Matematychni Studii最新文献_第7页

Generalized derivations of order $2$ on multilinear polynomials in prime rings 素环中多元线性多项式上$2$阶的广义导数

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.26-35

B. Prajapati, C. Gupta

引用次数: 0

Continued $mathbf{A_2}$-fractions and singular functions 续$mathbf{A_2}$-分数和奇异函数

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.3-12

M. Pratsiovytyi, Y. Goncharenko, I. Lysenko, S. Ratushniak

引用次数: 2

On linear sections of orthogonally additive operators 关于正交加法算子的线性截面

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.94-102

A. Gumenchuk, I. Krasikova, M. Popov

引用次数: 0

Non-periodic groups with the restrictions on the norm of cyclic subgroups of non-prime order 具有非素数阶循环子群范数约束的非周期群

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.36-44

M. Drushlyak, T. Lukashova

{"title":"Non-periodic groups with the restrictions on the norm of cyclic subgroups of non-prime order","authors":"M. Drushlyak, T. Lukashova","doi":"10.30970/ms.58.1.36-44","DOIUrl":"https://doi.org/10.30970/ms.58.1.36-44","url":null,"abstract":"One of the main directions in group theory is the study of the impact of characteristic subgroups on the structure of the whole group. Such characteristic subgroups include different $Sigma$-norms of a group. A $Sigma$-norm is the intersection of the normalizers of all subgroups of a system $Sigma$. The authors study non-periodic groups with the restrictions on such a $Sigma$-norm -- the norm $N_{G}(C_{bar{p}})$ of cyclic subgroups of non-prime order, which is the intersection of the normalizers of all cyclic subgroups of composite or infinite order of $G$. It was proved that if $G$ is a mixed non-periodic group, then its norm $N_{G}(C_{bar{p}})$ of cyclic subgroups of non-prime order is either Abelian (torsion or non-periodic) or non-periodic non-Abelian. Moreover, a non-periodic group $G$ has the non-Abelian norm $N_{G}(C_{bar{p}})$of cyclic subgroups of non-prime order if and only if $G$ is non-Abelian and every cyclic subgroup of non-prime order of a group $G$ is normal in it, and $G=N_{G}(C_{bar{p}})$.Additionally the relations between the norm $N_{G}(C_{bar{p}})$ of cyclic subgroups of non-prime order and the norm $N_{G}(C_{infty})$ of infinite cyclic subgroups, which is the intersection of the normalizers of all infinite cyclic subgroups, in non-periodic groups are studied. It was found that in a non-periodic group $G$ with the non-Abelian norm $N_{G}(C_{infty})$ of infinite cyclic subgroups norms $N_{G}(C _{infty})$ and $N_{G}(C _{bar{p}})$ coincide if and only if $N_{G}(C _{infty})$ contains all elements of composite order of a group $G$ and does not contain non-normal cyclic subgroups of order 4.In this case $N_{G}(C_{bar {p}})=N_{G}(C_{infty})=G$.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46189507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Essential spectra in non-Archimedean fields 非阿基米德场的基本光谱

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.82-93

A. Ammar, F. Boutaf, A. Jeribi

引用次数: 0

On modulus inequality of the order $p$ for the inner dilatation 关于内扩张的$p$阶模不等式

Matematychni Studii Pub Date : 2022-04-16 DOI: 10.30970/ms.59.2.141-155

R. Salimov, E. Sevost’yanov, V. Targonskii

{"title":"On modulus inequality of the order $p$ for the inner dilatation","authors":"R. Salimov, E. Sevost’yanov, V. Targonskii","doi":"10.30970/ms.59.2.141-155","DOIUrl":"https://doi.org/10.30970/ms.59.2.141-155","url":null,"abstract":"The article is devoted to mappings with boundedand finite distortion of planar domains. Our investigations aredevoted to the connection between mappings of the Sobolev class andupper bounds for the distortion of the modulus of families of paths.For this class, we have proved the Poletsky-type inequality withrespect to the so-called inner dilatation of the order~$p.$ Weseparately considered the situations of homeomorphisms and mappingswith branch points. In particular, we have established thathomeomorphisms of the Sobolev class satisfy the upper estimate ofthe distortion of the modulus at the inner and boundary points ofthe domain. In addition, we have proved that similar estimates ofcapacity distortion occur at the inner points of the domain for opendiscrete mappings. Also, we have shown that open discrete and closedmappings satisfy some estimates of the distortion of the modulus offamilies of paths at the boundary points. The results of themanuscript are obtained mainly under the condition that theso-called inner dilatation of mappings is locally integrable. Themain approach used in the proofs is the choice of admissiblefunctions, using the relations between the modulus and capacity, andconnections between different modulus of families of paths (similarto Hesse, Ziemer and Shlyk equalities). In this context, we haveobtained some lower estimate of the modulus of families of paths inSobolev classes. The manuscript contains some examples related toapplications of obtained results to specific mappings.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42113188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Some class of numerical radius peak $n$-linear mappings on $l_p$-spaces l_p$-空间上的一类数值半径峰$n$-线性映射

