/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Real and Complex Analysis

This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

Convex Analysis: (pms-28)

This chapter relates the notions of mutations with the concept of graphical derivatives of set-valued maps and more generally links the above results of morphological analysis with some basic facts of set-valued analysis that we shall recall.

Set-valued analysis

Value and ambiguity are two parameters which were introduced to represent fuzzy numbers. In this paper, we find the nearest trapezoidal approximation and the nearest symmetric trapezoidal approximation to a given fuzzy number, with respect to the average Euclidean distance, preserving the value and ambiguity. To avoid the laborious calculus associated with the Karush-Kuhn-Tucker theorem, the working tool in some recent papers, a less sophisticated method is proposed. Algorithms for computing the approximations, many examples, proofs of continuity and two applications to ranking of fuzzy numbers and estimations of the defect of additivity for approximations are given.

Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value

Approximation by Max-Product Type Operators

Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity

http://gagolewski.rexamine.com/publications/2013plfnknot1.pdf

Nearest piecewise linear approximation of fuzzy numbers

Starting from the study of the Shepard nonlinear operator of max-prod type by Bede et al. (2006, 2008), in the book by Gal (2008), Open Problem 5.5.4, pages 324&#x2013;326, the Bernstein max-prod-type operator is introduced and the question of the approximation order by this operator is raised. In recent paper, Bede and Gal by using a very complicated method to this open question an answer is given by obtaining an upper estimate of the approximation error of the form 𝐶𝜔1√(𝑓;1/𝑛) (with an unexplicit absolute constant 𝐶g0) and the question of improving the order of approximation 𝜔1√(𝑓;1/𝑛) is raised. The first aim of this note is to obtain this order of approximation but by a simpler method, which in addition presents, at least, two advantages: it produces an explicit constant in front of 𝜔1√(𝑓;1/𝑛) and it can easily be extended to other max-prod operators of Bernstein type. However, for subclasses of functions 𝑓 including, for example, that of concave functions, we find the order of approximation 𝜔1(𝑓;1/𝑛), which for many functions 𝑓 is essentially better than the order of approximation obtained by the linear Bernstein operators. Finally, some shape-preserving properties are obtained.

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Lucian Coroianu

Papers

Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value

Approximation by Max-Product Type Operators

Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity

Nearest piecewise linear approximation of fuzzy numbers

Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind