فصلنامه مدل سازی پیشرفته ریاضی
سال دهم شماره 2 (پاییز و زمستان 1399)

Choosing the most suitable fitted model on data is one of the common challenges in statistical modeling. Maximum a posteriori (MAP) criterion is a method used in both frequentist and Bayesian approaches. Additionally, the utility of the model is used as a tool to compare the performances of methods. In this paper, the MAP method is applied for the Gaussian model and its performance is compared to that of frequentist approach. Also, an analytical form of utility estimation is proposed. Besides, using simulation studies, it is shown that the Gaussian model has better performance, based on both utility and mean of squared errors (MSE) criteria, when it is used by the Bayesian approach. However, both frequentist and Bayesian approaches avoid over-fitting by increasing the sample size. Also, by increasing correlation among covariates, MSE increases, while the tendency of choosing fewer covariates is raised. Eventually, the study on a real dataset is shown that in both frequentist and Bayesian approaches, MSE of selected models decreases when the size of sample increases.

The two most important numerical methods, finite difference, and finite element methods have some limitations in solving some problems arising in partial differential equations. A meshless method can be used to overcome these limitations. In these methods, no mesh required in the domain to solve the problem, and just scattered points are used for the approximation of the unknown function. In this paper, the two-dimensional telegraph equation is solved using a direct meshless local Petrov-Galerkin (DMLPG) method based on generalized moving least squares. To measure the accuracy of this method, the comparison of the results with the theoretical solution and other methods has been used, which results indicate the high accuracy of the proposed method.

Social networks have a great role in viral marketing by which, a company selects a few influential users as seeds to introduce a new product with the hope that the influence is cascaded throughout the network within a finite number of time-stages. This paper addresses the problem of spreading influence in a competitive network in which the users are affected by both positive and negative propaganda. First, some users are selected as seeds by the leader, and then, the follower, with the full knowledge of the leader's decisions, selects some other users as negative seeds. Afterwards, the positive and negative influences spread throughout the network. The leader's objective is to maximize the number of positive active users. However, the follower's objective is to minimize this value. First, the problem is formulated as a bilevel programming model, and then, an exact decomposition-based algorithm is developed to solve it. Computational results evaluates the performance of the proposed model and algorithm on some instances taken from the literature.

Although Data envelopment analysis is a powerful technique for evaluation of decision making units with multiple inputs and outputs, internal activities are neglected and each unit treats as "black box" by considering only initial input and output in the basic DEA models. However, in this paper, a network DEA model for multi stages units was designed as a tool for considering the importance of internal relations. At first a new production possibility set was defined for two-stage units and introduced a new method for evaluation of two-stage units. Since, one of the most important issues in economical decision makings is RTS, a new algorithm for specify the RTS in two-stage units was presented by using of the new PPS, and then the proposed algorithm on empirical study was applied and the final results were analyzed.

Let X be a quasi-compact and semi-separated scheme and QcoX be the category of all quasi-coherent sheaves of O_X -modules. We show that any flat complex of cotorsion quasi-coherent sheaves of O_X -modules is contractible. As an application, it is shown that the homotopy category of cotorsion flat quasi-coherent sheaves of O_X -modules is the natural replacement of the homotopy category of projectives.

One of the relevant problem in the reliability theory is stochastic comparison of coherent systems. Several results have been obtained in stochastic comparison of systems with independent and identically (IID) components. In this paper, we focus on $ k $-out-of-$ n $ systems that play an important role in study of the reliability of engineering systems. We obtain some results on distribution-free comparisons of $ k $-out-of-$ n $ systems, with possibly dependent component lifetimes, based on the concept of distortion function. We provide some conditions on distorted distributions of $ k $-out-of-$ n $ systems or their residual lifetimes that conclude ordering between their lifetimes ‎or their residual lifetimes‎. As a special case we consider two common survival copula (Farlie-Gumbel-Morgenstern and Clayton–Oakes) to derive more details on stochastic comparison of $ k $-out-of-$ n $ systems with respect to $ k $ and $ n $. Some illustrative examples are also presented to ‎show that some of results for stochastic comparison of $ k $-out-of-$ n $ systems with i.i.d ‎components ‎are violated ‎in ‎dependent ‎case.

