Pub Date : 2021-04-01DOI: 10.37394/23206.2021.20.10
A. Abdel-Salam, M. Khalifa Saad
In this paper, we study the families of relatives of pedals and evolutes in the Minkowski spacetime plane R1. We obtain some relationships between these families which turn out to be different from Euclidean plane. Also, we classify and generalize these notions to the category of frontal curves in R1. Finally, some computational examples in support of our main results are given and plotted. Key–Words: Minkowski space-time, plane curve, evolute, evolutoids, pedal, pedaloids.
{"title":"Classification of Evolutoids and Pedaloids in Minkowski Space-time Plane","authors":"A. Abdel-Salam, M. Khalifa Saad","doi":"10.37394/23206.2021.20.10","DOIUrl":"https://doi.org/10.37394/23206.2021.20.10","url":null,"abstract":"In this paper, we study the families of relatives of pedals and evolutes in the Minkowski spacetime plane R1. We obtain some relationships between these families which turn out to be different from Euclidean plane. Also, we classify and generalize these notions to the category of frontal curves in R1. Finally, some computational examples in support of our main results are given and plotted. Key–Words: Minkowski space-time, plane curve, evolute, evolutoids, pedal, pedaloids.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132273618","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}
Pub Date : 2021-03-19DOI: 10.37394/23206.2021.20.8
Robert Gieroba, Łukasz Kruk
Ageneral multi-resource network with users requiring service from a number of shared resources simultaneously is considered. It is demonstrated that the Shortest Remaining Processing Time (SRPT) service protocol minimizes, in a suitable sense, the system resource idleness with respect to customers with residual service times not greater than any threshold value on every network route. Our arguments are pathwise, with no assumptions on the model stochastic primitives and the network topology. Key-Words: Queuing, resource sharing, SRPT, minimality, residual file sizes, partial ordering, service protocols
{"title":"Minimality of SRPT Networks With Resource Sharing","authors":"Robert Gieroba, Łukasz Kruk","doi":"10.37394/23206.2021.20.8","DOIUrl":"https://doi.org/10.37394/23206.2021.20.8","url":null,"abstract":"Ageneral multi-resource network with users requiring service from a number of shared resources simultaneously is considered. It is demonstrated that the Shortest Remaining Processing Time (SRPT) service protocol minimizes, in a suitable sense, the system resource idleness with respect to customers with residual service times not greater than any threshold value on every network route. Our arguments are pathwise, with no assumptions on the model stochastic primitives and the network topology. Key-Words: Queuing, resource sharing, SRPT, minimality, residual file sizes, partial ordering, service protocols","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130190585","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}
Pub Date : 2021-03-18DOI: 10.37394/23206.2021.20.7
Yu. K. Dem’yanovich
The purpose of this work is to obtain an effective evaluation of the speed of convergence for multidimensional approximations of the functions define on the differential manifold. Two approaches to approximation of functions, which are given on the manifold, are considered. The firs approach is the direct use of the approximation relations for the discussed manifold. The second approach is related to using the atlas of the manifold to utilise a well-designed approximation apparatus on the plane (finit element approximation, etc.). The firs approach is characterized by the independent construction and direct solution of the approximation relations. In this case the approximation relations are considered as a system of linear algebraic equations (with respect to the unknowns basic functions ωj(ζ)). This approach is called direct approximation construction . In the second approach, an approximation on a manifold is induced by the approximations in tangent spaces, for example, the Courant or the Zlamal or the Argyris fla approximations. Here we discuss the Courant fla approximations. In complex cases (in the multidimensional case or for increased requirements of smoothness) the second approach is more convenient. Both approaches require no processes cutting the manifold into a finit number of parts and then gluing the approximations obtained on each of the mentioned parts. This paper contains two examples of Courant type approximations. These approximations illustrate the both approaches mentioned above. Key–Words:approximation, manifold, simplicial subdivision, splines Received: February 18, 2021. Revised: March 10, 2021. Accepted: March 15, 2021. Published: March 18, 2021.
