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A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity.
In calculus and real analysis, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central operations of calculus—differentiation and integration.
John Cardy in 1988 considered the possibility to generalise C-theorem to higher-dimensional quantum field theory.He conjectured [2] that in four spacetime dimensions, the quantity behaving monotonically under renormalization group flows, and thus playing the role analogous to the central charge c in two dimensions, is a certain anomaly coefficient which came to be denoted as a.
Version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001. Implementations of the specification appeared in Amaya 1.1 , Mozilla 1.0 and Opera 9.5 . [ 5 ] [ 6 ] In October 2003, the second edition of MathML Version 2.0 was published as the final release by the W3C Math Working Group .
Michael Danos and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984. [14] [15] The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas (except for the first and the two last original chapters, which were dropped), but reducing the numerical tables to a minimum, [14] which, by this time, could ...
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function.Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined the function becomes divergent.
The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem.