Institute of Mathematics AS CR, v. v. i.
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Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces
No full textsummary:We prove the boundedness of the generalized fractional maximal operator and the generalized fractional integral operator on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces
Some extensions of Chu's formulas and further combinatorial identities
Get PDFsummary:We present some extensions of Chu's formulas and several striking generalizations of some well-known combinatorial identities. As applications, some new identities on binomial sums, harmonic numbers, and the generalized harmonic numbers are also derived
Modely a paradoxy teorie her, úvahy o vězňově dilematu
Get PDFsummary:V článku představujeme některé základní pojmy teorie her na klasické úloze vězňova dilematu. Úloha je snadno formulovatelná, přesto má zejména v ekonomii významné aplikace. Pozoruhodné na ní je zejména to, že různé přístupy k modelování rozhodování vedou k velmi různým výsledkům, ke kterým se musí přistupovat s opatrností. Kromě modelů zmíníme i experimenty
Multi-step-length gradient iterative method for separable nonlinear least squares problems
Get PDFsummary:Separable nonlinear least squares (SNLLS) problems are critical in various research and application fields, such as image restoration, machine learning, and system identification. Solving such problems presents a challenge due to their nonlinearity. The traditional gradient iterative algorithm often zigzags towards the optimal solution and is sensitive to the initial guesses of unknown parameters. In this paper, we improve the convergence rate of the traditional gradient method by implementing a multi-step-length gradient iterative algorithm. Moreover, we incorporate the variable projection (VP) strategy, taking advantage of the separable structure observed in SNLLS problems. We propose a multi-step-length gradient iterative-based VP (Mul-GI-VP) method to solve such nonlinear optimization problems. Our simulation results verify the feasibility and high efficiency of the proposed algorithm
Rings in which elements are sum of a central element and an element in the Jacobson radical
No full textsummary:An element in a ring is called CJ if it is of the form , where belongs to the center and is an element from the Jacobson radical. A ring is called CJ if each element of is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show that the subring is always a CJ ring and that if is a CJ ring then satisfies the Köthe conjecture
Images of locally nilpotent derivations of bivariate polynomial algebras over a domain
No full textsummary:We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let be a domain containing a field of characteristic zero. We prove that, when is a one-dimensional unique factorization domain, the image of any locally nilpotent -derivation of the bivariate polynomial algebra is a Mathieu-Zhao subspace. Moreover, we prove that, when is a Dedekind domain, the image of a locally nilpotent -derivation of with some additional conditions is a Mathieu-Zhao subspace
Nonlinear fourth order problems with asymptotically linear nonlinearities
Get PDFsummary:We investigate some nonlinear elliptic problems of the form \Delta ^{2}v + \sigma (x) v= h(x,v)\quad \mbox {in}\ \Omega ,\quad v=\Delta v=0 \quad \mbox {on}\ \partial \Omega , \eqno ({\rm P}) where is a regular bounded domain in , , a positive function in , and the nonlinearity is indefinite. We prove the existence of solutions to the problem (P) when the function is asymptotically linear at infinity by using variational method but without the Ambrosetti-Rabinowitz condition. Also, we consider the case when the nonlinearities are superlinear and subcritical
Non-homogeneous directional equations: Slice solutions belonging to functions of bounded -index in the unit ball
Get PDFsummary:For a given direction we study non-homogeneous directional linear higher-order equations whose all coefficients belong to a class of joint continuous functions which are holomorphic on intersection of all directional slices with a unit ball. Conditions are established providing boundedness of -index in the direction with a positive continuous function satisfying some behavior conditions in the unit ball. The provided conditions concern every solution belonging to the same class of functions as the coefficients of the equation. Our considerations use some estimates involving a directional logarithmic derivative and distribution of zeros on all directional slices in the unit ball
Expected value in problems at secondary schools
No full textsummary:Teorie pravděpodobnosti patří mezi klasické partie školské matematiky, která navíc nabízí přímé spojení se světem hazardních her kolem nás. Při analýzách takových her se však na střední škole zpravidla omezujeme pouze na určení pravděpodobnosti výher a neřešíme otázku, zda se sázení kvůli vysokým výhrám přece jen z dlouhodobého hlediska nevyplatí. V tomto článku představujeme možnost, jak se i ve třídě touto otázkou zabývat. Nejprve s důrazem na motivaci zavedeme pojem střední hodnoty a následně na čtveřici úloh s reálným kontextem ilustrujeme její význam k hlubšímu porozumění hazardním hrám.summary:The probability theory is a classic part of school mathematics, which also provides a direct connection with the world of gambling around us. During analyses of gambling at secondary schools we usually restrict ourselves to count probability of winnings and omit question whether betting is profitable in the long term due to high winnings. In this paper we present a possibility of how can this question be dealt with in class. Firstly we introduce the notion of expected value with emphasis on motivation and subsequently we illustrate with four real-life context problems its significance to deeper understanding of gambling