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On the Nilpotency of Some Modules Over Group Rings 论群环上某些模块的无势性
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-06 DOI: 10.1007/s11253-024-02279-x
{"title":"On the Nilpotency of Some Modules Over Group Rings","authors":"","doi":"10.1007/s11253-024-02279-x","DOIUrl":"https://doi.org/10.1007/s11253-024-02279-x","url":null,"abstract":"<p>We study <em>RG</em>-modules that do not contain nonzero <em>G</em>-perfect factors. In particular, it is shown that if a group <em>G</em> is finite and <em>R</em> is a Dedekind domain with some additional restrictions, then these <em>RG</em>-modules are <em>G</em>-nilpotent.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140597008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Theory of Moduli Of The Surfaces 论曲面模量理论
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02271-5
{"title":"On the Theory of Moduli Of The Surfaces","authors":"","doi":"10.1007/s11253-024-02271-5","DOIUrl":"https://doi.org/10.1007/s11253-024-02271-5","url":null,"abstract":"<p>We continue the development of the theory of moduli of the families of surfaces, in particular, of strings of various dimensions <em>m</em> = 1<em>,</em> 2<em>, . . . ,n −</em> 1 in Euclidean spaces <span> <span>({mathbb{R}}^{n})</span> </span><em>, n</em> ≥ 2<em>.</em> On the basis of the proof of the lemma on the relationships between the moduli and Lebesgue measures, we prove the corresponding analog of the Fubini theorem in terms of moduli that extends the well-known Väisälä theorem for the families of curves to the families of surfaces of arbitrary dimensions. It should be emphasized that the crucial role in the proof of the mentioned lemma is played by a proposition on measurable (Borel) hulls of sets in Euclidean spaces. In addition, we also prove a similar lemma and a proposition for the families of concentric balls.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds on the Parameters of Non-L-Borderenergetic Graphs 非 L 边能图参数的界限
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02268-0
Cahit Dede, Ayşe Dilek Maden
{"title":"Bounds on the Parameters of Non-L-Borderenergetic Graphs","authors":"Cahit Dede, Ayşe Dilek Maden","doi":"10.1007/s11253-024-02268-0","DOIUrl":"https://doi.org/10.1007/s11253-024-02268-0","url":null,"abstract":"<p>We consider graphs whose Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an <i>L</i>-borderenergetic graph. First, we study the graphs with degree sequence consisting of at most three distinct integers and give new bounds for the number of vertices of these graphs to be non-<i>L</i>-borderenergetic. Second, by using Koolen–Moulton and McClelland inequalities, we give new bounds for the number of edges of a non-<i>L</i>-borderenergetic graph. Third, we use recent bounds established by Milovanovic, et al. for the Laplacian energy to get similar conditions for non-<i>L</i>-borderenergetic graphs. Our bounds depend only on the degree sequence of a graph, which is much easier than computing the spectrum of the graph. In other words, we develop a faster approach to exclude non-<i>L</i>-borderenergetic graphs.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Jordan Homoderivation Behavior of Generalized Derivations in Prime Rings 素环中广义衍生的乔丹同源行为
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02265-3
Nripendu Bera, Basudeb Dhara
{"title":"Jordan Homoderivation Behavior of Generalized Derivations in Prime Rings","authors":"Nripendu Bera, Basudeb Dhara","doi":"10.1007/s11253-024-02265-3","DOIUrl":"https://doi.org/10.1007/s11253-024-02265-3","url":null,"abstract":"<p>Suppose that <i>R</i> is a prime ring with char(<i>R</i>) <i>≠</i> 2 and <i>f</i>(ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub>) is a noncentral multilinear polynomial over <i>C</i>(= <i>Z</i>(<i>U</i>))<i>,</i> where <i>U</i> is the Utumi quotient ring of <i>R.</i> An additive mapping <i>h</i> : <i>R</i> ⟶<i> R</i> is called homoderivation if <i>h</i>(<i>ab</i>) = <i>h</i>(<i>a</i>)<i>h</i>(<i>b</i>)+<i>h</i>(<i>a</i>)<i>b</i>+<i>ah</i>(<i>b</i>) for all <i>a, b</i> ∈ <i>R.</i> We investigate the behavior of three generalized derivations <i>F, G,</i> and <i>H</i> of <i>R</i> satisfying the condition</p><p><span>(Fleft({xi }^{2}right)=Gleft({xi }^{2}right)+Hleft(xi right)xi +xi Hleft(xi right))</span></p><p>for all ξ ∈<i> f</i>(<i>R</i>) = {<i>f</i>(ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub>) <i>|</i> ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub> ∈<i> R</i>}<i>.</i></p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences 双序列求和加权平均法的一些陶伯定理
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02272-4
{"title":"Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences","authors":"","doi":"10.1007/s11253-024-02272-4","DOIUrl":"https://doi.org/10.1007/s11253-024-02272-4","url":null,"abstract":"<p>Let <em>p</em> = (<em>p</em><sub><em>j</em></sub>) and <em>q</em> = (<em>q</em><sub><em>k</em></sub>) be real sequences of nonnegative numbers with the property that</p> <p><span> <span>(begin{array}{ccccccc}{P}_{m}=sum_{j=0}^{m}{p}_{j}ne 0&amp; {text{and}}&amp; {Q}_{m}=sum_{k=0}^{n}{q}_{k}ne 0&amp; mathrm{for all}&amp; m&amp; {text{and}}&amp; n.end{array})</span> </span></p> <p>Also let (<em>P</em><sub><em>m</em></sub>) and (<em>Q</em><sub><em>n</em></sub>) be regularly varying positive indices. Assume that (<em>u</em><sub><em>mn</em></sub>) is a double sequence of complex (real) numbers, which is (<span> <span>(overline{N })</span> </span><em>, p, q</em>; <em>α, β</em>)-summable and has a finite limit, where (<em>α, β</em>) = (1<em>,</em> 1)<em>,</em> (1<em>,</em> 0)<em>,</em> or (0<em>,</em> 1)<em>.</em> We present some conditions imposed on the weights under which (<em>u</em><sub><em>mn</em></sub>) converges in Pringsheim’s sense. These results generalize and extend the results obtained by the authors in [<em>Comput. Math. Appl.</em>, <strong>62</strong>, No. 6, 2609–2615 (2011)].</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Smooth Rigidity for Higher-Dimensional Contact Anosov Flows 高维接触阿诺索夫流的平滑刚性
