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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
On Exponential Dichotomy for Abstract Differential Equations with Delayed Argument 论具有延迟论证的抽象微分方程的指数二分法
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02263-x
Andrii Chaikovs’kyi, Oksana Lagoda
{"title":"On Exponential Dichotomy for Abstract Differential Equations with Delayed Argument","authors":"Andrii Chaikovs’kyi, Oksana Lagoda","doi":"10.1007/s11253-023-02263-x","DOIUrl":"https://doi.org/10.1007/s11253-023-02263-x","url":null,"abstract":"<p>We consider linear differential equations of the first order with delayed arguments in a Banach space. We establish conditions for the operator coefficients necessary for the existence of exponential dichotomy on the real axis. It is proved that the analyzed differential equation is equivalent to a difference equation in a certain space. It is shown that, under the conditions of existence and uniqueness of a solution bounded on the entire real axis, the condition of exponential dichotomy is also satisfied for any known bounded function. We also deduce the explicit formula for projectors, which form this dichotomy in the case of a single delay.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554122","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
Stochastic Bernoulli Equation on the Algebra of Generalized Functions 广义函数代数上的随机伯努利方程
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02258-8
Hafedh Rguigui
{"title":"Stochastic Bernoulli Equation on the Algebra of Generalized Functions","authors":"Hafedh Rguigui","doi":"10.1007/s11253-023-02258-8","DOIUrl":"https://doi.org/10.1007/s11253-023-02258-8","url":null,"abstract":"<p>Based on the topological dual space <span>({mathcal{F}}_{theta }^{*}left({mathcal{S}{prime}}_{mathbb{C}}right))</span> of the space of entire functions with θ-exponential growth of finite type, we introduce a generalized stochastic Bernoulli–Wick differential equation (or a stochastic Bernoulli equation on the algebra of generalized functions) by using the Wick product of elements in <span>({mathcal{F}}_{theta }^{*}left({mathcal{S}{prime}}_{mathbb{C}}right))</span>. This equation is an infinite-dimensional analog of the classical Bernoulli differential equation for stochastic distributions. This stochastic differential equation is solved and exemplified by several examples.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554435","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
S-Colocalization and Adams Cocompletion S-定位和亚当斯共同完成
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02262-y
Snigdha Bharati Choudhury, A. Behera
{"title":"S-Colocalization and Adams Cocompletion","authors":"Snigdha Bharati Choudhury, A. Behera","doi":"10.1007/s11253-023-02262-y","DOIUrl":"https://doi.org/10.1007/s11253-023-02262-y","url":null,"abstract":"<p>A relationship between the <i>S</i>-colocalization of an object and the Adams cocompletion of the same object in a complete small <i>𝒰</i> -category (<i>𝒰</i> is a fixed Grothendieck universe) is established together with a specific set of morphisms <i>S.</i></p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554176","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 Generalized Derivations Involving Prime Ideals with Involution 论涉及有卷积的质数理想的广义衍生
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02257-9
N. Rehman, Hafedh M. Alnoghashi, Motoshi Hongan
{"title":"On Generalized Derivations Involving Prime Ideals with Involution","authors":"N. Rehman, Hafedh M. Alnoghashi, Motoshi Hongan","doi":"10.1007/s11253-023-02257-9","DOIUrl":"https://doi.org/10.1007/s11253-023-02257-9","url":null,"abstract":"","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588657","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 Class of Fractional Integral Operators Involving a Certain General Multiindex Mittag-Leffler Function 一类涉及特定通用多指数 Mittag-Leffler 函数的分数积分算子
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02259-7
H. M. Srivastava, Manish Kumar Bansal, Priyanka Harjule
{"title":"A Class of Fractional Integral Operators Involving a Certain General Multiindex Mittag-Leffler Function","authors":"H. M. Srivastava, Manish Kumar Bansal, Priyanka Harjule","doi":"10.1007/s11253-023-02259-7","DOIUrl":"https://doi.org/10.1007/s11253-023-02259-7","url":null,"abstract":"<p>The paper is essentially motivated by the demonstrated potential for applications of the presented results in numerous widespread research areas, such as the mathematical, physical, engineering, and statistical sciences. The main object is to introduce and investigate a class of fractional integral operators involving a certain general family of multiindex Mittag-Leffler functions in their kernel. Among other results obtained in the paper, we establish several interesting expressions for the composition of well-known fractional integral and fractional derivative operators, such as (e.g.) the Riemann–Liouville fractional integral and fractional derivative operators, the Hilfer fractional derivative operator, and the above-mentioned fractional integral operator involving the general family of multiindex Mittag-Leffler functions in its kernel. Our main result is a generalization of the results obtained in earlier investigations in this field. We also present some potentially useful integral representations for the product of two members of the general family of multiindex Mittag-Leffler functions in terms of the well-known Fox–Wright hypergeometric function <sub><i>p</i></sub>Ψ <sub><i>q</i></sub> with <i>p</i> numerator and <i>q</i> denominator parameters.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554433","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: 1
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