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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":"30 1","pages":""},"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":"16 1","pages":""},"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":"153 1","pages":""},"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
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":"234 1","pages":""},"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
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":"1 1","pages":""},"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
Embeddings Into Countably Compact Hausdorff Spaces 嵌入可数紧凑豪斯多夫空间
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-11 DOI: 10.1007/s11253-023-02254-y
Taras Banakh, Serhii Bardyla, Alex Ravsky
{"title":"Embeddings Into Countably Compact Hausdorff Spaces","authors":"Taras Banakh, Serhii Bardyla, Alex Ravsky","doi":"10.1007/s11253-023-02254-y","DOIUrl":"https://doi.org/10.1007/s11253-023-02254-y","url":null,"abstract":"<p>We consider the problem of characterization of topological spaces embedded into countably compact Hausdorff topological spaces. We study the separation axioms for subspaces of Hausdorff countably compact topological spaces and construct an example of a regular separable scattered topological space that cannot be embedded into an Urysohn countably compact topological space.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"46 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567796","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
Centralizers of Linear and Locally Nilpotent Derivations 线性和局部无势衍生的中心点
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-11 DOI: 10.1007/s11253-023-02255-x
Leonid Bedratyuk, Anatolii Petravchuk, Evhen Chapovskyi
{"title":"Centralizers of Linear and Locally Nilpotent Derivations","authors":"Leonid Bedratyuk, Anatolii Petravchuk, Evhen Chapovskyi","doi":"10.1007/s11253-023-02255-x","DOIUrl":"https://doi.org/10.1007/s11253-023-02255-x","url":null,"abstract":"<p>Let 𝕂 be an algebraically closed field of characteristic zero, let 𝕂[<i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>] be the polynomial algebra, and let <i>W</i><sub><i>n</i></sub>(𝕂) be the Lie algebra of all 𝕂-derivations on 𝕂[<i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>]<i>.</i> For any derivation <i>D</i> with linear components, we describe the centralizer of <i>D</i> in <i>W</i><sub><i>n</i></sub>(𝕂) and propose an algorithm for finding the generators of this centralizer regarded as a module over the ring of constants of the derivation <i>D</i> in the case where <i>D</i> is a basic Weitzenböck derivation. In a more general case where a finitely generated integral domain <i>A</i> over the field 𝕂 is considered instead of the polynomial algebra 𝕂[<i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>] and <i>D</i> is a locally nilpotent derivation on <i>A,</i> we prove that the centralizer C<sub>Der<i>A</i></sub>(<i>D</i>) of <i>D</i> in the Lie algebra Der<i>A</i> of all 𝕂-derivations on <i>A</i> is a “large” subalgebra of Der <i>A.</i> Specifically, the rank of C<sub>Der<i>A</i></sub>(<i>D</i>) over <i>A</i> is equal to the transcendence degree of the field of fractions Frac(<i>A</i>) over the field 𝕂.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"46 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889268","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
A Modulus of Smoothness for Some Banach Function Spaces 某些巴拿赫函数空间的平滑度模量
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-11 DOI: 10.1007/s11253-023-02253-z
Ramazan Akgün
{"title":"A Modulus of Smoothness for Some Banach Function Spaces","authors":"Ramazan Akgün","doi":"10.1007/s11253-023-02253-z","DOIUrl":"https://doi.org/10.1007/s11253-023-02253-z","url":null,"abstract":"<p>Based on the Steklov operator, we consider a modulus of smoothness for functions in some Banach function spaces, which can be not translation invariant, and establish its main properties. A constructive characterization of the Lipschitz class is obtained with the help of the Jackson-type direct theorem and the inverse theorem on trigonometric approximation. As an application, we present several examples of related (weighted) function spaces.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"170 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138568171","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
Adomian’s Decomposition Method in the Theory of Nonlinear Autonomous Boundary-Value Problems 非线性自治边值问题理论中的阿多米分解法
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-11 DOI: 10.1007/s11253-023-02256-w
Oleksandr Boichuk, Serhii Chuiko, Dar’ya Diachenko
{"title":"Adomian’s Decomposition Method in the Theory of Nonlinear Autonomous Boundary-Value Problems","authors":"Oleksandr Boichuk, Serhii Chuiko, Dar’ya Diachenko","doi":"10.1007/s11253-023-02256-w","DOIUrl":"https://doi.org/10.1007/s11253-023-02256-w","url":null,"abstract":"<p>For a nonlinear autonomous boundary-value problem posed for an ordinary differential equation in the critical case, we establish constructive conditions for its solvability and propose a scheme for the construction of solutions based on the use of Adomian’s decomposition method.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"12 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567810","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
Generalized Weakly Demicompact and S-Demicompact Linear Relations and Their Spectral Properties 广义弱半紧密和 S 半紧密线性关系及其谱特性
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02261-z
Majed Fakhfakh, Aref Jeribi
{"title":"Generalized Weakly Demicompact and S-Demicompact Linear Relations and Their Spectral Properties","authors":"Majed Fakhfakh, Aref Jeribi","doi":"10.1007/s11253-023-02261-z","DOIUrl":"https://doi.org/10.1007/s11253-023-02261-z","url":null,"abstract":"<p>We extend the concept of generalized weakly demicompact and relatively weakly demicompact operators on linear relations and present some outstanding results. Moreover, we address the theory of Fredholm and upper semi-Fredholm relations and make an attempt to establish connections with these operators.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"129 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138559556","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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