Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80885220160521A fresh view on the interaction of growth rates and diffusion coefficients of cancer tumor modelsA fresh view on the interaction of growth rates and diffusion coefficients of cancer tumor models1231202610.22055/jamm.2016.12026FAKhosroSayevandFaculty memberKazemPichaghchiJournal Article20150715In this paper, the growth of cancer tumor cells as a prototype problems in real life will be discussed. Several different cases of the net killing rate are taken into consideration. These patterns are including the cases where net killing rate of the cancer cells are dependent on the concentration of the cells. Our proposed approach which is introduced for these observation is based on a modification of fractional Laplace iterative transformations scheme. The fractional derivative is in the local fractional sense. The obtained results enables us to give some recommendations on the effects of modeling of the cancer tumor.In this paper, the growth of cancer tumor cells as a prototype problems in real life will be discussed. Several different cases of the net killing rate are taken into consideration. These patterns are including the cases where net killing rate of the cancer cells are dependent on the concentration of the cells. Our proposed approach which is introduced for these observation is based on a modification of fractional Laplace iterative transformations scheme. The fractional derivative is in the local fractional sense. The obtained results enables us to give some recommendations on the effects of modeling of the cancer tumor.Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80885220160521Computing the pareto frontier of a linear Multiobjective bi-level modelComputing the pareto frontier of a linear Multiobjective bi-level model25451202710.22055/jamm.2016.12027FAAbbasMehrabaniHabibeSadeghiJournal Article20150617Bilevel programming is the model for hierarchical optimization problems in which there are two decision makers that have different objective functions, variables and constraints. Alves et al in[1], proposed a method for computing the Pareto frontier of bilevel linear problem with biobjective at the upper level and a single objective function at the lower level. In this paper, we extend their method for the situation in which there exists more than two objective function at both levels, and then by using a suitable exchange variable, we proposed a new method for computing the Pareto frontier of bilevel linear problem with fractional multi-objective at the upper level. Finally we will show the efficiency of the propsed approaches by solving a few numerical examples and comparing the results with other methods.Bilevel programming is the model for hierarchical optimization problems in which there are two decision makers that have different objective functions, variables and constraints. Alves et al in[1], proposed a method for computing the Pareto frontier of bilevel linear problem with biobjective at the upper level and a single objective function at the lower level. In this paper, we extend their method for the situation in which there exists more than two objective function at both levels, and then by using a suitable exchange variable, we proposed a new method for computing the Pareto frontier of bilevel linear problem with fractional multi-objective at the upper level. Finally we will show the efficiency of the propsed approaches by solving a few numerical examples and comparing the results with other methods.Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80885220160521A new formulation for extrapolation of seismic wave field response and its derivativesA new formulation for extrapolation of seismic wave field response and its derivatives47581202810.22055/jamm.2016.12028FAFarzadMoradpouriدانشگاه صنعتی شاهرودAliMoradzadehReynam CruzPestanaMehrdadSoleimani MonfaredJournal Article20150628The aim of this study is to present a new symplectic integrator for the case of spatially varying velocity based on Leapfrog (L) and Rapid Expansion Methods (REM). First of all, approximation of the wave field at each time step has been considered using rapid expansion method. Then the wave equation is rewrite as Hamiltonian system. It can provide an accurate solution for the acoustic wave equation to simulate the wave field response at each time. After that, for much more accurate and stable solution to extrapolate the wave field and its derivative, a new formulation based on leapfrog and rapid expansion methods has been presented. The obtained results of simple model indicate that this new formulation provides a very high level of accuracy and stability for estimation of wave field response and its derivatives.The aim of this study is to present a new symplectic integrator for the case of spatially varying velocity based on Leapfrog (L) and Rapid Expansion Methods (REM). First of all, approximation of the wave field at each time step has been considered using rapid expansion method. Then the wave equation is rewrite as Hamiltonian system. It can provide an accurate solution for the acoustic wave equation to simulate the wave field response at each time. After that, for much more accurate and stable solution to extrapolate the wave field and its derivative, a new formulation based on leapfrog and rapid expansion methods has been presented. The obtained results of simple model indicate that this new formulation provides a very high level of accuracy and stability for estimation of wave field response and its derivatives.Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80885220160521Make Improvements and Optimal Allocation of Budget in Order to Increase safety of The Shiraz-Abadeh RoadMake Improvements and Optimal Allocation of Budget in Order to Increase safety of The Shiraz-Abadeh Road59721202910.22055/jamm.2016.12029FAJournal Article20140803Regarding the importance of difficulties that made by accidents in the transportation between the cities, this paper presents a way for optimal budget allocation to improve disaster points of the Shiraz-Abadeh road for increasing its traffic safety. For this aim, two possible kinds of improvements (continuous and discrete) are considered and the problem is modeled as a mixed integer programming with continues and binary variables in which its aim is to obtain the optimal allocation and maximizes the reducing rate of accidents. Regarding the difficulties caused by high dimensionality of the problem, we present a new solution method based on the bender decomposition technique to illustrate the optimal allocation. First, the original problem is split into two smaller problems. Then, in an iterative procedure, in each iteration a new constraint is introduced and added to the problem. Thus, in each step, the current solution comes nearer to the optimal one; based on the existed theorem, after a finite number of iterations, the algorithm converges to the optimal solutionRegarding the importance of difficulties that made by accidents in the transportation between the cities, this paper presents a way for optimal budget allocation to improve disaster points of the Shiraz-Abadeh road for increasing its traffic safety. For this aim, two possible kinds of improvements (continuous and discrete) are considered and the problem is modeled as a mixed integer programming with continues and binary variables in which its aim is to obtain the optimal allocation and maximizes the reducing rate of accidents. Regarding the difficulties caused by high dimensionality of the problem, we present a new solution method based on the bender decomposition technique to illustrate the optimal allocation. First, the original problem is split into two smaller problems. Then, in an iterative procedure, in each iteration a new constraint is introduced and added to the problem. Thus, in each step, the current solution comes nearer to the optimal one; based on the existed theorem, after a finite number of iterations, the algorithm converges to the optimal solutionShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80885220160521Preliminary Test Estimation in Two-parameter Exponential Model
Under Progressively Type-II CensoringPreliminary Test Estimation in Two-parameter Exponential Model
Under Progressively Type-II Censoring73891203010.22055/jamm.2016.12030FAAkbarAsgharzadeh0000-0001-6714-4533MohammadSharifiJournal Article20150929In this paper, the preliminary test estimators for the location and scale parameters of the two-parameter <br />exponential model are presented based on progressively Type II censored samples. The biases and mean squared <br />errors of the proposed estimators are given. It is shown that the proposed estimators dominate the corresponding <br />classical estimators in the neighborhood of null hypothesis. We also provide the range of the parameters for which <br />the proposed estimators dominate the corresponding classical estimators for different sample sizes and level of <br />significance. Finally, a numerical example is given to illustrate the results.In this paper, the preliminary test estimators for the location and scale parameters of the two-parameter <br />exponential model are presented based on progressively Type II censored samples. The biases and mean squared <br />errors of the proposed estimators are given. It is shown that the proposed estimators dominate the corresponding <br />classical estimators in the neighborhood of null hypothesis. We also provide the range of the parameters for which <br />the proposed estimators dominate the corresponding classical estimators for different sample sizes and level of <br />significance. Finally, a numerical example is given to illustrate the results.Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80885220160521Presenting a mathematical model and investigating effects of contaminated needle sharing on prevalence of HIV/AIDS diseasePresenting a mathematical model and investigating effects of contaminated needle sharing on prevalence of HIV/AIDS disease911081203110.22055/jamm.2016.12031FAAfshinBabaeiHosseinJafari0000-0001-6807-6675MasumehAhmadiJournal Article20150828In this paper, a mathematical model for studying HIV/AIDS dynamics is presented. Based on this model, the effects of contaminated needle sharing in addicted population on spread of HIV/AIDS is investigated. For this purpose, first, the effective reproduction number is obtained by using the next generation operator method. Then, the reproduction number is examined in two cases, one with sharing needles and the other one with not sharing needles. The optimal control problem is formulated by applying some controls on the disease model including use of non-shared and sterile needles, use of prevention methods, screening of unaware infectives and treating patients. Necessary conditions for optimal control is determined by using Pontryagin’s minimum principle. Finally, numerical results is obtained by the Runge–Kutta fourth-order method. The results show a significant difference in control of prevalence of disease between the cases applying and not applying control on the disease.In this paper, a mathematical model for studying HIV/AIDS dynamics is presented. Based on this model, the effects of contaminated needle sharing in addicted population on spread of HIV/AIDS is investigated. For this purpose, first, the effective reproduction number is obtained by using the next generation operator method. Then, the reproduction number is examined in two cases, one with sharing needles and the other one with not sharing needles. The optimal control problem is formulated by applying some controls on the disease model including use of non-shared and sterile needles, use of prevention methods, screening of unaware infectives and treating patients. Necessary conditions for optimal control is determined by using Pontryagin’s minimum principle. Finally, numerical results is obtained by the Runge–Kutta fourth-order method. The results show a significant difference in control of prevalence of disease between the cases applying and not applying control on the disease.