{"title":"Approximation on Manifold","authors":"Yu. K. Dem’yanovich","doi":"10.37394/23206.2021.20.7","DOIUrl":"https://doi.org/10.37394/23206.2021.20.7","url":null,"abstract":"The purpose of this work is to obtain an effective evaluation of the speed of convergence for multidimensional approximations of the functions define on the differential manifold. Two approaches to approximation of functions, which are given on the manifold, are considered. The firs approach is the direct use of the approximation relations for the discussed manifold. The second approach is related to using the atlas of the manifold to utilise a well-designed approximation apparatus on the plane (finit element approximation, etc.). The firs approach is characterized by the independent construction and direct solution of the approximation relations. In this case the approximation relations are considered as a system of linear algebraic equations (with respect to the unknowns basic functions ωj(ζ)). This approach is called direct approximation construction . In the second approach, an approximation on a manifold is induced by the approximations in tangent spaces, for example, the Courant or the Zlamal or the Argyris fla approximations. Here we discuss the Courant fla approximations. In complex cases (in the multidimensional case or for increased requirements of smoothness) the second approach is more convenient. Both approaches require no processes cutting the manifold into a finit number of parts and then gluing the approximations obtained on each of the mentioned parts. This paper contains two examples of Courant type approximations. These approximations illustrate the both approaches mentioned above. Key–Words:approximation, manifold, simplicial subdivision, splines Received: February 18, 2021. Revised: March 10, 2021. Accepted: March 15, 2021. Published: March 18, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134282907","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}
Pub Date : 2021-03-03DOI: 10.37394/23206.2021.20.4
D. K. Nagar, E. Zarrazola, Yohana Tabares-Herrera
Abstract: The doubly non-central generalized beta type 1 and type 2 distributions have been derived by using two independent non-central gamma variables with different scale parameters. These distributions generalize several well known central and non-central beta distributions. The doubly non-central generalized beta densities are much more flexible than many exiting beta models and can assume a large variety of shapes. Several properties of these distributions have been studied.
{"title":"Doubly Non-Central Generalized Beta Distributions","authors":"D. K. Nagar, E. Zarrazola, Yohana Tabares-Herrera","doi":"10.37394/23206.2021.20.4","DOIUrl":"https://doi.org/10.37394/23206.2021.20.4","url":null,"abstract":"Abstract: The doubly non-central generalized beta type 1 and type 2 distributions have been derived by using two independent non-central gamma variables with different scale parameters. These distributions generalize several well known central and non-central beta distributions. The doubly non-central generalized beta densities are much more flexible than many exiting beta models and can assume a large variety of shapes. Several properties of these distributions have been studied.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127527603","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}
Pub Date : 2021-03-02DOI: 10.37394/23206.2021.20.1
S. Jafari, A. E. El-Atik, Raja Mohammad Latif, M. El-Bably
Soft relation is a basic mathematical model that can be related to several real-life data. Throughout many fields, soft relations are used to build soft topological structures. In addition, soft topological constructs are generalized methods to calculate similarity and dissimilarity of objects. Within this article, we present a new approach for directly producing a soft topology by soft relation without using base or subbase. This process is important technique for applications of soft topology. There is investigations into the relationship between soft set topologies and different relations and some of their properties are obtained. Key–Words: Soft sets, soft topology, soft topological spaces, soft relations.
{"title":"Soft Topological Spaces Induced via Soft Relations","authors":"S. Jafari, A. E. El-Atik, Raja Mohammad Latif, M. El-Bably","doi":"10.37394/23206.2021.20.1","DOIUrl":"https://doi.org/10.37394/23206.2021.20.1","url":null,"abstract":"Soft relation is a basic mathematical model that can be related to several real-life data. Throughout many fields, soft relations are used to build soft topological structures. In addition, soft topological constructs are generalized methods to calculate similarity and dissimilarity of objects. Within this article, we present a new approach for directly producing a soft topology by soft relation without using base or subbase. This process is important technique for applications of soft topology. There is investigations into the relationship between soft set topologies and different relations and some of their properties are obtained. Key–Words: Soft sets, soft topology, soft topological spaces, soft relations.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122769563","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}
Pub Date : 2021-03-02DOI: 10.37394/23206.2021.20.2
I. Burova
The present paper is devoted to the application of local polynomial and non-polynomial interpolation splines of the third order of approximation for the numerical solution of the Volterra integral equation of the second kind. Computational schemes based on the use of the splines include the ability to calculate the integrals over the kernel multiplied by the basis function which are present in the computational methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra integral equations is also discussed. The results of the numerical experiments are presented. Key-Words: Volterra integral equation, non-polynomial spline, polynomial spline Received: December 21, 2019. Revised: January 25, 2021. Accepted: February 19, 2021. Published: March 2, 2021.
