Researches in Mathematics
https://vestnmath.dnu.dp.ua/index.php/rim
<table><tbody><tr><td><img src="/files/pics/gen_issue_cover.png" alt="" width="100px" height="150px" /></td><td style="padding-left: 16px; vertical-align: top;"><p>The journal publishes, semiannually, research articles in basic areas of theoretical and applied mathematics, including, but not limited to: analysis, algebra, geometry, topology, probability theory and mathematical statistics, differential equations and mathematical physics.</p><p>The journal was published annually from 1963 to 1997 under the title “Researches on modern problems of summation and approximation of functions and their applications” and from 1998 to 2018 under the title “Dnipro University Mathematics Bulletin”.</p><p>In 2022, the journal was included to Scopus.</p><p><em>Attention:</em> The template of the submission (.tex and .cls files) was updated on 28.05.2023. Please proceed to <a href="/index.php/rim/about/submissions#authorGuidelines">Author Guidelines</a> to download and use the latest version.</p></td></tr></tbody></table>Oles Honchar Dnipro National Universityen-USResearches in Mathematics2664-4991Authors who publish with this journal agree to the following terms:<ol><li>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" target="_new">Creative Commons Attribution License</a> that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li><li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li><li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See <a href="http://opcit.eprints.org/oacitation-biblio.html" target="_new">The Effect of Open Access</a>).</li></ol>Preamble
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/394
Editors Editors
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2023-06-192023-06-1931112On Landau-Kolmogorov type inequalities for charges and their applications
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/395
In this article we prove sharp Landau-Kolmogorov type inequalities on a class of charges defined on Lebesgue measurable subsets of a cone in $$$\mathbb{R}^d$$$, $$$d\geqslant 1$$$, that are absolutely continuous with respect to the Lebesgue measure. In addition we solve the Stechkin problem of approximation of the Radon-Nikodym derivative of such charges by bounded operators and two related problems. As an application, we also solve these extremal problems on classes of essentially bounded functions $$$f$$$ such that their distributional partial derivative $$$\frac{\partial ^d f}{\partial x_1\ldots\partial x_d}$$$ belongs to the Sobolev space $$$W^{1,\infty}$$$.V.F. BabenkoV.V. BabenkoO.V. KovalenkoN.V. Parfinovych
Copyright (c) 2023 V.F. Babenko, V.V. Babenko, O.V. Kovalenko, N.V. Parfinovych
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2023-06-192023-06-1931131610.15421/242301Application of spectral decomposition to establish inequalities for operators
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/396
We give specific examples of the spectral decomposition of self-adjoint operators in application to establish sharp inequalities for their powers.R. BilichenkoS. Zhir
Copyright (c) 2023 R. Bilichenko, S. Zhir
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2023-06-192023-06-19311172210.15421/242302On the structure of some nilpotent braces
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/397
We prove a criteria for nilpotency of left braces in terms of the $$$\star$$$-central series and also discuss Noetherian braces, obtaining some of their elementary properties. We also show that if a finitely generated brace $$$A$$$ is Smoktunowicz-nilpotent, then the additive and multiplicative groups of $$$A$$$ are likewise finitely generated.M.R. DixonL.A. Kurdachenko
Copyright (c) 2023 M.R. Dixon, L.A. Kurdachenko
