177 Sentences With "exact value" | Random Sentence Generator

The companies didn't provide an exact value for the merger.

The exact value of the fines was not unveiled in the statement.

The exact value of the assets will not be known until it is all sold.

Its exact value can never be calculated, and it doesn't seem to have a pattern.

The artifacts are gold-plated and adorned in precious stones and pearls though their exact value is unknown.

In an interview with the Times, the agency refused to identify the exact value of Epstein's tax breaks.

The exact value doesn't matter; so long as it is high enough nobody will be paying the tax.

For recovery purposes and due to pending litigation, we cannot provide an exact value of the missing materials.

While the exact value of Reebok today is unknown, 14 years ago, Adidas bought the shoemaker for $3.8 billion.

Some include behind-the-scenes or other special access so it's hard to attach an exact value to them.

But an exact value was impossible because they had been purchased years earlier, and there were no comparable sales.

Neither BuzzFeed nor the RNC would confirm the exact value of the deal, reported by Politico to be $1.3 million.

But the wave function does not give us the exact value for any of the particle's properties, such as its position.

Although neither TAG nor the league disclosed the exact value of the deal, it is estimated to be around $7.3 million.

While it's difficult to assign an exact value to Membership Rewards points,The Points Guysubjectively estimates each point as worth 2 cents.

The exact value of Prince's estate has not yet been disclosed, but his music catalog alone has been estimated at over $500 million.

Mahendran declined to give the exact value of securities handled by Entrust Securities but said the amount was manageable without disrupting the market.

The exact value of the book deal is unknown, but three officials close to the negotiations told AP that it "topped $2 million."

The exact value of Prince's estate has not yet been disclosed but his music catalog alone has been estimated at more than $500 million.

APG also declined to comment on the exact value of the transaction, but said it was one of their largest ever in renewable energy.

The downside to excluding them is that while one can debate the exact value of work-provided health insurance, the value clearly isn't zero.

While the exact value of Amazon's stake hasn't been disclosed, reports have said the company invested $500 million into Deliveroo as part of the deal.

Guedes did not go into details about the accord, and the source declined to comment on the exact value that Petrobras would receive from the government.

Shinil Group told CNN it believes the ship is worth 1 billion won ($884,000), but was unclear about the exact value of the gold on board.

While the exact value of the relic has not been specified, previous sales have seen items from the ancient kingdom valued at hundreds of thousands of dollars.

Little is known about the exact value of the government's real estate and property holdings, but these assets are also understood to be worth billions of dollars.

Relying on the perceived difficulty of determining the exact value of the foreign help Trump is seeking is no longer an option for those charged with enforcing the law.

An IBM spokesperson confirmed to CNBC that the multibillion-dollar deal will extend "over several years," but didn't specify the exact value of the agreement or the time frame.

It's not an exact value, but the mere presence of a solid inner core says something important—it helps scientists better understand how the planet generates its magnetic field.

Lockheed Martin and Raytheon each won 54-month technology maturation and risk reduction contracts in August, but the Air Force would not release the exact value of the deals.

This electrical signal is passed along to the mercury ions, trapped in electric fields, which in turn begin to vibrate, providing an exact value for the frequency of the transition.

The exact value of Conaway's investment isn't clear, given that congressional ethics forms only show a range of amounts, and Conaway's office did not respond to a request for comment.

The exact value of Comcast's new bid for the Fox assets is not yet clear, although the $60 billion in new financing indicates it is seeking significant firepower to outbid Disney.

Dividends for Hainan Cihang's shareholding in HNA Group is likely to provide additional funding, Roesler said, adding that an evaluation of the "exact value" of the 29.5 percent stake was now underway.

The exact value of Discovery's offer could not be learned, but sources said it is a cash-and-stock bid, comprising mostly cash, and valuing Scripps in the region of $90 per share.

By using the pen to measure and siphon the exact value of the three inks — and mixing it with makeup base powder (all sold by Mink) — you can create custom eye shadow, lip gloss, blush, and more.

The exact value of the bureau's real estate and other assets is not made public, but its Bangkok holdings alone were estimated at $137 billion in a 240 biography of his father "King Bhumibol, A Life's Work".

Frankly, that's not always the simplest task, given that most websites require you to create codes that contain special characters, uppercase letters, or something bizarre like the exact value of Pi. This is why tools like PasswordWrench exist.

Some have argued it's not possible to calculate the exact value of specific pieces of data in a high-volume marketplace across an industry that uses data across dozens of platforms, all delivering different services with different business models.

The exact value of the assets owned by the Guards is unknown, though this is often cited in the tens of billions of dollars, or 30 percent of the country's gross national product, according to a 2016 report by KPMG.

Though the exact value of China's spending on its space programs remains shrouded in secrecy, many analysts peg its civilian space budget at around $22015 billion annually in recent years, a fraction of the $2150 billion the United States allocated to NASA in 2016.

But for years after "Eat Pray Love" was published, critics gnashed their teeth over her privilege and silky prose, and questioned the depths of her suffering and the extent of her faith, all the while calculating the exact value of her very good fortune.

Digging deeper, China agreed to purchase a variety of goods from each major industry, including but not limited to the following: Finer detail, such as the exact value of specific farm purchases (such as soybeans or pork) promised by China over the next two years, could not be ascertained.

Five furlongs are about 1 kilometre ( is the exact value, according to the international conversion).

Schmuland's paper explains why this probability is so close to, but not exactly, . The exact value of this probability is given by the infinite cosine product integral divided by .

However, AT&T; foolishly deleted from Campbell's proposed patent application all the tables and graphs detailing the exact value of inductance that would be required before the patent was submitted.Brittain pp.

The bank also agrees to pay large shareholders the exact value of the note on a weekly basis through redemption, which helps the ETNs track very closely to the underlying index return.

OED There is currently a movement within the Islamic world to revive the Dirham as a unit of mass for measuring silver, although the exact value is disputed (either 3 or 2.975 grams).

An advantage of these methods is that in the favorable cases it can find the exact value of the joint spectral radius and provide a certificate that this is the exact value. The second family of methods approximate the extremal norm with modern optimization techniques, such as ellipsoid norm approximation,Vincent D. Blondel, Yurii Nesterov and Jacques Theys, On the accuracy of the ellipsoid norm approximation of the joint spectral radius, Linear Algebra and its Applications, 394:1, pp. 91–107, 2005.

Although the exact value of energy density of a superflywheel would depend on the material used, it could theoretically be as high as 1200 Wh (4.4 MJ) per kg of mass for graphene superflywheels.

In statistics, truncation results in values that are limited above or below, resulting in a truncated sample.Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms. OUP. A random variable y is said to be truncated from below if, for some threshold value c, the exact value of y is known for all cases y > c, but unknown for all cases y \leq c. Similarly, truncation from above means the exact value of y is known in cases where y < c, but unknown when y \geq c.

The exact value is unknown, the prominence given is a minimum, but it could be around 19 m greater. It was estimated from the separation of 20 metre contour lines from the 1:10,000 scale topographic map.

Second, the giving and exchanging of seeruarisai, which usually consists of gifts such as a scooter, dressing table, sofa set or utensils. Normally the bridegroom’s parents will give to the bride, more or less, the exact value of the seervarisai given by the bride’s household to the brid-groom. Third, the exact value of the dowry, which the bride’s parents must give to the groom or his parents is determined. The local Muslim term for dowry is the kaikooli or the hibbath, whereas the Hindus call it varadatchanai.

