The paper discusses corrected Simpson-type inequalities on fractal sets. Based on an introduced identity, we establish some error bounds for the considered formula using the generalized s-convexity and s-concavity of the local fractional derivative. Finally, we present some graphical representations justifying the established theoretical framework as well as some applications.
本文讨论了分形集上的修正辛普森式不等式。基于引入的特性，我们利用局部分形导数的广义 s 凸性和 s 凹性为所考虑的公式建立了一些误差边界。最后，我们给出了一些图形表示，证明了所建立的理论框架以及一些应用。
{"title":"On corrected Simpson-type inequalities via local fractional integrals","authors":"Abdelghani Lakhdari, Badreddine Meftah, Wedad Saleh","doi":"10.1515/gmj-2024-2030","DOIUrl":"https://doi.org/10.1515/gmj-2024-2030","url":null,"abstract":"The paper discusses corrected Simpson-type inequalities on fractal sets. Based on an introduced identity, we establish some error bounds for the considered formula using the generalized <jats:italic>s</jats:italic>-convexity and <jats:italic>s</jats:italic>-concavity of the local fractional derivative. Finally, we present some graphical representations justifying the established theoretical framework as well as some applications.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532129","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}
Let m,n{m,n} be the fixed positive integers and let ℛ{mathcal{R}} be a ring. In 1978, Herstein proved that a 2-torsion free prime ring ℛ{mathcal{R}} is commutative if there is a nonzero derivation d of R such that [d(ϱ),d(ξ)]=0{[d(varrho),d(xi)]=0} for all ϱ,ξ∈R{varrho,xiin R}. In this article, we study the above mentioned classical result for higher derivations and describe the structure of semiprime rings by using the invariance property of prime ideals under higher derivations. Precisely, apart from proving some other important results, we prove the following. Let (di)
设 m , n {m,n} 是固定的正整数，设 ℛ {mathcal{R}} 是一个环。1978 年，赫斯坦证明，如果 R 有一个非零派生 d，使得 [ d ( ϱ ) , d ( ξ ) ] = 0 {[d(varrho),d(xi)]=0} 对于所有 ϱ , ξ∈ R {varrho,xiin R} 而言，那么 2 个无扭素数环ℛ {mathcal{R}} 是交换环。 .在本文中，我们将研究上述关于高阶引申的经典结果，并利用素理想在高阶引申下的不变性来描述半素环的结构。确切地说，除了证明其他一些重要结果之外，我们还证明了以下内容。设 ( d i ) i∈ ℕ {(d_{i})_{iinmathbb{N}}} 和 ( g j ) j∈ ℕ {(g_{j})_{jinmathbb{N}}} 是半椭圆环 ℛ {mathcal{R}} 的两个高阶衍，使得 [ d n ( ϱ ) 、 g m ( ξ ) ] ∈ Z ( ℛ ) {[d_{n}(varrho),g_{m}(xi)]in Z(mathcal{R})} for all ϱ , ξ ∈ ℐ {varrho,xiinmathcal{I}} 其中ℐ {mathcal{I}} 是ℛ {mathcal{R}} 的理想。 .那么，要么ℛ {mathcal{R}} 是交换式的，要么 ( d i ) i∈ ℕ {(d_{i})_{iinmathbb{N}}} 的某个线性组合将 Z ( ℛ ) {Z(mathcal{R})} 为零，或者 ( g j ) j∈ ℕ {(g_{j})_{jinmathbb{N}} 的某个线性组合使 Z ( ℛ ) {Z(mathcal{R})} 为零。我们用实例来丰富我们的结果，证明其假设的必要性。最后，我们以进一步研究的方向结束本文。
{"title":"Action of higher derivations on semiprime rings","authors":"Shakir Ali, Vaishali Varshney","doi":"10.1515/gmj-2024-2026","DOIUrl":"https://doi.org/10.1515/gmj-2024-2026","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0341.png\"/> <jats:tex-math>{m,n}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the fixed positive integers and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0224.png\"/> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a ring. In 1978, Herstein proved that a 2-torsion free prime ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0224.png\"/> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is commutative if there is a nonzero derivation <jats:italic>d</jats:italic> of <jats:italic>R</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ϱ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ξ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">]</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0157.png\"/> <jats:tex-math>{[d(varrho),d(xi)]=0}</jats:tex-math> </jats:alternatives> </jats:inline-formula> for all <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>ϱ</m:mi> <m:mo>,</m:mo> <m:mi>ξ</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>R</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0243.png\"/> <jats:tex-math>{varrho,xiin R}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In this article, we study the above mentioned classical result for higher derivations and describe the structure of semiprime rings by using the invariance property of prime ideals under higher derivations. Precisely, apart from proving some other important results, we prove the following. Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msub> <m:mi>d</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo stretchy=\"false\">)</m:mo","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504361","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}
In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform ℬα{mathscr{B}_{alpha}} in the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian equation and the time-dependent Dunkl–Schrödinger equation. The resolution of these types of problems is based on the techniques of the transmutation operators on the Dunkl-type Fock space ℱα(ℂd){mathscr{F}_{alpha}(mathbb{C}^{d})}.
