Displaying similar documents to “Investigation of the algorithms determining the optimum rational function of the ADI-method”

Characterization of linear rational preference structures.

Jacinto González Pachón, Sixto Ríos-Insua (1992)

Extracta Mathematicae

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We consider the multiobjective decision making problem. The decision maker's (DM) impossibility to take consciously a preference or indifference attitude with regard to a pair of alternatives leads us to what we have called doubt attitude. So, the doubt may be revealed in a conscient way by the DM. However, it may appear in an inconscient way, revealing judgements about her/his attitudes which do not follow a certain logical reasoning. In this paper, doubt will be considered...

Cauchy type functional equations related to some associative rational functions

Katarzyna Domańska (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.

Niven’s Theorem

Artur Korniłowicz, Adam Naumowicz (2016)

Formalized Mathematics

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This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9].

Rational semimodules over the max-plus semiring and geometric approach to discrete event systems

Stéphane Gaubert, Ricardo Katz (2004)

Kybernetika

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We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule 𝒮 n over a semiring 𝒮 is rational if it has a generating family that is a rational subset of 𝒮 n , 𝒮 n being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational...