A. Olutimo, I. D. Omoko, A. A. Abdurasid, A.F. Abass
Two coupled circuits are extensively used in radio electronics and communication. The problem of stability analysis of state variables describing system of two coupled circuits is very critical as unstable circuit causes damage to electrical systems. Analysis of stability and boundedness behavior of the state variables characterizing system of two coupled circuits is carried out using the Lyapunov's second method. We provide in simple form, less restrictive conditions that are implementable at the development stage and which ensure the stability and boundedness of the state variables describing system considered. For illustration, the behaviours of the system of two coupled circuits with response and its bounded output are shown.
双耦合电路广泛应用于无线电电子和通信领域。描述双耦合电路系统的状态变量的稳定性分析问题非常关键，因为不稳定的电路会对电气系统造成损害。利用 Lyapunov's second 方法对描述两个耦合电路系统的状态变量的稳定性和有界性行为进行了分析。我们以简单的形式提供了可在开发阶段实施的限制性较小的条件，这些条件确保了描述所考虑系统的状态变量的稳定性和有界性。为便于说明，我们展示了两个耦合电路系统的响应行为及其有界输出。
{"title":"STABILITY AND BOUNDEDNESS ANALYSIS OF A STATE–DEPENDENT DIFFERENTIAL EQUATIONS FOR A SYSTEM OF TWO COUPLED CIRCUITS","authors":"A. Olutimo, I. D. Omoko, A. A. Abdurasid, A.F. Abass","doi":"10.37418/amsj.13.1.3","DOIUrl":"https://doi.org/10.37418/amsj.13.1.3","url":null,"abstract":"Two coupled circuits are extensively used in radio electronics and communication. The problem of stability analysis of state variables describing system of two coupled circuits is very critical as unstable circuit causes damage to electrical systems. Analysis of stability and boundedness behavior of the state variables characterizing system of two coupled circuits is carried out using the Lyapunov's second method. We provide in simple form, less restrictive conditions that are implementable at the development stage and which ensure the stability and boundedness of the state variables describing system considered. For illustration, the behaviours of the system of two coupled circuits with response and its bounded output are shown.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"16 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140442952","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 purpose of this paper is the determination of some centralizers in $A_{1}$, the first Weyl Algebra. Some authors have done their studies in the case of zero characteristic field. As far as we're concerned, we have decided to work in 2 or 3 characteristic field. Doing so, we show that if $uin A_{1}$ is a minimal element, $C$-primitive and without constant term, then its centralizer $Z(u)=mathbb{L}[u]cap A_{1}$ where $mathbb{L}$ is the fractions field of $C$, the center of $A_{1}$. Particularly, when $u$ is ad-invertible, i.e there exists $vin A_{1}$ such that $[u,v]=1$, then we have $Z(u)=C[u]$ which is a result analogous to that of cite{JJC}.
{"title":"CENTRALIZERS IN THE FIRST WEYL ALGEBRA OVER A 2 OR 3-CHARACTERISTIC FIELD","authors":"B.S.B. Kouame, K.M. Kouakou","doi":"10.37418/amsj.13.1.2","DOIUrl":"https://doi.org/10.37418/amsj.13.1.2","url":null,"abstract":"The purpose of this paper is the determination of some centralizers in $A_{1}$, the first Weyl Algebra. Some authors have done their studies in the case of zero characteristic field. As far as we're concerned, we have decided to work in 2 or 3 characteristic field. Doing so, we show that if $uin A_{1}$ is a minimal element, $C$-primitive and without constant term, then its centralizer $Z(u)=mathbb{L}[u]cap A_{1}$ where $mathbb{L}$ is the fractions field of $C$, the center of $A_{1}$. Particularly, when $u$ is ad-invertible, i.e there exists $vin A_{1}$ such that $[u,v]=1$, then we have $Z(u)=C[u]$ which is a result analogous to that of cite{JJC}.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"548 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139833917","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 purpose of this paper is the determination of some centralizers in $A_{1}$, the first Weyl Algebra. Some authors have done their studies in the case of zero characteristic field. As far as we're concerned, we have decided to work in 2 or 3 characteristic field. Doing so, we show that if $uin A_{1}$ is a minimal element, $C$-primitive and without constant term, then its centralizer $Z(u)=mathbb{L}[u]cap A_{1}$ where $mathbb{L}$ is the fractions field of $C$, the center of $A_{1}$. Particularly, when $u$ is ad-invertible, i.e there exists $vin A_{1}$ such that $[u,v]=1$, then we have $Z(u)=C[u]$ which is a result analogous to that of cite{JJC}.