Practitioners who use the classical regression model have been realized that many of its assumptions seldom hold. We then need flexible models to capture the real intrinsic properties of data. The class of generalized additive models for location, scale, and shape is very flexible in analyzing the inherent complexity of the data. This class of models provides the ability to do regression modeling beyond the mean of the response variable. Indeed, to admit outliers in the modeling framework is vital. Where we have a few outliers, the model could be too complicated by using heavy-tailed distributions. To overcome this issue, in this paper, we introduce a new location-scale semiparametric regression that is constructed based on a semi-heavy-tailed distribution, named hyperbolic secant, in the considered class of the models. We explore the performance of the proposed model by a simulation study and compare the results with a classical normal model. We also illustrate the model in a real application.

This paper is devoted to the study of the multiplicity results of solutions for a class of difference equations. Indeed, we will use variational methods for smooth functionals, defined on the reflexive Banach spaces in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are non-negative, we will prove that the solutions are non-negative. Finally, by presenting one example, we will ensure the applicability of our results.

This paper examines the problem of stochasticcomparisons of $(n-k+1)$-out-of-$n$ systems, and in the special cases, series and parallel systems with independent and heterogeneous Log-logistic components. Using concepts of majorization, weak supermajorization and p-larger order, we establish usual stochastic order, hazard rate and reversed hazard rate order between these systems. We also discuss the stochastic comparisons of two vector of order statistics arising from two independent and heterogeneous Log-logistic samples.

With the development of biosensor technology in various sciences, mathematical modeling of biosensors seems to be an important and necessary issue. In this paper, we present the numerical simulation of the mathematical model of amperometric biosensor based on the enzyme. This model is based on reaction-diffusion equations containing a nonlinear term of the Michaelis-Menten enzymatic reaction. The governing equations are discretized with the multi-quadric radial basis functions collocation method in space variable and semi-implicit backward Euler scheme in time. The effect of the reaction- diffusion parameter on other parameters of the mathematical model and biosensor response is investigated. The direct relationship, the current density with the maximal enzymatic rate, and the coefficient of reaction- diffusion are studied. The more stable effect of biosensor behavior with a thicker of enzyme layer than its similar type with a thinner layer has also been shown. In this study, the maximal enzymatic rate and thickness of the enzymatic layer are considered in the range of 10^-9 to 10^-3 and 0.005 to 0.09 , respectively.

One of the most important physical phenomena caused by surface adhesion forces is capillary property. Capillarity can be briefly explained by considering the effects of two opposing forces: adhesion, i.e. the attractive (or repulsive) force between the molecules of the liquid and those of the container; and cohesion, i.e. the attractive force between the molecules of the liquid. In this paper, we study a class of boundary value problems obtained from a capillary phenomenon modeling. Indeed, using a three critical points theorem, we will prove the existence of three weak solutions for a model of nonlinear differential equations with variable exponent. In this method which is based on the variational method, we correspond the differential equation with a nonlinear operator such that the critical points of this operator are weak solutions to the desired differential equation. As can be seen in the next section, there are two control parameters in the differential equation. We find intervals like and such that for and our problem has three bounded weak solutions in a Sobolev space with variable exponent.

Either Producers’ competition or consumers’ manner, influence on variation of market structure. To investigate this variation, a comprehensive model is required that covers all attitudes and interactions of both sides. Review the studies in literature cleared that the previous works have focused on modeling of duopoly or oligopoly markets, based on limited features and aspects. For instance, only one of the subjects of these markets such as consumer behavior, producer behavior, firms R&D game and firms competition by pricing or advertising has been studied. Hence, to investigate the markets perfectly and to study the integration among the elements of them, a comprehensive model is needed. In introduced such model in this study, we used theory of differential game for modeling of firms competition, approach of agent-based modeling and learning models for modeling of consumers behaviors. By developed model, it is feasible to investigate the market shares variations of two firms in a duopoly influenced by firms’ policies or consumers’ behaviors. The results of running the model in a numerical example demonstrate that firstly, learning models of consumers influence on firms’ market shares. Secondly, by even very partial simplifying in the sub model of firms competition, considerable and sensitive differences occur in the pattern of market shares.