In this study, we determine the isoparametric surfaces and we give the Gauss map of these surfaces by semi symmetric matrix, in Lorentz space. Also we define any chord property and we show that the surfaces which have the chord property corresponds to isoparametric surfaces. Moreover, we consider the chord property locally and we give some examples in the Euclidean space.
{"title":"Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space","authors":"E. Öztürk","doi":"10.33401/fujma.643374","DOIUrl":"https://doi.org/10.33401/fujma.643374","url":null,"abstract":"In this study, we determine the isoparametric surfaces and we give the Gauss map of these surfaces by semi symmetric matrix, in Lorentz space. Also we define any chord property and we show that the surfaces which have the chord property corresponds to isoparametric surfaces. Moreover, we consider the chord property locally and we give some examples in the Euclidean space.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122937774","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 pseudoblocks is borrowed from [1] and introduced to finite-dimensional algebras. We determine the pseudoblocks for several known algebras such as the triangular algebra and the cyclic group algebra. Also, we determine the pseudoblocks for the group algebra of the special linear group $SL(2,p)$ in the natural characteristic being the only finite group of Lie type of finite representation type.
{"title":"Pseudoblocks of Finite Dimensional Algebras","authors":"Ahmed A. Khammash, Afaf Alharthi","doi":"10.33401/fujma.691602","DOIUrl":"https://doi.org/10.33401/fujma.691602","url":null,"abstract":"The notion of pseudoblocks is borrowed from [1] and introduced to finite-dimensional algebras. We determine the pseudoblocks for several known algebras such as the triangular algebra and the cyclic group algebra. Also, we determine the pseudoblocks for the group algebra of the special linear group $SL(2,p)$ in the natural characteristic being the only finite group of Lie type of finite representation type.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127681179","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 essential goal of this manuscript is to investigate some novel sequence spaces of $p_{infty }left( Delta right) $, $p_{c}left( Delta right) $ and $p_{0}left( Delta right) $ which are comprised by all sequence spaces whose differences are in Pascal sequence spaces $p_{infty }$, $p_{c}$ and $p_{0}$, respectively. Furthermore, we determine both $gamma $-, $beta $-, $alpha $- duals of newly defined difference sequence spaces of $p_{infty }left( Delta right) $, $% p_{c}left( Delta right) $ and $p_{0}left( Delta right) $. We also obtain bases of the newly defined difference sequence spaces of $p_{c}left( Delta right) $ and $p_{0}left( Delta right) $. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes $(p_{c}left( Delta right) :l_{infty })$ and $(p_{c}left( Delta right) :c)$ are characterized.
{"title":"Difference Sequence Spaces Derived by using Pascal Transform","authors":"Saadettin Aydın, Harun Polat","doi":"10.33401/FUJMA.541721","DOIUrl":"https://doi.org/10.33401/FUJMA.541721","url":null,"abstract":"The essential goal of this manuscript is to investigate some novel sequence spaces of $p_{infty }left( Delta right) $, $p_{c}left( Delta right) $ and $p_{0}left( Delta right) $ which are comprised by all sequence spaces whose differences are in Pascal sequence spaces $p_{infty }$, $p_{c}$ and $p_{0}$, respectively. Furthermore, we determine both $gamma $-, $beta $-, $alpha $- duals of newly defined difference sequence spaces of $p_{infty }left( Delta right) $, $% p_{c}left( Delta right) $ and $p_{0}left( Delta right) $. We also obtain bases of the newly defined difference sequence spaces of $p_{c}left( Delta right) $ and $p_{0}left( Delta right) $. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes $(p_{c}left( Delta right) :l_{infty })$ and $(p_{c}left( Delta right) :c)$ are characterized.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":" 43","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113952365","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 concept of UP-bialgebras was introduced and analyzed by Mosrijai and Iampan at the beginning of 2019. Theorem that we can look at as the First theorem on UP-biisomorphism between the UP-bialgebras is given in our forthcoming text [9]. In this article we construct a form of the third theorem on UP-biisomorphism between UP-bialgebras.
{"title":"The Third Isomorphism Theorem on UP-Bialgebras","authors":"D. Romano","doi":"10.33401/FUJMA.552192","DOIUrl":"https://doi.org/10.33401/FUJMA.552192","url":null,"abstract":"The concept of UP-bialgebras was introduced and analyzed by Mosrijai and Iampan at the beginning of 2019. Theorem that we can look at as the First theorem on UP-biisomorphism between the UP-bialgebras is given in our forthcoming text [9]. In this article we construct a form of the third theorem on UP-biisomorphism between UP-bialgebras.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"250 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117233322","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 bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.
{"title":"Neimark-Sacker Bifurcation of a Third Order Difference Equation","authors":"M. Aloqeili, A. Shareef","doi":"10.33401/FUJMA.527572","DOIUrl":"https://doi.org/10.33401/FUJMA.527572","url":null,"abstract":"In this paper, we investigate the bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122169274","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 seek to investigate the effect of inflation on the optimal investment strategies for DC Pension. Our model permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest in risk-free asset and two risky assets. A stochastic differential equation of the pension wealth that takes into account certainly agreed proportions of the plan member's salary, paid as a contribution towards the pension fund, is presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation has significant negative effect on optimal investment strategy, particularly, the CCRA is not constant with the investment strategy since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategy.