{"title":"CENTRALIZERS IN THE FIRST WEYL ALGEBRA OVER A 2 OR 3-CHARACTERISTIC FIELD","authors":"B.S.B. Kouame, K.M. Kouakou","doi":"10.37418/amsj.13.1.2","DOIUrl":"https://doi.org/10.37418/amsj.13.1.2","url":null,"abstract":"The purpose of this paper is the determination of some centralizers in $A_{1}$, the first Weyl Algebra. Some authors have done their studies in the case of zero characteristic field. As far as we're concerned, we have decided to work in 2 or 3 characteristic field. Doing so, we show that if $uin A_{1}$ is a minimal element, $C$-primitive and without constant term, then its centralizer $Z(u)=mathbb{L}[u]cap A_{1}$ where $mathbb{L}$ is the fractions field of $C$, the center of $A_{1}$. Particularly, when $u$ is ad-invertible, i.e there exists $vin A_{1}$ such that $[u,v]=1$, then we have $Z(u)=C[u]$ which is a result analogous to that of cite{JJC}.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"20 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774231","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, I work on expanding the Jensen $(Gamma_{1},Gamma_{2})$-function inequalities by relying on the general Jensen functional equation with 3k-variables on the complex Banach space. That's the main result in this.
{"title":"ESTABLISH OF THE JENSEN TYPE ( Γ_1, Γ_2 )-FUNCTIONAL INEQUATITIES BASED ON JENSEN TYPE FUNCTIONAL EQUATION WITH 3k-VARIABLES IN COMPLEX BANACH SPACE","authors":"Ly Van An","doi":"10.37418/amsj.13.1.1","DOIUrl":"https://doi.org/10.37418/amsj.13.1.1","url":null,"abstract":"In this paper, I work on expanding the Jensen $(Gamma_{1},Gamma_{2})$-function inequalities by relying on the general Jensen functional equation with 3k-variables on the complex Banach space. That's the main result in this.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"137 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139604480","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 purpose of this paper is to present the proof that the determinant of any matrix of order higher than 2 ($k > 2$) where elements are consecutive numbers or numbers following an arithmetic progression will always be zero.
{"title":"THE CONSECUTIVE MATRIX THEOREM - A PROPERTY OF DETERMINANTS","authors":"Pablo Roberto Dias","doi":"10.37418/amsj.12.12.1","DOIUrl":"https://doi.org/10.37418/amsj.12.12.1","url":null,"abstract":"The purpose of this paper is to present the proof that the determinant of any matrix of order higher than 2 ($k > 2$) where elements are consecutive numbers or numbers following an arithmetic progression will always be zero.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"20 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138597867","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 show if $R$ be a ring in which every element is sum of three commuting tripotents then for every $kin R$ we have $(k-3)(k-2)^2(k-1)^2k^2(k+1)^2(k+2)^2(k+3)=0$, if every element of $R$ is sum of four commuting tripotents then for every $kin R$ we have $(k-4)(k-3)(k-2)^2(k-1)^2k^4(k+1)^2(k+2)^2(k+3)(k+4)=0$, if every element of $R$ is sum of five commuting tripotents then for every $kin R$ we have $(k-5)(k-4)(k-3)^2(k-2)^3(k-1)^3k^4(k+1)^3(k+2)^3(k+3)^2(k+4)(k+5)=0$. Then we discuss the properties of these type of ring. Finally we find the general structure of a ring in which every element is sum of $n$ commuting tripotents and discuss the properties of it.