Mpxplay on DOS requires a ~100 MHz i486 (or faster) CPU for real-time playback (the exact value depends mostly on the format of the file being played), 4-8 MiB RAM, and MS-DOS 5.00+ or equivalent (FreeDOS, DR-DOS).

The run-time of the procedure is, technically, infinite, since Austin's procedure involves two knives moving continuously, and this procedure cannot be discretized. The number of cuts is bounded, though. Austin's procedure requires 2 cuts to divide a cake between 2 people with an exact value of 1/2; each of these pieces should be divided with 2 more cuts to generate the 4 pieces with exact value of 1/4. So in total, 6 cuts are needed for step A. A single cut is done in step B and 6 more cuts in step C, for a total of 13 cuts.

The NOP opcode can be used to form a NOP slide, which allows code to execute when the exact value of the instruction pointer is indeterminate (e.g., when a buffer overflow causes a function's return address on the stack to be overwritten).

Most important works of Bloch belong to complex analysis. His early contribution is known as Bloch's theorem. This theorem asserts the existence of certain absolute constant which is called the Bloch constant. The exact value of the Bloch constant is still unknown .

One way of doing this is to keep the n largest eigenvalues at each step, for some fixed n. In most cases, the sequence of approximations obtained by taking n = 1,2,3,... converges rapidly, and to the exact value (for an exactly solvable model).

In Bohm's original work he notes that the fraction 1/16 is not exact; in particular "the exact value of [the diffusion coefficient] is uncertain within a factor of 2 or 3." Lyman Spitzer considered this fraction as a factor related to plasma instability.

Near inferior conjunction the planet typically fades to about magnitude −3 although the exact value depends on the phase angle. The typical range in apparent brightness for Venus over the course of one apparition is less than a factor of 10 or merely 1% that of Mercury.

Campbell's delay in filing was due to the slow internal machinations of AT&T.;Brittain, p44 However, AT&T; foolishly deleted from Campbell's proposed patent application all the tables and graphs detailing the exact value of inductance that would be required before the patent was submitted.

To find the minimax value, MTD(f) calls AlphaBeta a number of times, converging towards it and eventually finding the exact value. A transposition table stores and retrieves the previously searched portions of the tree in memory to reduce the overhead of re-exploring parts of the search tree.

Said differently, a one-Megalithic-arcsecond- thick 'slice' of Earth (at the equator) weighs almost exactly , as though, according to the authors, the exact value of the pound had been adjusted so as to be a round subdivision of a one-arcsecond-thick slice of Earth in the Megalithic geometry.

This conjecture would determine the linear arboricity exactly for graphs of odd degree, as in that case both expressions are equal. For graphs of even degree it would imply that the linear arboricity must be one of only two possible values, but determining the exact value among these two choices is NP-complete.

By contrast, the fine structure constant can be measured via the anomalous magnetic dipole moment of electron with a precision of a few parts per 1010. Also, the meter and second are now defined in a way such that has an exact value by definition. Hence the precision of depends only on that of , and .

From there, the whistler waves are reflected back to the hemisphere from which they started. The energy is almost perfectly reflected from earth surface 4 or 5 times with increase dispersion and diminishing amplitude. Along such long paths the speed of propagation of energy is between c/10 to c/100 and the exact value depends upon frequency.

Many superconductors are non-stoichiometric. For example, yttrium barium copper oxide, arguably the most notable high-temperature superconductor, is a non- stoichiometric solid with the formula YxBa2Cu3O7−x. The critical temperature of the superconductor depends on the exact value of x. The stoichiometric species has x = 0, but this value can be as great as 1.

In contrast, the probability of a statement about the degree of confirmation could be unknown, in the sense that one may miss the correct logical method to evaluate its exact value. But, such a statement can always receive a certain logical value, given the fact that this value only depends on the meaning of its symbols.

Because of the International yard and pound agreement, one troy ounce (oz t) equals exactly grams. It also equals avoirdupois ounces, or exactly , about 10% larger. The international yard and pound agreement did not define any troy weights. Rather, it defined the avoirdupois pound in metric terms, from which we can derive an exact value for the troy ounce.

Thus, the reduction of the total tripping energy is lower, about 30%, although the exact value depends on the application and the operating mechanism. Depending on the specific case, either the double motion or the single motion technique can be cheaper. Other considerations, such as rationalization of the circuit breaker range, can also influence the cost.

The canada () was the unit of liquid volume of the ancient Portuguese measurement system. It was used in Portugal, Brazil and other parts of the Portuguese Empire until the adoption of the metric system. It was equivalent to 4 quartilhos (pints). The exact value of the canada varied from region to region, the canada of Lisbon being equivalent to 1.4 litres.

For u->∞, a tabulation exists for an exact value of Q (see link). A word of caution is needed here: notations for Q and R are not the same throughout literature, where Q is sometimes denoted as the shortest significant interval, and R as the significant quantile for studentized range distribution (Duncan's 1955 paper uses both notations in different parts).

NGC certification offers significant protection against counterfeiting, misattribution, overgrading, and damage, but does not necessarily determine exact value. Even within the same grade, coins can have widely differing values. The NGC grading scale is based on the 70-point Sheldon coin grading scale. Strike designations include Prooflike and Deep Prooflike for circulation issue coins and Cameo and Ultra Cameo for Proof coins.

The lower bound 1/72 in Bloch's theorem is not the best possible. The number B defined as the supremum of all b for which this theorem holds, is called the Bloch's constant. Bloch's theorem tells us B ≥ 1/72, but the exact value of B is still unknown. The similarly defined optimal constant L in Landau's theorem is called the Landau's constant.

Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find x such that : f(x)=b.\, Given an approximation x0 of x, the residual is : b - f(x_0)\, whereas the error is : x - x_0\, If the exact value of x is not known, the residual can be computed, whereas the error cannot.

He concluded by asking whether the exact value of the original constant was chosen through derivation or trial and error. Lomont said that the magic number for 64-bit IEEE754 size type double is 0x5FE6EC85E7DE30DA, but it was later shown by Matthew Robertson to be exactly 0x5FE6EB50C7B537A9. A complete mathematical analysis for determining the magic number is now available for single-precision floating-point numbers.

The hob (South Korea) or hop (North Korea) is a traditional Korean unit based on the ge which is equal to doe (SK) or toe (NK). Its exact value has varied over time with the size of the doe. During its occupation, Korea's native measures were standardized to their Japanese equivalents. The present-day hob is litres (6.1floz or 0.328dry pt), the same as the Japanese gō.

Since it depends on the density parameter \Omega, its value depends on the cosmological model used. In an Einstein–de Sitter model it equals 18\pi^2\approx 178. This definition is not universal, however, as the exact value of \Delta_c depends on the cosmology. In an Einstein–de Sitter model, it is assumed that the density parameter is due to matter only, where \Omega_m=1.

As an example, if the exact value is 50 and the approximation is 49.9, then the absolute error is 0.1 and the relative error is 0.1/50 = 0.002 = 0.2%. Another example would be if, in measuring a 6 mL beaker, the value read was 5 mL. The correct reading being 6 mL, this means the percent error in that particular situation is, rounded, 16.7%.

Since for all k, this shows that . Davenport showed that in 1939, by demonstrating that any sufficiently large number congruent to 1 through 14 mod 16 could be written as a sum of 14 fourth powers (Vaughan in 1985 and 1989 reduced the 14 successively to 13 and 12). The exact value of G(k) is unknown for any other k, but there exist bounds.

