Georgian Mathematical Journal最新文献

{"title":"Double lacunary statistical convergence of Δ-measurable functions on product time scales","authors":"Hemen Dutta, Pallav Bhattarai","doi":"10.1515/gmj-2023-2068","DOIUrl":"https://doi.org/10.1515/gmj-2023-2068","url":null,"abstract":"Abstract We first present a notion of a double lacunary sequence on product time scales. Using this notion, we define the notions of the double lacunary statistical convergence and double lacunary strongly p -Cesàro summability of 2-multiple functions on product time scales and we study some fundamental properties of both notions. We also present a theorem that connects the above-mentioned two concepts. Furthermore, we define a refinement of a double lacunary sequence on product time scales and provide some fundamental properties as well as inclusion theorems for a refined and a non-refined double lacunary sequence on product time scales.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547567","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}

{"title":"The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring","authors":"Malik Jaradat, Khaldoun Al-Zoubi","doi":"10.1515/gmj-2023-2075","DOIUrl":"https://doi.org/10.1515/gmj-2023-2075","url":null,"abstract":"Abstract Let G be a group. Let R be a G -graded commutative ring and let M be a graded R -module. A proper graded submodule Q of M is called a graded quasi-primary submodule if whenever <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>r</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mi>h</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>R</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {rin h(R)} and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>m</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mi>h</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {min h(M)} with <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>r</m:mi> <m:mo>⁢</m:mo> <m:mi>m</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>Q</m:mi> </m:mrow> </m:math> {rmin Q} , then either <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>r</m:mi> <m:mo>∈</m:mo> <m:mi>Gr</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>Q</m:mi> <m:msub> <m:mo>:</m:mo> <m:mi>R</m:mi> </m:msub> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {rinoperatorname{Gr}((Q:_{R}M))} or <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>m</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:msub> <m:mi>Gr</m:mi> <m:mi>M</m:mi> </m:msub> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>Q</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {minoperatorname{Gr}_{M}(Q)} . The graded quasi-primary spectrum <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mrow> <m:mi>qp</m:mi> <m:mo>.</m:mo> <m:mi>Spec</m:mi> </m:mrow> <m:mi>g</m:mi> </m:msub> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {mathop{rm qp.Spec}nolimits_{g}(M)} is defined to be the set of all graded quasi-primary submodules of M . In this paper, we introduce and study a topology on <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mrow> <m:mi>qp</m:mi> <m:mo>.</m:mo> <m:mi>Spec</m:mi> </m:mrow> <m:mi>g</m:mi> </m:msub> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {mathop{rm qp.Spec}nolimits_{g}(M)} , called the quasi-Zariski topology, and investigate the properties of this topology and some conditions under which <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>qp</m:mi> <m:mo>.</m:mo> <m:mi>Spec</m:mi> </m:mrow> <m:mi>g</m:mi> </m:msub> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> <m:mo>.</m:mo> <m:msup> <m:mi>τ</m:mi> <m:m","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547509","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}

{"title":"Solution of generalized fractional kinetic equations with generalized Mathieu series","authors":"Mehar Chand, Özen Özer, Jyotindra C. Prajapati","doi":"10.1515/gmj-2023-2064","DOIUrl":"https://doi.org/10.1515/gmj-2023-2064","url":null,"abstract":"Abstract We develop a new generalized form of the fractional kinetic equation involving the generalized Mathieu series. By using the Sumudu transform, a solution of these generalized fractional kinetic equation is obtained in terms of the Mittag-Leffler function. The numerical results and graphical interpretation are also presented.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135548382","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}

{"title":"The generalized Drazin inverse of an operator matrix with commuting entries","authors":"Huanyin Chen, Marjan Sheibani Abdolyousefi","doi":"10.1515/gmj-2023-2074","DOIUrl":"https://doi.org/10.1515/gmj-2023-2074","url":null,"abstract":"Abstract We present new results for the generalized Drazin inverse of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>2</m:mn> <m:mo>×</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {2times 2} anti-triangular matrices with commuting entries over a Banach algebra. As an application, the g -Drazin invertibility of block-operator matrices is obtained under new wider conditions.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135549143","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}

{"title":"New approach on the study of operator matrix","authors":"Ines Marzouk, Ines Walha","doi":"10.1515/gmj-2023-2071","DOIUrl":"https://doi.org/10.1515/gmj-2023-2071","url":null,"abstract":"Abstract In the present paper, a new technique is presented to study the problem of invertibility of unbounded block <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>3</m:mn> <m:mo>×</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> {3times 3} operator matrices defined with diagonal domain. Sufficient criteria are established to guarantee our interest and to prove some interaction between such a model of an operator matrix and its diagonal operator entries. The effectiveness of the proposed new technique is shown by a physical example of an integro differential equation named the neutron transport equation with partly elastic collision operators. In particular, the obtained results answer the question in [H. Zguitti, A note on Drazin invertibility for upper triangular block operators, Mediterr. J. Math. 10 2013, 3, 1497–1507] and the conjecture in [A. Bahloul and I. Walha, Generalized Drazin invertibility of operator matrices, Numer. Funct. Anal. Optim. 43 2022, 16, 1836–1847].","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547569","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}

{"title":"Frontmatter","authors":"","doi":"10.1515/gmj-2023-frontmatter5","DOIUrl":"https://doi.org/10.1515/gmj-2023-frontmatter5","url":null,"abstract":"","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134934698","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}

