In this paper, we equip the partition lattice of the positive integers with a metric structure, and study the properties of this metric. We show, that this new space is complete, compact and separable. We also investi...
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In this paper, we equip the partition lattice of the positive integers with a metric structure, and study the properties of this metric. We show, that this new space is complete, compact and separable. We also investigate how continuous functions look like in this structure.(c) 2023 Elsevier B.V. All rights reserved.
It is well known that the bidual of C(X)for a compact space X, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to C( X)forsome compact space X. The space X is unique up to homeomorphis...
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It is well known that the bidual of C(X)for a compact space X, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to C( X)forsome compact space X. The space X is unique up to homeomorphism. We es tablisha similar result for realcompact spaces: The order bidual of C(X)for a rea lcompact space X, when supplied with the Arens product, is isomorphic as anf-algebra to C( X)for some real compact space X. The space X is unique up to homeomorphism
Migrating birds optimization algorithm is a promising metaheuristic algorithm recently introduced to the optimization community. In this study, we propose a superior version of the migrating birds optimization algorit...
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Migrating birds optimization algorithm is a promising metaheuristic algorithm recently introduced to the optimization community. In this study, we propose a superior version of the migrating birds optimization algorithm by hybridizing it with the simulated annealing algorithm which is one of the most popular metaheuristics. The new algorithm, called MBOx, is compared with the original migrating birds optimization and four well-known metaheuristics, including the simulated annealing, differential evolution, genetic algorithm and recently proposed harris hawks optimization algorithm. The extensive experiments are conducted on problem instances from both discrete and continuous domains;feature selection problem, obstacle neutralization problem, quadratic assignment problem and continuous functions. On problems from discrete domain, MBOx outperforms the original MBO and others by up to 20.99%. On the continuous functions, it is observed that MBOx does not lead the competition but takes the second position. As a result, MBOx provides a significant performance improvement and therefore, it is a promising solver for computational optimization problems.
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. Special attention is given to modelling such functions by system...
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The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. Special attention is given to modelling such functions by systems of functional equations.
The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension m...
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The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection of uniformly closed subspaces (respectively, sublattices) of codimension one. Every uniformly closed sublattice of codimension n contains a uniformly closed ideal of codimension at most 2n. If the vector lattice is uniformly complete then every ideal of finite codimension is uniformly closed. Results of the paper extend (and are motivated by) results of Abramovich Y.A., Lipecki Z. [On ideals and sublattices in linear lattices and F-lattices. Math Proc Cambridge Philos Soc. 1990;108(1):79-87.;On lattices and algebras of simple functions. Comment Math Univ Carolin. 1990;31(4):627-635.], as well as Kakutani's characterization of closed sublattices of C(K) spaces.
The article presents a mathematical proof for the problem of a real-valued continuous function on a compact interval using the notion of maximal intervals.
The article presents a mathematical proof for the problem of a real-valued continuous function on a compact interval using the notion of maximal intervals.
In this work, we establish a sequential characterization of the notion of relatively weak compactness of Banach algebras introduced recently by J. Banas and L. Olszowy. Moreover, we show that this structure is one of ...
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In this work, we establish a sequential characterization of the notion of relatively weak compactness of Banach algebras introduced recently by J. Banas and L. Olszowy. Moreover, we show that this structure is one of the most important properties which could be lifted from a Banach algebra X to C(K, X) and L1(mu, X). In addition, fixed point theorems for the product of two nonlinear operators acting on RWC-Banach algebra are proved by the help of the De Blasi measure of weak noncompactness.(c) 2022 Elsevier Inc. All rights reserved.
The article focuses on the proof of the First Fundamental Theorem of Calculus (FTC1) for continuous functions. It states that continuous functions have been proven to be Riemann-integrable whereas Darboux integral of ...
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The article focuses on the proof of the First Fundamental Theorem of Calculus (FTC1) for continuous functions. It states that continuous functions have been proven to be Riemann-integrable whereas Darboux integral of a bounded function as the infimum of all upper sums of a function and the supremum of lower sums are equal. It mentions that proof of FTC1 works without modification for upper and lower integrals.
Given a closed subset E of Lebesgue measure zero on the unit circle T there is a function f on T with uniformly convergent symmetric Fourier series Sn(f , zeta) = Sigma(k=-n) (f) over cap (k)zeta(k) paired right arrow...
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Given a closed subset E of Lebesgue measure zero on the unit circle T there is a function f on T with uniformly convergent symmetric Fourier series Sn(f , zeta) = Sigma(k=-n) (f) over cap (k)zeta(k) paired right arrows(T) integral(zeta) , such that for every continuous function g on E , there is a subsequence of partial power sums Sn + ( f , zeta )= Sigma(k=0)(f) over cap (k)zeta(k), of f, which converges to g uniformly on E. Here (f) over cap (k) = integral(T)zeta(-k) f(zeta)dm(zeta) , and m is the normalized Lebesgue measure on T. (c) 2023 Elsevier Inc. All rights reserved. MSC: 30D55;42A20;42B30;46A22;46E15;46E35;46J15
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