There is no known way of measuring directly, and CODATA does not report an estimate of its value. The above estimate is calculated from the CODATA values of and . While is known to one part in and has an exact value by definition, is only known to one part in (mainly because is known to only one part in ). Hence αG is known to only four significant digits.

Alignment uncertainty stems from two main sources: near-optimal alignments and evolutionary parameter uncertainty. Evolutionary parameters include branch lengths, substitution rates, insertion/deletion rates, and the phylogeny itself. If the exact value for these parameters is unknown, and the alignment estimate is sensitive to the parameter, then the alignment cannot be known with confidence. Even when evolutionary parameters are fully known, many different alignments may be optimal, or nearly optimal.

Censoring should not be confused with the related idea truncation. With censoring, observations result either in knowing the exact value that applies, or in knowing that the value lies within an interval. With truncation, observations never result in values outside a given range: values in the population outside the range are never seen or never recorded if they are seen. Note that in statistics, truncation is not the same as rounding.

In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealisation of real-life furniture-moving problems and asks for the rigid two-dimensional shape of largest area A that can be maneuvered through an L-shaped planar region with legs of unit width. The area A thus obtained is referred to as the sofa constant. The exact value of the sofa constant is an open problem.

In order to value assets belong to Indonesian Railways (not the government), internal revaluation of assets has been done by the Ministry of Transportation. Indonesian Railways own Rp.35 trillion ($4.1 billion) as land and Rp.22 trillion ($2.6 billion) as other assets (bridges, signals, etc.). The exact value was to be determined by the end of 2011 or 2012, based on an audit by the Ministry of Finance.

In metrology it is used to define the kilogram in SI units., p. 131 The Planck constant is defined to have the exact value At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but predictions of the frequency distribution of the radiation by then-existing theories diverged significantly at higher frequencies. In 1900, Max Planck empirically derived a formula for the observed spectrum.

This allowed the pumper to get to high values relatively fast and then still get to the exact value they wanted. While it was still being sold, the Cozmo was marketed heavily towards young people, and included many features that made it easy for teenagers and preteens to use. It came in a variety of neon colors, including ice blue and purple, and allowed users to "name" their pumps.

This stadium was used for Bratislava regional championship until the stadium for I. Čsl. ŠK Bratislava was built in the end of the 1920s. More than 100 years later Artmedia still used to play their home matches at the same place – named Štadión za Starým mostom. Today's estimated capacity is 10,000; it is however impossible to give the exact value, because older part of the stadium still remains for standing visitors.

The US purchase of silver in the International market increase the price of silver, causing an outflow of silver in China who based the economy on silver standard currency, which forces China to abandon the silver standard. Hong Kong abandoned the silver standard in September 1935. Hong Kong then adopted the gold exchange standard and the Hong Kong dollar took on the exact value of one shilling and three pence (1s 3d) sterling.

The Bolsterlanger Horn is a grass mountain in the Allgäu Alps in Bavaria. Because its 1,586-metre-high summit rises above Bolsterlang, it is the local mountain (Hausberg) of this village. The Bolsterlanger Horn is part of the Hörner group and its southernmost peak. The topographic prominence of the Bolsterlanger Horn is at least 46 metres,The exact value is unknown; the given value is a minimum (- it could be around 19 m more).

It is hard to place an exact value on the money stolen through insurance fraud. Insurance fraud is deliberately undetectable, unlike visible crimes such as robbery or murder. As such, the number of cases of insurance fraud that are detected is much lower than the number of acts that are actually committed. The best that can be done is to provide an estimate for the losses that insurers suffer due to insurance fraud.

Another problem is the Mulliken charges are explicitly sensitive to the basis set choice. In principle, a complete basis set for a molecule can be spanned by placing a large set of functions on a single atom. In the Mulliken scheme, all the electrons would then be assigned to this atom. The method thus has no complete basis set limit, as the exact value depends on the way the limit is approached.

The more massive supergiants lose mass much more rapidly and all red supergiants appear to reach a similar mass of the order of by the time their cores collapse. The exact value depends on the initial chemical makeup of the star and its rotation rate. Most red supergiants show some degree of visual variability, but only rarely with a well-defined period or amplitude. Therefore, they are usually classified as irregular or semiregular variables.

Graph of f(x) = e^x (blue) with its linear approximation P_1(x) = 1 + x (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0. The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because: #the measurement of the data is not precise due to the instruments. (e.g.

The IRF gives the probability that a person with a given ability level will answer correctly. Persons with lower ability have less of a chance, while persons with high ability are very likely to answer correctly; for example, students with higher math ability are more likely to get a math item correct. The exact value of the probability depends, in addition to ability, on a set of item parameters for the IRF.

If we know the exact value of the treatment effect, there is no need to do the experiment. To address this issue, we can consider conditional power in a Bayesian setting by considering the treatment effect parameter to be a random variable. Taking the expected value of the conditional power with respect to the posterior distribution of the parameter gives the predictive power. Predictive power can also be calculated in a frequentist setting.

Experimental determination of the gravitational potential at the geoid surface is a task in physical geodesy. In 2000, the IAU very slightly altered the definition of TT by adopting an exact value for the ratio between TT and TCG time, as Resolution B1.9 of the IAU XXIV General Assembly, 2000 (As measured on the geoid surface, the rate of TCG is very slightly faster than that of TT, see below, Relativistic relationships of TT).

The relationship of e and d means that d = (1 + k.\phi(n))/e, where the exact value of k is unknown but 0 < k < e. Using this fact and the approximation \phi'(n) , the attacker can enumerate a set of possible values for the top half of the binary representation of d for each possible value of k. These binary patterns can be tested for many orders of magnitude faster than performing a trail decryption.

The PV diagram is a particularly useful visualization of a quasi-static process, because the area under the curve of a process is the amount of work done by the system during that process. Thus work is considered to be a process variable, as its exact value depends on the particular path taken between the start and end points of the process. Similarly, heat may be transferred during a process, and it too is a process variable.

A Zen butsuden is 5 ken across The is a traditional Japanese unit of length, equal to six Japanese feet (shaku). The exact value has varied over time and location but has generally been a little shorter than .JAANUS It is now standardized as meter. Although mostly supplanted by the metric system, this unit is a common measurement in Japanese architecture, where it is used as a proportion for the intervals between the pillars of traditional-style buildings.

Instead of 100 points per image, the score was varied to reward higher specificity. "Man" might get 50 points whereas "Bill Gates" might get 140 points. On August 7, 2007 another change was made: instead of simply showing the point values of each match as the match occurs, the value of each match was shown next to the matching word at the end of the game. This made it much easier to see the exact value of specific versus general labeling.

In the aftermath of the fire, the market was closed for entry for days. The shop owners were allowed to set up temporary shops on the pavements adjoining the market. While the exact value of losses of the shop owners are not known, it is inferred that many of the small shop owners have lost their lifetime savings in the fire. Many of them were reported to be on the lookout for alternate employment and seeking relief from the state government.

It is advantageous not to discard the part of the histogram that exceeds the clip limit but to redistribute it equally among all histogram bins. 300 px The redistribution will push some bins over the clip limit again (region shaded green in the figure), resulting in an effective clip limit that is larger than the prescribed limit and the exact value of which depends on the image. If this is undesirable, the redistribution procedure can be repeated recursively until the excess is negligible.

