Let $L$ be a finite Orthomodular Lattice and $T$ be the Formal Context of $L$. Then, considering $T$ as a binary symmetric matrix, we find the determinant of the formal context of the atomic amalgam $B_n+B_m$ of two Boolean algebras $mathbf{B_{n}}$ and $mathbf{B_{m}}$ consisting of $n$ and $m$ atoms, respectively using the Schur complement formulacite{p28}. We present the proofs of some preliminary results on the determinant of the context table of the Boolean algebra $B_{n}$ and the characteristic polynomial of $B_{n}$. These preliminary results are used in many applications in graph theory.
{"title":"PROPERTIES OF THE FORMAL CONTEXT OF ORTHOMODULAR LATTICES","authors":"S. Shabnam, Ramananda Hs, Harsha Aj","doi":"10.37418/amsj.11.10.8","DOIUrl":"https://doi.org/10.37418/amsj.11.10.8","url":null,"abstract":"Let $L$ be a finite Orthomodular Lattice and $T$ be the Formal Context of $L$. Then, considering $T$ as a binary symmetric matrix, we find the determinant of the formal context of the atomic amalgam $B_n+B_m$ of two Boolean algebras $mathbf{B_{n}}$ and $mathbf{B_{m}}$ consisting of $n$ and $m$ atoms, respectively using the Schur complement formulacite{p28}. We present the proofs of some preliminary results on the determinant of the context table of the Boolean algebra $B_{n}$ and the characteristic polynomial of $B_{n}$. These preliminary results are used in many applications in graph theory.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124750915","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 the present paper, a new characterization of the orthogonality of a monic polynomials sequence $left{ Q_{n}right} _{ngeq 0}$ is obtained. This is defined as a linear combination of another monic orthogonal polynomials sequence $left{ P_{n}right} _{ngeq 0}$ such as% begin{equation*} Q_{n}(x)+r_{n}Q_{n-1}(x)=P_{n}(x)+s_{n}P_{n-1}(x)+t_{n}P_{n-2}left( xright) +v_{n}P_{n-3}left( xright) +w_{n}P_{n-4}(x), ngeq 0 end{equation*}% where $w_{n}r_{n}neq 0,$ for every $ngeq 5.$ Futhermore, the relation between the corresponding linear functionals is showed to be begin{equation*} kleft( x-cright) u=left( x^{4}+ax^{3}+bx^{2}+dx+eright) v end{equation*}% where $c,$ $a,$ $b,$ $d,$ $ein mathbb{C}$ and $kin mathbb{C}backslash{0}.$ Finally, an illustration using special case of the above type relation is given.
本文给出了一元多项式序列$left{ Q_{n}right} _{ngeq 0}$正交性的一个新性质。这被定义为另一个单正交多项式序列$left{ P_{n}right} _{ngeq 0}$的线性组合，例如% begin{equation*} Q_{n}(x)+r_{n}Q_{n-1}(x)=P_{n}(x)+s_{n}P_{n-1}(x)+t_{n}P_{n-2}left( xright) +v_{n}P_{n-3}left( xright) +w_{n}P_{n-4}(x), ngeq 0 end{equation*}% where $w_{n}r_{n}neq 0,$ for every $ngeq 5.$ Futhermore, the relation between the corresponding linear functionals is showed to be begin{equation*} kleft( x-cright) u=left( x^{4}+ax^{3}+bx^{2}+dx+eright) v end{equation*}% where $c,$ $a,$ $b,$ $d,$ $ein mathbb{C}$ and $kin mathbb{C}backslash{0}.$ Finally, an illustration using special case of the above type relation is given.
{"title":"A COMBINATION OF ORTHOGONAL POLYNOMIALS SEQUENCES: 2-5 TYPE RELATION","authors":"A. Belkebir, M. Bouras","doi":"10.37418/amsj.11.10.7","DOIUrl":"https://doi.org/10.37418/amsj.11.10.7","url":null,"abstract":"In the present paper, a new characterization of the orthogonality of a monic polynomials sequence $left{ Q_{n}right} _{ngeq 0}$ is obtained. This is defined as a linear combination of another monic orthogonal polynomials sequence $left{ P_{n}right} _{ngeq 0}$ such as% begin{equation*} Q_{n}(x)+r_{n}Q_{n-1}(x)=P_{n}(x)+s_{n}P_{n-1}(x)+t_{n}P_{n-2}left( xright) +v_{n}P_{n-3}left( xright) +w_{n}P_{n-4}(x), ngeq 0 end{equation*}% where $w_{n}r_{n}neq 0,$ for every $ngeq 5.$ Futhermore, the relation between the corresponding linear functionals is showed to be begin{equation*} kleft( x-cright) u=left( x^{4}+ax^{3}+bx^{2}+dx+eright) v end{equation*}% where $c,$ $a,$ $b,$ $d,$ $ein mathbb{C}$ and $kin mathbb{C}backslash{0}.$ Finally, an illustration using special case of the above type relation is given.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125409603","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}
The notion of compatible mappings of type $(K)$ in metric space has been introduced by K. Jha, V. Popa, and K.B. Manandhar in 2014. In this paper, we use Meir-Keeler contractive type condition and establish a common fixed point theorem in Menger probabilistic metric space by using compatible mappings of type $(K)$. Our results generalize and improve several similar known results in the literature.
