In this paper, we introduce a numerical method to construct the inverse of a square matrix whose elements are trapezoidal or triangular fuzzy numbers (FNs). A set of fuzzy linear equations is required to be solved in order to determine the fuzzy inverse matrix. The proposed technique first iteratively searches the possible solution intervals and then narrows those too-wide estimated intervals via bisection. Using interval arithmetic in left and right matrix multiplication, we aim to approximate the identity matrix as a result of product operations. The dissimilarity of the endpoints of intervals belonging to multiplication matrices with the identity matrix is considered to be an error function to be minimized. In this way, even if the entries of a matrix are uncertain, the fuzzy inverse matrix containing all inverse matrices can be found quickly with the use of computer technology. The method is explained and comparisons are drawn with inverse stable examples from the literature.
{"title":"Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection","authors":"Hande Günay Akdemir","doi":"10.33401/fujma.1195121","DOIUrl":"https://doi.org/10.33401/fujma.1195121","url":null,"abstract":"In this paper, we introduce a numerical method to construct the inverse of a square matrix whose elements are trapezoidal or triangular fuzzy numbers (FNs). A set of fuzzy linear equations is required to be solved in order to determine the fuzzy inverse matrix. The proposed technique first iteratively searches the possible solution intervals and then narrows those too-wide estimated intervals via bisection. Using interval arithmetic in left and right matrix multiplication, we aim to approximate the identity matrix as a result of product operations. The dissimilarity of the endpoints of intervals belonging to multiplication matrices with the identity matrix is considered to be an error function to be minimized. In this way, even if the entries of a matrix are uncertain, the fuzzy inverse matrix containing all inverse matrices can be found quickly with the use of computer technology. The method is explained and comparisons are drawn with inverse stable examples from the literature.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"134 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128730437","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 form of the solution of the following systems of difference equations of order two xn+1 = (x_{n}*y{n−1})/(x_{n}+y_{n-1}) , yn+1 =( y_{n}*x_{n-1})/(pm y_{n} pm x_{n-1}) with nonzero real numbers initial conditions.
{"title":"The Form of Solutions and Periodic Nature for Some System of Difference Equations","authors":"E. Elsayed, J. Al-Juaid","doi":"10.33401/fujma.1166022","DOIUrl":"https://doi.org/10.33401/fujma.1166022","url":null,"abstract":"In this paper we study the form of the solution of the following systems of difference equations of order two xn+1 = (x_{n}*y{n−1})/(x_{n}+y_{n-1}) , yn+1 =( y_{n}*x_{n-1})/(pm y_{n} pm x_{n-1}) \u0000 \u0000with nonzero real numbers initial conditions.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123523794","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 investigate the new traveling wave solutions for the sixth-order Boussinesq equation using the tanh-coth method. Such a method is a type of expansion method that represents the solutions of partial differential equations as polynomials of tanh and coth functions. We discover several new traveling wave solutions for the sixth-order Boussinesq equation with different parameters, which are of fundamental importance for various applications.
{"title":"New Traveling Wave Solutions for the Sixth-Order Boussinesq Equation","authors":"He Yang","doi":"10.33401/fujma.1144277","DOIUrl":"https://doi.org/10.33401/fujma.1144277","url":null,"abstract":"In this paper, we investigate the new traveling wave solutions for the sixth-order Boussinesq equation using the tanh-coth method. Such a method is a type of expansion method that represents the solutions of partial differential equations as polynomials of tanh and coth functions. We discover several new traveling wave solutions for the sixth-order Boussinesq equation with different parameters, which are of fundamental importance for various applications.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122828240","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}
Afractional order system of evolution partial differential equations with a constant delay is considered. By exploiting the Lie symmetry method, we give a complete group classification of the system. Furthermore, we establish the corresponding symmetry reductions and construct some analytical solutions to the system.
