Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220170219A Bootstrap Test for Symmetry based on Cumulative EntropyA Bootstrap Test for Symmetry based on Cumulative Entropy1141299010.22055/jamm.2017.12990FAVali ZardashtDepartment of Statistics, University of Mohaghegh Ardabili, Ardabil, IranJournal Article20151205The symmetry assumption plays an important role in nonparametric statistical inference methods. Using different measure of asymmetry, various test statistics has proposed for testing the symmetry hypothesis. In this paper, we apply the cumulative residual entropy to introduce a new skewness measure and construct a distribution–free test for the hypothesis. Bootstrap re-sampling from a symmetric empirical distribution function is used to calculate the p-value of the test. The power of the new test statistic is compared with two existing tests in a simulation study. The results show that the proposed test preserves its level and it has reasonable power properties on the family of distribution evaluated.The symmetry assumption plays an important role in nonparametric statistical inference methods. Using different measure of asymmetry, various test statistics has proposed for testing the symmetry hypothesis. In this paper, we apply the cumulative residual entropy to introduce a new skewness measure and construct a distribution–free test for the hypothesis. Bootstrap re-sampling from a symmetric empirical distribution function is used to calculate the p-value of the test. The power of the new test statistic is compared with two existing tests in a simulation study. The results show that the proposed test preserves its level and it has reasonable power properties on the family of distribution evaluated.https://jamm.scu.ac.ir/article_12990_976536d2b8569acaf9e8075d3456c176.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220170219An Iterative Finite Difference Approach with Time Variable Steps for the Numerical Investigation of the Model of Drug Diffusion Through Polymeric SpheresAn Iterative Finite Difference Approach with Time Variable Steps for the Numerical Investigation of the Model of Drug Diffusion Through Polymeric Spheres15291299410.22055/jamm.2017.12994FAMorteza GarshasbiSchool of Mathematics, Iran University of Science and Technology, Tehran, IranParastoo Reihani ArdabiliPayame Noor University of Tehran, Tehran Shargh Unit, IranJournal Article20150721In this paper, a mathematical model of drug diffusion in spherical polymeric drug delivery devices is considered and investigated numerically. The proposed model considered as a moving boundary parabolic equation with nonlinear condition at the moving boundary. Because of the nonlinearity of the problem and existence of a moving boundary in proposed problem, a new iterative finite differences approach with time variable steps is established to solve this problem. The closed form of solution of the proposed problem has not been derived and to show the ability of the method, the numerical results have been compared with asymptotic solutions and the results of the paper [14].In this paper, a mathematical model of drug diffusion in spherical polymeric drug delivery devices is considered and investigated numerically. The proposed model considered as a moving boundary parabolic equation with nonlinear condition at the moving boundary. Because of the nonlinearity of the problem and existence of a moving boundary in proposed problem, a new iterative finite differences approach with time variable steps is established to solve this problem. The closed form of solution of the proposed problem has not been derived and to show the ability of the method, the numerical results have been compared with asymptotic solutions and the results of the paper [14].https://jamm.scu.ac.ir/article_12994_7f9405cf8e16e74f2e974e4e40bdb46a.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220170219〖 H〗_(∞ )Technique for Five Story Buildings Under Seismic Loads and Uncertainty Process Using Synchronized Control〖 H〗_(∞ )Technique for Five Story Buildings Under Seismic Loads and Uncertainty Process Using Synchronized Control31531299510.22055/jamm.2017.12995FAAlaeddin MalekDepartment of Applied Mathematics, Tarbiat Modares University, Tehran, IranJavad MesbahiDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20150530In this paper, synchronized control is used for five story structure of Kajima Shizuoka under the EL - Centro earthquake load ( 1940) seismic record. According to coupled values of displacement, drift and position error the related partial differential equation for motion and state is solved successfully. The Riccati equation is solved based on the close loop transfer function with respect to uncertainty parameters and random dynamic processes. Numerical simulations along with comparisons are made to evaluate the efficiency of this hybrid technique.In this paper, synchronized control is used for five story structure of Kajima Shizuoka under the EL - Centro earthquake load ( 1940) seismic record. According to coupled values of displacement, drift and position error the related partial differential equation for motion and state is solved successfully. The Riccati equation is solved based on the close loop transfer function with respect to uncertainty parameters and random dynamic processes. Numerical simulations along with comparisons are made to evaluate the efficiency of this hybrid technique.https://jamm.scu.ac.ir/article_12995_9e7d9eac7b694a8e8abb69c3ee3119f9.