V.S.V. Krishna Murty, C. Jaya Subba Reddy, K. Sukanya
Consider a 2-torsion-free semiprime (Gamma)-near ring (N). Assume that (sigma) and (tau) are automorphisms on (N). An additive map (d_1: N to N) is called a ((sigma, tau))-derivation if it satisfies [d_1(u alpha v) = d_1(u) alpha sigma(v) + tau(u) alpha d_1(v) ]for all (u, v in N) and (alpha in Gamma). An additive map (D_1: N to N) is termed a generalized ((sigma, tau))-derivation associated with the ((sigma, tau))-derivation (d_1) if [D_1(u alpha v) = D_1(u) alpha sigma(v) + tau(u) alpha d_1(v)]for all (u, v in N) and (alpha in Gamma). Consider two generalizedhspace{0.1cm} ((sigma, tau))-derivations (D_1) and (D_2) on (N). This paper introduces the concept of the orthogonality of two generalized ((sigma, tau))-derivations (D_1) and (D_2) and presents several results regarding the orthogonality of generalized ((sigma, tau))-derivations and ((sigma, tau))-derivations in a (Gamma)-near ring.
考虑一个无二扭的半环（Gamma）-近环（N）。假设(sigma) 和(tau)是(N)上的自变量。一个加法映射 （d_1：如果它满足[d_1(u alpha v) = d_1(u) alpha sigma(v) + tau(u) alpha d_1(v) ] for all (u, v in N) and(alpha in Gamma)，那么它就叫做一个（（（sigma, tau））衍生。）一个加法映射 （D_1：N到N）被称为与（（（西格玛、D_1(u α v) = D_1(u) α sigma(v) + tau(u) α d_1(v)]for all (u, v in N) and(alpha in Gamma).考虑两个广义空间{0.1cm｝上的（D_1）和（D_2）的衍生。本文介绍了两个广义的（(sigma, tau)）支点（（D_1）和（D_2））的正交性概念，并给出了关于广义的（(sigma, tau)）支点和（(sigma, tau)）支点在（Gamma）近环中的正交性的几个结果。
{"title":"ORTHOGONAL GENERALIZED ( 𝜎 , 𝜏 ) (σ,τ)-DERIVATIONS IN SEMIPRIME Γ Γ-NEAR RINGS","authors":"V.S.V. Krishna Murty, C. Jaya Subba Reddy, K. Sukanya","doi":"10.37418/amsj.13.3.4","DOIUrl":"https://doi.org/10.37418/amsj.13.3.4","url":null,"abstract":"Consider a 2-torsion-free semiprime (Gamma)-near ring (N). Assume that (sigma) and (tau) are automorphisms on (N). An additive map (d_1: N to N) is called a ((sigma, tau))-derivation if it satisfies [d_1(u alpha v) = d_1(u) alpha sigma(v) + tau(u) alpha d_1(v) ]for all (u, v in N) and (alpha in Gamma). An additive map (D_1: N to N) is termed a generalized ((sigma, tau))-derivation associated with the ((sigma, tau))-derivation (d_1) if [D_1(u alpha v) = D_1(u) alpha sigma(v) + tau(u) alpha d_1(v)]for all (u, v in N) and (alpha in Gamma). Consider two generalizedhspace{0.1cm} ((sigma, tau))-derivations (D_1) and (D_2) on (N). This paper introduces the concept of the orthogonality of two generalized ((sigma, tau))-derivations (D_1) and (D_2) and presents several results regarding the orthogonality of generalized ((sigma, tau))-derivations and ((sigma, tau))-derivations in a (Gamma)-near ring.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"31 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141640033","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 proposes a new method for solving solid transportation problem under uncertainty environments. The fully fuzzy solid transportation problem has been formulated. To reduce the model into crisp equivalent, we have used existing method for approximation of fuzzy numbers by interval numbers and its arithmatics. A simplex method and existing method for solving Interval Linear Programming problems are used for solving solid transportation problem with fuzzy parameters and decision variables. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy and reasonable.
{"title":"A NOVEL METHOD FOR SOLVING FULLY FUZZY SOLID TRANSPORTATIONS PROBLEMS","authors":"H. Bado, L. Diabaté, D. Diawara, L. v","doi":"10.37418/amsj.13.3.2","DOIUrl":"https://doi.org/10.37418/amsj.13.3.2","url":null,"abstract":"In this paper, we proposes a new method for solving solid transportation problem under uncertainty environments. The fully fuzzy solid transportation problem has been formulated. To reduce the model into crisp equivalent, we have used existing method for approximation of fuzzy numbers by interval numbers and its arithmatics. A simplex method and existing method for solving Interval Linear Programming problems are used for solving solid transportation problem with fuzzy parameters and decision variables. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy and reasonable.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"13 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639923","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, a crack in a heated plate is investigated, subjected to normal stress. Employing the relationship between the uniform and perturbation fields, as well as complex potential functions and stresses, the problems of heat conduction and heat stress are modeled as singular integral equations. The derivatives of the crack opening displacement function and the temperature jump function serve as the unknown functions. Gauss integration rules are applied to solve the obtained equations numerically. Analysis of the stress intensity factors(SIFs) for some particular crack configurations is presented.
{"title":"SINGULAR INTEGRAL EQUATIONS FOR A CRACK SUBJECTED NORMAL STRESS IN A HEATED PLATE","authors":"S.K. Zhuang, N. N. Nik Long, K. Hamzah, N. Senu","doi":"10.37418/amsj.13.3.3","DOIUrl":"https://doi.org/10.37418/amsj.13.3.3","url":null,"abstract":"In this paper, a crack in a heated plate is investigated, subjected to normal stress. Employing the relationship between the uniform and perturbation fields, as well as complex potential functions and stresses, the problems of heat conduction and heat stress are modeled as singular integral equations. The derivatives of the crack opening displacement function and the temperature jump function serve as the unknown functions. Gauss integration rules are applied to solve the obtained equations numerically. Analysis of the stress intensity factors(SIFs) for some particular crack configurations is presented.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"35 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639963","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 give characterizations of timelike normal, rectifying and osculating helices in Minkowski space $E_{1}^{3}.$ Moreover, we examine the characterization of timelike helices whose axis $U$ perpendicular to the $F$-constant vector field $X$, which is a generalization of these helices$.$
{"title":"SOME CHARACTERIZATIONS OF TIMELIKE HELICES WITH THE $F$-CONSTANT VECTOR FIELD IN MINKOWSKI SPACE $E_{1}^{3}$}","authors":"Derya Sa˘glam, Duygu Bada","doi":"10.37418/amsj.13.3.1","DOIUrl":"https://doi.org/10.37418/amsj.13.3.1","url":null,"abstract":"In this paper we give characterizations of timelike normal, rectifying and osculating helices in Minkowski space $E_{1}^{3}.$ Moreover, we examine the characterization of timelike helices whose axis $U$ perpendicular to the $F$-constant vector field $X$, which is a generalization of these helices$.$","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"80 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682163","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}
D. Ampini, Challoum Dyaus, Elohe Mouanda, C. Mouanda
In this work, we construct a functional related to a hyperbolic problem with polynomial non linearity and homogeneous Neuwman conditions and its differentiability in the Frechet sense.
{"title":"DIFFERENTIABILITY IN THE FRECHET SENSE OF A FUNCTIONAL RELATED TO A HYPERBOLIC PROBLEM WITH POLYNOMIAL NONLINEARITY","authors":"D. Ampini, Challoum Dyaus, Elohe Mouanda, C. Mouanda","doi":"10.37418/amsj.13.2.4","DOIUrl":"https://doi.org/10.37418/amsj.13.2.4","url":null,"abstract":"In this work, we construct a functional related to a hyperbolic problem with polynomial non linearity and homogeneous Neuwman conditions and its differentiability in the Frechet sense.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":" 54","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141367735","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}
Christophe Fotso, Duplex Elvis, Houpa Danga, Daniel Tieudjo
The choice of a convenient approach to be used is one important issue when attempting to develop methods or obtain results in the setting of Probability on general metric spaces. In this paper, we extend the mean-sets probabilistic approach formally introduced by Mosina on locally finite graphs, and hence (via Cayley graphs) on finitely generated groups, to the field of Negatively Curved Convex Combination Polish (NCCCP) metric spaces. We construct an appropriated Vertex-Weighted Metric (VWM) graph in the framework of this class of geometrical structures. We define a function called convexification function on the direct product of $ n $ copies of the vertex-set of this graph (for a given fixed integer $ ngeq 2$), using the natural convexification operator of the metric space concerned. This function is then used to construct a weighted mean-set that generalizes the notion of convex combination (CC) mean in the sense of Ter{'a}n and Molchanov, the mean-set concept according to Mosina and the ordinary notion of $ k $-means ($kgeq 2$) of independent identically distributed (i.i.d.) random elements of the metric space. Two numerical examples are given for the cases when the metric space $ X= [0,1]$ and $ X=mathbf{R}^{2} $. Moreover, an analogue of the Strong Law of Large Numbers (SLLN), the consistency problem and the Chebyshev's inequality for NCCCP spaces are established.
{"title":"AN APPROACH OF MEAN-SETS THEORY FOR NEGATIVELY CURVED CONVEX COMBINATION POLISH METRIC SPACES","authors":"Christophe Fotso, Duplex Elvis, Houpa Danga, Daniel Tieudjo","doi":"10.37418/amsj.13.2.3","DOIUrl":"https://doi.org/10.37418/amsj.13.2.3","url":null,"abstract":"The choice of a convenient approach to be used is one important issue when attempting to develop methods or obtain results in the setting of Probability on general metric spaces. In this paper, we extend the mean-sets probabilistic approach formally introduced by Mosina on locally finite graphs, and hence (via Cayley graphs) on finitely generated groups, to the field of Negatively Curved Convex Combination Polish (NCCCP) metric spaces. We construct an appropriated Vertex-Weighted Metric (VWM) graph in the framework of this class of geometrical structures. We define a function called convexification function on the direct product of $ n $ copies of the vertex-set of this graph (for a given fixed integer $ ngeq 2$), using the natural convexification operator of the metric space concerned. This function is then used to construct a weighted mean-set that generalizes the notion of convex combination (CC) mean in the sense of Ter{'a}n and Molchanov, the mean-set concept according to Mosina and the ordinary notion of $ k $-means ($kgeq 2$) of independent identically distributed (i.i.d.) random elements of the metric space. Two numerical examples are given for the cases when the metric space $ X= [0,1]$ and $ X=mathbf{R}^{2} $. Moreover, an analogue of the Strong Law of Large Numbers (SLLN), the consistency problem and the Chebyshev's inequality for NCCCP spaces are established.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"51 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141382099","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}
R. A. Oderinu, K.A. Salaudeen, W.A. Tijani, S.O. Sangoniyi
In this paper, we propose a new method called Dual Simultaneous Co-Inertia Analysis Type 2 (DSCIA2), which is both a new approach to DSCIA in the context of two horizontal multi-tables and Dual of SCIA2 method. The aim is to study the variability of the proximity between pairs of tables with the same variables, by constructing the common axes of representation of the variables and the individuals simultaneously, i.e. constructing in one go an orthogonal matrix containing the solutions. An example of this method consisting being studied of the compared economic evolution of the countries of the Economic Monetary Community of Central Africa (EMCCA) and the West African Economic Monetary Union(WAEMU) is given.
{"title":"SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS BY A DEFORMATION BASED SAWI’S TRANSFORM","authors":"R. A. Oderinu, K.A. Salaudeen, W.A. Tijani, S.O. Sangoniyi","doi":"10.37418/amsj.13.2.1","DOIUrl":"https://doi.org/10.37418/amsj.13.2.1","url":null,"abstract":"In this paper, we propose a new method called Dual Simultaneous Co-Inertia Analysis Type 2 (DSCIA2), which is both a new approach to DSCIA in the context of two horizontal multi-tables and Dual of SCIA2 method. The aim is to study the variability of the proximity between pairs of tables with the same variables, by constructing the common axes of representation of the variables and the individuals simultaneously, i.e. constructing in one go an orthogonal matrix containing the solutions. An example of this method consisting being studied of the compared economic evolution of the countries of the Economic Monetary Community of Central Africa (EMCCA) and the West African Economic Monetary Union(WAEMU) is given.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"346 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140698065","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}
R.M. Taghiyev, S.S. Farajova, A.T. Ramazonova, R. N. Allahverdiyev, M.Y. Shalimov
The paper studies the solvability of an inverse boundary value problem with an unknown time-dependent coefficient for the equation of forced vibrations of a cantilever beam with the integral. Bending transverse vibrations of a homogeneous beam under the action of an external force in the absence of rotational motion during bending are described by a fourth-order differential equation. The purpose of the work is to determine the unknown coefficient and solve the problem under consideration. THIS problem under consideration is reduced to an auxiliary equivalent problem. Next, the existence and uniqueness of a solution to the equivalent problem is proved using the contraction mapping principle. As a result, using equivalence, the uniqueness of the existence of the classical solution is proved.