{"title":"Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations","authors":"Fethi Soltani, Meriem Nenni","doi":"10.1515/gmj-2024-2031","DOIUrl":"https://doi.org/10.1515/gmj-2024-2031","url":null,"abstract":"In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">ℬ</m:mi> <m:mi>α</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2031_eq_0181.png\"/> <jats:tex-math>{mathscr{B}_{alpha}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> in the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian equation and the time-dependent Dunkl–Schrödinger equation. The resolution of these types of problems is based on the techniques of the transmutation operators on the Dunkl-type Fock space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi mathvariant=\"script\">ℱ</m:mi> <m:mi>α</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msup> <m:mi>ℂ</m:mi> <m:mi>d</m:mi> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2031_eq_0190.png\"/> <jats:tex-math>{mathscr{F}_{alpha}(mathbb{C}^{d})}</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504360","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}
Let H be a subgroup of a group G. We say that H is c-subnormal in G if there exists a subnormal subgroup T of G such that HT=G{HT=G} and H∩T⩽HG{Hcap Tleqslant H_{G}}, where HG{H_{G}} is the maximal normal subgroup of G which is contained in H. In this paper, we investigate the structure of a finite group G under the assumption that all maximal subgroups are c-subnormal subgroups and present some new conditions for supersolvability.
如果存在一个 G 的子正则子群 T，使得 H T = G {HT=G}，并且 H ∩ T ⩽ H G {Hcap Tleqslant H_{G}} ，我们就说 H 在 G 中是 c 正则子群。 本文研究了在所有最大子群都是 c-subnormal 子群的假设下有限群 G 的结构，并提出了一些新的超可溶条件。
{"title":"The influence of c-subnormality subgroups on the structure of finite groups","authors":"Dana Jaraden, Ali Ateiwi, Jehad Jaraden","doi":"10.1515/gmj-2024-2036","DOIUrl":"https://doi.org/10.1515/gmj-2024-2036","url":null,"abstract":"Let <jats:italic>H</jats:italic> be a subgroup of a group <jats:italic>G</jats:italic>. We say that <jats:italic>H</jats:italic> is <jats:italic>c</jats:italic>-subnormal in <jats:italic>G</jats:italic> if there exists a subnormal subgroup <jats:italic>T</jats:italic> of <jats:italic>G</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo></m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0064.png\"/> <jats:tex-math>{HT=G}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>∩</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>⩽</m:mo> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0065.png\"/> <jats:tex-math>{Hcap Tleqslant H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0073.png\"/> <jats:tex-math>{H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the maximal normal subgroup of <jats:italic>G</jats:italic> which is contained in <jats:italic>H</jats:italic>. In this paper, we investigate the structure of a finite group <jats:italic>G</jats:italic> under the assumption that all maximal subgroups are <jats:italic>c</jats:italic>-subnormal subgroups and present some new conditions for supersolvability.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532130","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}
Abstract We are interested in the solution of the Björling problem for timelike surfaces in R 1 4 mathbb{R}_{1}^{4} . The main contribution of the paper is to present new and many examples of timelike zero mean curvature surfaces and give their explicit parametric equations. In particular cases, one observes that the parametric equations of these surfaces coincide with the timelike minimal surfaces in Lorentz–Minkowski 3-space.