This effect is exploited in models of large extra dimensions. The exact value of the grand unification energy (if grand unification is indeed realized in nature) depends on the precise physics present at shorter distance scales not yet explored by experiments. If one assumes the Desert and supersymmetry, it is at around 1016 GeV. The most powerful collider to date, the Large Hadron Collider (LHC), is designed to reach a center of mass energy of 1.4x104 GeV in proton-proton collisions.

This process was known as 'rocking the brushes'. Various developments took place to automate the process of adjusting the commutation and minimizing the sparking at the brushes. One of these was the development of 'high resistance brushes', or brushes made from a mixture of copper powder and carbon.Higher Electrical Engineering: Shepherd, Morton & Spence Although described as high resistance brushes, the resistance of such a brush was of the order of milliohms, the exact value dependent on the size and function of the machine.

Another man is asked to kill this little girl to save the life of a seriously ill child. Old Marcella, in exchange for healing her Alzheimer's husband, must perpetrate a massacre in a crowded place with an explosive device that she must assemble herself. Young Martina has to commit a burglary for an exact value of 100,000 euros and 5 cents if she wants to become more beautiful. Blind Fulvio wants to regain his sight and is assigned to rape a woman.

The data given for each planet is taken from the latest published paper on the planet to have that data. In many cases it is not possible to have an exact value, and an estimated range is instead provided. The lightest, coldest, and oldest planet directly imaged is Proxima Centauri c, which has a mass of 7 MEarth, an effective temperature of 39 K, and an age of about 4.8 Ga. This list includes the four members of the multi-planet system that orbit HR 8799.

The tonne of oil equivalent (toe) is a unit of energy defined as the amount of energy released by burning one tonne of crude oil. It is approximately 42 gigajoules or 11.630 megawatt-hours, although as different crude oils have different calorific values, the exact value is defined by convention; several slightly different definitions exist. The toe is sometimes used for large amounts of energy. Multiples of the toe are used, in particular the megatoe (Mtoe, one million toe) and the gigatoe (Gtoe, one billion toe).

See E19 -- De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt, from The Euler Archive, which includes a scanned copy of the original article. Euler further discovered some of the gamma function's important functional properties, including the reflection formula. James Stirling, a contemporary of Euler, also attempted to find a continuous expression for the factorial and came up with what is now known as Stirling's formula. Although Stirling's formula gives a good estimate of , also for non-integers, it does not provide the exact value.

As a rule of thumb, if the condition number \kappa(A) = 10^k, then you may lose up to k digits of accuracy on top of what would be lost to the numerical method due to loss of precision from arithmetic methods. However, the condition number does not give the exact value of the maximum inaccuracy that may occur in the algorithm. It generally just bounds it with an estimate (whose computed value depends on the choice of the norm to measure the inaccuracy).

In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value in the above equations. Although the estimates of the covariance may be considered optimal in some sense, this does not mean that the resulting discriminant obtained by substituting these values is optimal in any sense, even if the assumption of normally distributed classes is correct.

Each of the colonies had their own currencies. Although modelled on the British system of pounds- shillings-pence, the exact value of each currency could vary, depending on the legislation of each colony. There was the Canadian pound, used in Upper and Lower Canada, and then the Province of Canada; the New Brunswick pound; the Newfoundland pound; the Nova Scotian pound; and the Prince Edward Island pound. They were all gradually replaced with decimal systems of currency linked to the US and Spanish dollars.

The exact value of the stone cannot be determined until it is decided how it will be cut and more details about its colour are known. Former diamond-mining geologist Phil Swinfen estimates, based on other similar sales, that the stone could be sold for $40–60 million. The process of selling and cutting the diamond "will likely take years to complete". In May 2016, Sotheby's in London announced that the Lesedi La Rona diamond would be offered in a stand-alone auction on 29 June 2016.

The reaction catalyzed by carbonic anhydrase is: :HCO3− \+ H+ CO2 \+ H2O Carbonic acid has a pKa of around 6.36 (the exact value depends on the medium), so at pH 7 a small percentage of the bicarbonate is protonated. Carbonic anhydrase is one of the fastest enzymes, and its rate is typically limited by the diffusion rate of its substrates. Typical catalytic rates of the different forms of this enzyme ranging between 104 and 106 reactions per second. The uncatalyzed reverse reaction is relatively slow (kinetics in the 15-second range).

While the neutron lifetime has been studied for decades, there currently exists a lack of consilience on its exact value, due to different results from two experimental methods ("bottle" versus "beam"). While the error margin was once overlapping, increasing refinement in technique which should have resolved the issue has failed to demonstrate convergence to a single value. The difference in mean lifetime values obtained as of 2014 was approximately 9 seconds. Further, a prediction of the value based on quantum chromodynamics as of 2018 is still not sufficiently precise to support one over the other.

The exact value of the CCD depends on the solubility of calcium carbonate which is determined by temperature, pressure and the chemical composition of the water – in particular the amount of dissolved in the water. Calcium carbonate is more soluble at lower temperatures and at higher pressures. It is also more soluble if the concentration of dissolved is higher. Adding a reactant to the above chemical equation pushes the equilibrium towards the right producing more products: Ca2+ and HCO3−, and consuming more reactants and calcium carbonate according to Le Chatelier's principle.

This disparity is not a significant departure from accuracy, and USSA1976 uses this value of R∗ for all the calculations of the standard atmosphere. When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and an increase of 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in). Also note that this was well before the 2019 SI redefinition which gave the constant an exact value.

The map encompasses almost all of the Mediterranean inside two circles, one for the western Mediterranean, one for the eastern. These circles are divided into sixteen parts, providing the map with sixteen corresponding wind directions. Furthermore, it comprises a two- directional scale subdivided into several segments corresponding to 200, 50, 10, and 5 miles. The exact value of these "portolan miles" is difficult to calculate in present-day units, given discrepancies between geographical areas on this map and others; but it is conventionally accepted to be around 1.25 kilometers.

The minimum number of flips required to sort any stack of pancakes has been shown to lie between and (approximately 1.07n and 1.64n,) but the exact value is not known. The simplest pancake sorting algorithm performs at most flips. In this algorithm, a kind of selection sort, we bring the largest pancake not yet sorted to the top with one flip; take it down to its final position with one more flip; and repeat this process for the remaining pancakes. In 1979, Bill Gates and Christos Papadimitriou gave an upper bound of .

The US fluid gallon is about 14.1% smaller than the dry gallon, while the Imperial fluid gallon is about 3.2% larger. Its implicit value in the US system was originally one eighth of the Winchester bushel, which was a cylindrical measure of in diameter and in depth, which made the dry gallon an irrational number in cubic inches whose value to seven significant digits was , or exact cubic inches. Since the bushel was later defined to be exactly 2150.42 cubic inches, this figure became the exact value for the dry gallon ( gives exactly ).

ATR uses a property of total internal reflection resulting in an evanescent wave. A beam of infrared light is passed through the ATR crystal in such a way that it reflects at least once off the internal surface in contact with the sample. This reflection forms the evanescent wave which extends into the sample. The penetration depth into the sample is typically between 0.5 and 2 micrometres, with the exact value determined by the wavelength of light, the angle of incidence and the indices of refraction for the ATR crystal and the medium being probed.

The relative heights of the peaks in the total histogram are representative of the populations of various types of E/2 having differing factors. The heights are approximately inversely proportional to \Pi\,p, the products of the lowest factors. Thus the height of the peak marked (3,5) in the overall histogram is about 1/15 of the main peak. Heights may vary from this by about 20%; their exact value is a complex function of the way in which the peaks are constituted from their components and of their varying width.

