structure, are crucial to identifying the values of the complement functions relative to the syntactic quadruple. Type 1 categories, contained in the marking structure, may also play a role in the identification of syntactic function values.
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A Vietoris–Rips complex of a set of 23 points in the Euclidean plane. This complex has sets of up to four points: the points themselves (shown as red circles), pairs of points (black edges), triples of points (pale blue triangles), and quadruples of points (dark blue tetrahedrons). In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is an abstract simplicial complex that can be defined from any metric space M and distance δ by forming a simplex for every finite set of points that has diameter at most δ. That is, it is a family of finite subsets of M, in which we think of a subset of k points as forming a (k − 1)-dimensional simplex (an edge for two points, a triangle for three points, a tetrahedron for four points, etc.); if a finite set S has the property that the distance between every pair of points in S is at most δ, then we include S as a simplex in the complex.
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There is a natural correspondence between circles in the plane and points in three-dimensional projective space; a line in this space corresponds to a one-dimensional continuous family of circles, hence a pencil of points in this space is a pencil of circles in the plane. Specifically, the equation of a circle of radius centered at a point (), : (x-p)^2 + (y-q)^2 = r^2, may be rewritten as : \alpha(x^2 + y^2) - 2\beta x - 2\gamma y + \delta = 0, where . In this form, multiplying the quadruple () by a scalar produces a different quadruple that represents the same circle; thus, these quadruples may be considered to be homogeneous coordinates for the space of circles.. Straight lines may also be represented with an equation of this type in which and should be thought of as being a degenerate form of a circle. When , we may solve for , and ; the latter formula may give (in which case the circle degenerates to a point) or equal to an imaginary number (in which case the quadruple () is said to represent an imaginary circle).
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193 Scientist James Richards from the University of Delaware stated that successful jumps depend upon "how much angular momentum do you leave the ice with, how small can you make your moment of inertia in the air, and how much time you can spend in the air". He found that many skaters, although they were able to gain the necessary angular momentum for takeoff, had difficulty gaining enough rotational speed to complete the jump. For example, a skater could successfully complete a jump by making small changes to his or her arm position partway through the rotation, and a small bend in the hips and knees allows a skater "to land with a lower center of mass than they started with, perhaps eking out a few precious degrees of rotation and a better body position for landing". A skater tends to spend the same amount of time in the air regardless of whether he or she completes triple or quadruple jumps, but his or her angular momentum at the start of triples and quadruples is slightly higher than it is for double jumps.
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