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.10-15

S. Kim

{"title":"Some class of numerical radius peak $n$-linear mappings on $l_p$-spaces","authors":"S. Kim","doi":"10.30970/ms.57.1.10-15","DOIUrl":"https://doi.org/10.30970/ms.57.1.10-15","url":null,"abstract":"For $ngeq 2$ and a real Banach space $E,$ ${mathcal L}(^n E:E)$ denotes the space of all continuous $n$-linear mappings from $E$ to itself.Let $$Pi(E)=Big{[x^*, (x_1, ldots, x_n)]: x^{*}(x_j)=|x^{*}|=|x_j|=1~mbox{for}~{j=1, ldots, n}Big}.$$For $Tin {mathcal L}(^n E:E),$ we define $$qopnamerelax o{Nr}({T})=Big{[x^*, (x_1, ldots, x_n)]in Pi(E): |x^{*}(T(x_1, ldots, x_n))|=v(T)Big},$$where $v(T)$ denotes the numerical radius of $T$.$T$ is called {em numerical radius peak mapping} if there is $[x^{*}, (x_1, ldots, x_n)]in Pi(E)$ such that $qopnamerelax o{Nr}({T})={pm [x^{*}, (x_1, ldots, x_n)]}.$In this paper, we investigate some class of numerical radius peak mappings in ${mathcalL}(^n l_p:l_p)$ for $1leq p<infty.$ Let $(a_{j})_{jin mathbb{N}}$ be a bounded sequence in $mathbb{R}$ such that $sup_{jin mathbb{N}}|a_j|>0.$Define $Tin {mathcal L}(^n l_p:l_p)$ by$$TBig(sum_{iin mathbb{N}}x_i^{(1)}e_i, cdots, sum_{iin mathbb{N}}x_i^{(n)}e_i Big)=sum_{jin mathbb{N}}a_{j}~x_{j}^{(1)}cdots x_{j}^{(n)}~e_j.qquadeqno(*)$$In particular is proved the following statements:$1.$ If $1< p<+infty$ then $T$ is a numerical radius peak mapping if and only if there is $j_0in mathbb{N}$ such that$$|a_{j_0}|>|a_{j}|~mbox{for every}~jin mathbb{N}backslash{j_0}.$$ \u0000$2.$ If $p=1$ then $T$ is not a numerical radius peak mapping in ${mathcal L}(^n l_1:l_1).$","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48763694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Slice holomorphic functions in the unit ball: boundedness of $L$-index in a direction and related properties 单位球上的切片全纯函数:L -指标在一个方向上的有界性及相关性质

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.68-78

Andriy Ivanovych Bandura, T. Salo, O. Skaskiv

{"title":"Slice holomorphic functions in the unit ball: boundedness of $L$-index in a direction and related properties","authors":"Andriy Ivanovych Bandura, T. Salo, O. Skaskiv","doi":"10.30970/ms.57.1.68-78","DOIUrl":"https://doi.org/10.30970/ms.57.1.68-78","url":null,"abstract":"Let $mathbf{b}inmathbb{C}^nsetminus{mathbf{0}}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice ${z^0+tmathbf{b}: tinmathbb{C}}$ with the unit ball $mathbb{B}^n={zinmathbb{C}^: |z|:=sqrt{|z|_1^2+ldots+|z_n|^2}<1}$ for any $z^0inmathbb{B}^n$. For this class of functions we consider the concept of boundedness of $L$-index in the direction $mathbf{b},$ where $mathbf{L}: mathbb{B}^ntomathbb{R}_+$ is a positive continuous function such that $L(z)>frac{beta|mathbf{b}|}{1-|z|}$ and $beta>1$ is some constant.For functions from this class we deduce analog of Hayman's Theorem. It is criterion useful in applications todifferential equations. We introduce a concept of function having bounded value $L$-distribution in direction forthe slice holomorphic functions in the unit ball. It is proved that slice holomorphic function in the unit ball has bounded value $L$-distribution in a direction if and only if its directional derivative has bounded $L$-index in the same direction. Other propositions concern existence theorems. We show that for any slice holomorphic function $F$ with bounded multiplicities of zeros on any slice in the fixed direction there exists such a positive continuous function $L$that the function $F$ has bounded $L$-index in the direction.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41822251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 extent of a topological space 拓扑空间范围的界

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.62-67

A. Ravsky, T. Banakh

引用次数: 0

An exact constant on the estimation of the approximation of classes of periodic functions of two variables by Ceśaro means 用Ceśaro方法估计两个变量的周期函数类的近似的一个精确常数

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.3-9

O. Rovenska

{"title":"An exact constant on the estimation of the approximation of classes of periodic functions of two variables by Ceśaro means","authors":"O. Rovenska","doi":"10.30970/ms.57.1.3-9","DOIUrl":"https://doi.org/10.30970/ms.57.1.3-9","url":null,"abstract":"In the present work, we study problem related to the approximation of continuous $2pi$-periodic functions by linear means of their Fourier series. The simplest example of a linear approximation of periodic function is the approximation of this function by partial sums of the Fourier series. However, as well known, the sequence of partial Fourier sums is not uniformly convergent over the class of continuous $2pi$-periodic functions. Therefore, a significant number of papers is devoted to the research of the approximative properties of different approximation methods, which are generated by some transformations of the partial sums of the Fourier series. The methods allow us to construct sequence of trigonometrical polynomials that would be uniformly convergent for all functions $f in C$. Particularly, Ceśaro means and Fejer sums have been widely studied in past decades.One of the important problems in this field is the study of the exact constant in an inequality for upper bounds of linear means deviations of the Fourier sums on fixed classes of periodic functions. Methods of investigation of integral representations for trigonometric polynomial deviations are generated by linear methods of summation of the Fourier series. They were developed in papers of Nikolsky, Stechkin, Nagy and others. \u0000The paper presents known results related to the approximation of classes of continuous functions by linear means of the Fourier sums and new facts obtained for some particular cases.In the paper, it is studied the approximation by the Ceśaro means of Fourier sums in Lipschitz class. In certain cases, the exact inequalities are found for upper bounds of deviations in the uniform metric of the second order rectangular Ceśaro means on the Lipschitz class of periodic functions in two variables.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47765626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0