{"title":"Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind","authors":"I. Burova","doi":"10.37394/23206.2021.20.2","DOIUrl":"https://doi.org/10.37394/23206.2021.20.2","url":null,"abstract":"The present paper is devoted to the application of local polynomial and non-polynomial interpolation splines of the third order of approximation for the numerical solution of the Volterra integral equation of the second kind. Computational schemes based on the use of the splines include the ability to calculate the integrals over the kernel multiplied by the basis function which are present in the computational methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra integral equations is also discussed. The results of the numerical experiments are presented. Key-Words: Volterra integral equation, non-polynomial spline, polynomial spline Received: December 21, 2019. Revised: January 25, 2021. Accepted: February 19, 2021. Published: March 2, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132646384","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}
Pub Date : 2021-03-02DOI: 10.37394/23206.2021.20.3
N. Abughazalah, Majid Khan
The basic requirement by adding confusion is to ensure the confidentiality of the secret information. In the present article, we have suggested new methodology for the construction of nonlinear confusion component. This confusion component is used for enciphering the secret information and hiding it in a cover medium by proposed scheme. The proposed scheme is based on ring structure instead of Galois field mechanism. To provide multi-layer security, secret information is first encrypted by using confusion component and then utilized three different substitution boxes (S-boxes) to hide into the cover medium.
{"title":"An Efficient Information Hiding Mechanism Based on Confusion Component over Local Ring and Moore-Penrose Pseudo Inverse","authors":"N. Abughazalah, Majid Khan","doi":"10.37394/23206.2021.20.3","DOIUrl":"https://doi.org/10.37394/23206.2021.20.3","url":null,"abstract":"The basic requirement by adding confusion is to ensure the confidentiality of the secret information. In the present article, we have suggested new methodology for the construction of nonlinear confusion component. This confusion component is used for enciphering the secret information and hiding it in a cover medium by proposed scheme. The proposed scheme is based on ring structure instead of Galois field mechanism. To provide multi-layer security, secret information is first encrypted by using confusion component and then utilized three different substitution boxes (S-boxes) to hide into the cover medium.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127846403","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}
Pub Date : 2021-02-09DOI: 10.37394/23206.2020.19.74
Samir Belhadj, M. Goubi
Abstract: In this work, we are interested by Vasyunin cotangent-sum V (p/q) encountered in computation of the inner product arising in the Baez-Duarte-Balazard criterion for Riemann hypothesis. By hint of generating functions theory and introduction of double Euclidean algorithm, we give series expansions of V (p/q) and the symmetric sum S (p, q) = V (p/q)+V (q/p) . These calculus permit to deduce another reformulation of Vasyunin formula. This study is a complement of the recent work of M. Goubi concerning special case V (1/q).