The usual rule for performing floating-point arithmetic is that the exact mathematical value is calculated,Computer hardware doesn't necessarily compute the exact value; it simply has to produce the equivalent rounded result as though it had computed the infinitely precise result. and the result is then rounded to the nearest representable value in the specified precision. This is in fact the behavior mandated for IEEE-compliant computer hardware, under normal rounding behavior and in the absence of exceptional conditions. For ease of presentation and understanding, 7-digit precision will be used in the examples.

It is not known precisely how the exact value for the magic number was determined. Chris Lomont developed a function to minimize approximation error by choosing the magic number over a range. He first computed the optimal constant for the linear approximation step as 0x5F37642F, close to 0x5F3759DF, but this new constant gave slightly less accuracy after one iteration of Newton's method. Lomont then searched for a constant optimal even after one and two Newton iterations and found 0x5F375A86, which is more accurate than the original at every iteration stage.

The results of either test can be converted into the more traditional "dependence vector" form, but since this abstraction provides less precision, much of the information about the dependence will be lost. Both techniques produce exact information for programs with affine control and subscript expressions, and must approximate for many programs outside this domain (i.e., in the presence of non-affine subscripts such as index arrays). The original work of Feautrier focused on describing true dependences, which would be referred to as exact value-based flow dependences by the Omega Project.

In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function. The most common type of asymptotic expansion is a power series in either positive or negative powers.

The Timor Gap refers to the 60,000 square kilometre “coffin-shaped” area between Australia and East Timor. The area contains several oil and gas reserves. The exact value of the resources contained in the Timor Gap is unknown, but three of the largest reserves, Elang-Kakatua, Bayu-Undan and Sunrise-Troubadour are estimated to hold US$17 billion worth of oil. The Timor Gap does not refer to any geographical landmark but is instead the area of continental shelf that was subject to negotiations between Indonesia, Australia and Portugal in the early 1970s.

According to one paradigm, the leading edge of a gravity current 'controls' the flow behind it: it provides a boundary condition for the flow. In this phase the propagation rate of the current is approximately constant with time. For many flows of interest, the leading edge moves at a Froude number of about 1; estimates of the exact value vary between about 0.7 and 1.4. As the driving fluid depletes as a result of the current spreading into the environment, the driving head decreases until the flow becomes laminar.

In a break from tradition, Washington College announced the winner at the Poets House in New York City where Sophie Kerr lived for more than 40 years. The first Sophie Kerr Prize, valued at $9,000, was awarded to a Washington College senior in 1968. The exact value varies according to the return on the endowment. Since its inception, the Sophie Kerr Endowment has provided more than $1.4 million in prize money to promising young writers and has brought literary stars such as Toni Morrison, Katherine Ann Porter, Edward Albee, Natasha Trethewey, and Colum McCann to the Washington College campus.

The economist Joseph Schumpeter disagreed with the Marxist explanation of the origin of capital, because Schumpeter did not believe in exploitation. In liberal economic theory, the market returns to each person the exact value she added into it; capitalists are just people who are very adept at saving and whose contributions are especially magnificent, and they do not take anything away from other people or the environment. Liberals believe that capitalism has no internal flaws or contradictions; only outside threats. To liberals, the idea of the necessity of violent primitive accumulation to capital is particularly incendiary.

In the centimetre–gram–second system of units (CGS), it is .This is derived from the National Institute of Standards and Technology value and uncertainty, using the fact that one coulomb is exactly statcoulombs. The conversion factor is ten times the numerical speed of light in metres per second. Making the value of the elementary charge exact implies that the value of ε0 (electric constant), which was an exact value before, is now subject to experimental determination: ε0 had an exactly defined value until the 2019 SI redefinition, after which it has become a subject of experimental refinement over time.

Plastic limit theorems in continuum mechanics provide two bounds that can be used to determine whether material failure is possible by means of plastic deformation for a given external loading scenario. According to the theorems, to find the range within which the true solution must lie, it is necessary to find both a stress field that balances the external forces and a velocity field or flow pattern that corresponds to those stresses. If the upper and lower bounds provided by the velocity field and stress field coincide, the exact value of the collapse load is determined.

In the everyday world, it is natural and intuitive to think of every object being in its own eigenstate. This is another way of saying that every object appears to have a definite position, a definite momentum, a definite measured value, and a definite time of occurrence. However, the uncertainty principle says that it is impossible to measure the exact value for the momentum of a particle like an electron, given that its position has been determined at a given instant. Likewise, it is impossible to determine the exact location of that particle once its momentum has been measured at a particular instant.

When a physical process is parameterized, two choices have to be made: what is the structural form (for instance, two variables can be related linearly) and what is the exact value of the parameters (for instance, the constant of proportionality). The process of determining the exact values of the parameters in a parameterization is called calibration, or sometimes less precise, tuning. Calibration is a difficult process, and different strategies are used to do it. One popular method is to run a model, or a submodel, and compare it to a small set of selected metrics, such as temperature.

It is possible to use rounded arithmetic to evaluate the exact value of a function with integer domain and range. For example, if we know that an integer is a perfect square, we can compute its square root by converting to a floating-point value , computing the approximate square root of with floating point, and then rounding to the nearest integer . If is not too big, the floating-point round-off error in will be less than 0.5, so the rounded value will be the exact square root of . This is essentially why slide rules could be used for exact arithmetic.

On 20 May 2019, the kelvin was redefined so that its value is now determined by the definition of the Boltzmann constant rather than being defined by the triple point of VSMOW. This means that the triple point is now a measured value, not a defined value. The newly-defined exact value of the Boltzmann constant was selected so that the measured value of the VSMOW triple point is exactly the same as the older defined value to within the limits of accuracy of contemporary metrology. The degree Celsius remains exactly equal to the kelvin, and 0 K remains exactly −273.15 °C.

Babylonian mathematics usually approximated to 3, sufficient for the architectural projects of the time (notably also reflected in the description of Solomon's Temple in the Hebrew Bible).See #Imputed biblical value. "There has been concern over the apparent biblical statement of ≈ 3 from the early times of rabbinical Judaism, addressed by Rabbi Nehemiah in the 2nd century." The Babylonians were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near Susa in 1936 (dated to between the 19th and 17th centuries BCE) gives a better approximation of as = 3.125, about 0.528 percent below the exact value.

Experiments and computer simulations have shown that the most compact way to pack hard perfect spheres randomly gives a maximum volume fraction of about 64%, i.e., approximately 64% of the volume of a container is occupied by the spheres. It seems as if because it is not possible to precisely define 'random' in this sense it is not possible to give an exact value. The random close packing value is significantly below the maximum possible close-packing of (equal sized) hard spheres into a regular crystalline arrangements, which is 74.04% Modes of wall induced granular crystallisation in vibrational packing.

Inexpensive analog multimeter with a galvanometer needle display A multimeter may be implemented with a galvanometer meter movement, or less often with a bargraph or simulated pointer such as an liquid-crystal display (LCD) or vacuum fluorescent display. Analog multimeters were common; a quality analog instrument would cost about the same as a DMM. Analog multimeters had the precision and reading accuracy limitations described above, and so were not built to provide the same accuracy as digital instruments. Analog meters were intuitive where the trend of a measurement was more important than an exact value obtained at a particular moment.