{"title":"On Complete Group Classification of Time Fractional Systems Evolution Differential Equation with a Constant Delay","authors":"Kassimu Mpungu, Aminu Ma’aruf Nass","doi":"10.33401/fujma.1147657","DOIUrl":"https://doi.org/10.33401/fujma.1147657","url":null,"abstract":"Afractional order system of evolution partial differential equations with a constant delay is considered. By exploiting the Lie symmetry method, we give a complete group classification of the system. Furthermore, we establish the corresponding symmetry reductions and construct some analytical solutions to the system.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126173575","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 aim of the present paper is to study holomorphically planar conformal vector fields(HPCV) on almost alpha-cosymplectic (k,m)-spaces. This is done assuming various conditions such as i) U is pointwise collinear with xi ( in this case the integral manifold of the distribution D is totally geodesic or totally umbilic), ii) M has a constant xi-sectional curvature (under this condition the integral manifold of the distribution D is totally geodesic (or totally umbilic) or the manifold is isometric to sphere S2n+1(pc) of radius 1 pc ), iii) M an almost alpha-cosymplectic (k,m)-spaces ( in this case the manifold is constant negative curvature or the integral manifold of the distribution D is totally geodesic(or totally umbilic) or U is an eigenvector of h).
{"title":"Holomorphically planar conformal vector fields on almost alpha-cosymplectic (k,m)-spaces","authors":"M. Yıldırım, N. Aktan","doi":"10.33401/fujma.1153224","DOIUrl":"https://doi.org/10.33401/fujma.1153224","url":null,"abstract":"The aim of the present paper is to study holomorphically planar conformal vector fields(HPCV) on almost alpha-cosymplectic (k,m)-spaces. This is done assuming various conditions such as i) U is pointwise collinear with xi ( in this case the integral manifold of the distribution D is totally geodesic or totally umbilic), ii) M has a constant xi-sectional curvature (under this condition the integral manifold of the distribution D is totally geodesic (or totally umbilic) or the manifold is isometric to sphere S2n+1(pc) of radius 1 pc ), iii) M an almost alpha-cosymplectic (k,m)-spaces ( in this case the manifold is constant negative curvature or the integral manifold of the distribution D is totally geodesic(or totally umbilic) or U is an eigenvector of h).","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128052394","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 motivation of this article is to define approximately near rings, some types of approximately near rings, approximately $N$-groups, approximately ideals and approximately near rings of all descriptive approximately cosets. Moreover, some properties of these approximately algebraic structures are given. Furthermore, approximately near ring homomorphisms are introduced and their some properties are investigated.
{"title":"Approximately Near Rings in Proximal Relator Spaces","authors":"E. Inan, Ayşegül Kocamaz","doi":"10.33401/fujma.1117103","DOIUrl":"https://doi.org/10.33401/fujma.1117103","url":null,"abstract":"The motivation of this article is to define approximately near rings, some types of approximately near rings, approximately $N$-groups, approximately ideals and approximately near rings of all descriptive approximately cosets. Moreover, some properties of these approximately algebraic structures are given. Furthermore, approximately near ring homomorphisms are introduced and their some properties are investigated.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"151 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":"134457335","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}
An undirected mathematical graph, G = (V,E) where V is a set of vertices and E = V ×V is the set of edges, can model a computer network. By this consideration we search for solutions to real computer network problems with a theoretical approach. This approach is based on labelling each edge by a subset of a universal set, and then encoding a path as the union of the labels of its edges. We label each vertex v ∈V by using a subset of universal set U , then we present a way to encode shortest paths in the graph G by using a way optimizing the data. By mathematical approach, it is provable that the labelling method we introduced eliminates the errors from the shortest paths in the graph. We aim to obtain the results in a more efficient use of network resources and to reduce network traffic. This shows how our theoretical approach works in real world network systems.
