Matematychni Studii最新文献_第6页

Identities on additive mappings in semiprime rings 半素环上加性映射的恒等式

Matematychni Studii Pub Date : 2023-01-16 DOI: 10.30970/ms.58.2.133-141

A. Z. Ansari, N. Rehman

引用次数: 0

3D geometric moment invariants from the point of view of the classical invariant theory 从经典不变量理论的角度研究三维几何矩不变量

Matematychni Studii Pub Date : 2023-01-16 DOI: 10.30970/ms.58.2.115-132

L. P. Bedratyuk, A. I. Bedratyuk

引用次数: 2

On regular variation of entire Dirichlet series 关于整个Dirichlet级数的正则变分

Matematychni Studii Pub Date : 2023-01-16 DOI: 10.30970/ms.58.2.174-181

P. Filevych, O. B. Hrybel

{"title":"On regular variation of entire Dirichlet series","authors":"P. Filevych, O. B. Hrybel","doi":"10.30970/ms.58.2.174-181","DOIUrl":"https://doi.org/10.30970/ms.58.2.174-181","url":null,"abstract":"Consider an entire (absolutely convergent in $mathbb{C}$) Dirichlet series $F$ with the exponents $lambda_n$, i.e., of the form $F(s)=sum_{n=0}^infty a_ne^{slambda_n}$, and, for all $sigmainmathbb{R}$, put $mu(sigma,F)=max{|a_n|e^{sigmalambda_n}:nge0}$ and $M(sigma,F)=sup{|F(s)|:operatorname{Re}s=sigma}$. Previously, the first of the authors and M.M.~Sheremeta proved that if $omega(lambda)<C(rho)$, then the regular variation of the function $lnmu(sigma,F)$ with index $rho$ implies the regular variation of the function $ln M(sigma,F)$ with index $rho$, and constructed examples of entire Dirichlet series $F$, for which $lnmu(sigma,F)$ is a regularly varying function with index $rho$, and $ln M(sigma,F)$ is not a regularly varying function with index $rho$. For the exponents of the constructed series we have $lambda_n=lnln n$ for all $nge n_0$ in the case $rho=1$, and $lambda_nsim(ln n)^{(rho-1)/rho}$ as $ntoinfty$ in the case $rho>1$. In the present article we prove that the exponents of entire Dirichlet series with the same property can form an arbitrary sequence $lambda=(lambda_n)_{n=0}^infty$ not satisfying $omega(lambda)<C(rho)$. More precisely, if $omega(lambda)ge C(rho)$, then there exists a regularly varying function $Phi(sigma)$ with index $rho$ such that, for an arbitrary positive function $l(sigma)$ on $[a,+infty)$, there exists an entire Dirichlet series $F$ with the exponents $lambda_n$, for which $ln mu(sigma, F)simPhi(sigma)$ as $sigmato+infty$ and $M(sigma,F)ge l(sigma)$ for all $sigmagesigma_0$.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46614713","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

On a semitopological semigroup $boldsymbol{B}_{omega}^{mathscr{F}}$ when a family $mathscr{F}$ consists of inductive non-empty subsets of $omega$ 关于半拓扑半群$boldsymbol{B}_｛omega｝^｛mathscr｛F｝｝$当一个族$mathscr{F｝$由$omega的归纳非空子集组成时$