{"title":"STRUCTURE OF A RING IN WHICH EVERY ELEMENT IS SUM OF 3, 4 OR 5 COMMUTING TRIPOTENTS","authors":"Kumar Napoleon, Deka, Helen K. Saikia","doi":"10.37418/amsj.12.11.4","DOIUrl":"https://doi.org/10.37418/amsj.12.11.4","url":null,"abstract":"In this paper we show if $R$ be a ring in which every element is sum of three commuting tripotents then for every $kin R$ we have $(k-3)(k-2)^2(k-1)^2k^2(k+1)^2(k+2)^2(k+3)=0$, if every element of $R$ is sum of four commuting tripotents then for every $kin R$ we have $(k-4)(k-3)(k-2)^2(k-1)^2k^4(k+1)^2(k+2)^2(k+3)(k+4)=0$, if every element of $R$ is sum of five commuting tripotents then for every $kin R$ we have $(k-5)(k-4)(k-3)^2(k-2)^3(k-1)^3k^4(k+1)^3(k+2)^3(k+3)^2(k+4)(k+5)=0$. Then we discuss the properties of these type of ring. Finally we find the general structure of a ring in which every element is sum of $n$ commuting tripotents and discuss the properties of it.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"24 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139205817","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}
Graph is a easy way to represent the real life situation. Graph is a combination of Points and Lines. In network analysis, the degree of a point plays a prominent role in Graph Theory. The degree of a point is the number of connections it has with the other points in the point set. Among the degrees of all the points in graph $G^*$, the minimum value is denoted by $delta(G^*)$. In this article, a new abstraction of fuzzy graph is initiated by combining the parameters, degree of a point and minimum degree of the graph and termed it is as $delta_d$-fuzzy graphs. Order and Size on $delta_d$-fuzzy graphs were studied and Handshaking Lemma were explained with illustration. Idea on $delta_d$-regular fuzzy graph were interpreted using the theorems. Also operations on graphs such as union, intersection, complement, cartesian product, Tensor Product, Corona are extended for $delta_d$-fuzzy graphs.
{"title":"AN INTRO TO $delta_d$-FUZZY GRAPHS","authors":"J. Jeromi Jovita, O. Uma Maheswari, N. Meenal","doi":"10.37418/amsj.12.11.3","DOIUrl":"https://doi.org/10.37418/amsj.12.11.3","url":null,"abstract":"Graph is a easy way to represent the real life situation. Graph is a combination of Points and Lines. In network analysis, the degree of a point plays a prominent role in Graph Theory. The degree of a point is the number of connections it has with the other points in the point set. Among the degrees of all the points in graph $G^*$, the minimum value is denoted by $delta(G^*)$. In this article, a new abstraction of fuzzy graph is initiated by combining the parameters, degree of a point and minimum degree of the graph and termed it is as $delta_d$-fuzzy graphs. Order and Size on $delta_d$-fuzzy graphs were studied and Handshaking Lemma were explained with illustration. Idea on $delta_d$-regular fuzzy graph were interpreted using the theorems. Also operations on graphs such as union, intersection, complement, cartesian product, Tensor Product, Corona are extended for $delta_d$-fuzzy graphs.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139220691","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 work, we investigate the algebraic and geometric properties of centrosymmetric matrices over the positive reals. We show that the set of centrosymmetric matrices, denoted as $mathcal{C}_n$, forms a Lie algebra under the Hadamard product with the Lie bracket defined as $[A, B] = A circ B - B circ A$. Furthermore, we prove that the set $mathcal{C}_n$ of centrosymmetric matrices over $mathbb{R}^+$ is an open connected differentiable manifold with dimension $lceil frac{n^2}{2}rceil$. This result is achieved by establishing a diffeomorphism between $mathcal{C}_n$ and a Euclidean space $mathbb{R}^{lceil frac{n^2}{2}rceil}$, and by demonstrating that the set is both open and path-connected. This work provides insight into the algebraic and topological properties of centrosymmetric matrices, paving the way for potential applications in various mathematical and engineering fields.
在这项工作中，我们研究了正实数上中心对称矩阵的代数和几何性质。我们证明，中心对称矩阵的集合（表示为 $mathcal{C}_n$）在哈达玛积下构成一个列代数，其列括号定义为 $[A, B] = A circ B - B circ A$。此外，我们还证明了在 $mathbb{R}^+$ 上的中心对称矩阵集合 $mathcal{C}_n$ 是维数为 $lceil frac{n^2}{2}rceil$ 的开放连通可微流形。这一结果是通过在 $mathcal{C}_n$ 与欧几里得空间 $mathbb{R}^{lceil frac{n^2}{2}rceil}$ 之间建立差分同构，并证明该集合既是开放的又是路径连接的而得到的。这项研究深入揭示了中心对称矩阵的代数和拓扑性质，为其在数学和工程领域的潜在应用铺平了道路。
{"title":"ON TOPOLOGY OF CENTROSYMMETRIC MATRICES WITH APPLICATIONS","authors":"S. Koyuncu, C. Ozel, M. Albaity","doi":"10.37418/amsj.12.11.2","DOIUrl":"https://doi.org/10.37418/amsj.12.11.2","url":null,"abstract":"In this work, we investigate the algebraic and geometric properties of centrosymmetric matrices over the positive reals. We show that the set of centrosymmetric matrices, denoted as $mathcal{C}_n$, forms a Lie algebra under the Hadamard product with the Lie bracket defined as $[A, B] = A circ B - B circ A$. Furthermore, we prove that the set $mathcal{C}_n$ of centrosymmetric matrices over $mathbb{R}^+$ is an open connected differentiable manifold with dimension $lceil frac{n^2}{2}rceil$. This result is achieved by establishing a diffeomorphism between $mathcal{C}_n$ and a Euclidean space $mathbb{R}^{lceil frac{n^2}{2}rceil}$, and by demonstrating that the set is both open and path-connected. This work provides insight into the algebraic and topological properties of centrosymmetric matrices, paving the way for potential applications in various mathematical and engineering fields.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"128 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139265058","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 paper presents a numerical solution for the two-dimensional Lane-Emden problem using two-dimensional Boubaker polynomials. The method involves utilizing the operational matrix of differentiation and collocation method to convert the problem into a system of algebraic equations. The proposed approach, based on two-dimensional Boubaker polynomials operational matrices, is shown to be straightforward and effective. The validity and applicability of the method are demonstrated through illustrative examples.