无向数学图G = (V,E)，其中V是一组顶点，E = V ×V是一组边，可以模拟计算机网络。通过这种考虑，我们用理论方法寻找解决实际计算机网络问题的方法。该方法基于用泛域集的子集标记每条边，然后将路径编码为其边的标签的并集。我们用泛域集U的一个子集来标记每个顶点v∈v，然后用优化数据的方法给出了图G中最短路径的编码方法。通过数学方法证明了所引入的标记方法可以消除图中最短路径的误差。我们的目标是在更有效地利用网络资源和减少网络流量的情况下获得结果。这显示了我们的理论方法是如何在现实世界的网络系统中工作的。
{"title":"Encoding the Shortest Paths in a King's Graph","authors":"Gokce CAYLAK KAYATURAN","doi":"10.33401/fujma.1091736","DOIUrl":"https://doi.org/10.33401/fujma.1091736","url":null,"abstract":"An undirected mathematical graph, G = (V,E) where V is a set of vertices and E = V ×V \u0000is the set of edges, can model a computer network. By this consideration we search for \u0000solutions to real computer network problems with a theoretical approach. This approach \u0000is based on labelling each edge by a subset of a universal set, and then encoding a path \u0000as the union of the labels of its edges. We label each vertex v ∈V by using a subset of \u0000universal set U , then we present a way to encode shortest paths in the graph G by using a \u0000way optimizing the data. By mathematical approach, it is provable that the labelling method \u0000we introduced eliminates the errors from the shortest paths in the graph. We aim to obtain \u0000the results in a more efficient use of network resources and to reduce network traffic. This \u0000shows how our theoretical approach works in real world network systems.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"40 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":"131263696","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 obtain exact solutions of the (2+1)-dimensional combined KdV-mKdV equation by using symbol calculation approach. First, we give some background on the equation. Second, the exp(-varphi(z))-expansion method will be introduced to solve the equation. After, using the exp(-varphi(z))-expansion method to solve the equation, we can get four types of exact solutions, which are hyperbolic, trigonometric, exponential, and rational function solutions. Finally, we can observe the characteristics of the exact solutions via computer simulation more easily.
{"title":"Employing the exp(-varphi(z))-expansion method to find analytical solutions for a (2+1)-dimensional combined KdV-mKdV equation","authors":"Baixin Chen, Yongyi Gu","doi":"10.33401/fujma.1125858","DOIUrl":"https://doi.org/10.33401/fujma.1125858","url":null,"abstract":"In this paper, we obtain exact solutions of the (2+1)-dimensional combined KdV-mKdV equation by using symbol calculation approach. First, we give some background on the equation. Second, the exp(-varphi(z))-expansion method will be introduced to solve the equation. After, using the exp(-varphi(z))-expansion method to solve the equation, we can get four types of exact solutions, which are hyperbolic, trigonometric, exponential, and rational function solutions. Finally, we can observe the characteristics of the exact solutions via computer simulation more easily.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128567220","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 study, some existing results dealing with the weak approximation property of Banach spaces are considered for the $p$-weak approximation property. Also, an observation on the bounded weak approximation and the $p$-bounded weak approximation properties is given. Moreover, the proof of the solution of the duality problem for the $p$-weak approximation property which exists in the literature is given in a shorter way as an alternative.
{"title":"Some Results on the p-Weak Approximation Property in Banach Spaces","authors":"Ayşegül Keten Çopur, Adalet Satar","doi":"10.33401/fujma.1099840","DOIUrl":"https://doi.org/10.33401/fujma.1099840","url":null,"abstract":"In this study, some existing results dealing with the weak approximation property of Banach spaces are considered for the $p$-weak approximation property. Also, an observation on the bounded weak approximation and the $p$-bounded weak approximation properties is given. Moreover, the proof of the solution of the duality problem for the $p$-weak approximation property which exists in the literature is given in a shorter way as an alternative.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131140911","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 consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.
{"title":"Constacyclic and Negacyclic Codes over F_2+uF_2+vF_2 and Equivalents of Codes in F_2","authors":"M. Özkan, Berk Yeni̇ce, Ayşe Tuğba Güroğlu","doi":"10.33401/fujma.1124502","DOIUrl":"https://doi.org/10.33401/fujma.1124502","url":null,"abstract":"In this work, we consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127803543","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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