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 formulation of the model, is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated.

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 details see inset, fig. 5.

For a few details of the system the lines are 1-1/4'' '' X-Tru-Coat, a product of Republic Steel Corp., and all lines are welded.

For more details of this early work, see Alpha particle # History of discovery and use.

For many years, the events described in " The Curse of Akkad " were thought, like the details of Sargon's birth, to be purely fictional.

For example a target acquisition element can send a message with target details which is automatically routed through the tactical and technical fire control elements to deliver firing data to the gun's laying system and the gun automatically laid.

For details of monumental evidence the articles on Crete, Mycenae, Tiryns, Troad, Cyprus, etc., must be consulted.

For details, see " Polybutadiene ".

For details on specific bicycle parts, see list of bicycle parts and: Category: bicycle parts.

For more details, see Cooper pairs.

For more details on geological crystal formation, see above.

For example, a payroll file might contain information concerning all the employees in a company and their payroll details ; each record in the payroll file concerns just one employee, and all the records have the common trait of being related to payroll — this is very similar to placing all payroll information into a specific filing cabinet in an office that does not have a computer.

For example, a financial department of a company needs the payment details of all employees as part of the company's expenses, but not other many details about employees, that are the interest of the human resources department.

For example, each record in a " Faculty and Their Courses " table might contain a Faculty ID, Faculty Name, Faculty Hire Date, and Course Code — thus we can record the details of any faculty member who teaches at least one course, but we cannot record the details of a newly hired faculty member who has not yet been assigned to teach any courses except by setting the Course Code to null.

For more details see: NI Neighbourhood Information Service

For more details, visit: http :// wikitravel. org / en / Glenfinnan

For more details, see lead glass.

( For details, see Typography ).

For details on the various matrix addressing schemes see Passive-matrix and active-matrix addressed LCDs.

For details refer to Blue Phase Mode LCD.

For more details see Radon measure.

For details of the specific operations defined in different languages, see the modulo operation page.

For full details, see The Programming Language Oberon-07.

For later plays such as Othello, Shakespeare probably used the 1599 English translation of Gasparo Contarini's The Commonwealth and Government of Venice for some details about Venice's laws and customs.