Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Monte Carlo Method for Solving Becker-Doring Equations with Constant MonomersMonte Carlo Method for Solving Becker-Doring Equations with Constant Monomers11110012FAAlireza SoheiliDepartment of Applied Mathematics, Ferdowsi University of Mashhad,
Mashhad, IranHussian HassaniDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, IranJournal Article20130610Stochastic differential equations (SDE) play a relevant role in many application areas such as collision, population and polymer dynamics, genetic regulation, investment ﬁnance and biology. The procedure of <br />collision among particles was modeled by an inﬁnite dimensional diﬀerential system (in the discrete case) and a nonlinear partial integro-diﬀerential equation (in the continuous case). The discrete case may be approximated with a parabolic partial diﬀerential equation. In this paper, using the Monte-Carlo method, we obtain an approximation for solving the parabolic diﬀerential equation in the continuous form. Stochastic differential equations (SDE) play a relevant role in many application areas such as collision, population and polymer dynamics, genetic regulation, investment ﬁnance and biology. The procedure of <br />collision among particles was modeled by an inﬁnite dimensional diﬀerential system (in the discrete case) and a nonlinear partial integro-diﬀerential equation (in the continuous case). The discrete case may be approximated with a parabolic partial diﬀerential equation. In this paper, using the Monte-Carlo method, we obtain an approximation for solving the parabolic diﬀerential equation in the continuous form. https://jamm.scu.ac.ir/article_10012_132aec29d7979aa65a6454470dc098bf.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Modules with Krull Dimension of at Most αModules with Krull Dimension of at Most α132610018FANasrin ShiraliDepartment of Mathematics, Shahid Chamran University, Ahvaz, IranJournal Article20130610In this article we have introduced and studied the notation of α-loewy modules (0-loewy modules is just a loewy module). Using this concept we extend some of the basic results of loewy modules to α-loewy modules and we find a universal upper bound for Krull dimension over ߙ- loewy rings. In particular, we show that module M has Krull dimension α if and only if each factor module of M is lambda-loewy modules for some lambda <=α and has finite Goldie dimension.In this article we have introduced and studied the notation of α-loewy modules (0-loewy modules is just a loewy module). Using this concept we extend some of the basic results of loewy modules to α-loewy modules and we find a universal upper bound for Krull dimension over ߙ- loewy rings. In particular, we show that module M has Krull dimension α if and only if each factor module of M is lambda-loewy modules for some lambda <=α and has finite Goldie dimension.https://jamm.scu.ac.ir/article_10018_0761692a643ea78221774298808849f2.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Simultaneously determining the optimal control and state in an vibrating circular surface system by a discretization methodSimultaneously determining the optimal control and state in an vibrating circular surface system by a discretization method274210013FAAlireza FakharzadehjahromiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranParviz ElahiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranNadimeh JafarpoorDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranJournal Article20130610Presenting a new method for simultaneous determination of the control and trajectory functions in an optimal control problem governed by a vibrating circular surface system, is the main purpose of this paper. First, by identifying the form of the trajectory function, doing discretization and using the properties of measure, the problem is linearized. Then, by doing some approximation steps, the nearly optimal pair of trajectory and control with the optimal value of the objective function are obtained via solving a finite linear programming problem. A numerical example is also presented.Presenting a new method for simultaneous determination of the control and trajectory functions in an optimal control problem governed by a vibrating circular surface system, is the main purpose of this paper. First, by identifying the form of the trajectory function, doing discretization and using the properties of measure, the problem is linearized. Then, by doing some approximation steps, the nearly optimal pair of trajectory and control with the optimal value of the objective function are obtained via solving a finite linear programming problem. A numerical example is also presented.https://jamm.scu.ac.ir/article_10013_798db8826993aac3dc44315bf9c7a433.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Application of Latent Class Regression Model for Modeling Factors Associated with Inter-Province ImmigrationsApplication of Latent Class Regression Model for Modeling Factors Associated with Inter-Province Immigrations436310014FAJamshid JamaliMashhad university of Medical Sciences, Mashhad, IranAwat FeiziDepartment of Biostatistics and Epidemiology, Isfahan university of Medical Sciences, Isfahan IranJournal Article20130610In the present research, inter-provinces immigration and its determinants in a 40 years period in Iran was investigated, using the latent class regression. The analyzed data were extracted from reliable governmental resources (Iran statistical center, ministry of industry and mining and ministry of agriculture). According to obtained results, Iran’s provinces were classified in two migrator and immmigrator categories. The pattern of immigration during 1345 to 1385 showed that the Tehran, Isfahan, Quem, Mazandaran, Boushehr, Semnan and Yazd provinces were immigrator. The most important related predictors were: civilization level, level of education, sex ratio, family dimension, Industrial development coefficient, unemployment rate. Accordingly, the obtained results in this study can be used for developing suitable strategy in order to managing immigration and diminishing its side effects.In the present research, inter-provinces immigration and its determinants in a 40 years period in Iran was investigated, using the latent class regression. The analyzed data were extracted from reliable governmental resources (Iran statistical center, ministry of industry and mining and ministry of agriculture). According to obtained results, Iran’s provinces were classified in two migrator and immmigrator categories. The pattern of immigration during 1345 to 1385 showed that the Tehran, Isfahan, Quem, Mazandaran, Boushehr, Semnan and Yazd provinces were immigrator. The most important related predictors were: civilization level, level of education, sex ratio, family dimension, Industrial development coefficient, unemployment rate. Accordingly, the obtained results in this study can be used for developing suitable strategy in order to managing immigration and diminishing its side effects.https://jamm.scu.ac.ir/article_10014_b9919fb8e78d07b158d8cb763304a8c4.