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Ukrainian Mathematical Journal最新文献

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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":"1 1","pages":""},"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":"82 1","pages":""},"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":"39 1","pages":""},"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":"47 33","pages":""},"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":"17 1","pages":""},"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
On the Variational Statement of One Boundary-Value Problem with Free Interface 论自由界面一个边值问题的变式表述
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI: 10.1007/s11253-023-02260-0
Aleksander Timokha
{"title":"On the Variational Statement of One Boundary-Value Problem with Free Interface","authors":"Aleksander Timokha","doi":"10.1007/s11253-023-02260-0","DOIUrl":"https://doi.org/10.1007/s11253-023-02260-0","url":null,"abstract":"<p>With the help of Clebsch’s potentials, we propose a Bateman–Luke-type variational principle for a boundary- value problem with a free (unknown) interface between two ideal compressible barotropic fluids (liquid and gas) admitting rotational flows.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554121","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 Tangent Inequality Over Primes 质数上的正切不等式
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-11-28 DOI: 10.1007/s11253-023-02245-z
S. I. Dimitrov
{"title":"A Tangent Inequality Over Primes","authors":"S. I. Dimitrov","doi":"10.1007/s11253-023-02245-z","DOIUrl":"https://doi.org/10.1007/s11253-023-02245-z","url":null,"abstract":"<p>We introduce a new Diophantine inequality with prime numbers. Let <span>(1&lt;c&lt;frac{10}{9}.)</span> We show that, for any fixed <i>θ &gt;</i> 1<i>,</i> every sufficiently large positive number <i>N,</i> and a small constant <i>ε &gt;</i> 0<i>,</i> the tangent inequality\u0000</p><span>$$left|{p}_{1}^{c} {mathrm{tan}}^{theta }left(mathrm{log}{p}_{1}right)+{p}_{2}^{c} {mathrm{tan}}^{theta }left(mathrm{log}{p}_{2}right)+{p}_{3}^{c} {mathrm{tan}}^{theta }left(mathrm{log}{p}_{3}right)-Nright|&lt;varepsilon $$</span><p>has a solution in prime numbers <i>p</i><sub>1</sub><i>, p</i><sub>2</sub><i>,</i> and <i>p</i><sub>3</sub><i>.</i></p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516370","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
Determination of Some Properties of Starlike and Close-to-Convex Functions According to Subordinate Conditions with Convexity of a Certain Analytic Function 根据具有一定解析函数凸性的从属条件确定星形和近凸函数的一些性质
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-11-28 DOI: 10.1007/s11253-023-02251-1
Hasan Şahin, İsmet Yildiz
{"title":"Determination of Some Properties of Starlike and Close-to-Convex Functions According to Subordinate Conditions with Convexity of a Certain Analytic Function","authors":"Hasan Şahin, İsmet Yildiz","doi":"10.1007/s11253-023-02251-1","DOIUrl":"https://doi.org/10.1007/s11253-023-02251-1","url":null,"abstract":"<p>Investigation of the theory of complex functions is one of the most fascinating aspects of the theory of complex analytic functions of one variable. It has a huge impact on all areas of mathematics. Numerous mathematical concepts are explained when viewed through the theory of complex functions. Let <span>(fleft(zright)in A, fleft(zright)=z+{sum }_{nge 2}^{infty }{a}_{n}{z}^{n},)</span> be an analytic function in an open unit disc <i>U</i> = {<i>z</i> : <i>|z| &lt;</i> 1<i>, z</i> ∈ ℂ} normalized by <i>f</i>(0) = 0 and <i>f</i>′(0) = 1<i>.</i> For close-to-convex and starlike functions, new and different conditions are obtained by using subordination properties, where <i>r</i> is a positive integer of order <span>({2}^{-r}left(0&lt;{2}^{-r}le frac{1}{2}right).)</span> By using subordination, we propose a criterion for <i>f</i>(<i>z</i>) ∈ <i>S</i><sup>*</sup>[<i>a</i><sup><i>r</i></sup><i>, b</i><sup><i>r</i></sup>]<i>.</i> The relations for starlike and close-to-convex functions are investigated under certain conditions according to their subordination properties. At the same time, we analyze the convexity of some analytic functions and study their regional transformations. In addition, the properties of convexity are examined for <i>f</i>(<i>z</i>) ∈ <i>A</i>.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"44 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516371","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
Weighted Discrete Hardy’s Inequalities 加权离散Hardy不等式
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-11-28 DOI: 10.1007/s11253-023-02252-0
Pascal Lefèvre
{"title":"Weighted Discrete Hardy’s Inequalities","authors":"Pascal Lefèvre","doi":"10.1007/s11253-023-02252-0","DOIUrl":"https://doi.org/10.1007/s11253-023-02252-0","url":null,"abstract":"<p>We give a short proof of a weighted version of the discrete Hardy inequality. This includes the known case of classical monomial weights with optimal constant. The proof is based on the ideas of the short direct proof given recently in [P. Lefèvre, <i>Arch. Math. (Basel)</i>, <b>114</b>, No. 2, 195–198 (2020)].</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"23 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516374","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: 6
Uncertainty Principles for the q-Hankel–Stockwell Transform q-Hankel-Stockwell变换的不确定性原理
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2023-11-28 DOI: 10.1007/s11253-023-02244-0
Kamel Brahim, Hédi Ben Elmonser
{"title":"Uncertainty Principles for the q-Hankel–Stockwell Transform","authors":"Kamel Brahim, Hédi Ben Elmonser","doi":"10.1007/s11253-023-02244-0","DOIUrl":"https://doi.org/10.1007/s11253-023-02244-0","url":null,"abstract":"<p>By using the <i>q</i>-Jackson integral and some elements of the <i>q</i>-harmonic analysis associated with the <i>q</i>-Hankel transform, we introduce and study a <i>q</i>-analog of the Hankel–Stockwell transform. We present some properties from harmonic analysis (Plancherel formula, inversion formula, reproducing kernel, etc.). Furthermore, we establish a version of Heisenberg’s uncertainty principles. Finally, we study the <i>q</i>-Hankel–Stockwell transform on a subset of finite measure.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"10072 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516378","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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