Matematychni Studii Pub Date : 2022-12-11 DOI: 10.30970/ms.59.1.20-28

O. Gutik, M. Mykhalenych

{"title":"On a semitopological semigroup $boldsymbol{B}_{omega}^{mathscr{F}}$ when a family $mathscr{F}$ consists of inductive non-empty subsets of $omega$","authors":"O. Gutik, M. Mykhalenych","doi":"10.30970/ms.59.1.20-28","DOIUrl":"https://doi.org/10.30970/ms.59.1.20-28","url":null,"abstract":"Let $boldsymbol{B}_{omega}^{mathscr{F}}$ be the bicyclic semigroup extension for the family $mathscr{F}$ of ${omega}$-closed subsets of $omega$ which is introduced in cite{Gutik-Mykhalenych=2020}.We study topologizations of the semigroup $boldsymbol{B}_{omega}^{mathscr{F}}$ for the family $mathscr{F}$ of inductive ${omega}$-closed subsets of $omega$. We generalize Eberhart-Selden and Bertman-West results about topologizations of the bicyclic semigroup cite{Bertman-West-1976, Eberhart-Selden=1969} and show that every Hausdorff shift-continuous topology on the semigroup $boldsymbol{B}_{omega}^{mathscr{F}}$ is discrete and if a Hausdorff semitopological semigroup $S$ contains $boldsymbol{B}_{omega}^{mathscr{F}}$ as a proper dense subsemigroup then $Ssetminusboldsymbol{B}_{omega}^{mathscr{F}}$ is an ideal of $S$. Also, we prove the following dichotomy: every Hausdorff locally compact shift-continuous topology on $boldsymbol{B}_{omega}^{mathscr{F}}$ with an adjoined zero is either compact or discrete. As a consequence of the last result we obtain that every Hausdorff locally compact semigroup topology on $boldsymbol{B}_{omega}^{mathscr{F}}$ with an adjoined zero is discrete and every Hausdorff locally compact shift-continuous topology on the semigroup $boldsymbol{B}_{omega}^{mathscr{F}}sqcup I$ with an adjoined compact ideal $I$ is either compact or the ideal $I$ is open, which extent many results about locally compact topologizations of some classes of semigroups onto extensions of the semigroup $boldsymbol{B}_{omega}^{mathscr{F}}$.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46389928","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

On the trace of permuting tri-derivations on rings 环上置换三导的迹

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.20-25

D. Yılmaz, H. Yazarli

引用次数: 0

Note on boundedness of the $L$-index in the direction of the composition of slice entire functions 注意在切片整个函数的合成方向上$L$-索引的有界性

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.58-68

V. Baksa, Andriy Ivanovych Bandura, T. Salo, O. Skaskiv

{"title":"Note on boundedness of the $L$-index in the direction of the composition of slice entire functions","authors":"V. Baksa, Andriy Ivanovych Bandura, T. Salo, O. Skaskiv","doi":"10.30970/ms.58.1.58-68","DOIUrl":"https://doi.org/10.30970/ms.58.1.58-68","url":null,"abstract":"We study a composition of two functions belonging to a class of slice holomorphic functions in the whole $n$-dimensional complex space. The slice holomorphy in the space means that for some fixed direction $mathbf{b}inmathbb{C}^nsetminus{mathbf{0}}$ and for every point $z^0inmathbb{C}^n$ the function is holomorphic on its restriction on the slice ${z^0+tmathbf{b}: tinmathbb{C}}.$ An additional assumption on joint continuity for these functions allows to construct an analog of theory of entire functions having bounded index. The analog is applicable to study properties of slice holomorphic solutions of directional differential equations, describe local behavior and value distribution.In particular, we found conditions providing boundedness of $L$-index in the direction $mathbf{b}$ for a function $f(underbrace{Phi(z),ldots,Phi(z)}_{mtext{ times}}),$where $f: mathbb{C}^ntomathbb{C}$ is a slice entire function, $Phi: mathbb{C}^ntomathbb{C}$ is a slice entire function,${L}: mathbb{C}^ntomathbb{R}_+$ is a continuous function.The obtained results are also new in one-dimensional case, i.e. for $n=1,$ $m=1.$ They are deduced using new approach in this area analog of logarithmic criterion.For a class of nonvanishing outer functions in the composition the sufficient conditions obtained by logarithmic criterion are weaker than the conditions by the Hayman theorem.","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":"47041447","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

Minimal growth of entire functions with prescribed zeros outside exceptional sets 例外集外具有指定零的整函数的最小增长

