Consider the triple $ left(M, g, dmuright)$ as a smooth metric measure space and $ M $ is an $n$-dimensional compact Riemannian manifold without boundary, also $dmu = e^{-f(x)}dV$ is a weighted measure. We are going to investigate the evolution problem for the first eigenvalue of the weighted $left(p, qright)$-Laplacian system along the rescaled Yamabe flow and we hope to find some monotonic quantities.
{"title":"Evolution of the first eigenvalue of the weighted $(p,q)$-Laplacian system under rescaled Yamabe flow","authors":"M. H. M. Kolaei, S. Azami","doi":"10.30495/JME.V0I0.1672","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1672","url":null,"abstract":"Consider the triple $ left(M, g, dmuright)$ as a smooth metric measure space and $ M $ is an $n$-dimensional compact Riemannian manifold without boundary, also $dmu = e^{-f(x)}dV$ is a weighted measure. We are going to investigate the evolution problem for the first eigenvalue of the weighted $left(p, qright)$-Laplacian system along the rescaled Yamabe flow and we hope to find some monotonic quantities.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49188953","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}
In this paper, we present a general version of operator Bellman inequality. Also, the refinement of inequality due to J. Aujla and F. Silva for the convex functions is given as well.
{"title":"New Bellman-type inequalities","authors":"R. Pashaei, M. Asgari","doi":"10.30495/JME.V0I0.1573","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1573","url":null,"abstract":"In this paper, we present a general version of operator Bellman inequality. Also, the refinement of inequality due to J. Aujla and F. Silva for the convex functions is given as well.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46979555","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}
Let G be a group and Aut^{phi}(G) denote the group of all automorphisms of G centralizing G/phi(G) elementwise. In this paper, we give a necessary and sufficient condition on a finite p-group G for the group Aut^{phi}(G) to be elementary abelian.
{"title":"A note on automorphisms of finite p-groups","authors":"R. Soleimani","doi":"10.30495/JME.V0I0.1484","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1484","url":null,"abstract":"Let G be a group and Aut^{phi}(G) denote the group of all automorphisms of G centralizing G/phi(G) elementwise. In this paper, we give a necessary and sufficient condition on a finite p-group G for the group Aut^{phi}(G) to be elementary abelian.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49081303","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}
Let $(R,mathfrak{m})$ is a $d$-dimensional Noetherian local ring and $T$ be a commutative strict algebra with unit element $1_T$ over $R$ such that $mathfrak{m}Tneq T$. We define almost exact sequences of $T$-modules and characterize almost flat $T$-modules. Moreover, we define almost (faithfully) flat homomorphisms between $R$-algebras $T$ and $W$, where $W$ has similar properties that $T$ has as an $R$-algebra. By almost (faithfully) flat homomorphisms and almost flat modules, we investigate Cousin complexes of $T$ and $W$-modules. Finally, for a finite filtration of length less than $d$ of $mathrm{Spec}(T)$, $mathcal{F}=(F_i)_{igeq0}$ such that admits a $T$-module $X$, we show that $^Imathrm{E}_{p,q}^2:=mathrm{Tor}_p^T left(M,mathrm{H}^{d-q}left(mathcal{C}_Tleft(mathcal{F},Xright)right)right) stackrel{p}{Rightarrow}mathrm{H}_{p+q}(mathrm{Tot}(mathcal{T}))$ and $^{II}mathrm{E}_{p,q}^2:=mathrm{H}^{d-p}left(mathrm{Tor}_q^Tleft(M,mathcal{C}_Tleft(mathcal{F},Xright)right)right) stackrel{p}{Rightarrow}mathrm{H}_{p+q}(mathrm{Tot}(mathcal{T}))$, where $M$ is an any flat $T$-module and as result we show that $^Imathrm{E}_{p,q}^2$ and $^{II}mathrm{E}_{p,q}^2$ are almost zero, when $M$ is almost flat.
{"title":"Cousin Complexes and almost flat rings","authors":"Nesa Eshagh Nimvari, S. O. Faramarzi","doi":"10.30495/JME.V0I0.1504","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1504","url":null,"abstract":"Let $(R,mathfrak{m})$ is a $d$-dimensional Noetherian local ring and $T$ be a commutative strict algebra with unit element $1_T$ over $R$ such that $mathfrak{m}Tneq T$. We define almost exact sequences of $T$-modules and characterize almost flat $T$-modules. Moreover, we define almost (faithfully) flat homomorphisms between $R$-algebras $T$ and $W$, where $W$ has similar properties that $T$ has as an $R$-algebra. By almost (faithfully) flat homomorphisms and almost flat modules, we investigate Cousin complexes of $T$ and $W$-modules. Finally, for a finite filtration of length less than $d$ of $mathrm{Spec}(T)$, $mathcal{F}=(F_i)_{igeq0}$ such that admits a $T$-module $X$, we show that $^Imathrm{E}_{p,q}^2:=mathrm{Tor}_p^T left(M,mathrm{H}^{d-q}left(mathcal{C}_Tleft(mathcal{F},Xright)right)right) stackrel{p}{Rightarrow}mathrm{H}_{p+q}(mathrm{Tot}(mathcal{T}))$ and $^{II}mathrm{E}_{p,q}^2:=mathrm{H}^{d-p}left(mathrm{Tor}_q^Tleft(M,mathcal{C}_Tleft(mathcal{F},Xright)right)right) stackrel{p}{Rightarrow}mathrm{H}_{p+q}(mathrm{Tot}(mathcal{T}))$, where $M$ is an any flat $T$-module and as result we show that $^Imathrm{E}_{p,q}^2$ and $^{II}mathrm{E}_{p,q}^2$ are almost zero, when $M$ is almost flat.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48580008","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}
We study weighted Dirichlet type spaces in the unit disk. We prove that analytic polynomials are dense in weighted Dirichlet type spaces if the (non-radial) weight function is super-biharmonic and satisfies a growth condition up to the boundary.
