Institute of Mathematics AS CR, v. v. i.
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No full textsummary:Marián Fabian 75letý. Jiří Bičák (7. 1. 1942-26. 1. 2024). Prof. Jan Mlynář (1966-2023)
Robert Andrews Millikan (1868–1953) – stanovil hodnoty dvou základních fyzikálních konstant
Get PDFsummary:Článek pojednává o základních výsledcích práce amerického fyzika Roberta Millikana – metodách určení velikosti náboje elektronu a hodnoty Planckovy konstanty. Jsou zmíněni i někteří Millikanovi spolupracovníci
An approach to solve a fuzzy bi-objective multi-index fixed charge transportation problem
Get PDFsummary:In this paper, we propose a novel approach for solving a fuzzy bi-objective multi-index fixed-charge transportation problem where the aim is to minimize two objectives: the total transportation cost and transportation time. The parameters of the problem, such as fixed cost, variable cost, and transportation time are represented as fuzzy numbers. To extract crisp values from these parameters, a linear ranking function is used. The proposed approach initially separates the main problem into sub-problems. Then, it solves each sub-problem using different algorithms. After that, it determines the Pareto optimal solutions and trade-off pairs. To evaluate the performance of the proposed approach, various numerical problems of different sizes were solved. The results obtained are encouraging and show the efficiency of our approach
Energy norm error estimates and convergence analysis for a stabilized Maxwell's equations in conductive media
No full textsummary:The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell's equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme
A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration
No full textsummary:The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms incorporate strong Wolfe line search conditions to ensure effective convergence. Through numerical comparisons with other conjugate gradient algorithms, our modified approach demonstrates superior performance. The results highlight the improved efficacy of the HZF algorithm compared to the FR and three-term FR conjugate gradient methods. The new algorithm was applied to the problem of image restoration and proved to be highly effective in image restoration compared to other algorithms
regularity for elliptic equations with the general nonstandard growth conditions
No full textsummary:We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on . We prove the global regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case
On zero-symmetric nearrings with identity whose additive groups are simple
No full textsummary:We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay's characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group as its additive group
Distributed dual averaging algorithm for multi-agent optimization with coupled constraints
Get PDFsummary:This paper investigates a distributed algorithm for the multi-agent constrained optimization problem, which is to minimize a global objective function formed by a sum of local convex (possibly nonsmooth) functions under both coupled inequality and affine equality constraints. By introducing auxiliary variables, we decouple the constraints and transform the multi-agent optimization problem into a variational inequality problem with a set-valued monotone mapping. We propose a distributed dual averaging algorithm to find the weak solutions of the variational inequality problem with an convergence rate, where is the number of iterations. Moreover, we show that weak solutions are also strong solutions that match the optimal primal-dual solutions to the considered optimization problem. A numerical example is given for illustration