Georgian Mathematical Journal最新文献

{"title":"Existence and exponential stability of solutions for a Balakrishnan–Taylor quasilinear wave equation with strong damping and localized nonlinear damping","authors":"Zayd Hajjej","doi":"10.1515/gmj-2023-2105","DOIUrl":"https://doi.org/10.1515/gmj-2023-2105","url":null,"abstract":"Abstract In the paper, we study a Balakrishnan–Taylor quasilinear wave equation | z t | α ⁢ z t ⁢ t - Δ ⁢ z t ⁢ t - ( ξ 1 + ξ 2 ⁢ ∥ ∇ ⁡ z ∥ 2 + σ ⁢ ( ∇ ⁡ z , ∇ ⁡ z t ) ) ⁢ Δ ⁢ z - Δ ⁢ z t + β ⁢ ( x ) ⁢ f ⁢ ( z t ) + g ⁢ ( z ) = 0 |z_{t}|^{alpha}z_{tt}-Delta z_{tt}-bigl{(}xi_{1}+xi_{2}|nabla z|^{2}+% sigma(nabla z,nabla z_{t})bigr{)}Delta z-Delta z_{t}+beta(x)f(z_{t})+g(% z)=0 in a bounded domain of ℝ n {mathbb{R}^{n}} with Dirichlet boundary conditions. By using Faedo–Galerkin method, we prove the existence of global weak solutions. By the help of the perturbed energy method, the exponential stability of solutions is also established.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138943947","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":"A new fuzzy approach of vehicle routing problem for disaster-stricken zones","authors":"Gia Sirbiladze, Bezhan Ghvaberidze, Bidzina Midodashvili, Bidzina Matsaberidze, Irina Khutsishvili","doi":"10.1515/gmj-2023-2097","DOIUrl":"https://doi.org/10.1515/gmj-2023-2097","url":null,"abstract":"Route planning problems are among the activities that have the highest impact in emergency logistical planning, goods transportation and facility location-distribution because of their effects on efficiency in resource management, service levels and client satisfaction. In the extreme conditions, such as disaster-stricken zones, the difficulty of vehicle movement between nearest different affected areas (demand points) on planning routes cause the imprecision of time of movement and the uncertainty of feasibility of movement. In this paper, the imprecision is presented by triangular fuzzy numbers and the uncertainty is presented by a possibility measure. A new two-stage, fuzzy bi-criterion optimization approach for the vehicle routing problem (VRP) is considered. On the first stage, the sample of so-called “promising” closed routes are selected based on a “constructive” approach. On the second stage, triangular fuzzy valued Choquet aggregation (TFCA) operator is constructed for the selected closed routes. The evaluation of constructed routes, levels of failure and possibility of vehicle movement on the roads are aggregated by the TFCA operator by the new criterion – minimization of infeasibility of movement. The new criterion together with the classic criterion – minimization of the total distance traveled – creates a bi-criteria fuzzy VRP. The constructed VRP is reduced to the bi-criteria fuzzy partitioning problem, and an 𝜀-constraint approach is developed for solving it. For numerical experiments, a parallel algorithm is created on the basis of D. Knuth’s algorithm of Dancing Links (DLX). An example is presented with the results of our approach for the VRP, where all Pareto-optimal solutions are found from the set of promising routes. The optimal solutions tend to avoid roads that are problematic because of extreme situations.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579260","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":"Identities with generalized derivations on Lie ideals and Banach algebras","authors":"Abderrahman Hermas, Lahcen Oukhtite","doi":"10.1515/gmj-2023-2101","DOIUrl":"https://doi.org/10.1515/gmj-2023-2101","url":null,"abstract":"Let 𝑅 be a prime ring and 𝐿 a non-central Lie ideal of 𝑅. In this paper, we aim to classify the generalized derivations of 𝑅 satisfying some algebraic identities with power values on 𝐿. Moreover, the same identities are studied locally on a two nonvoid open subsets of a prime Banach algebra.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579564","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":"Additivity of multiplicative (generalized) skew semi-derivations on rings","authors":"Sk Aziz, Arindam Ghosh, Om Prakash","doi":"10.1515/gmj-2023-2100","DOIUrl":"https://doi.org/10.1515/gmj-2023-2100","url":null,"abstract":"In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it skew semi-derivation. Furthermore, we present a study of the conditions under which this type of multiplicative derivation becomes additive.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579478","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":"Concerning the Nakayama property of a module","authors":"Somayeh Karimzadeh, Esmaeil Rostami, Somayeh Hadjirezaei","doi":"10.1515/gmj-2023-2102","DOIUrl":"https://doi.org/10.1515/gmj-2023-2102","url":null,"abstract":"In this paper, we thoroughly study the Nakayama property and some related concepts. Also, we describe multiplication modules that, among other things, satisfy the Nakayama property. Next, we show that a ring 𝑅 is a Max ring if and only if all modules that can be generated by a finite or countable set have the weak Nakayama property. We prove that a ring 𝑅 is a perfect ring if and only if every module that can be generated by a finite or countable set has the Nakayama property. Finally, we present some categorical results on the aforementioned properties.