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.51-57

I. Andrusyak, P. Filevych, O. Oryshchyn

引用次数: 0

The sharp bound of the third Hankel determinants for inverse of starlike functions with respect to symmetric points 关于对称点的星形函数逆的第三汉克尔行列式的锐界

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.45-50

B. Ráth, D. V. Krishna, K. S. Kumar, G. K. S. Viswanadh

引用次数: 3

On the convergence of Kurchatov-type methods using recurrent functions for solving equations 用递归函数求解方程的kurchatov型方法的收敛性

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.103-112

I. Argyros, S. Shakhno, H. Yarmola

引用次数: 1

On graded WAG2-absorbing submodule 梯度wag2吸收子模块

Matematychni Studii Pub Date : 2022-10-31 DOI: 10.30970/ms.58.1.13-19

K. Al-Zoubi, Mariam Al-Azaizeh

{"title":"On graded WAG2-absorbing submodule","authors":"K. Al-Zoubi, Mariam Al-Azaizeh","doi":"10.30970/ms.58.1.13-19","DOIUrl":"https://doi.org/10.30970/ms.58.1.13-19","url":null,"abstract":"Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded $WAG2$-absorbing submodule. A number of results concerning of these classes of graded submodules and their homogeneous components are given. \u0000Let $N=bigoplus _{hin G}N_{h}$ be a graded submodule of $M$ and $hin G.$ We say that $N_{h}$ is a $h$-$WAG2$-absorbing submodule of the $R_{e}$-module $M_{h}$ if $N_{h}neq M_{h}$; and whenever $r_{e},s_{e}in R_{e}$ and $m_{h}in M_{h}$ with $0neq r_{e}s_{e}m_{h}in N_{h}$, then either $%r_{e}^{i}m_{h}in N_{h}$ or $s_{e}^{j}m_{h}in N_{h}$ or $%(r_{e}s_{e})^{k}in (N_{h}:_{R_{e}}M_{h})$ for some $i,$ $j,$ $k$ $inmathbb{N}.$ We say that $N$ is {a graded }$WAG2${-absorbing submodule of }$M$ if $Nneq M$; and whenever $r_{g},s_{h}in h(R)$ and $%m_{lambda }in h(M)$ with $0neq r_{g}s_{h}m_{lambda }in N$, then either $r_{g}^{i}m_{lambda }in N$ or $s_{h}^{j}m_{lambda }in N$ or $%(r_{g}s_{h})^{k}in (N:_{R}M)$ for some $i,$ $j,$ $k$ $in mathbb{N}.$ In particular, the following assertions have been proved: \u0000Let $R$ be a $G$-graded ring, $M$ a graded cyclic $R$-module with $%Gr((0:_{R}M))=0$ and $N$ a graded submodule of $M.$ If $N$ is a graded $WAG2$% {-absorbing submodule of }$M,$ thenlinebreak $Gr((N:_{R}M))$ is a graded $WAG2$% -absorbing ideal of $R$ (Theorem 4).Let $R_{1}$ and $R_{2}$ be a $G$-graded rings. Let $R=R_{1}bigoplus R_{2}$ be a $G$-graded ring and $M=M_{1}bigoplus M_{2}$ a graded $R$-module. Let $N_{1},$ $N_{2}$ be a proper graded submodule of $M_{1}$, $M_{2}$ respectively. If $N=N_{1}bigoplus N_{2}$ is a graded $WAG2$-absorbing submodule of $M,$ then $N_{1}$ and $N_{2}$ are graded weakly primary submodule of $R_{1}$-module $M_{1},$ $R_{2}$-module $M_{2},$ respectively. Moreover, If $N_{2}neq 0$ $(N_{1}neq 0),$ then $N_{1}$ is a graded weak primary submodule of $R_{1}$-module $M_{1}$ $(N_{2}$ is a graded weak primary submodule of $R_{2}$-module $M_{2})$ (Theorem 7).","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":"43887036","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