摘要:在本文中，我们对黎曼假设的Baez-Duarte-Balazard准则中计算内积时遇到的Vasyunin共切和V (p/q)感兴趣。利用生成函数理论的提示和二重欧几里得算法的引入，给出了V (p/q)的级数展开式和对称和S (p, q) = V (p/q)+V (q/p)。这些演算可以推导出瓦苏宁公式的另一种重新表述。本研究是对最近Goubi先生关于特例V (1/q)的研究的补充。
{"title":"On the Vasyunin Cotangent sums related to Riemann Hypothesis","authors":"Samir Belhadj, M. Goubi","doi":"10.37394/23206.2020.19.74","DOIUrl":"https://doi.org/10.37394/23206.2020.19.74","url":null,"abstract":"Abstract: In this work, we are interested by Vasyunin cotangent-sum V (p/q) encountered in computation of the inner product arising in the Baez-Duarte-Balazard criterion for Riemann hypothesis. By hint of generating functions theory and introduction of double Euclidean algorithm, we give series expansions of V (p/q) and the symmetric sum S (p, q) = V (p/q)+V (q/p) . These calculus permit to deduce another reformulation of Vasyunin formula. This study is a complement of the recent work of M. Goubi concerning special case V (1/q).","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116474144","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}
Pub Date : 2020-04-27DOI: 10.37394/23206.2020.19.21
García Planas, M. Isabel
M. I. GARCÍA-PLANAS Universitat Politècnica de Catalunya Departament de Matemàtiques Mineria 1, 08038 Barcelona SPAIN maria.isabel.garcia@upc.edu Abstract: In this paper, a review of the simultaneous diagonalization of n-tuples of matrices for its applications in sciences is presented. For example, in quantum mechanics, position and momentum operators do not have a shared base that can represent the states of the system because they not commute, which is why switching operators form a key element of quantum physics since they define quantities that are compatible, that is, defined simultaneously. We are going to study this kind of family of linear operators using geometric constructions such as the principal bundles and associating them with a cohomology class measuring the deviation of the local product structure from the global product structure.
m.i. GARCÍA-PLANAS Catalunya polititat cnica departmentde Matemàtiques Mineria 1, 08038 Barcelona SPAIN maria.isabel.garcia@upc.edu摘要:本文综述了n元组矩阵的同时对角化及其在科学中的应用。例如，在量子力学中，位置和动量算符没有一个可以表示系统状态的共享基，因为它们不能交换，这就是为什么切换算符形成量子物理学的关键要素，因为它们定义的量是兼容的，即同时定义的。我们将使用诸如主束之类的几何结构来研究这类线性算子，并将它们与测量局部积结构与全局积结构偏差的上同调类联系起来。
{"title":"The Bundle of Simultaneously Diagonalizable N-tuples of Matrices","authors":"García Planas, M. Isabel","doi":"10.37394/23206.2020.19.21","DOIUrl":"https://doi.org/10.37394/23206.2020.19.21","url":null,"abstract":"M. I. GARCÍA-PLANAS Universitat Politècnica de Catalunya Departament de Matemàtiques Mineria 1, 08038 Barcelona SPAIN maria.isabel.garcia@upc.edu Abstract: In this paper, a review of the simultaneous diagonalization of n-tuples of matrices for its applications in sciences is presented. For example, in quantum mechanics, position and momentum operators do not have a shared base that can represent the states of the system because they not commute, which is why switching operators form a key element of quantum physics since they define quantities that are compatible, that is, defined simultaneously. We are going to study this kind of family of linear operators using geometric constructions such as the principal bundles and associating them with a cohomology class measuring the deviation of the local product structure from the global product structure.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134557116","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}
Pub Date : 2020-04-07DOI: 10.37394/23206.2020.19.16
Raja Mohammad Latif
In 2014 Mubarki, Al-Rshudi, and Al-Juhani introduced and studied the notion of a set in general topology called β * - open sets and investigated its fundamental properties and studied the relationships between β * - open set and other topological sets including β * - continuity in topological spaces. The objective of this paper is to introduce the new concepts called β * - compact space, countably β * - compact space, β * - Lindelof space, almost β * - compact space, mildly β * - compact space and β * - connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.
{"title":"β* - Compactness and β* - Connectedness","authors":"Raja Mohammad Latif","doi":"10.37394/23206.2020.19.16","DOIUrl":"https://doi.org/10.37394/23206.2020.19.16","url":null,"abstract":"In 2014 Mubarki, Al-Rshudi, and Al-Juhani introduced and studied the notion of a set in general topology called β * - open sets and investigated its fundamental properties and studied the relationships between β * - open set and other topological sets including β * - continuity in topological spaces. The objective of this paper is to introduce the new concepts called β * - compact space, countably β * - compact space, β * - Lindelof space, almost β * - compact space, mildly β * - compact space and β * - connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126086079","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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