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Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications 广义Orlicz-Sobolev空间中的插值不等式及其应用
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0595
Rui Wu, Songbai Wang
{"title":"Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications","authors":"Rui Wu, Songbai Wang","doi":"10.1515/math-2022-0595","DOIUrl":"https://doi.org/10.1515/math-2022-0595","url":null,"abstract":"Abstract Let m ∈ N min {mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces W m , φ ( R n ) {W}^{m,varphi }left({{mathbb{R}}}^{n}) . As applications, we established a compact Sobolev embedding on domain and a Landau-Kolmogorov-type inequality in generalized Orlicz spaces. And we introduced the Sobolev φ varphi -capacity and studied some of its properties.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49017020","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
Remarks on hyponormal Toeplitz operators with nonharmonic symbols 关于具有非调和符号的次正规Toeplitz算子的注记
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0114
Sumin Kim, Jongrak Lee
{"title":"Remarks on hyponormal Toeplitz operators with nonharmonic symbols","authors":"Sumin Kim, Jongrak Lee","doi":"10.1515/math-2023-0114","DOIUrl":"https://doi.org/10.1515/math-2023-0114","url":null,"abstract":"Abstract In this article, we present some necessary or sufficient conditions for the hyponormality of Toeplitz operator T φ {T}_{varphi } on the Bergman space A 2 ( D ) {A}^{2}left({mathbb{D}}) . In particular, we consider the Toeplitz operator T φ {T}_{varphi } with nonharmonic symbols φ varphi under certain assumptions.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49224333","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 multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering 逆散射中Steklov特征值问题的一种基于移位逆迭代的多网格离散化方法
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0607
Jiali Xie, H. Bi
{"title":"A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering","authors":"Jiali Xie, H. Bi","doi":"10.1515/math-2022-0607","DOIUrl":"https://doi.org/10.1515/math-2022-0607","url":null,"abstract":"Abstract Numerical methods for computing Steklov eigenvalues have attracted the attention of academia for their important physical background and wide applications. In this article we discuss the multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering, and give the error estimation of the proposed scheme. In addition, on the basis of the a posteriori error indicator, we design an adaptive multigrid algorithm. Finally, we present numerical examples to show the efficiency of the proposed scheme.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47328027","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
Note on differential identities on σ-prime rings with involution 有对合的σ-素环上的微分恒等式
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1142/s2811007223500050
M. Madni, M. R. Mozumder, W. Ahmed, A. Abbasi̇, A. Ramesh
{"title":"Note on differential identities on σ-prime rings with involution","authors":"M. Madni, M. R. Mozumder, W. Ahmed, A. Abbasi̇, A. Ramesh","doi":"10.1142/s2811007223500050","DOIUrl":"https://doi.org/10.1142/s2811007223500050","url":null,"abstract":"The major goal of this paper is to investigate the structure of [Formula: see text]-prime rings with involution, satisfying certain [Formula: see text]-differential identities involving [Formula: see text]-centralizing and some special type of products. We also provide an example which shows that center of [Formula: see text]-prime ring is not free from zero divisors.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"31 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76053136","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
Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications 完备CAT(0)空间中非扩张映射序列的平均遍历定理及其应用
4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0121
Sakan Termkaew, Parin Chaipunya, Fumiaki Kohsaka
{"title":"Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications","authors":"Sakan Termkaew, Parin Chaipunya, Fumiaki Kohsaka","doi":"10.1515/math-2023-0121","DOIUrl":"https://doi.org/10.1515/math-2023-0121","url":null,"abstract":"Abstract In this article, we prove ergodic convergence for a sequence of nonexpansive mappings in Hadamard (complete <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"normal\">CAT</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {rm{CAT}}left(0) ) spaces. Our result extends the nonlinear ergodic theorem by Baillon for nonexpansive mappings from Hilbert spaces to Hadamard spaces. We further establish the standard nonlinear ergodic theorem and apply our results to the problem of finding a common fixed point of a countable family of nonexpansive mappings. Finally, we propose some applications of our results to solve convex optimization problems in Hadamard spaces.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135913321","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 a class of stochastic differential equations driven by the generalized stochastic mixed variational inequalities 一类由广义随机混合变分不等式驱动的随机微分方程
4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0109
Qiaofeng Zeng, Chao Min, Feifei Fan