{"title":"INVERSE BOUNDARY PROBLEM FOR THE EQUATION OF FORCED VIBRATIONS OF A CANTILEVER BEAM WITH INTEGRAL CONDITIONS","authors":"R.M. Taghiyev, S.S. Farajova, A.T. Ramazonova, R. N. Allahverdiyev, M.Y. Shalimov","doi":"10.37418/amsj.13.1.6","DOIUrl":"https://doi.org/10.37418/amsj.13.1.6","url":null,"abstract":"The paper studies the solvability of an inverse boundary value problem with an unknown time-dependent coefficient for the equation of forced vibrations of a cantilever beam with the integral. Bending transverse vibrations of a homogeneous beam under the action of an external force in the absence of rotational motion during bending are described by a fourth-order differential equation. The purpose of the work is to determine the unknown coefficient and solve the problem under consideration. THIS problem under consideration is reduced to an auxiliary equivalent problem. Next, the existence and uniqueness of a solution to the equivalent problem is proved using the contraction mapping principle. As a result, using equivalence, the uniqueness of the existence of the classical solution is proved.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":" 48","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140385715","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.A. Oyewumi, R. A. Oderinu, A.W. Ogunsola, M. Taiwo, A.A. Yahaya
A combination of the Aboodh transform method and the reduced differential polynomial technique was employed in this work to solve the Navier-Stokes equations with the Caputo-Fabrizio derivative. Two illustrations are presented to show the efficacy of the used method. The results gotten are showcased with the aid of tables and graphs. It is discovered that the results derived are close to the actual solution of the problems illustrated. This work will thus make it simple to study nonlinear process that arise in various aspect of innovations and researches.
{"title":"A NUMERICAL SOLUTION OF THE FRACTIONAL NAVIER-STOKES EQUATION USING THE CAPUTO-FABRIZIO ABOODH TRANSFORM METHOD WITH THE REDUCED DIFFERENTIAL POLYNOMIALS","authors":"A.A. Oyewumi, R. A. Oderinu, A.W. Ogunsola, M. Taiwo, A.A. Yahaya","doi":"10.37418/amsj.13.1.5","DOIUrl":"https://doi.org/10.37418/amsj.13.1.5","url":null,"abstract":"A combination of the Aboodh transform method and the reduced differential polynomial technique was employed in this work to solve the Navier-Stokes equations with the Caputo-Fabrizio derivative. Two illustrations are presented to show the efficacy of the used method. The results gotten are showcased with the aid of tables and graphs. It is discovered that the results derived are close to the actual solution of the problems illustrated. This work will thus make it simple to study nonlinear process that arise in various aspect of innovations and researches.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":" 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140222032","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}
E. Choi, B. Chao, I. Choi, A. Chung, A. Mermigas, R. Shah
The emph{sub-defect} of $A$, defined as $mathrm{sd}(A) = lceil n - mbox{sum}(A) rceil,$ is the minimum number of rows and columns required to be added to transform a doubly substochastic matrix into a doubly stochastic matrix. Here, $n$ is the size of $A$ and $mbox{sum}(A)$ is the sum of all entries of matrix $A.$ In this paper, we show that for arbitrary doubly substochastic matrices $A$ and $B$, the Hadamard product $A circ B$ is also a doubly substochastic matrix, and $ max {sd(A),sd(B)}leq sd(A circ B) leq max{n, sd(A)+sd(B)}. $
{"title":"ON SUB-DEFECT OF HADAMARD PRODUCT OF DOUBLY SUBSTOCHASTIC MATRICES","authors":"E. Choi, B. Chao, I. Choi, A. Chung, A. Mermigas, R. Shah","doi":"10.37418/amsj.13.1.4","DOIUrl":"https://doi.org/10.37418/amsj.13.1.4","url":null,"abstract":"The emph{sub-defect} of $A$, defined as $mathrm{sd}(A) = lceil n - mbox{sum}(A) rceil,$ is the minimum number of rows and columns required to be added to transform a doubly substochastic matrix into a doubly stochastic matrix. Here, $n$ is the size of $A$ and $mbox{sum}(A)$ is the sum of all entries of matrix $A.$ In this paper, we show that for arbitrary doubly substochastic matrices $A$ and $B$, the Hadamard product $A circ B$ is also a doubly substochastic matrix, and $ max {sd(A),sd(B)}leq sd(A circ B) leq max{n, sd(A)+sd(B)}. $","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"14 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140244126","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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