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579492","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 Dirichlet problem in an infinite layer for a system of differential equations with shifts","authors":"Zinovii Nytrebych, Roman Shevchuk, Ivan Savka","doi":"10.1515/gmj-2023-2104","DOIUrl":"https://doi.org/10.1515/gmj-2023-2104","url":null,"abstract":"In this paper, we study the problem with data on the boundary of the infinite layer <jats:disp-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">{</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>t</m:mi> <m:mo>,</m:mo> <m:mi>x</m:mi> <m:mo rspace=\"0.278em\" stretchy=\"false\">)</m:mo> </m:mrow> <m:mo rspace=\"0.278em\">:</m:mo> <m:mrow> <m:mrow> <m:mi>t</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>h</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo rspace=\"0.337em\">,</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mi mathvariant=\"double-struck\">R</m:mi> <m:mi>s</m:mi> </m:msup> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">}</m:mo> </m:mrow> <m:mo rspace=\"1.167em\">,</m:mo> <m:mi>h</m:mi> </m:mrow> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> </m:mrow> <m:mo rspace=\"0.337em\">,</m:mo> <m:mrow> <m:mi>s</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant=\"double-struck\">N</m:mi> </m:mrow> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:math> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2104_eq_9999.png\" /> <jats:tex-math>{(t,x):tin(0,h),,xinmathbb{R}^{s}},quad h&gt;0,,sinmathbb{N},</jats:tex-math> </jats:alternatives> </jats:disp-formula> for the system of two differential equations of the second order in the time variable 𝑡 with shifts in the spatial variables <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi>x</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>x</m:mi> <m:mn>2</m:mn> </m:msub> <m:mo>,</m:mo> <m:mi mathvariant=\"normal\">…</m:mi> <m:mo>,</m:mo> <m:msub> <m:mi>x</m:mi> <m:mi>s</m:mi> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2104_ineq_0001.png\" /> <jats:tex-math>x_{1},x_{2},ldots,x_{s}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We propose a differential-symbol method of constructing a solution of the problem and identify a class of vector functions in which the obtained solution is unique. The method of solving the Dirichlet problem in the layer is illustrated by examples.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579385","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":"Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛","authors":"Mohd Rashid, Muzibur Rahman Mozumder, Mohd Anwar","doi":"10.1515/gmj-2023-2098","DOIUrl":"https://doi.org/10.1515/gmj-2023-2098","url":null,"abstract":"Let 𝑅 be a commutative ring with identity <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>1</m:mn> <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-2023-2098_ineq_0001.png\" /> <jats:tex-math>1neq 0</jats:tex-math> </jats:alternatives> </jats:inline-formula> and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>Z</m:mi> <m:mo>⁢</m:mo> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>R</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>′</m:mo> </m:msup> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2098_ineq_0002.png\" /> <jats:tex-math>Z(R)^{prime}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the set of all non-zero and non-unit elements of ring 𝑅. Further, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi mathvariant=\"normal\">Γ</m:mi> <m:mo>′</m:mo> </m:msup> <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:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2098_ineq_0003.png\" /> <jats:tex-math>Gamma^{prime}(R)</jats:tex-math> </jats:alternatives> </jats:inline-formula> denotes the cozero-divisor graph of 𝑅, is an undirected graph with vertex set <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>Z</m:mi> <m:mo>⁢</m:mo> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>R</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>′</m:mo> </m:msup> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2098_ineq_0002.png\" /> <jats:tex-math>Z(R)^{prime}</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:mi>w</m:mi> <m:mo>∉</m:mo> <m:mrow> <m:mi>z</m:mi> <m:mo>⁢</m:mo> <m:mi>R</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2098_ineq_0005.png\" /> <jats:tex-math>wnotin zR</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:mi>z</m:mi> <m:mo>∉</m:mo> <m:mrow> <m:mi>w</m:mi> <m:mo>⁢</m:mo> <m:mi>R</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2098_ineq_0006.png\" /> <jats:tex-math>znotin wR</jats:tex-math> </jats:alternatives> </jats:inline-formula> if and only if two distinct vertices 𝑤 and 𝑧 are adjacent, where <jats:","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138563869","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 a two-dimensional Dirichlet type problem for a linear hyperbolic equation of fourth order","authors":"Tariel Kiguradze, Reemah Alhuzally","doi":"10.1515/gmj-2023-2083","DOIUrl":"https://doi.org/10.1515/gmj-2023-2083","url":null,"abstract":"For a linear hyperbolic equation of fourth order, a Dirichlet type boundary problem in an orthogonally convex domain is investigated. Sharp sufficient conditions guaranteeing solvability and well-posedness of the problem under consideration are established.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517404","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 Euclidean operator radius","authors":"Mohammad W. Alomari, Mohammad Sababheh, Cristian Conde, Hamid Reza Moradi","doi":"10.1515/gmj-2023-2079","DOIUrl":"https://doi.org/10.1515/gmj-2023-2079","url":null,"abstract":"In this paper, we introduce the <jats:italic>f</jats:italic>-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the <jats:italic>q</jats:italic>-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504242","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":"Multi-dimensional almost automorphic type sequences and applications","authors":"Marko Kostić, Halis Can Koyuncuoğlu","doi":"10.1515/gmj-2023-2092","DOIUrl":"https://doi.org/10.1515/gmj-2023-2092","url":null,"abstract":"In this paper, we investigate several new classes of multi-dimensional almost automorphic type sequences and focus on their applications to various difference equations involving Volterra difference equations. We provide many structural results, illustrative examples and open problems about the notion under consideration.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517372","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}