{"title":"A COMMON FIXED POINT THEOREM IN MENGER SPACE WITH COMPATIBLE MAPPING OF TYPE (K)","authors":"A.J. Chaudhary, K. Jha, K. B. Manandhar","doi":"10.37418/amsj.11.10.6","DOIUrl":"https://doi.org/10.37418/amsj.11.10.6","url":null,"abstract":"The notion of compatible mappings of type $(K)$ in metric space has been introduced by K. Jha, V. Popa, and K.B. Manandhar in 2014. In this paper, we use Meir-Keeler contractive type condition and establish a common fixed point theorem in Menger probabilistic metric space by using compatible mappings of type $(K)$. Our results generalize and improve several similar known results in the literature.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116239603","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 establish the generalized $n^{th}$-Order Opial's integral inequality via (p,q)-calculus with some extensions. The other analytical tools used to establish the results were $(p,q)$-Cauchy repeated integration formula and $(p,q)$-Cauchy-Schwarz's integral inequality.
{"title":"GENERALIZATION OF THE $n^{th}$-ORDER OPIAL'S INEQUALITY IN $(p,q)$-CALCULUS","authors":"M. M. Iddrisu, B. Abubakari, J. López-Bonilla","doi":"10.37418/amsj.11.10.5","DOIUrl":"https://doi.org/10.37418/amsj.11.10.5","url":null,"abstract":"We establish the generalized $n^{th}$-Order Opial's integral inequality via (p,q)-calculus with some extensions. The other analytical tools used to establish the results were $(p,q)$-Cauchy repeated integration formula and $(p,q)$-Cauchy-Schwarz's integral inequality.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114420901","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 study the graphic topology $mathcal{T}_{G}$ for a fuzzy graph. We give some properties of this topology, in particular we prove that $mathcal{T}_{G}$ is an Alexandroff topology and when two graphs are isomorphic, their graphic topologies will be homeomorphic. We give some properties matching graphs and homeomorphic topology spaces. Finally, we investigate the connectedness of this topology and some relations between the connectedness of the graph and the topology $mathcal{T}_{G}$.
{"title":"GRAPHIC TOPOLOGY ON FUZZY GRAPHS","authors":"A. M. Alzubaidi, M. Dammak","doi":"10.37418/amsj.11.10.4","DOIUrl":"https://doi.org/10.37418/amsj.11.10.4","url":null,"abstract":"In this paper, we study the graphic topology $mathcal{T}_{G}$ for a fuzzy graph. We give some properties of this topology, in particular we prove that $mathcal{T}_{G}$ is an Alexandroff topology and when two graphs are isomorphic, their graphic topologies will be homeomorphic. We give some properties matching graphs and homeomorphic topology spaces. Finally, we investigate the connectedness of this topology and some relations between the connectedness of the graph and the topology $mathcal{T}_{G}$.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116823336","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 brief note, we provide, as far as we know, a simple way to demonstrate that when we multiply $ktimes n$ matrix with $ntimes k$ one, for $k>n$, we always obtain singular $ktimes k$ matrix as a result. Some additional results are also provided.
{"title":"A NOTE ABOUT THE WAY TO GENERATE SINGULAR MATRIX","authors":"E. Gómez–Déniz","doi":"10.37418/amsj.11.10.3","DOIUrl":"https://doi.org/10.37418/amsj.11.10.3","url":null,"abstract":"In this brief note, we provide, as far as we know, a simple way to demonstrate that when we multiply $ktimes n$ matrix with $ntimes k$ one, for $k>n$, we always obtain singular $ktimes k$ matrix as a result. Some additional results are also provided.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"238 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123740215","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 graph theory, the theory of domination has several applications in various fields of science and technology, which is considered as a turn up field of research. In real life, it is extremely important in fields like network desigh, wireless sensor networks,logistics, mobile computing, telecommunication and others, Problems with facility location, communication or electrical network monitoring can lead to dominance. Undirected graphs is one of the most excellent models in connection with distributed computation and parellel processing. A set $Ssubset V$ is said to be a dominating set of a graph $G$ if every vertex in $ V-S $ is adjacent to atleast one vertex in $S$. The domination number $gamma{(G)}$ of the graph $ G $ is the minimum cardinality of a dominating set of $ G $. An independent dominating set $ S subset V $ is exists if no edges in the induced subgraph $langle S rangle$ and the independent dominating number $gamma_i(G)$ is the minimum cardinality of an independent dominating set of $ G $. in this paper, some results on dominating sets and independent dominating sets of $uppercase{G}^{M}_{m,n}$ graph on a finite sebset of natural numbers are presented and the domination numbers are obtained for various values of $m,n$.
