In this article we study algebraic functions in {->, 1}-subreducts of MV-algebras, also known as Lukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equa...
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In this article we study algebraic functions in {->, 1}-subreducts of MV-algebras, also known as Lukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Lukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Lukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form for all there exists! Lambda p approximate to q within the variety generated by the 3-element chain.
In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analyti...
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In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.
It is well known that we can efficiently test whether a polynomial is identically zero or not by examining the values of the polynomial at well-chosen points. Both deterministic and efficient probabilistic algorithms ...
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It is well known that we can efficiently test whether a polynomial is identically zero or not by examining the values of the polynomial at well-chosen points. Both deterministic and efficient probabilistic algorithms have been devised for this purpose. It is not so well recognized that algebraic functions can be similarly tested for zeroness. The need for zero testing black boxes representing algebraic functions has recently arisen in the area of self-testing/self-correcting programs. Given a black box B-alpha that represents an algebraic function alpha and a few additional parameters about alpha, we show how to test if alpha is equal to the zero function. (C) 1997 Elsevier Science B.V.
作者：
Epple, MUNIV MAINZ
FACHBEREICH MATH 17AG GESCHICHTE MATHD-55099 MAINZGERMANY
Many of the key ideas which formed modern topology grew out of ''normal research'' in one of the mainstream fields of 19th-century mathematical thinking, the theory of complex algebraic functions. Thes...
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Many of the key ideas which formed modern topology grew out of ''normal research'' in one of the mainstream fields of 19th-century mathematical thinking, the theory of complex algebraic functions. These ideas were eventually divorced from their original context. The present study discusses an example illustrating this process. During the years 1895-1905, the Austrian mathematician, Wilhelm Wirtinger, tried to generalize Felix Klein's View of algebraic functions to the case of several variables. An investigation of the monodromy behavior of such functions in the neighborhood of singular points led to the first computation of a knot group. Modern knot theory was then formed after a shift in mathematical perspective took place regarding the types of problems investigated by Wirtinger, resulting in an elimination of the context of algebraic functions. This shift, clearly visible in Max Dehn's pioneering work on knot theory, was related to a deeper change in the normative horizon of mathematical practice which brought about mathematical modernity. (C) 1996 Academic Press, Inc.
Let f be a rational function on an algebraic curve over the complex numbers. For a point p and local parameter x we can consider the Taylor series for f in the variable x. In this paper we give an upper bound on the f...
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Let f be a rational function on an algebraic curve over the complex numbers. For a point p and local parameter x we can consider the Taylor series for f in the variable x. In this paper we give an upper bound on the frequency with which the terms in the Taylor series have 0 as their coefficient.
We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermedi...
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We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions.
We study algebraic properties of the Wiener algebra of absolutely convergent power series on the closed unit disc. In particular, we prove a form of Weierstrass preparation for algebraic functions in this algebra.
We study algebraic properties of the Wiener algebra of absolutely convergent power series on the closed unit disc. In particular, we prove a form of Weierstrass preparation for algebraic functions in this algebra.
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of non-negative, constant description-complexity algebraic functions. We fi...
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ISBN:
(纸本)9780898717013
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of non-negative, constant description-complexity algebraic functions. We first give a FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions, and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum area hulls.
We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric fun...
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We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In particular, we show that there are no irreducible algebraic functions if the number of boundary points is sufficiently large and A is not a pyramid. (C) 2013 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
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