Kouame Beranger Edja, K. A. Touré, Brou Jean-Claude Koua
In this paper, we study the quenching behavior of semidiscretizations of the heat equation with nonlinear boundary conditions. We obtain some conditions under which the positive solution of the semidiscrete problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time and obtain some results on numerical quenching rate. Finally we give some numerical results to illustrate our analysis.
{"title":"Numerical quenching of a heat equation with nonlinear boundary conditions","authors":"Kouame Beranger Edja, K. A. Touré, Brou Jean-Claude Koua","doi":"10.22436/jnsa.013.01.06","DOIUrl":"https://doi.org/10.22436/jnsa.013.01.06","url":null,"abstract":"In this paper, we study the quenching behavior of semidiscretizations of the heat equation with nonlinear boundary conditions. We obtain some conditions under which the positive solution of the semidiscrete problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time and obtain some results on numerical quenching rate. Finally we give some numerical results to illustrate our analysis.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87478179","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 optimal asset allocation strategy for a defined contribution (DC) pension fund with return of premium clause under Heston’s volatility model in mean-variance utility frame work. In this model, members’ next of kin are allowed to withdraw their family members’ accumulated premium with predetermined interest. Also, investments in one risk free asset and one risky asset are considered to help increase the accumulated funds of the remaining members in order to meet their retirement needs. Using the actuarial symbol, we formulize the problem as a continuous time mean-variance stochastic optimal control problem. We establish an optimization problem from the extended Hamilton Jacobi Bellman equations using the game theoretic approach and solve the optimization problem to obtain the optimal allocation strategy for the two assets, the optimal fund size and also the efficient frontier of the pension members. We analyze numerically the effect of some parameters on the optimal allocation strategy and deduce that as the initial wealth, predetermined interest rate and risk averse level increases, the optimal allocation policy for the risky asset (equity) decreases. Furthermore, we give a theoretical comparison of our result with an existing result and observed that the optimal allocation policy whose return is with predetermined interest is higher compared to that without predetermined interest.
{"title":"On the optimal asset allocation strategy for a defined contribution pension system with refund clause of premium with predetermined interest under Heston's volatility model","authors":"Edikan E. Akpanibah, B. Osu, S. Ihedioha","doi":"10.22436/jnsa.013.01.05","DOIUrl":"https://doi.org/10.22436/jnsa.013.01.05","url":null,"abstract":"In this paper, we study optimal asset allocation strategy for a defined contribution (DC) pension fund with return of premium clause under Heston’s volatility model in mean-variance utility frame work. In this model, members’ next of kin are allowed to withdraw their family members’ accumulated premium with predetermined interest. Also, investments in one risk free asset and one risky asset are considered to help increase the accumulated funds of the remaining members in order to meet their retirement needs. Using the actuarial symbol, we formulize the problem as a continuous time mean-variance stochastic optimal control problem. We establish an optimization problem from the extended Hamilton Jacobi Bellman equations using the game theoretic approach and solve the optimization problem to obtain the optimal allocation strategy for the two assets, the optimal fund size and also the efficient frontier of the pension members. We analyze numerically the effect of some parameters on the optimal allocation strategy and deduce that as the initial wealth, predetermined interest rate and risk averse level increases, the optimal allocation policy for the risky asset (equity) decreases. Furthermore, we give a theoretical comparison of our result with an existing result and observed that the optimal allocation policy whose return is with predetermined interest is higher compared to that without predetermined interest.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85375747","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}
H. Yousof, Mahdi Rasekhi, M. Alizadeh, G. Hamedani
In this paper, we propose and study a new class of continuous distributions called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, 84 (1997), 641–652]. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. Some characterizations for the new family are presented. Maximum likelihood estimation for the model parameters under uncensored and censored data is addressed in Section 5 as well as a simulation study to assess the performance of the estimators. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.
{"title":"The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications, and characterizations","authors":"H. Yousof, Mahdi Rasekhi, M. Alizadeh, G. Hamedani","doi":"10.22436/jnsa.013.01.04","DOIUrl":"https://doi.org/10.22436/jnsa.013.01.04","url":null,"abstract":"In this paper, we propose and study a new class of continuous distributions called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, 84 (1997), 641–652]. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. Some characterizations for the new family are presented. Maximum likelihood estimation for the model parameters under uncensored and censored data is addressed in Section 5 as well as a simulation study to assess the performance of the estimators. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86467204","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 Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is a three-dimensional phenomenon. [The paper is published in an international journal.]
{"title":"Modeling turbulence with the Navier-Stokes equations","authors":"B. Wong","doi":"10.22436/jnsa.013.02.03","DOIUrl":"https://doi.org/10.22436/jnsa.013.02.03","url":null,"abstract":"The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is a three-dimensional phenomenon. [The paper is published in an international journal.]","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87744148","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 obtain some fixed point and common fixed point theorems of comparable maps satisfying certain contractive conditions on partially ordered cone b-metric space over Banach algebras. Some examples are also provided to illustrate the main results presented in this paper, which extend and generalize several known results in cone b-metric spaces.