{"title":"On a class of stochastic differential equations driven by the generalized stochastic mixed variational inequalities","authors":"Qiaofeng Zeng, Chao Min, Feifei Fan","doi":"10.1515/math-2023-0109","DOIUrl":"https://doi.org/10.1515/math-2023-0109","url":null,"abstract":"Abstract A new class of stochastic differential equations (SDEs) is introduced in this article, which is driven by the generalized stochastic mixed variational inequality (GS-MVI). First, the property of the solution sets of the GS-MVI is proved by Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem and Aumann’s measurable selection theorem. Next, we obtain the Carathéodory property of the solution set, with which the discussed SDEs can be transformed to stochastic differential inclusions (SDIs). The solution set of the proposed SDEs is proved to be nonempty through the existence of the solutions of the corresponding SDIs by the tools of fixed point theorem.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136209861","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
Relay fusion frames in Banach spaces 巴拿赫空间中的中继融合帧
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0554
G. Hong, Pengtong Li
{"title":"Relay fusion frames in Banach spaces","authors":"G. Hong, Pengtong Li","doi":"10.1515/math-2022-0554","DOIUrl":"https://doi.org/10.1515/math-2022-0554","url":null,"abstract":"Abstract The relay fusion frames have been recently introduced in Hilbert spaces to model sensor relay networks and distributed sensor relay systems, which are deeply connected with compressed sensing. In this article, we introduce the notions of relay fusion frames and Banach relay fusion frames in Banach spaces and study certain attractive properties of relay fusion frames in this more general setting. In a particular sense, Schauder frames can be shown to be a special case of relay fusion frames. Moreover, the stability issue of relay fusion frames and Banach relay fusion frames will be addressed.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42208237","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
Finite spectrum of fourth-order boundary value problems with boundary and transmission conditions dependent on the spectral parameter 边界条件和传输条件依赖于谱参数的四阶边值问题的有限谱
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0110
Na Zhang, Ji-jun Ao
{"title":"Finite spectrum of fourth-order boundary value problems with boundary and transmission conditions dependent on the spectral parameter","authors":"Na Zhang, Ji-jun Ao","doi":"10.1515/math-2023-0110","DOIUrl":"https://doi.org/10.1515/math-2023-0110","url":null,"abstract":"Abstract A kind of fourth-order boundary value problem with eigenparameter-dependent boundary and transmission conditions is investigated. By constructing the characteristic function, we prove that the problems consist of a finite number of eigenvalues. We obtain that the number of eigenvalues of the problems not only depend on the order of the equation but also depend on the partition of the domain interval, the boundary conditions, and the eigenparameter-dependent transmission conditions.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42444548","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 unified perspective on some autocorrelation measures in different fields: A note 对不同领域一些自相关测度的统一观点:注
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0574
H. Yamada
{"title":"A unified perspective on some autocorrelation measures in different fields: A note","authors":"H. Yamada","doi":"10.1515/math-2022-0574","DOIUrl":"https://doi.org/10.1515/math-2022-0574","url":null,"abstract":"Abstract Using notions from linear algebraic graph theory, this article provides a unified perspective on some autocorrelation measures in different fields. They are as follows: (a) Orcutt’s first serial correlation coefficient, (b) Anderson’s first circular serial correlation coefficient, (c) Moran’s r 11 {r}_{11} , and (d) Moran’s I I . The first two are autocorrelation measures for one-dimensional data equally spaced, such as time series data, and the last two are for spatial data. We prove that (a)–(c) are a kind of (d). For example, we show that (d) such that its spatial weight matrix equals the adjacency matrix of a path graph is the same as (a). The perspective is beneficial because studying the properties of (d) leads to studying the properties of (a)–(c) at the same time. For example, the bounds of (a)–(c) can be found from the bounds of (d).","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47608467","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 2r-ideals in commutative rings with zero-divisors 零因子交换环中的2r理想
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0576
Khaled Alhazmy, F. Almahdi, E. M. Bouba, M. Tamekkante
{"title":"On 2r-ideals in commutative rings with zero-divisors","authors":"Khaled Alhazmy, F. Almahdi, E. M. Bouba, M. Tamekkante","doi":"10.1515/math-2022-0576","DOIUrl":"https://doi.org/10.1515/math-2022-0576","url":null,"abstract":"Abstract In this article, we are interested in uniformly p r pr -ideals with order ≤ 2 le 2 (which we call 2 r 2r -ideals) introduced by Rabia Üregen in [On uniformly pr-ideals in commutative rings, Turkish J. Math. 43 (2019), no. 4, 18781886]. Several characterizations and properties of these ideals are given. Moreover, the comparison between the (nonzero) 2 r 2r -ideals and certain classes of classical ideals gives rise to characterizations of certain rings based only on the properties of the ideals consisting only of zero-divisors. Namely, among other things, we compare the class of (nonzero) 2 r 2r -ideals with the class of (minimal) prime ideals, the class of minimal prime ideals and their squares, and the class of primary ideals. The study of 2 r 2r -ideal in polynomial rings allows us to give a new characterization of the rings satisfying the famous A A -property.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46609677","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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