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On Algebras of Hausdorff Operators on the Real Line

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arXiv 2023年第2期271卷 109-114页

关键词： Fourier transforms

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On σ-semipermutable Subgroups of Finite Groups

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Acta Mathematica Sinica,English Series 2018年第9期34卷 1379-1390页

作者： Wen Bin GUO Alexander N. SKIBA Department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel 246019 Belarus

Let a = {σi｜ i ∈ I} be some partition of the set of all primes P, G a finite group and σ（G） = {σi｜σi ∩ π （G） ≠ Ф}. A set H of subgroups of G is said to be a complete Hall or-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some σi ∈ σ and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ（G）. A subgroup H of G is said to be： σ-semipermutablc in G with respect to H if HHi x = Hi x H for all x ∈ G and all x ∈ G and all Hi ∈H such that （｜H｜, ｜Hi｜） = 1; σ-semipermutable in G if H is σ-semipermutable in G with respect to some complete Hall σ-set of G. We study the structure of G being based on the assumption that some subgroups of G are σ-semipermutable in G.

关键词： Finite group Hall subgroup p-soluble group p-supersoluble group σ-semipermutable subgroup

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Is Every Nontrivial Hausdorff Operator on Lebesgue Space a Non-Riesz Operator?

Is Every Nontrivial Hausdorff Operator on Lebesgue Space a N...

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International Scientific Conference on Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis, OTHA 2020

作者： Mirotin, A.R. Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel Belarus

ISBN: (纸本)9783030774929

We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In particular, it cannot be represented as a sum of a quasinilpotent and compact operators. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Compact operator Hausdorff operator Lebesgue space Quasinilpotent operator Riesz operator

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Finite groups whose n-maximal subgroups are σ-subnormal

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Science China mathematics 2019年第7期62卷 1355-1372页

作者： Wenbin Guo Alexander N. Skiba School of Mathematical Sciences University of Science and Technology of China Hefei 230026 China Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel 246019 Belarus

Let σ={σi | i ∈ I} be some partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G, for some i ∈ I, and H contains exactly one Hall σi-subgroup of G for every σi ∈σ(G). A subgroup H of G is said to be:σ-permutable or σ-quasinormal in G if G possesses a complete Hall σ-set H such that HAx= AxH for all A ∈ H and x ∈ G:σ-subnormal in G if there is a subgroup chain A = A0≤A1≤···≤ At = G such that either Ai-1■Ai or Ai/(Ai-1)Ai is a finite σi-group for some σi ∈σ for all i = 1,..., *** Mn < Mn-1 <···< M1 < M0 = G, where Mi is a maximal subgroup of Mi-1, i = 1, 2,..., n, then Mn is said to be an n-maximal subgroup of G. If each n-maximal subgroup of G is σ-subnormal(σ-quasinormal,respectively) in G but, in the case n > 1, some(n-1)-maximal subgroup is not σ-subnormal(not σ-quasinormal,respectively) in G, we write mσ(G)= n(mσq(G)= n, respectively).In this paper, we show that the parameters mσ(G) and mσq(G) make possible to bound the σ-nilpotent length lσ(G)(see below the definitions of the terms employed), the rank r(G) and the number |π(G)| of all distinct primes dividing the order |G| of a finite soluble group G. We also give the conditions under which a finite group is σ-soluble or σ-nilpotent, and describe the structure of a finite soluble group G in the case when mσ(G)=|π(G)|. Some known results are generalized.

关键词： finite group n-maximal subgroup σ-subnormal subgroup σ-quasinormal subgroup σ-soluble group σ-nilpotent group

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An Algorithm for Decentralized Multi-agent Feasibility Problems 22nd

An Algorithm for Decentralized Multi-agent Feasibility Prob...

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22nd International Conference on Mathematical Optimization Theory and Operations Research , MOTOR 2023

作者： Pinyagina, Olga Department of Data Mining and Programming Technologies Institute of Computational Mathematics and Information Technologies Kazan Federal University Kazan Russia

ISBN: (纸本)9783031432569

We consider the feasibility problem in a multi-agent decentralized form, where each agent has the personal information of the feasible subset, which is unknown to other agents. The common feasible set is composed of the agents’ feasible subsets. For solving this problem, we reformulate it in the form of a variational inequality and propose an algorithm based on the projection method. Preliminary test calculations confirm the efficiency of the proposed approach. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Multi agent systems