In an attempt to demonstrate that the thickness of the p/q-limb is zero, David Boll carried out a computer experiment in 1991, where he computed the number of iterations required for the series to diverge for z = − + iε (− being the location thereof). As the series doesn't diverge for the exact value of z = −, the number of iterations required increases with a small ε. It turns out that multiplying the value of ε with the number of iterations required yields an approximation of π that becomes better for smaller ε. For example, for ε = 0.0000001 the number of iterations is 31415928 and the product is 3.1415928.

Measurements most commonly use the International System of Units (SI) as a comparison framework. The system defines seven fundamental units: kilogram, metre, candela, second, ampere, kelvin, and mole. Six of these units are defined without reference to a particular physical object which serves as a standard (artifact-free), while the kilogram is still embodied in an artifact which rests at the headquarters of the International Bureau of Weights and Measures in Sèvres near Paris. Artifact-free definitions fix measurements at an exact value related to a physical constant or other invariable phenomena in nature, in contrast to standard artifacts which are subject to deterioration or destruction.

It is then normalized by the duration of the finite-time sample and also by a numerical constant in the order of 1 to get its exact value. This procedure gives correct spectral data only deeply within the frequency window determined by the reciprocal of the duration of the finite-time sample (low-frequency end) and the digital sampling rate of the noise (high-frequency end). Thus the upper and the lower half decades of the obtained power density spectrum are usually discarded from the spectrum. Conventional spectrum analyzers that sweep a narrow filtered band over the signal have good signal-to-noise ratio (SNR), since they are narrow-band instruments.

The exact value of the adhesion force of a spatula varies with the surface energy of the substrate to which it adheres. Recent studies have moreover shown that the component of the surface energy derived from long-range forces, such as van der Waals forces, depends on the material's structure below the outermost atomic layers (up to 100 nm beneath the surface); taking that into account, the adhesive strength can be inferred. Apart from the setae, phospholipids—fatty substances produced naturally in their bodies—also come into play. These lipids lubricate the setae and allow the gecko to detach its foot before the next step.

Whenever a ray of light moves from one medium to another (for example, when light enters a sheet of glass after travelling through air), some portion of the light is reflected from the surface (known as the interface) between the two media. This can be observed when looking through a window, for instance, where a (weak) reflection from the front and back surfaces of the window glass can be seen. The strength of the reflection depends on the ratio of the refractive indices of the two media, as well as the angle of the surface to the beam of light. The exact value can be calculated using the Fresnel equations.

Therefore, computing the resultant makes sense only for polynomials whose coefficients belong to a field or are polynomials in few indeterminates over a field. In the case of input polynomials with coefficients in a field, the exact value of the resultant is rarely important, only its equality (or not) to zero matters. As the resultant is zero if and only if the rank of the Macaulay matrix is lower than its number of its rows, this equality to zero may by tested by applying Gaussian elimination to the Macaulay matrix. This provides a computational complexity d^{O(n)}, where is the maximum degree of input polynomials.

Past debates on the exact value of the exponent are settled in part because the observed variability in the metabolic scaling exponent is consistent with a 'relaxed' version of metabolic scaling theory where additional selective pressures lead to a constrained set of variation around the predicted optimal exponent . Much of past debate have focused on two particular types of mechanisms. One of these assumes energy or resource transport across the external surface area of three-dimensional organisms is the key factor driving the relationship between metabolic rate and body size. The surface area in question may be skin, lungs, intestines, or, in the case of unicellular organisms, cell membranes.

Its exact value will depend on the eventual value of Kluge's estate at the time of his death; however, the generous donation has helped change financial aid policy at Columbia. Annual gifts, fund-raising, and an increase in spending from the university's endowment have allowed Columbia to extend generous financial aid packages to qualifying students. , undergraduates from families with incomes as high as $60,000 a year will have the projected cost of attending the university, including room, board, and academic fees, fully paid for by the university. That same year, the university ended loans for incoming and then-current students who were on financial aid, replacing loans that were traditionally part of aid packages with grants from the university.

MichaeliMichaeli, D.: WO00068647 (2000). proposed that ICP should be inferred from the magnitude and shape of pulsations of the third ventricle synchronous with the cardiac cycle or respiration, where the pulsations are measured along the propagation axis of an ultrasound wave. The method so far has not been independently validated, and the author provides no exact data from which one could estimate the accuracy of the method. However, the discussion in the body of the patent document suggests that the method is able to distinguish among three ranges of ICP (<20, 20–40 and >40mmHg) but cannot provide an exact value of ICP within the range because of the impossibility of the calibration to the individual patient.

An interesting element of Calcutta auctions is in determining an appropriate wager for each contestant, as the payoff will directly hinge on the size of the pot and thereby the size of the bids being placed. Thus the value of each team fluctuates during the course of the betting. For example, even if a bidder knew the University of North Carolina would be the tournament winner and thus pay out 32% of the pool, he would still be unsure of the exact value of the team (unless it was the last team being bid on) since the payout depends on the sum total of all winning bids, i.e. the final size of the pool.

To determine the direction to the spin active nucleus from the localized unpaired electron (remember: unpaired electrons are, themselves, spin active) one employs the principle of magnetic angle selection. The exact value of θ is calculated as follows to the right: Hyperfine tensor of dipolar couplingAt θ = 0˚ the ENDOR spectra contain only the component of hyperfine coupling that is parallel to the axial protons and perpendicular to the equatorial protons. At θ = 90˚ ENDOR spectra contain only the component of hyperfine coupling that is perpendicular to the axial protons and parallel to the equatorial protons. The electron nuclear distance (R), in meters, along the direction of the interaction is determined by point-dipole approximation.

In statistics and econometrics, set identification (or partial identification) extends the concept of identifiability (or "point identification") in statistical models to situations where the distribution of observable variables is not informative of the exact value of a parameter, but instead constrains the parameter to lie in a strict subset of the parameter space. Statistical models that are set identified arise in a variety of settings in economics, including game theory and the Rubin causal model. Though the use of set identification dates to a 1934 article by Ragnar Frisch, the methods were significantly developed and promoted by Charles Manski starting in the 1990s. Manski developed a method of worst-case bounds for accounting for selection bias.

Gregory stated that without a relationship of debt, there is no reciprocity, and that this is what distinguishes a gift economy from a "true gift" given with no expectation of return (something Sahlins calls "generalized reciprocity": see below). Marshall Sahlins, an American cultural anthropologist, identified three main types of reciprocity in his book Stone Age Economics (1972). Gift or generalized reciprocity is the exchange of goods and services without keeping track of their exact value, but often with the expectation that their value will balance out over time. Balanced or Symmetrical reciprocity occurs when someone gives to someone else, expecting a fair and tangible return at a specified amount, time, and place.

At very high temperatures, as in the environment of a black hole or neutron star, high energy photon interactions with nuclei or even with other photons, can create an electron-positron plasma. In that situation the combined mass of the positive-negative charge carrier pair is approximately 918 times smaller (the proton to electron mass ratio), while the radiation pressure on the positrons doubles the effective upward force per unit mass, so the limiting luminosity needed is reduced by a factor of ≈918×2. The exact value of the Eddington luminosity depends on the chemical composition of the gas layer and the spectral energy distribution of the emission. A gas with cosmological abundances of hydrogen and helium is much more transparent than gas with solar abundance ratios.