{"title":"Fixed point and common fixed point theorems on ordered cone b-metric space over Banach algebra","authors":"Sharafat Hussain","doi":"10.22436/jnsa.013.01.03","DOIUrl":"https://doi.org/10.22436/jnsa.013.01.03","url":null,"abstract":"In this work, we obtain some fixed point and common fixed point theorems of comparable maps satisfying certain contractive conditions on partially ordered cone b-metric space over Banach algebras. Some examples are also provided to illustrate the main results presented in this paper, which extend and generalize several known results in cone b-metric spaces.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75620782","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, differential transform method (DTM) is presented to solve Tumor-immune system at two initial conditions where two different cases of the interaction between tumor cells and effector cells. The system is presented to show the ability of the method for non-linear systems of differential equations. By using small iteration, the results of DTM are near the results of Runge-Kutta fourth-fifth order method (ode45 solver in MATLAB) and better than the results of Runge-Kutta second-third order method (ode23 solver in MATLAB). Also, the residual error of DTM’s solutions approach zero. Therefore, DTM’s solutions approximate exact solutions. Finally, we conclude formulae that we can find DTM’s solutions, better than the results of RungeKutta second-third order method, in any interval we need.
{"title":"Solution of the tumor-immune system by differential transform method","authors":"M. Kassem, A. A. Hemeda, M. Abdeen","doi":"10.22436/jnsa.013.01.02","DOIUrl":"https://doi.org/10.22436/jnsa.013.01.02","url":null,"abstract":"In this paper, differential transform method (DTM) is presented to solve Tumor-immune system at two initial conditions where two different cases of the interaction between tumor cells and effector cells. The system is presented to show the ability of the method for non-linear systems of differential equations. By using small iteration, the results of DTM are near the results of Runge-Kutta fourth-fifth order method (ode45 solver in MATLAB) and better than the results of Runge-Kutta second-third order method (ode23 solver in MATLAB). Also, the residual error of DTM’s solutions approach zero. Therefore, DTM’s solutions approximate exact solutions. Finally, we conclude formulae that we can find DTM’s solutions, better than the results of RungeKutta second-third order method, in any interval we need.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84460395","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}
{"title":"Solvability of the functional integro-differential equation with self-reference and state-dependence","authors":"A. El-Sayed, Reda Gamal Aahmed","doi":"10.22436/JNSA.013.01.01","DOIUrl":"https://doi.org/10.22436/JNSA.013.01.01","url":null,"abstract":"","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78952316","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 present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gasdust cloud. We consider two special initial conditions for density and velocity. We take an analytical Cole-Hopf transformation method to study the dynamics of a gravitating system of a gas-dust cloud. The technique is employed to simplify the equations of dynamics, and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The obtained results in this study are presented in graphics.
{"title":"Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud","authors":"M. Abobaker","doi":"10.22436/JNSA.012.12.06","DOIUrl":"https://doi.org/10.22436/JNSA.012.12.06","url":null,"abstract":"In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gasdust cloud. We consider two special initial conditions for density and velocity. We take an analytical Cole-Hopf transformation method to study the dynamics of a gravitating system of a gas-dust cloud. The technique is employed to simplify the equations of dynamics, and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The obtained results in this study are presented in graphics.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85777525","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}
Charyulu L. N. Rompicharla, V. Putcha, G. V. S. R. Deekshithulu
In this paper, sufficient conditions for the controllability of the fuzzy dynamical discrete system with the use of fuzzy rule base are established. Further, a sufficient condition for the fuzzy dynamical discrete system to be observable is constructed. The main advantage of this approach is that the rule base for the initial value can be determined without actually solving the system. Difference inclusions approach is adopted in the construction of these conditions. All the established theories are consolidated and explained with the help of examples.
{"title":"Controllability and observability of fuzzy matrix discrete dynamical systems","authors":"Charyulu L. N. Rompicharla, V. Putcha, G. V. S. R. Deekshithulu","doi":"10.22436/JNSA.012.12.04","DOIUrl":"https://doi.org/10.22436/JNSA.012.12.04","url":null,"abstract":"In this paper, sufficient conditions for the controllability of the fuzzy dynamical discrete system with the use of fuzzy rule base are established. Further, a sufficient condition for the fuzzy dynamical discrete system to be observable is constructed. The main advantage of this approach is that the rule base for the initial value can be determined without actually solving the system. Difference inclusions approach is adopted in the construction of these conditions. All the established theories are consolidated and explained with the help of examples.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"41 4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87680979","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}
Poly-Cauchy numbers c n (n > 0, k > 1) have explicit expressions in terms of the Stirling numbers of the first kind. When the index is negative, there exists a different expression. However, the sequence {c n }n>0 seem quite irregular for a fixed integer k > 2. In this paper we establish a certain kind of recurrence relations among the sequence {c n }n>0, analyzing the structure of poly-Cauchy numbers. We also study those of poly-Cauchy numbers of the second kind, poly-Euler numbers, and poly-Euler numbers of the second kind. Some different proofs are given. As applications, some leaping relations are shown.
{"title":"Some recurrence relations of poly-Cauchy numbers","authors":"T. Komatsu","doi":"10.22436/JNSA.012.12.05","DOIUrl":"https://doi.org/10.22436/JNSA.012.12.05","url":null,"abstract":"Poly-Cauchy numbers c n (n > 0, k > 1) have explicit expressions in terms of the Stirling numbers of the first kind. When the index is negative, there exists a different expression. However, the sequence {c n }n>0 seem quite irregular for a fixed integer k > 2. In this paper we establish a certain kind of recurrence relations among the sequence {c n }n>0, analyzing the structure of poly-Cauchy numbers. We also study those of poly-Cauchy numbers of the second kind, poly-Euler numbers, and poly-Euler numbers of the second kind. Some different proofs are given. As applications, some leaping relations are shown.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"06 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85850794","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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