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ON A UNIQUE TWO-DIMENSIONAL INTEGRAL OPERATOR HOMOGENEOUS WITH RESPECT TO ALL ORIENTATION PRESERVING LINEAR TRANSFORMATIONS

arXiv

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arXiv 2025年

作者： Avetisyan, Zhirayr Karapetyants, Alexey Mirotin, Adolf Department of Mathematics: Analysis Logic and Discrete Mathematics University of Ghent Krijgslaan 281 Building S8 GhentB 9000 Belgium Regional Mathematical Center Southern Federal University Rostov-on-Don344090 Russia Institute of Mathematics Mechanics and Computer Sciences Regional Mathematical Center Southern Federal University Rostov-on-Don344090 Russia Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel246019 Belarus

In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces;conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are *** Codes 44A05, 44A15 Copyright © 2025, The Authors. All rights reserved.

关键词： Linear transformations

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A Generalization of σ-Permutability

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Communications in mathematics and Statistics 2022年第3期10卷 565-579页

作者： Zhigang Wang Jin Guo Inna N.Safonova Alexander N.Skiba School of Science Hainan UniversityHaikou 570228HainanPeople’s Republic of China Department of Applied Mathematics and Computer Science Belarusian State University220030 MinskBelarus Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University246019 GomelBelarus

Throughout this paper,all groups are finite and G always denotes a finite group;σis some partition of the set of all primes P.A group G is said to beσ-primary if G is aπ-group for someπ∈σ.Aπ-semiprojector of G[29]is a subgroup H of G such that HN/N is a maximalπ-subgroup of G/N for all normal subgroups N of ***П⊆σ.Then we say thatχ={X_(1),...,X_(t)}is aП-covering subgroup system for a subgroup H in G if all members of the setχareσ-primary subgroups of G and for eachπ∈Пwithπ∩π(H)≠φthere are an index i and aπ-semiprojector U of H such that U≤X_(i).We study the embedding properties of subgroups H of G under the hypothesis that G has aП-covering subgroup systemχsuch that H permutes with X^(x)for all X∈χand x∈*** well-known results are generalized.

关键词： Finite group σ-nilpotent group П-semiprojector П-covering subgroup system σ-subnormal subgroup

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Development of Adaptive Coding Means, Decoding of Data in Real Time Using Barker-Like Codes 4

Development of Adaptive Coding Means, Decoding of Data in Re...

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4th IEEE International Conference on Advanced Information and Communication technologies, AICT 2021

作者： Riznvk, Oleg Tsmots, Ivan Noga, Ynrii Myaus, Olga Lviv Polytechnic National University Department of Publishing Information Technologies Lviv Ukraine Lviv Polytechnic National University Department of Computational Mathematics and Programming Lviv Ukraine

ISBN: (纸本)9781665406185

An improved method for quickly finding such interference-resistant code sequences that are capable of finding and correcting errors according to the length of the resulting code sequence is considered. The methods make it possible to create coding systems with improved quality indicators in terms of power and noise immunity. The considered noise sequences are of practical interest, as on the basis of the obtained code sequence there is an opportunity to easily and quickly find (up to 50%) and correct (up to 25%) distorted characters (from the length of the noise code sequence). © 2021 IEEE.

关键词： Binary sequences

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ON THE SYMBOL CALCULUS FOR MULTIDIMENSIONAL HAUSDORFF OPERATORS

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Journal of Mathematical Sciences (United States) 2024年第1期280卷 23-32页

作者： Liflyand, E. Mirotin, A. Department of Mathematics Bar-Ilan University Ramat-Gan 52900 Israel Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel Belarus Regional Mathematical Center Southern Federal University Rostov-on-Don Russian Federation

The aim of this work is to derive a symbol calculus on L2(Rn) for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices a... 详细信息

The aim of this work is to derive a symbol calculus on L²(Rⁿ) for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorff operator elaborated earlier by the second named author. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Commutative algebra Commuting family Convolution Fourier transform Fractional power Hausdorff operator Holomorphic function Matrix symbol Positive definiteness Primary 47B38 Secondary 42B10 Symbol

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Hausdorff operators: problems and solutions

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Journal of Mathematical Sciences (United States) 2024年第6期280卷 1065-1114页

作者： Liflyand, Elijah Mirotin, Adolf Department of Mathematics Bar-Ilan University Ramat-Gan 5290002 Israel Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel Belarus Regional Mathematical Center Southern Federal University Rostov-on-Don 344090 Russian Federation

We overview basic results in the field of Hausdorff operators obtained during the last decade. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

关键词： Approximation Atomic decomposition Automorphism Averaging Hausdorff operator Locally compact group Normal operator Real Hardy space Riesz operator Spectrum

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