{"title":"Effect of Inflation on Stochastic Optimal Investment Strategies for DC Pension under the Affine Interest Rate Model","authors":"B. Osu, K. Njoku","doi":"10.33401/FUJMA.409748","DOIUrl":"https://doi.org/10.33401/FUJMA.409748","url":null,"abstract":" In this paper, we seek to investigate the effect of inflation on the optimal investment strategies for DC Pension. Our model permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest in risk-free asset and two risky assets. A stochastic differential equation of the pension wealth that takes into account certainly agreed proportions of the plan member's salary, paid as a contribution towards the pension fund, is presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation has significant negative effect on optimal investment strategy, particularly, the CCRA is not constant with the investment strategy since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategy.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130731062","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, the efficient numerical solutions of a class of system of Fredholm integral equations are solved by the Nystrom method, which discretizes the system of integral equations into solving a linear system. The existence and uniqueness of the exact solutions are proved by the Banach fixed point theorem. The format of the Nystrom solutions is given, especially with the composite Trapezoidal and Simpson rules. The results of error estimation and convergence analysis are obtained in the infinite norm sense. The validity and reliability of the theoretical analysis are verified by numerical experiments.
{"title":"The Nyström Method and Convergence Analysis for System of Fredholm Integral Equations","authors":"Huimin Zhou, Qi-sheng Wang","doi":"10.33401/FUJMA.486878","DOIUrl":"https://doi.org/10.33401/FUJMA.486878","url":null,"abstract":"In this paper, the efficient numerical solutions of a class of system of Fredholm integral equations are solved by the Nystrom method, which discretizes the system of integral equations into solving a linear system. The existence and uniqueness of the exact solutions are proved by the Banach fixed point theorem. The format of the Nystrom solutions is given, especially with the composite Trapezoidal and Simpson rules. The results of error estimation and convergence analysis are obtained in the infinite norm sense. The validity and reliability of the theoretical analysis are verified by numerical experiments.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116293178","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 three-dimensional quasi-Sasakian manifolds admitting the Schouten-van Kampen connection. Also, we study D-homothetic deformations on three-dimensional quasi-Sasakian manifolds admitting Schouten-van connection and projectively flat three-dimensional quasi-Sasakian manifolds admitting scv connection.
{"title":"On Quasi-Sasakian Manifolds","authors":"A. Sazak, A. Yildiz","doi":"10.33401/FUJMA.527465","DOIUrl":"https://doi.org/10.33401/FUJMA.527465","url":null,"abstract":"In this paper we study three-dimensional quasi-Sasakian manifolds admitting the Schouten-van Kampen connection. Also, we study D-homothetic deformations on three-dimensional quasi-Sasakian manifolds admitting Schouten-van connection and projectively flat three-dimensional quasi-Sasakian manifolds admitting scv connection.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124044393","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 objective of this study is to extend the usage of Newton's method for Banach space valued operators. We use our new idea of restricted convergence domain in combination with the center Lipschitz hypothesis on the Frechet-derivatives where the center is not necessarily the initial point. This way our semi-local convergence analysis is tighter than in earlier works (since the new majorizing function is at least as tight as the ones used before) leading to weaker criteria, better error bounds more precise information on the solution. These improvements are obtained under the same computational effort.
{"title":"Extended Semi-Local Convergence of Newton's Method using the Center Lipschitz Condition and the Restricted Convergence Domain","authors":"I. K. Argyros, S. George","doi":"10.33401/FUJMA.503716","DOIUrl":"https://doi.org/10.33401/FUJMA.503716","url":null,"abstract":"The objective of this study is to extend the usage of Newton's method for Banach space valued operators. We use our new idea of restricted convergence domain in combination with the center Lipschitz hypothesis on the Frechet-derivatives where the center is not necessarily the initial point. This way our semi-local convergence analysis is tighter than in earlier works (since the new majorizing function is at least as tight as the ones used before) leading to weaker criteria, better error bounds more precise information on the solution. These improvements are obtained under the same computational effort.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"12367 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123016139","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}
Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in $x$ and $t$. For each positive integer $N$, the numerator is a polynomial of degree $N(N+1)-2$ in $x$ and $t$, while the denominator is a polynomial of degree $N(N+1)$ in $x$ and $t$. So we obtain a hierarchy of rational solutions depending on an integer $N$ called the order of the solution. We construct explicit expressions of these rational solutions for $N=1$ to $4$.
{"title":"Rational Solutions to the Boussinesq Equation","authors":"P. Gaillard","doi":"10.33401/FUJMA.512333","DOIUrl":"https://doi.org/10.33401/FUJMA.512333","url":null,"abstract":"Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in $x$ and $t$. For each positive integer $N$, the numerator is a polynomial of degree $N(N+1)-2$ in $x$ and $t$, while the denominator is a polynomial of degree $N(N+1)$ in $x$ and $t$. So we obtain a hierarchy of rational solutions depending on an integer $N$ called the order of the solution. We construct explicit expressions of these rational solutions for $N=1$ to $4$.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"2 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131991019","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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