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2023-06-192023-06-19311233910.15421/242303A sharp Remez type inequalities for the functions with asymmetric restrictions on the oldest derivative
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/398
<p>For odd $$$r\in \mathbb{N}$$$; $$$\alpha, \beta >0$$$; $$$p\in [1, \infty]$$$; $$$\delta \in (0, 2 \pi)$$$, any $$$2\pi$$$-periodic function $$$x\in L^r_{\infty}(I_{2\pi})$$$, $$$I_{2\pi}:=[0, 2\pi]$$$, and arbitrary measurable set $$$B \subset I_{2\pi},$$$ $$$\mu B \leqslant \delta/\lambda,$$$ where $$$\lambda=$$$ $$$\left({\left\|\varphi_{r}^{\alpha, \beta}\right\|_{\infty} \left\| {\alpha^{-1}}{x_+^{(r)}} + {\beta^{-1}}{x_-^{(r)}}\right\|_\infty}{E^{-1}_0(x)_\infty}\right)^{1/r}$$$, we obtain sharp Remez type inequality $$E_0(x)_\infty \leqslant \frac{\|\varphi_r^{\alpha, \beta}\|_\infty}{E_0(\varphi_r^{\alpha, \beta})^{\gamma}_{L_p(I_{2\pi} \setminus B_\delta)}} \left\|x \right\|^{\gamma}_{{L_p} \left(I_{2\pi} \setminus B \right)}\left\| {\alpha^{-1}}{x_+^{(r)}} + {\beta^{-1}}{x_-^{(r)}}\right\|_\infty^{1-\gamma},$$ where $$$\gamma=\frac{r}{r+1/p},$$$ $$$\varphi_r^{\alpha, \beta}$$$ is non-symmetric ideal Euler spline of order $$$r$$$, $$$B_\delta:= \left[M- \delta_2, M+ \delta_1 \right]$$$, $$$M$$$ is the point of local maximum of spline $$$\varphi_r^{\alpha, \beta}$$$ and $$$\delta_1 > 0$$$, $$$\delta_2 > 0$$$ are such that $$$\varphi_r^{\alpha, \beta}(M+ \delta_1) = \varphi_r^{\alpha, \beta}(M- \delta_2), \;\; \delta_1 + \delta_2 = \delta .$$$<br />In particular, we prove the sharp inequality of Hörmander-Remez type for the norms of intermediate derivatives of the functions $$$x\in L^r_{\infty}(I_{2\pi})$$$.</p>V.A. KofanovA.V. Zhuravel
Copyright (c) 2023 V.A. Kofanov, A.V. Zhuravel
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2023-06-192023-06-19311405110.15421/242304Description of the automorphism groups of some Leibniz algebras
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/399
Let $$$L$$$ be an algebra over a field $$$F$$$ with the binary operations $$$+$$$ and $$$[,]$$$. Then $$$L$$$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $$$[[a,b],c]=[a,[b,c]]-[b,[a,c]]$$$ for all elements $$$a,b,c\in L$$$. A linear transformation $$$f$$$ of $$$L$$$ is called an endomorphism of $$$L$$$, if $$$f([a,b])=[f(a),f(b)]$$$ for all elements $$$a,b\in L$$$. A bijective endomorphism of $$$L$$$ is called an automorphism of $$$L$$$. It is easy to show that the set of all automorphisms of the Leibniz algebra is a group with respect to the operation of multiplication of automorphisms. The description of the structure of the automorphism groups of Leibniz algebras is one of the natural and important problems of the general Leibniz algebra theory. The main goal of this article is to describe the structure of the automorphism group of a certain type of nilpotent three-dimensional Leibniz algebras.L.A. KurdachenkoO.O. PypkaM.M. Semko
Copyright (c) 2023 L.A. Kurdachenko, O.O. Pypka, M.M. Semko
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2023-06-192023-06-19311526110.15421/242305On the algebra of derivations of some nilpotent Leibniz algebras
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/400
We describe the algebra of derivations of some nilpotent Leibniz algebra, having dimensionality 3.L.A. KurdachenkoM.M. SemkoV.S. Yashchuk
Copyright (c) 2023 L.A. Kurdachenko, M.M. Semko, V.S. Yashchuk
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2023-06-192023-06-19311627110.15421/242306On the structure of groups admitting faithful modules with certain conditions of primitivity
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/401
In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear group $$$G$$$ of finite rank admits a fully primitive fully faithful module then $$$G$$$ has infinite $$$FC$$$-centre.A.V. Tushev
Copyright (c) 2023 A.V. Tushev
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2023-06-192023-06-19311727810.15421/242307