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02266-2
{"title":"Smooth Rigidity for Higher-Dimensional Contact Anosov Flows","authors":"","doi":"10.1007/s11253-024-02266-2","DOIUrl":"https://doi.org/10.1007/s11253-024-02266-2","url":null,"abstract":"<p>We apply the technique of matching functions in the setting of contact Anosov flows satisfying a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman and Ornstein [<em>Ergodic Theory Dynam. Syst.</em>, <strong>7</strong>, No. 1, 49–72 (1987)]. Namely, we show that if two Anosov flow of this kind are <em>C</em><sup>0</sup> conjugate, then they are <em>C</em><sup><em>r</em></sup> conjugate for some <em>r</em> ∈ [1<em>,</em> 2) or even <em>C</em><sup>∞</sup> conjugate under certain additional assumptions. This, e.g., applies to geodesic flows on compact Riemannian manifolds of 1<em>/</em>4-pinched negative sectional curvature. We can also use our result to recover Hamendstädt’s marked length spectrum rigidity result for real hyperbolic manifolds.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cohomology and Formal Deformations of n-Hom–Lie Color Algebras n-Hom-Lie色彩代数的同调与形式变形
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02264-4
K. Abdaoui, R. Gharbi, S. Mabrouk, A. Makhlouf
{"title":"Cohomology and Formal Deformations of n-Hom–Lie Color Algebras","authors":"K. Abdaoui, R. Gharbi, S. Mabrouk, A. Makhlouf","doi":"10.1007/s11253-024-02264-4","DOIUrl":"https://doi.org/10.1007/s11253-024-02264-4","url":null,"abstract":"<p>We provide a cohomology of <i>n</i>-Hom–Lie color algebras, in particular, a cohomology governing oneparameter formal deformations. Then we also study formal deformations of the <i>n</i>-Hom–Lie color algebras and introduce the notion of Nijenhuis operator on an <i>n</i>-Hom–Lie color algebra, which may give rise to infinitesimally trivial (<i>n −</i> 1)th-order deformations. Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure on <i>n</i>-Hom–Lie color algebras.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Quantum Hermite–Hadamard-Type Inequalities for p-Convex Functions Involving Recently Defined Quantum Integrals 涉及最近定义的量子积分的 p 凸函数的新量子赫米特-哈达马德式不等式
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02267-1
Ghazala Gulshan, Hüseyin Budak, Rashida Hussain, Muhammad Aamir Ali
{"title":"New Quantum Hermite–Hadamard-Type Inequalities for p-Convex Functions Involving Recently Defined Quantum Integrals","authors":"Ghazala Gulshan, Hüseyin Budak, Rashida Hussain, Muhammad Aamir Ali","doi":"10.1007/s11253-024-02267-1","DOIUrl":"https://doi.org/10.1007/s11253-024-02267-1","url":null,"abstract":"<p>We develop new Hermite–Hadamard-type integral inequalities for <i>p</i>-convex functions in the context of <i>q</i>-calculus by using the concept of recently defined <i>T</i><sub><i>q</i></sub>-integrals. Then the obtained Hermite–Hadamard inequality for <i>p</i>-convex functions is used to get a new Hermite–Hadamard inequality for coordinated <i>p</i>-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the proposed ideas and techniques may stimulate further research in this field.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence of Baum–Katz Series for Sums Whose Terms are Elements of a Linear mth Order Autoregressive Sequence 项为线性 mth 阶自回归序列元素之和的鲍姆-卡茨数列的收敛性
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02269-z
Maryna Ilienko, Anastasiia Polishchuk
{"title":"Convergence of Baum–Katz Series for Sums Whose Terms are Elements of a Linear mth Order Autoregressive Sequence","authors":"Maryna Ilienko, Anastasiia Polishchuk","doi":"10.1007/s11253-024-02269-z","DOIUrl":"https://doi.org/10.1007/s11253-024-02269-z","url":null,"abstract":"<p>We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear <i>m</i>th order autoregressive sequences of random variables.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Schmidt Rank and Singularities 施密特等级和奇异性
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-02-20 DOI: 10.1007/s11253-024-02270-6
David Kazhdan, Amichai Lampert, Alexander Polishchuk
{"title":"Schmidt Rank and Singularities","authors":"David Kazhdan, Amichai Lampert, Alexander Polishchuk","doi":"10.1007/s11253-024-02270-6","DOIUrl":"https://doi.org/10.1007/s11253-024-02270-6","url":null,"abstract":"<p>We revisit Schmidt’s theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also establish a sharper result for this kind for homogeneous polynomials, assuming that the characteristic does not divide the degree. Further, we use this to relate the Schmidt rank of a homogeneous polynomial (resp., a collection of homogeneous polynomials of the same degree) with the codimension of the singular locus of the corresponding hypersurface (resp., intersection of hypersurfaces). This gives an effective version of Ananyan–Hochster’s theorem [<i>J. Amer. Math. Soc.</i>, <b>33</b>, No. 1, 291–309 (2020), Theorem A].</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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