In addition, there are also plans to integrate the nuclear-capable Nirbhay missile with the aircraft as well. As part of a different effort for modernisation, the 'Super Sukhoi' programs aims to modernise the entire Indian air force Su-30MKI fleet with new active electronically scanned array (AESA) Zhuk radars, onboard computers, and advanced electronic warfare systems. The exact value of the contract has yet to be disclosed however. An initial 42 fighters will be upgraded before the rest of the Indian Air Force Su-30MKI fleet. In March 2010, India and France finalised the long delayed deal to upgrade all of India's Mirage 2000H to Mirage 2000-5 Mk 2 variant with new radar systems, a new weapon suite, missiles, electronic warfare system etc.

In 1905, Richards A. H. proved the existence of bromous acid through a series of experiments involving silver nitrate (AgNO3) and bromine. The reaction of excess cold aqueous to form hypobromous acid (HBrO), silver bromide (AgBr) and nitric acid (HNO3): :Br2 \+ AgNO3 \+ H2O → HBrO + AgBr + HNO3 Richards discovered that the effect of adding excess liquid bromine in a concentrated silver nitrate (AgNO3) resulted in a different reaction mechanism. From numbers of equivalent portions of acid bromine formed from the previous reaction, the ratio between oxygen and bromine was calculated, with the exact value of O:Br (0.149975:0.3745), suggesting the acid compound contains two oxygen atom to one bromine atom. Thus, the chemical structure of the acid compound was deducted as HBrO2.

Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the ¾ power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M the animal's mass, then Kleiber's law states that q0 ~ M¾. Thus, over the same timespan, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses. The exact value of the exponent in Kleiber's law is unclear, in part because there is currently no completely satisfactory theoretical explanation for the law. Kleiber's plot comparing body size to metabolic rate for a variety of species.

Naturally occurring beryllium, save for slight contamination by the cosmogenic radioisotopes, is isotopically pure beryllium-9, which has a nuclear spin of . Beryllium has a large scattering cross section for high- energy neutrons, about 6 barns for energies above approximately 10 keV. Therefore, it works as a neutron reflector and neutron moderator, effectively slowing the neutrons to the thermal energy range of below 0.03 eV, where the total cross section is at least an order of magnitude lower – exact value strongly depends on the purity and size of the crystallites in the material. The single primordial beryllium isotope 9Be also undergoes a (n,2n) neutron reaction with neutron energies over about 1.9 MeV, to produce 8Be, which almost immediately breaks into two alpha particles.

NICMOS data show that the telescope background exceeds the > zodiacal background at wavelengths longer than λ ≈ 1.6μm, the exact value > depending on the pointing on the sky and on the position of the Earth on its > orbit. Despite this, the combination of Hubble's mirror and NICMOS offered never- before seen levels of quality in near-infrared performance at that time. Dedicated infrared telescopes like the Infrared Space Observatory were ground- breaking in their own way, but had a smaller primary mirror, and were also out of service at the time of NICMOS installation because they ran out of coolant. NICMOS later overcame this problem by using a machine chiller like a refrigerator, which allowed it operate for years until it went offline in 2008.

Diving with and handling nitrox raise a number of potentially fatal dangers due to the high partial pressure of oxygen (ppO2). Nitrox is not a deep-diving gas mixture owing to the increased proportion of oxygen, which becomes toxic when breathed at high pressure. For example, the maximum operating depth of nitrox with 36% oxygen, a popular recreational diving mix, is to ensure a maximum ppO2 of no more than . The exact value of the maximum allowed ppO2 and maximum operating depth varies depending on factors such as the training agency, the type of dive, the breathing equipment and the level of surface support, with professional divers sometimes being allowed to breathe higher ppO2 than those recommended to recreational divers.

In 2005 the CIPM embarked on a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous methodology. In particular, the committee proposed redefining the kelvin such that Boltzmann constant takes the exact value . The committee had hoped that the programme would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger programme. The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition, but was finally adopted at the 26th CGPM in late 2018, with a value of = .

However, the exact value of these new units (zhang, chi and cun) was never stipulated, but can be deduced by the context in which they are used. For example, the spectacular passing of Halley's comet in 837 indicates that the tail of the comet measured 8 zhang. Even if it is not possible to know the angular size of the comet at the time it passed, it is certain that 8 zhang correspond to 180 degrees at the most (maximum visible angle on the celestial sphere), which means that one zhang can hardly exceed 20 degrees, and therefore one cun cannot exceed 0.2 degrees. A more rigorous estimation was made from 1972 on the basis of references of minimal separations expressed in chi or cun between two stars in the case of various conjunctions.

These definitions meant that the value of the Avogadro number depended on the experimentally determined value of the mass (in grams) of one atom of those elements, and therefore it was known only to a limited number of decimal digits. However, in its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro number as the exact value , and redefined the mole as the amount of a substance under consideration that contains N constituent particles of the substance. Under the new definition, the mass of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is N times the average mass of one of its constituent particles—a physical quantity whose precise value has to be determined experimentally for each substance.

Since then, only five more of these values have been found.. In the same 1955 paper, Greenwood and Gleason also computed the multicolor Ramsey number R(3,3,3): the smallest number r such that, if a complete graph on r vertices has its edges colored with three colors, then it necessarily contains a monochromatic triangle. As they showed, R(3,3,3) = 17; this remains the only nontrivial multicolor Ramsey number whose exact value is known. As part of their proof, they used an algebraic construction to show that a 16-vertex complete graph can be decomposed into three disjoint copies of a triangle-free 5-regular graph with 16 vertices and 40 edges. . (sometimes called the Greenwood–Gleason graph).. Ronald Graham writes that the paper by Greenwood and Gleason "is now recognized as a classic in the development of Ramsey theory".

The "conventional" volt, V90, defined in 1987 by the 18th General Conference on Weights and Measures and in use from 1990, is implemented using the Josephson effect for exact frequency-to-voltage conversion, combined with the caesium frequency standard. For the Josephson constant, KJ = 2e/h (where e is the elementary charge and h is the Planck constant), a "conventional" value KJ-90 = 0.4835979 GHz/μV was used for the purpose of defining the volt. As a consequence of the 2019 redefinition of SI base units, the Josephson constant was redefined in 2019 to have an exact value of = , which replaced the conventional value . This standard is typically realized using a series-connected array of several thousand or tens of thousands of junctions, excited by microwave signals between 10 and 80 GHz (depending on the array design).

In 1834, he was elected a foreign member of the Royal Swedish Academy of Sciences. At this period he also rapidly obtained a large and lucrative practice and from time to time wrote on surgical questions, contributing numerous papers to the Medical and Chirurgical Society and to the medical journals. His most important work is widely acknowledged to be the 1818 treatise Pathological and Surgical Observations on the Diseases of the Joints, in which he attempts to trace the beginnings of disease in the different tissues that form a joint and to give an exact value to the symptom of pain as evidence of organic disease. This volume led to the adoption by surgeons of more conservative measures in the treatment of diseases of the joints, with consequent reduction in the number of amputations and the saving of many limbs and lives.

In the book Civilization One, Butler and Knight contend that the basic units of volume and mass of the imperial system, the Imperial pint and the avoirdupois pound, are also derived from their Megalithic Yard. Just like the litre is the tenth part of the metre to the cubic power, the tenth part of the Megalithic Yard to the cubic power produces a volume of (82.96 cm∕10)3 = 570.96 mL, a very close approximation of the modern pint of 568.26 mL. Similarly, they argue that this theoretical Megalithic pint, if filled with barley dry seeds, weighs on average a number close to 453.59 grams, which is the exact value of the avoirdupois pound. They also argue that division of the Earth mass into 366 equal parts, then again into 60 equal parts, and then again into 6 equal parts, yields a result that is almost exactly : ∕(366 × 60 × 6) = = .