{"title":"Density of polynomials in certain weighted Dirichlet type spaces","authors":"A. Abkar","doi":"10.30495/JME.V0I0.1771","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1771","url":null,"abstract":"We study weighted Dirichlet type spaces in the unit disk. We prove that analytic polynomials are dense in weighted Dirichlet type spaces if the (non-radial) weight function is super-biharmonic and satisfies a growth condition up to the boundary.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43371990","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}
Abstract. The concept of 2-normed spaces and 2-Banach spacesare considerd as generalization of normed and Banach spaces. Inthe present paper we have studied the existence of square rootsand quasi square roots of some elements of a 2-Banach algebra.Also relation between nth roots and quasi nth root of elements of2-Banach algebras are considered.
{"title":"ON SQUARE ROOTS AND QUASI-SQUARE ROOTS OF ELEMENTS OF 2-NORMED ALGEBRAS","authors":"A. Zohri","doi":"10.30495/JME.V0I0.1545","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1545","url":null,"abstract":"Abstract. The concept of 2-normed spaces and 2-Banach spacesare considerd as generalization of normed and Banach spaces. Inthe present paper we have studied the existence of square rootsand quasi square roots of some elements of a 2-Banach algebra.Also relation between nth roots and quasi nth root of elements of2-Banach algebras are considered.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43744949","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}
Recently, absolute value equations (AVEs) are lied in theconsideration center of some researchers since they are very suitable al-ternatives for many frequently occurring optimization problems. There-fore, nding a fast solution method for these type of problems is verysignicant. In this paper, based on the mixed-type splitting (MTS) ideafor solving linear system of equations, a new fast algorithm for solvingAVEs is presented. This algorithm has two auxiliary matrices whichare limited to be nonnegative strictly lower triangular and nonnega-tive diagonal matrices. The convergence of the algorithm is discussedvia some theorems. In addition, it is shown that by suitable choice ofthe auxiliary matrices, the convergence rate of this algorithm is fasterthan that of the SOR, AOR, Generalized Newton, Picard and SOR-like methods. Eventually, some numerical results for dierent size ofproblem dimensionality are presented which admit the credibility of theproposed algorithm.
{"title":"An efficient algorithm for solving absolute value equations","authors":"A. Fakharzadeh, N. Shams","doi":"10.30495/JME.V0I0.1393","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1393","url":null,"abstract":"Recently, absolute value equations (AVEs) are lied in theconsideration center of some researchers since they are very suitable al-ternatives for many frequently occurring optimization problems. There-fore, nding a fast solution method for these type of problems is verysignicant. In this paper, based on the mixed-type splitting (MTS) ideafor solving linear system of equations, a new fast algorithm for solvingAVEs is presented. This algorithm has two auxiliary matrices whichare limited to be nonnegative strictly lower triangular and nonnega-tive diagonal matrices. The convergence of the algorithm is discussedvia some theorems. In addition, it is shown that by suitable choice ofthe auxiliary matrices, the convergence rate of this algorithm is fasterthan that of the SOR, AOR, Generalized Newton, Picard and SOR-like methods. Eventually, some numerical results for dierent size ofproblem dimensionality are presented which admit the credibility of theproposed algorithm.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"15 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41500149","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}
In this paper we will introduce the integral closure of a filtration relative to an injective module.
在本文中，我们将介绍关于内射模的过滤的积分闭包。
{"title":"INTEGRAL CLOSURE OF A FILTRATION RELATIVE TO AN INJECTIVE MODULE","authors":"F. Dorostkar","doi":"10.30495/JME.V0I0.1574","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1574","url":null,"abstract":"In this paper we will introduce the integral closure of a filtration relative to an injective module.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45469552","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}
In this paper,under growth conditions on the nonlinearity, we obtain the existence of at least three weak solutions for some singular elliptic Dirichlet problems involving the $p$-Laplacian. The approach is based on variational methods and critical point theory.
{"title":"Existence of three weak solutions for some singular elliptic problems with Hardy potential","authors":"M. R. H. Tavani, M. Khodabakhshi","doi":"10.30495/JME.V0I0.1571","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1571","url":null,"abstract":"In this paper,under growth conditions on the nonlinearity, we obtain the existence of at least three weak solutions for some singular elliptic Dirichlet problems involving the $p$-Laplacian. The approach is based on variational methods and critical point theory.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42149984","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}
In this paper, we introduce the concept of F-G-contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F-metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results.
{"title":"Some fixed point results for F-G-contraction in F-metric spaces endowed with a graph","authors":"H. Faraji, S. Radenović","doi":"10.30495/JME.V0I0.1513","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1513","url":null,"abstract":"In this paper, we introduce the concept of F-G-contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F-metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49057671","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}
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