Institute of Mathematics AS CR, v. v. i.
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The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem
No full textsummary:For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the Generalized Eigenvalue Complementarity Problem (GEiCP) derived from unilateral friction elastic systems. Numerical experiments show the efficiency of the proposed methods compared to the projected steepest descent method with less CPU time
Krocení jedné bijekce aneb o zipu a tkaničkách
Get PDFsummary:Tento text pojednává o jednom pozoruhodném vzájemně jednoznačném zobrazení mezi množinou všech bodů jednotkového čtverce a množinou všech bodů jednotkové úsečky. Existence tohoto zobrazení (bijekce) zaručuje (laicky řečeno) stejně velká nekonečna, řečeno matematicky – stejnou mohutnost dvou nekonečných množin
Česká matematická společnost
Get PDFsummary:Znáte Českou matematickou společnost? Víte, čím se zabývá? Pokud jste odpověděli ano, nebo dokonce s naší společností spolupracujete, pak jsme velice potěšeni a doufáme, že i pro vás je a bude ČMS přínosem. Jestliže si nejste jisti, jak odpovědět, ale zajímá vás matematika a chcete se dozvědět o nás a naší činnosti více, pak je tento článek určen právě vám
Musical Composition Typesetting
Get PDFsummary:TeX je užitečný nástroj pro sazbu textu, ale nemá v základu dobrou podporu pro sazbu skladeb. Na konferenci TUG 2022 zazněla přednáška o sazbě not, která porovnávala sazbu pomocí balíku MusiXTeX s nástroji Musescore a Flat, ale nezmínila preprocesory PMX a M-Tx, které sazbu zjednodušují. V tomto článku porovnám sazbu nástrojem MusiXTeX s jeho preprocesory a popíšu jejich užití. Dále rozeberu začlenění notových značek do textu odstavce. Po přečtení článku bude čtenář schopný vytvořit jednoduchý krátký úryvek hudebního díla a začlenit jej do TeXového dokumentu, či doplnit psaný text notovými značkami.summary:TeX is a useful tool for text typesetting; however, it doesn't feature a good support for composition typesetting at its core. The TUG 2022 conference featured a talk on notation typesetting which compared the MusiXTeX package with the MuseScore and Flat tools, but did not mention the PMX and M-Tx preprocessors. In this article, I compare typesetting using MusiXTeX and its preprocessors and describe its usage. In addition, I describe the incorporation of note symbols into a paragraph text. After reading the article, the reader will be able to create a short simple excerpt of a piece of music and incorporate it into a TeX document, as well as add musical symbols to a written text
Finitely silting comodules in quasi-finite comodule category
No full textsummary:We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules
Ding projective and Ding injective modules over trivial ring extensions
No full textsummary:Let be a trivial extension of a ring by an --bimodule such that , , and have finite flat dimensions. We prove that is a Ding projective left -module if and only if the sequence is exact and is a Ding projective left -module. Analogously, we explicitly describe Ding injective -modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms
Equations for the set of overrings of normal rings and related ring extensions
No full textsummary:We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards
A new inclusion interval for the real eigenvalues of real matrices
No full textsummary:By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) \hbox {B-matrices}, a new class of nonsingular matrices called CKV-type -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results
Some properties of algebras of real-valued measurable functions
Get PDFsummary:Let () be the -ring of all (bounded) real-measurable functions on a -measurable space , let be the family of all such that is compact, and let be all that is compact for any . We introduce realcompact subrings of , we show that is a realcompact subring of , and also is a realcompact if and only if is a compact measurable space. For every nonzero real Riesz map , we prove that there is an element such that for every if is a compact measurable space. We confirm that is equal to the intersection of all free maximal ideals of , and also is equal to the intersection of all free ideals of (or ). We show that and do not have free ideal