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Bayesian Inferences in Generalized Exponential DistributionBayesian Inferences in Generalized Exponential Distribution667810015FASediqeh Omidvar ShalmaniDepartment of Statistics, University of Tehran, Tehran, IranAhmad ParsianDepartment of Statistics, University of Tehran, Tehran, IranAli KarimnejadDepartment of Statistics, University of Tehran, Tehran, IranLeila GolparvarDepartment of Statistics, University of Tehran, Tehran, IranJournal Article20130610In this paper, we discuss minimaxity of Generalized Bayes estimator of the shape parameter of Generalized Exponential (GE) distribution under Weighted Square Error Loss (WSEL) function. A common approach to the prior uncertainty in Bayesian analysis is to choose a class of prior distributions and look for an optimal decision within this class. This is known as robust Bayesian methodology. We obtain Posterior Regret Gamma Minimax estimator of the shape parameter of GE distribution under WSEL function.In this paper, we discuss minimaxity of Generalized Bayes estimator of the shape parameter of Generalized Exponential (GE) distribution under Weighted Square Error Loss (WSEL) function. A common approach to the prior uncertainty in Bayesian analysis is to choose a class of prior distributions and look for an optimal decision within this class. This is known as robust Bayesian methodology. We obtain Posterior Regret Gamma Minimax estimator of the shape parameter of GE distribution under WSEL function.https://jamm.scu.ac.ir/article_10015_7df3a78019fb0aa1c4ce17442a40d262.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522The Structural Model of Learner Knowledge Based on Designing Instructional ObjectivesThe Structural Model of Learner Knowledge Based on Designing Instructional Objectives799710016FAElahe AminifarSchool of Mathematics, Shahid Rajaee Teacher Training University,
Tehran, IranBahram Saleh SedghpourSchool of Education, Shahid Rajaee Teacher Training University, Tehran, IranZahra SabaghzadehSchool of Mathematics, Shahid Rajaee Teacher Training University,
Tehran, IranJournal Article20130610The aim of this research was to find the structural model of learner knowledge based on designing instructional objectives of Second Order Non-Homogeneous Linear Differential Equations. To do this, the <br />instructional objectives of purposed subject were designed and their integrity was confirmed by three members of academic staff who teach this course for more than 10 years. In a pilot study, a test consists of 25 questions was given to thirty-one science and engineering students who were chosen randomly. Analyzing data with attention to Cronbach’s Alpha (0.834) confirmed that designed questions verified with mentioned instructional objectives of goal-content’s table. By using difficulty index, discrimination index and loop method unfit questions removed and 15 questions remained. engineering students who were chosen by cluster sampling. The empirical model of learner’s knowledge was compiled and results showed that there are meaningful relationships between ‘knowledge of definitions’ and ‘knowledge of method of undetermined coefficients’; ‘knowledge of method of variation of parameters’ and ‘knowledge of special methods’; and ‘knowledge of special methods’ and ‘knowledge of definitions’.The aim of this research was to find the structural model of learner knowledge based on designing instructional objectives of Second Order Non-Homogeneous Linear Differential Equations. To do this, the <br />instructional objectives of purposed subject were designed and their integrity was confirmed by three members of academic staff who teach this course for more than 10 years. In a pilot study, a test consists of 25 questions was given to thirty-one science and engineering students who were chosen randomly. Analyzing data with attention to Cronbach’s Alpha (0.834) confirmed that designed questions verified with mentioned instructional objectives of goal-content’s table. By using difficulty index, discrimination index and loop method unfit questions removed and 15 questions remained. engineering students who were chosen by cluster sampling. The empirical model of learner’s knowledge was compiled and results showed that there are meaningful relationships between ‘knowledge of definitions’ and ‘knowledge of method of undetermined coefficients’; ‘knowledge of method of variation of parameters’ and ‘knowledge of special methods’; and ‘knowledge of special methods’ and ‘knowledge of definitions’.https://jamm.scu.ac.ir/article_10016_3c8cdb234def3246d021e70c53be2d8a.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Testing Homogeneity of Mean Vectors against ordered restriction in Multivariate Normal DistributionTesting Homogeneity of Mean Vectors against ordered restriction in Multivariate Normal Distribution9911810017FAAbouzar BazyariDepartment of Statistics, Shahid Chamran University, Ahvaz, IranRahim ChinipardazDepartment of Statistics, Shahid Chamran University, Ahvaz, IranAli Akbar RasekhiDepartment of Statistics, Shahid Chamran University, Ahvaz, IranJournal Article20130610This paper concerned with the testing of homogeneity of mean vectors against ordered restriction in multivariate normal distribution. Three different cases for covariance matrices are considered. First when covariance matrices are known, second when it is assume that covariance matrices have an unknown scale factor and third when the covariance matrices are completely unknown and equal. In two first cases the critical values of test statistic are computed for bivariate and trivariate normal distribution. The power and p-value of the test statistic are estimated by simulation method. When the covariance matrices are completely unknown and equal some tests are presented which the computation of those probabilities can be used as the upper bonds of p-values.This paper concerned with the testing of homogeneity of mean vectors against ordered restriction in multivariate normal distribution. Three different cases for covariance matrices are considered. First when covariance matrices are known, second when it is assume that covariance matrices have an unknown scale factor and third when the covariance matrices are completely unknown and equal. In two first cases the critical values of test statistic are computed for bivariate and trivariate normal distribution. The power and p-value of the test statistic are estimated by simulation method. When the covariance matrices are completely unknown and equal some tests are presented which the computation of those probabilities can be used as the upper bonds of p-values.https://jamm.scu.ac.ir/article_10017_a387189c591951b5cee5798420016119.pdf