For those of the Cardinal, Melanchthon, and Dürer's final major work, a drawn portrait of the Nuremberg patrician Ulrich Starck, Dürer depicted the sitters in profile, perhaps reflecting a more mathematical approach.

For the proof of the equivalence of the four approaches the reader is referred to mathematical expositions like or.

For the mathematical definition, see Decimal representation.

For this, and other, reasons mathematical historian Kurt Vogel writes: “ Diophantus was not, as he has often been called, the father of algebra.

For the mathematical constant, see e ( mathematical constant ).

For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories such as string theory posit a physical dimension.

For the mathematical congress, Peano did not speak, but Padoa's memorable presentation has been frequently recalled.

For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Chaldeans from Babylonia.

For the purpose of facilitating jointly sponsored activities and jointly pursuing the objectives of the IMU, multinational mathematical societies and professional societies can join IMU as an Affiliate Member.

For instance, the inverse of the sine function is typically called the arcsine function, written as arcsin, which is, like sin, conventionally denoted in roman type and not in italics ( note that software libraries of mathematical functions often use the name < tt > asin </ tt >):

In 1991 he was awarded the Balzan Prize for Genetics and Evolution " For his powerful analysis of evolutionary theory and of the role of sexual reproduction as a critical factor in evolution and in the survival of species ; for his mathematical models applying the theory of games to evolutionary problems " ( motivation of the Balzan General Prize Committee ).

For example, if A is some mathematical statement that an intuitionist has not yet proved or disproved, then that intuitionist will not assert the truth of " A or not A ".

For games that directly involve mathematics in their play, see mathematical puzzle.

For instance, in the original version, the RSA algorithm was used to encrypt session keys ; RSA's security depends upon the one-way function nature of mathematical integer factoring.

For example, Spearman is a non-parametric test as it is computed from the order of the data regardless of the actual values, whereas Pearson is a parametric test as it is computed directly from the data and can be used to derive a mathematical relationship.

For example, Mancala is a mathematical game, because mathematicians can study it using combinatorial game theory, even though no mathematics is necessary in order to play it.

For a brief period in fact, complete normed linear spaces where referred to as " Banach-Wiener " spaces in mathematical literature, based on terminology introduced by Wiener himself.

For a given physical process, the selection of suitable independent local non-equilibrium macroscopic state variables for the construction of a thermodynamic description calls for qualitative physical understanding, rather than being a simply mathematical problem concerned with a uniquely determined thermodynamic description.

For example, devices such as cameras and scanners produce essentially continuous-tone raster graphics that are impractical to convert into vectors, and so for this type of work, an image editor will operate on the pixels rather than on drawing objects defined by mathematical expressions.

For example, the first 15 digits of the mathematical constant pi ( 3. 14159265358979 ) can be encoded as " Now I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics ".

For sound waves, Lord Rayleigh published a full mathematical analysis of propagation modes in his seminal work, “ The Theory of Sound ”.

For this work he was presented in 1826 with the Gold Medal of the Royal Astronomical Society ( which he won again in 1836 ), and with the Lalande Medal of the French Academy of Sciences in 1825, while in 1821 the Royal Society bestowed upon him the Copley Medal for his mathematical contributions to their Transactions.

For a precise mathematical description refer to the original paper by Erné et al.

For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms ( usually called a small category ), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets.

For example, Pepcid Complete includes calcium carbonate in its formulation, allowing it a faster onset of action.

For incumbent management, the contrary views of some of their members were not matters to be weighed in the balance and taken account of in formulation of policy.

For example, a defender of evolution may well accept that the current formulation of evolutionary theory is likely to be revised in the future, but she defends evolution because she believes current evolutionary theory is more likely than any current rival idea, such as Creationism.

* For overviews, see Standard Model, its field theoretical formulation, strong interactions, quarks and gluons, hadrons, confinement, QCD matter, or quark-gluon plasma.

For at least the IV formulation, a loading dose of 20 mg / kg is required.

For a mathematical description, see the article Standard Model ( mathematical formulation ).

For the above formulation and its huge impact in practice, Cortes and Vapnik received the 2008 ACM Paris Kanellakis Award.

For Defense officials, it ensured a continuing military voice in formulation of related foreign and domestic policies during peacetime.

For example, consider the recursive formulation for generating the Fibonacci series: F < sub > i </ sub >

For the best recordings and playback, an S-VHS VCR requires S-VHS videotape, which has a different oxide media formulation for higher magnetic coercivity.

For this reason, one must either modify the formulation to ensure that it's a minimization problem ( for example, by extremizing the square of the gradient of the Lagrangian as below ), or else use an optimization technique that finds stationary points ( such as Newton's method without an extremum seeking line search ) and not necessarily extrema.

For both forms of prophylaxis, an aerosolized formulation of pentamidine given by nebulizer once monthly in a dose of 300 mg is used.

For example, mathematicians opted that rings need not be commutative, which differed from Emmy Noether's original formulation.

For technical reasons the Itō integral is the most useful for general classes of processes but the related Stratonovich integral is frequently useful in problem formulation ( particularly in engineering disciplines.

For a limited number of words in Russian, though, a partitive expression has its own separate formulation ; this group is generally regarded as a special type of the genitive ( also called the " second genitive ") case.

For instance, the idea that recessions reflect inadequate aggregate demand and that Say's Law ( in Keynes's formulation, that " supply creates its own demand ") does not hold in a monetary economy.

For example, it is consistent with global mental – physical supervenience on the simple formulation described above for two worlds to have the same number of people in the same physical states, but for the mental states to be distributed over those people in different ways ( e. g. I have my father's thoughts in the other world, and he has my thoughts ).

Egg cream purists and fans of the original early 20th-century formulation of U-Bet seek out the Kosher For Passover version of the syrup.

But attempting to directly eliminate " is true " from this sentence, on the standard first-order interpretation of quantification in terms of objects, would result in the ungrammatical formulation For all P, if John says P, then P. It is ungrammatical because P must, in that case, be replaced by the name of an object and not a proposition.

For poorly water soluble compounds, Élan's proprietary NanoCrystal technology can enable formulation and improve compound activity and final product characteristics.

For a flow in transition region, where both viscous and Knudsen friction are present a new formulation is used, which is known as binary friction model

For instance, in classical mechanics in the action formulation, extremal solutions to the variational principle are on shell and the Euler-Lagrange equations are on shell equations ( i. e., they do not hold off shell ).

For example, a vaginal formulation of miconazole antifungal cream might irritate the skin less than an athlete foot formulation of miconazole cream.