{"title":"Generalized inverse equations and SEP elements in a ring with involution","authors":"Mengge Guan, Junchao Wei","doi":"10.1515/gmj-2023-2067","DOIUrl":"https://doi.org/10.1515/gmj-2023-2067","url":null,"abstract":"Abstract In this paper, the generalized inverses and the solution of the generalized inverse equation in a specific set are used to characterize the SEP element in a ring with involution.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46188265","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}

{"title":"Multiplicity of solutions for Schrödinger–Bopp–Podolsky systems","authors":"Chun-Rong Jia, Lin Li, Shang-Jie Chen, Donal O’Regan","doi":"10.1515/gmj-2023-2058","DOIUrl":"https://doi.org/10.1515/gmj-2023-2058","url":null,"abstract":"Abstract In this paper, we study the existence and multiplicity of solutions for the Schrödinger–Bopp–Podolsky system { - Δ ⁢ u + V ⁢ ( x ) ⁢ u + ϕ ⁢ u = f ⁢ ( u ) + λ ⁢ | u | 4 ⁢ u in ⁢ ℝ 3 , - Δ ⁢ ϕ + a 2 ⁢ Δ 2 ⁢ ϕ = 4 ⁢ π ⁢ u 2 in ⁢ ℝ 3 , left{begin{aligned} displaystyle{-}Delta u+V(x)u+phi u&displaystyle=f(u% )+lambda|u|^{4}u&&displaystylephantom{}text{in }mathbb{R}^{3}, displaystyle{-}Deltaphi+a^{2}Delta^{2}phi&displaystyle=4pi u^{2}&&% displaystylephantom{}text{in }mathbb{R}^{3},end{aligned}right. where x ∈ ℝ 3 {xinmathbb{R}^{3}} , a > 0 {a>0} , V ⁢ ( x ) ∈ 𝒞 ⁢ ( ℝ 3 , ℝ ) {V(x)inmathcal{C}(mathbb{R}^{3},mathbb{R})} . Using variational methods and the symmetric mountain pass theorem, we establish the existence of multiple solutions for this system.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42390490","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}

{"title":"Exponential stability of the von Kármán system with internal damping","authors":"C. Raposo, Roseane Martins, J. Ribeiro, O. Vera","doi":"10.1515/gmj-2023-2063","DOIUrl":"https://doi.org/10.1515/gmj-2023-2063","url":null,"abstract":"Abstract This work deals with a von Kármán system with internal damping. For the solution’s existence, we use nonlinear semigroup theory tools. We construct an evolution system by nonlinear Lipschitz perturbation of a semigroup of contractions. We apply the energy method for the asymptotic behavior, which uses suitable multipliers to construct a Lyapunov functional that leads to exponential decay.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43170448","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}

{"title":"On the characterization of generalized (m, n)-Jordan *-derivations in prime rings","authors":"Mohammad Aslam Siddeeque, Abbas Hussain Shikeh","doi":"10.1515/gmj-2023-2060","DOIUrl":"https://doi.org/10.1515/gmj-2023-2060","url":null,"abstract":"Abstract Let 𝒜 {mathcal{A}} be a prime ring equipped with an involution ‘ * {*} ’ of order 2 and let m ≠ n {mneq n} be some fixed positive integers such that 𝒜 {mathcal{A}} is 2 ⁢ m ⁢ n ⁢ ( m + n ) ⁢ | m - n | {2mn(m+n)|m-n|} -torsion free. Let 𝒬 m ⁢ s ⁢ ( 𝒜 ) {mathcal{Q}_{ms}(mathcal{A})} be the maximal symmetric ring of quotients of 𝒜 {mathcal{A}} and consider the mappings ℱ {mathcal{F}} and 𝒢 : 𝒜 → 𝒬 m ⁢ s ⁢ ( 𝒜 ) {mathcal{G}:mathcal{A}tomathcal{Q}_{ms}(mathcal{A})} satisfying the relations ( m + n ) ⁢ ℱ ⁢ ( a 2 ) = 2 ⁢ m ⁢ ℱ ⁢ ( a ) ⁢ a * + 2 ⁢ n ⁢ a ⁢ ℱ ⁢ ( a ) (m+n)mathcal{F}(a^{2})=2mmathcal{F}(a)a^{*}+2namathcal{F}(a) and ( m + n ) ⁢ 𝒢 ⁢ ( a 2 ) = 2 ⁢ m ⁢ 𝒢 ⁢ ( a ) ⁢ a * + 2 ⁢ n ⁢ a ⁢ ℱ ⁢ ( a ) (m+n)mathcal{G}(a^{2})=2mmathcal{G}(a)a^{*}+2namathcal{F}(a) for all a ∈ 𝒜 {ainmathcal{A}} . Using the theory of functional identities and the structure of involutions on matrix algebras, we prove that if ℱ {mathcal{F}} and 𝒢 {mathcal{G}} are additive, then 𝒢 = 0 {mathcal{G}=0} . We also show that, in case ‘ * * ’ is any nonidentity anti-automorphism, the same conclusion holds if either ‘ * {*} ’ is not identity on 𝒵 ⁢ ( 𝒜 ) {mathcal{Z}(mathcal{A})} or 𝒜 {mathcal{A}} is a PI-ring.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48068063","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}