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220160922A Cellular Automata Model of Tumor Growth Based on Cell CycleA Cellular Automata Model of Tumor Growth Based on Cell Cycle55741299610.22055/jamm.2016.12996FAFateme PourhasanzadeDepartment of Biomedical Engineering, Research Laboratory of Biomedical Signals and Sensors, Iran University of Sciences and Technology, Tehran, IranSeyed Hojjat SabzpoushanCancer Biology Research Center, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, Iran0000 0002 9477 2567Ali Mohammad AlizadehCancer Biology Research Center, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, IranReyhaneh ChamaniRadiation Oncology Department, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, IranReyhaneh ChamaniCancer Biology Research Center, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, IranJournal Article20160104Breast cancer is one of the major causes of death among women. Therefore, studying the morphology of cancer is necessary. Computer models and simulations may help scientists better understand this disease, and improve current treatments. In this paper, a model of breast cancer based on Cell Cycle is presented. Five states for each cell in a 2D square lattice is considered. The rules for updating the states of the model in the Moore neighborhood are stochastic. The results of our simulations are presented with/without considering immune system. The growth fraction and necrotic fraction are used as output parameters beside a 2-D graphical growth presentation. Moreover, we introduced a new in-vivo study to measure the output parameters by using Tetrazolium chloride. It can be observed that there is an acceptable compatibility between the experimental tests and simulation results.Breast cancer is one of the major causes of death among women. Therefore, studying the morphology of cancer is necessary. Computer models and simulations may help scientists better understand this disease, and improve current treatments. In this paper, a model of breast cancer based on Cell Cycle is presented. Five states for each cell in a 2D square lattice is considered. The rules for updating the states of the model in the Moore neighborhood are stochastic. The results of our simulations are presented with/without considering immune system. The growth fraction and necrotic fraction are used as output parameters beside a 2-D graphical growth presentation. Moreover, we introduced a new in-vivo study to measure the output parameters by using Tetrazolium chloride. It can be observed that there is an acceptable compatibility between the experimental tests and simulation results.https://jamm.scu.ac.ir/article_12996_230cdcf9df1d56a2483e463b8cf7d69a.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220170219On the existence of solutions to a class of semilinear Schrödinger equationsOn the existence of solutions to a class of semilinear Schrödinger equations75911299710.22055/jamm.2017.12997FAYaghoob JalilianDepartment of Mathematics, Razi University, Kermanshah, IranIraj DehsariDepartment of Mathematics, Razi University, Kermanshah, IranJournal Article20170619In this paper, we investigate the existence of a nontrivial weak solution for a class of quasilinear Schrödinger equations in the Sobolev space . First, we use a change of variables to obtain a well defined energy functional on . Then we find a manifold which is a natural constraint, and we prove that the restriction of the energy functional to this manifold attains its infimum. Finally, we show that this infimum point is a nontrivial weak solution for the equation.In this paper, we investigate the existence of a nontrivial weak solution for a class of quasilinear Schrödinger equations in the Sobolev space . First, we use a change of variables to obtain a well defined energy functional on . Then we find a manifold which is a natural constraint, and we prove that the restriction of the energy functional to this manifold attains its infimum. Finally, we show that this infimum point is a nontrivial weak solution for the equation.https://jamm.scu.ac.ir/article_12997_d4ab42cd3fe23af00e7154d1808d72d0.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220170219Empirical Comparison of Box-Jenkins Models, Artificial Neural Network and Singular Spectrum Analysis in Forecasting Time SeriesEmpirical Comparison of Box-Jenkins Models, Artificial Neural Network and Singular Spectrum Analysis in Forecasting Time Series931121299810.22055/jamm.2017.12998FAMasoud YarmohammadiDepartment of Statistics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran0000-0001-7038-7106Mahdi KalantariDepartment of Statistics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran0000-0003-4951-1402Rahim MahmoudvandDepartment of Statistics, Bu-Ali Sina University, Hamedan, IranJournal Article20161010The Box-Jenkins model is applied as a parametric method for time series analysis and fitting seasonal and non-seasonal autoregressive moving average models. But this procedure is not useful for short length and non stationary time series data. To overcome these problems, two nonparametric methods i.e. Artificial Neural Network and Singular Spectrum Analysis are introduced. These procedures do not require any statistical assumptions about normality of errors and could be used for short time series data. In this article, after introducing the above methods, their accuracy in forecasting sales of four types of food products, pharmaceutical and health care of a distribution Corporation are compared. Then using simulation studies, the effectiveness of these methods for short-term and long-term predictions are evaluated. The results show the superiority of Singular Spectrum Analysis compared to the other two methods in terms of the root mean square error of forecasting.The Box-Jenkins model is applied as a parametric method for time series analysis and fitting seasonal and non-seasonal autoregressive moving average models. But this procedure is not useful for short length and non stationary time series data. To overcome these problems, two nonparametric methods i.e. Artificial Neural Network and Singular Spectrum Analysis are introduced. These procedures do not require any statistical assumptions about normality of errors and could be used for short time series data. In this article, after introducing the above methods, their accuracy in forecasting sales of four types of food products, pharmaceutical and health care of a distribution Corporation are compared. Then using simulation studies, the effectiveness of these methods for short-term and long-term predictions are evaluated. The results show the superiority of Singular Spectrum Analysis compared to the other two methods in terms of the root mean square error of forecasting.https://jamm.scu.ac.ir/article_12998_224f43c37fa9630b1c183a95c8a490cd.pdf