منابع مشابه
Discrete Analytic Functions: An Exposition
Harmonic and analytic functions have natural discrete analogues. Harmonic functions can be defined on every graph, while analytic functions (or, more precisely, holomorphic forms) can be defined on graphs embedded in orientable surfaces. Many important properties of the “true” harmonic and analytic functions can be carried over to the discrete setting.
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V. L. Rvachev called R-functions “logically-charged functions” because they encode complete logical information within the standard setting of real analysis. He invented them in the 1960s as a means for unifying logic, geometry, and analysis within a common computational framework – in an effort to develop a new computationally effective language for modeling and solving boundary value problems...
متن کاملFurther Properties of Discrete Analytic Functions
for every point (x, y) E Z, X Z, . If Z, x Z, is identified with the lattice (h(m + in); m, 1z integers} embedded in the complex plane, then condition (1.1) is seen to be an “analyticity” condition: On each unit square of the lattice, the difference quotients along the two diagonals are the same. The above definition of analyticity was introduced by Ferrand [I] and many properties of such funct...
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Lf(m,n)=f(m,n)+if(m+1,n)+i~f(m+1,n+1)+i3f(m,n+ 1) =o. (1.1) The concept of a discrete analytic function was introduced by Ferrand [l] and many properties of discrete analytic functions were obtained by D&in [2]. A convolution product for discrete analytic functions was defined by DufEn and Duris [3] and an operational calculus was developed by Hayabara [4] and further extended by Deeter and Lor...
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Modeling complex gene interacting systems as Boolean networks lead to a significant simplification of computational investigation. This can be achieved by discretization of the expression level to ON or OFF states and classifying the interactions to inhibitory and activating. In this respect, Boolean functions are responsible for the evolution of the binary elements of the Boolean networks. In ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1963
ISSN: 0002-9947
DOI: 10.2307/1993711