Wyniki wyszukiwania - BazTech

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Równania rekurencyjne, szeregi oraz iloczyny nieskończone - zadania i problemy. Cz. II

Bartłomiejczyk Lech, Ludew Jakub J., Różański Michał, Smuda Adrian, Wituła Roman

MINUT Matematyka i Informatyka na Uczelniach Technicznych

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2023

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Nr 5

37-55

PL

W prezentowanej części drugiej pracy (w przygotowaniu jest już trzecia część pracy) przedstawiamy rozwiązania (pełne, bądź częściowe) wielu zadań i problemów z części pierwszej tej pracy. W wybranych rozwiązaniach sformułowano nowe zadania i problemy badawcze.

2

Równania rekurencyjne, szeregi oraz iloczyny nieskończone - zadania i problemy. Cz. III

Bartłomiejczyk Lech, Ludew Jakub J., Różański Michał, Smuda Adrian, Wituła Roman

MINUT Matematyka i Informatyka na Uczelniach Technicznych

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2023

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Nr 5

56-75

PL

W prezentowanej części trzeciej pracy, stanowiącej kontynuację części drugiej trylogii pod wspólnym tytułem: „Wybór zadań i problemów o ciągach, równaniach rekurencyjnych, szeregach oraz iloczynach nieskończonych”, przedstawiamy rozwiązania (pełne, bądź częściowe) wielu zadań i problemów z części pierwszej tej pracy. W wybranych rozwiązaniach sformułowano nowe zadania i problemy badawcze.

3

Experimental tests of laminated glass with embedded steel mesh subjected to in-plane loading

Kozłowski Marcin, Wasik Dominik

Architecture Civil Engineering Environment

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2023

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Vol. 16, no. 3

77--88

EN

This article presents the issue of the in-plane post-breakage capacity of laminated glass elements. It presents the results of an ongoing research project that aims to develop novel reinforced, laminated glass elements with embedded steel woven mesh and increased post-breakage capacity. The research was focused on tensile strength tests in a custom-made experimental set-up. The tests were carried out on laminated glass samples consisting of two glass panes with 8, 10 and 12 mm thicknesses, bonded with an EVA Clear interlayer (3.04 mm thick). A total of 36 reference and reinforced samples were tested (6 series of 6 samples each). During the tests, an increase in load after glass breakage was observed for all samples, however, the samples reinforced with steel mesh showed much better strength in the post-breakage phase. It was found that the steel woven mesh embedded in laminated glass increases the post-breakage capacity by approximately 300% compared to the reference samples.

4

Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

Alakoya Timilehin Opeyemi, Jolaoso Lateef Olakunle, Mewomo Oluwatosin Temitope

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

208--224

EN

In this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge o fthe Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

5

On a cubic integral equation of Urysohn type with linear perturbation of second kind

Awad H. K., Darwish M. A., Metwali M. M. A.

Journal of Mathematics and Applications

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2018

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Vol. 41

29--38

EN

In this paper, we concern by a very general cubic integral equation and we prove that this equation has a solution in C[0; 1]. We apply the measure of noncompactness introduced by Banaś and Olszowy and Darbo's fixed point theorem to establish the proof of our main result.

6

Measures of noncompactness in a Banach algebra and their applications

Dudek S.

Journal of Mathematics and Applications

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2017

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Vol. 40

69--84

EN

In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.

7

An inequality involving the gamma and digamma functions

Qi F., Guo B.-N.

Journal of Applied Analysis

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2016

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Vol. 22, nr 1

49--54

EN

In the paper, the authors establish an inequality involving the gamma and digamma functions and apply it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

8

Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow

Abolarinwa A.

Journal of Applied Analysis

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2015

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Vol. 21, nr 2

147--160

EN

We study the evolution and monotonicity of the eigenvalues of p-Laplace operator on an m-dimen-sional compact Riemannian manifold M whose metric g(t) evolves by the Ricci-harmonic flow. The first nonzero eigenvalue is proved to be monotonically nondecreasing along the flow and differentiable almost everywhere. As a corollary, we recover the corresponding results for the usual Laplace-Beltrami operator when p = 2. We also examine the evolution and monotonicity under volume preserving flow and it turns out that the first eigenvalue is not monotone in general.

9

Matrix interval monotonicity

Jayaraman S., Sivakumar K.

Demonstratio Mathematica

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2010

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Vol. 43, nr 1

1-10

EN

We propose new notions of monotonicity for real matrices in order to characterize a particular notion of interval boundedness of various generalized inverses.

10

Iterative learning control — monotonicity and optimization

Owens D. H., Daley S.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 3

279-293

EN

The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.

11

Wartości "proceduralne" gier kooperacyjnych

Malawski M.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2004

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Nr 982

1-18

PL

W pracy wprowadzamy nowe pojęcie "wartości proceduralnych" dla gier kooperacyjnych z wypłatami ubocznymi. Wartości takie są wyznaczone przez procedury podziału krańcowych wkładów graczy pomiędzy nich i graczy już obecnych w koalicji powstającej przy losowym uporządkowaniu graczy. Najprostszą wartościąproceduralną jest wartość Shapleya, otrzymywana przy procedurze, według której każdy gracz zachowuje całość swego wkładu; jednak inne zasady podziału prowadzą do różnych interesujących wartości, w tym do podziału równego i do "wartości solidarnej" Nowaka i Radzika. Zbiór wszystkich wartości proceduralnych zawiera się w zbiorze wartości efektywnych, symetrycznych, liniowych i lokalnie monotonicznych; w pracy pokazujemy, że jest jego właściwym podzbiorem. Onawiamy także krótko możliwe kierunki uogólnień.

EN

A new notion of a "procedural" value for cooperative TU games is proposed. A procedural value is determined by an underlying procedurę of sharing marginal contributions to koalicje that form by random ordering of players between the contributing player and his predecessors in the ordering. The simplest procedural value is the Shapley value obtaining under the procedurę of every player j ust re-taining his entire marginal contribution. But different sharing rules lead to other interesting values, including the "egalitarian solution" and the Nowak and Radzik "solidarity value". The set of all procedural values is a subset of all efficient, symmetric, linear and locally monotonie values, and it is shown that the subset is proper. Some possible generalizations arę also briefły discussed.