In September 2010, a preliminary report of the WTO found unfair Boeing payments broke WTO rules and should be withdrawn. In two separate findings issued in May 2011, the WTO found, firstly, that the US defence budget and NASA research grants could not be used as vehicles to subsidise the civilian aerospace industry and that Boeing must repay $5.3 billion of illegal subsidies. Secondly, the WTO Appellate Body partly overturned an earlier ruling that European Government launch aid constituted unfair subsidy, agreeing with the point of principle that the support was not aimed at boosting exports and some forms of public- private partnership could continue. Part of the $18bn in low interest loans received would have to be repaid eventually; however, there was no immediate need for it to be repaid and the exact value to be repaid would be set at a future date.

Also time will have passed, and the losing party may be bankrupt or have used the time to hide assets or otherwise frustrate efforts to collect on the judgment if they lose their appeal. Therefore, it is often either a requirement of the law, or an order of the court, that prior to commencing its appeal processes, the losing party must provide a surety bond – money it pays to the court or a third party, to demonstrate its good faith and commitment to paying judgment if it loses, and in some cases to show that their appeal is not frivolous or merely a tactic to delay or avoid payment. This is known as a supersedeas (or "appeal") bond, and shows that they can and will cover the damages or fees awarded – including any additional costs of the appeal. The bond may not be – and often is not – the exact value of the ruling.

Given a database in which each entry has multiple attributes (viewed as a 0–1 matrix with a row per database entry and a column per attribute) they use MinHash-based approximations to the Jaccard index to identify candidate pairs of attributes that frequently co-occur, and then compute the exact value of the index for only those pairs to determine the ones whose frequencies of co-occurrence are below a given strict threshold.. The MinHash algorithm has been adapted for bioinformatics, where the problem of comparing genome sequences has a similar theoretical underpinning to that of comparing documents on the web. MinHash-based tools allow rapid comparison of whole genome sequencing data with reference genomes (around 3 minutes to compare one genome with the 90000 reference genomes in RefSeq), and are suitable for speciation and maybe a limited degree of microbial sub-typing. There are also applications for metagenomics and the use of MinHash derived algorithms for genome alignment and genome assembly.

Writers need not explain the exact value of their fictional currencies or provide an exchange rate to modern money; they may rely on the intuitive grasp of their readers, for instance that one currency unit is probably of little value, but that millions of units will be worth a lot. Currencies in science fiction face particular problems due to futuristic technology allowing matter replication and hence forgery. Authors have proposed currencies that are incapable of replication such as the non-replicable "latinum" used by the Ferengi in the Star Trek universe, or the currency in Pandora's Millions by George O. Smith, which is booby-trapped to explode if scanned by a replicating machine. Money in fantasy fiction faces analogous challenges from the use of magic; in the Harry Potter series by J. K. Rowling, magically-created currency is time-limited, while in Ursula K. Le Guin's fictional realm of Earthsea, the world's equilibrium is unbalanced when something is created from nothing.

In mathematics, specifically in computational geometry, geometric nonrobustness is a problem wherein branching decisions in computational geometry algorithms are based on approximate numerical computations, leading to various forms of unreliability including ill-formed output and software failure through crashing or infinite loops. For instance, algorithms for problems like the construction of a convex hull rely on testing whether certain "numerical predicates" have values that are positive, negative, or zero. If an inexact floating-point computation causes a value that is near zero to have a different sign than its exact value, the resulting inconsistencies can propagate through the algorithm causing it to produce output that is far from the correct output, or even to crash. One method for avoiding this problem involves using integers rather than floating point numbers for all coordinates and other quantities represented by the algorithm, and determining the precision required for all calculations to avoid integer overflow conditions.

Some problems which do not have a PTAS may admit a randomized algorithm with similar properties, a polynomial-time randomized approximation scheme or PRAS. A PRAS is an algorithm which takes an instance of an optimization or counting problem and a parameter ε > 0 and, in polynomial time, produces a solution that has a high probability of being within a factor ε of optimal. Conventionally, "high probability" means probability greater than 3/4, though as with most probabilistic complexity classes the definition is robust to variations in this exact value (the bare minimum requirement is generally greater than 1/2). Like a PTAS, a PRAS must have running time polynomial in n, but not necessarily in ε; with further restrictions on the running time in ε, one can define an efficient polynomial-time randomized approximation scheme or EPRAS similar to the EPTAS, and a fully polynomial-time randomized approximation scheme or FPRAS similar to the FPTAS.

In macroeconomics, multiplier uncertainty is lack of perfect knowledge of the multiplier effect of a particular policy action, such as a monetary or fiscal policy change, upon the intended target of the policy. For example, a fiscal policy maker may have a prediction as to the value of the fiscal multiplier—the ratio of the effect of a government spending change on GDP to the size of the government spending change—but is not likely to know the exact value of this ratio. Similar uncertainty may surround the magnitude of effect of a change in the monetary base or its growth rate upon some target variable, which could be the money supply, the exchange rate, the inflation rate, or GDP. There are several policy implications of multiplier uncertainty: (1) If the multiplier uncertainty is uncorrelated with additive uncertainty, its presence causes greater cautiousness to be optimal (the policy tools should be used to a lesser extent).

The exact value of the magnetic declination is place-dependent and varies over time, though declination is frequently given on the map itself or obtainable on-line from various sites. If the hiker has been following the correct path, the compass' corrected (true) indicated bearing should closely correspond to the true bearing previously obtained from the map. A compass should be laid down on a level surface so that the needle only rests or hangs on the bearing fused to the compass casing – if used at a tilt, the needle might touch the casing on the compass and not move freely, hence not pointing to the magnetic north accurately, giving a faulty reading. To see if the needle is well leveled, look closely at the needle, and tilt it slightly to see if the needle is swaying side to side freely and the needle is not contacting the casing of the compass.

In the International System of Quantities (ISQ), the speed of light in vacuum, , is related to the magnetic constant and the electric constant (vacuum permittivity), , by the equation: .}} This relation can be derived using Maxwell's equations of classical electromagnetism in the medium of classical vacuum, but this relation is used by BIPM (International Bureau of Weights and Measures) and NIST (National Institute of Standards and Technology) as a definition of ε0 in terms of the defined numerical values for and , and is not presented as a derived result contingent upon the validity of Maxwell's equations.The exact numerical value is found at: This formula determining the exact value of is found in Table 1, p. 637 of Conversely, as the permittivity is related to the fine structure constant (\alpha), the permeability can be derived from the latter (using the Planck constant, h, and the elementary charge, e): In the new SI units, only the fine structure constant is a measured value in SI units in the expression on the right, since the remaining constants have defined values in SI units.

In the international yard and pound agreement of 1959, the United States and five countries of the Commonwealth of Nations defined the international yard to be exactly 0.9144 metre. The US authorities decided that, while the refined definition would apply nationally in all other respects, the US survey foot (and thus the survey acre) would continue 'until such a time as it becomes desirable and expedient to readjust [it]'. By inference, an "international acre" may be calculated as exactly square metres but it does not have a basis in any international agreement. Both the international acre and the US survey acre contain of a square mile or 4,840 square yards, but alternative definitions of a yard are used (see survey foot and survey yard), so the exact size of an acre depends upon which yard it is based. The US survey acre is about 4,046.872 square metres; its exact value ( m2) is based on an inch defined by 1 metre = 39.37 inches exactly, as established by the Mendenhall Order of 1922.