摘要 我们对 R 1 4 mathbb{R}_{1}^{4} 中时间状曲面的比约林问题的解很感兴趣。本文的主要贡献在于提出了许多新的时样零均值曲率曲面的例子，并给出了它们的显式参数方程。在特殊情况下，我们会发现这些曲面的参数方程与洛伦兹-闵科夫斯基 3 空间中的时间极小曲面重合。
{"title":"Timelike zero mean curvature surfaces in ℝ1 4","authors":"Seher Kaya","doi":"10.1515/gmj-2024-2028","DOIUrl":"https://doi.org/10.1515/gmj-2024-2028","url":null,"abstract":"Abstract We are interested in the solution of the Björling problem for timelike surfaces in R 1 4 mathbb{R}_{1}^{4} . The main contribution of the paper is to present new and many examples of timelike zero mean curvature surfaces and give their explicit parametric equations. In particular cases, one observes that the parametric equations of these surfaces coincide with the timelike minimal surfaces in Lorentz–Minkowski 3-space.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141360706","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}
Abstract In this study, the commutativity conditions with generalized derivations, which have not been examined before, are discussed. Under these conditions, the subject of generalized derivations in (semi)prime Banach algebras is studied. New fundamental results will be provided for researchers in this field and generalize some of the results found in the literature.
{"title":"Generalized derivation on semiprime and prime Banach algebras","authors":"Emine Koç Sögütcü","doi":"10.1515/gmj-2024-2027","DOIUrl":"https://doi.org/10.1515/gmj-2024-2027","url":null,"abstract":"Abstract In this study, the commutativity conditions with generalized derivations, which have not been examined before, are discussed. Under these conditions, the subject of generalized derivations in (semi)prime Banach algebras is studied. New fundamental results will be provided for researchers in this field and generalize some of the results found in the literature.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141357019","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}
Abstract In this paper, we are interested to formulate new assumptions on the entries of an unbounded 3 × 3 3times 3 block operator matrix defined with a maximal domain on the product of Banach spaces guaranteeing its corresponding Frobenius–Schur formula. Our approach allows us to derive some original stability results intervening in the theory of perturbed lower semi-Fredholm operators involving the concept of a measure of non-strict cosingularity perturbation. A new technique is presented to investigate the Weidmann and defect essential spectra of the closure of such model of operator matrix via new criterion of perturbation.
{"title":"On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix","authors":"S. Bouzidi, Ines Walha","doi":"10.1515/gmj-2024-2029","DOIUrl":"https://doi.org/10.1515/gmj-2024-2029","url":null,"abstract":"Abstract In this paper, we are interested to formulate new assumptions on the entries of an unbounded 3 × 3 3times 3 block operator matrix defined with a maximal domain on the product of Banach spaces guaranteeing its corresponding Frobenius–Schur formula. Our approach allows us to derive some original stability results intervening in the theory of perturbed lower semi-Fredholm operators involving the concept of a measure of non-strict cosingularity perturbation. A new technique is presented to investigate the Weidmann and defect essential spectra of the closure of such model of operator matrix via new criterion of perturbation.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141358483","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}
In this work, we establish a theorem concerning the extension of positive weak solutions for a stationary fractional Laplacian problem featuring weight functions that change sign. Additionally, we introduce novel conditions to ensure the existence of a positive solution for the given problem. These conditions are derived utilizing the approach of sub-super solutions, thereby extending and complementing existing results in the literature.
{"title":"Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions","authors":"R. Guefaifia, S. Boulaaras, Rashid Jan","doi":"10.1515/gmj-2024-2025","DOIUrl":"https://doi.org/10.1515/gmj-2024-2025","url":null,"abstract":"\u0000 In this work, we establish a theorem concerning the extension of positive weak solutions for a stationary fractional Laplacian problem featuring weight functions that change sign. Additionally, we introduce novel conditions to ensure the existence of a positive solution for the given problem. These conditions are derived utilizing the approach of sub-super solutions, thereby extending and complementing existing results in the literature.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140962280","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}
It is shown that there exists a Mazurkiewicz subset of the Euclidean plane containing the graph of some Sierpiński–Zygmund function.
研究表明，欧几里得平面存在一个马祖尔凯维奇子集，其中包含某个西尔皮斯基-齐格蒙函数的图形。
{"title":"A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function","authors":"Alexander Kharazishvili","doi":"10.1515/gmj-2024-2023","DOIUrl":"https://doi.org/10.1515/gmj-2024-2023","url":null,"abstract":"\u0000 It is shown that there exists a Mazurkiewicz subset of\u0000the Euclidean plane containing the graph of some Sierpiński–Zygmund function.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140659791","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}
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