在图论中，支配理论在科学技术的各个领域都有应用，被认为是一个新兴的研究领域。在现实生活中，它在网络设计、无线传感器网络、物流、移动计算、电信等领域极其重要，设施定位、通信或电网监控等问题可能导致主导地位。无向图是分布式计算和并行处理中最优秀的模型之一。如果$ V-S $中的每个顶点与$S$中的至少一个顶点相邻，则称集合$S子集V$是图$G$的支配集。图$ G $的支配数$gamma{(G)}$是$ G $的支配集的最小基数。如果诱导子图$langle $ S rangle$中没有边，且独立支配数$gamma_i(G)$是独立支配集$ G $的最小基数，则存在独立支配集$ S 子集V $。本文给出了有限自然数集上$uppercase{G}^{M}_{M,n}$图的支配集和独立支配集的一些结果，并得到了$ M,n$的不同值的支配数。
{"title":"ON THE DOMINATION AND INDEPENDENT SETS OF G^M_{m,n} GRAPH","authors":"K. Sravanthi, S. Parvathi","doi":"10.37418/amsj.11.10.2","DOIUrl":"https://doi.org/10.37418/amsj.11.10.2","url":null,"abstract":"In graph theory, the theory of domination has several applications in various fields of science and technology, which is considered as a turn up field of research. In real life, it is extremely important in fields like network desigh, wireless sensor networks,logistics, mobile computing, telecommunication and others, Problems with facility location, communication or electrical network monitoring can lead to dominance. Undirected graphs is one of the most excellent models in connection with distributed computation and parellel processing. A set $Ssubset V$ is said to be a dominating set of a graph $G$ if every vertex in $ V-S $ is adjacent to atleast one vertex in $S$. The domination number $gamma{(G)}$ of the graph $ G $ is the minimum cardinality of a dominating set of $ G $. An independent dominating set $ S subset V $ is exists if no edges in the induced subgraph $langle S rangle$ and the independent dominating number $gamma_i(G)$ is the minimum cardinality of an independent dominating set of $ G $. in this paper, some results on dominating sets and independent dominating sets of $uppercase{G}^{M}_{m,n}$ graph on a finite sebset of natural numbers are presented and the domination numbers are obtained for various values of $m,n$.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"65 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120817533","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 generalize the notion of vector fields on Weil bundle. Let $qgeq 2$ be an integer, we give equivalent definitions of a $q$-vector field on Weil bundle in terms of $q$-derivations. Further, we construct a Lie graded algebra structure of multivector fields on Weil bundle.
{"title":"EQUIVALENT DEFINITIONS OF MULTIVECTOR FIELDS ON WEIL BUNDLE","authors":"N.V. Borhen, M.M. Norbert, M. Ange","doi":"10.37418/amsj.11.10.1","DOIUrl":"https://doi.org/10.37418/amsj.11.10.1","url":null,"abstract":"In this paper, we generalize the notion of vector fields on Weil bundle. Let $qgeq 2$ be an integer, we give equivalent definitions of a $q$-vector field on Weil bundle in terms of $q$-derivations. Further, we construct a Lie graded algebra structure of multivector fields on Weil bundle.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"202 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121069187","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}
A nonlocal reaction-diffusion equation is presented in this article, based on a model proposed by J. Rubinstein and P. Sternberg [6] with a nonlinear strictly monotone operator. A dynamical boundary condition is considered, rather then the usual ones such as Neumann or Dirichlet boundary conditions. The well-posedness and the existence of a universal attractor of this problem, which describes the long time behavior of the solution, are established.
{"title":"UNIVERSAL ATTRACTOR FOR A NONLOCAL REACTION-DIFFUSION PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS","authors":"S. Boussaïd","doi":"10.37418/amsj.11.9.4","DOIUrl":"https://doi.org/10.37418/amsj.11.9.4","url":null,"abstract":"A nonlocal reaction-diffusion equation is presented in this article, based on a model proposed by J. Rubinstein and P. Sternberg [6] with a nonlinear strictly monotone operator. A dynamical boundary condition is considered, rather then the usual ones such as Neumann or Dirichlet boundary conditions. The well-posedness and the existence of a universal attractor of this problem, which describes the long time behavior of the solution, are established.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131443470","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 are interested by the study of asymptotic behaviour of the sequence of integral functionals using the direct method.
本文用直接方法研究了整泛函序列的渐近性质。
{"title":"EPICONVERGENCE OF A SEQUENCE OF INTEGRAL FUNCTIONALS DEFINED ON H^1(A)","authors":"M. Brahimi, M. Laouar","doi":"10.37418/amsj.11.9.3","DOIUrl":"https://doi.org/10.37418/amsj.11.9.3","url":null,"abstract":"In this paper, we are interested by the study of asymptotic behaviour of the sequence of integral functionals using the direct method.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116779777","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：