{"title":"A NUMERICAL STUDY OF 2D-LANE-EMDEN PROBLEM USING 2D-BOUBAKER POLYNOMIALS","authors":"Abdelkrim Bencheikh","doi":"10.37418/amsj.12.9.1","DOIUrl":"https://doi.org/10.37418/amsj.12.9.1","url":null,"abstract":"The paper presents a numerical solution for the two-dimensional Lane-Emden problem using two-dimensional Boubaker polynomials. The method involves utilizing the operational matrix of differentiation and collocation method to convert the problem into a system of algebraic equations. The proposed approach, based on two-dimensional Boubaker polynomials operational matrices, is shown to be straightforward and effective. The validity and applicability of the method are demonstrated through illustrative examples.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"163 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134360518","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}
G. S. Awe, M. A. Akanbi, R. Abdulganiy, A. Olutimo, Y. T. Oyebo
A family of K-step Trigonometrically-fitted Block Falkner Methods is considered for the direct solution of second order Oscillatory Initial value problems. As unique to Falkner methods, two main formulas (one for the method and one for the derivative) for each k-step and some additional formulas. This method shall be adapted to general oscillatory second order ordinary differential equations via the multistep collocation technique. The idea employed in this study is the generalized collocation technique based on fitting functions that are combination of trigonometric and algebraic polynomials, which is then implemented in a block mode to get approximations at all the grid points simultaneously. As in other block methods, there is no need of other procedures to provide starting values, and thus the methods are selfstarting (sharing this advantage of Runge-kutta methods). The study of the properties of the proposed adapted block Falkner methods reveals that they are consistent and zero-stable, and thus, convergent. Furthermore, the stability analysis and the algebraic order conditions of the proposed methods are established. As evident from the numerical results, the methods are efficient and accurate when compared with some recent methods in the literature.
{"title":"A FAMILY OF K-STEP TRIGONOMETRICALLY-FITTED BLOCK FALKNER METHODS FOR SOLVING SECOND-ORDER INITIAL-VALUE PROBLEMS WITH OSCILLATING SOLUTIONS","authors":"G. S. Awe, M. A. Akanbi, R. Abdulganiy, A. Olutimo, Y. T. Oyebo","doi":"10.37418/amsj.12.8.5","DOIUrl":"https://doi.org/10.37418/amsj.12.8.5","url":null,"abstract":"A family of K-step Trigonometrically-fitted Block Falkner Methods is considered for the direct solution of second order Oscillatory Initial value problems. As unique to Falkner methods, two main formulas (one for the method and one for the derivative) for each k-step and some additional formulas. This method shall be adapted to general oscillatory second order ordinary differential equations via the multistep collocation technique. The idea employed in this study is the generalized collocation technique based on fitting functions that are combination of trigonometric and algebraic polynomials, which is then implemented in a block mode to get approximations at all the grid points simultaneously. As in other block methods, there is no need of other procedures to provide starting values, and thus the methods are selfstarting (sharing this advantage of Runge-kutta methods). The study of the properties of the proposed adapted block Falkner methods reveals that they are consistent and zero-stable, and thus, convergent. Furthermore, the stability analysis and the algebraic order conditions of the proposed methods are established. As evident from the numerical results, the methods are efficient and accurate when compared with some recent methods in the literature.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124314308","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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