فصلنامه مدل سازی پیشرفته ریاضی
سال سیزدهم شماره 3 (پاییز 1402)

Missing values in time series data are one of the problems that sometimes arise in time series analysis. The more accurate imputation of these values, the better understanding of the structure of the time series will be obtained, and as a result, the recognition of its pattern and the prediction of future values will be more accurate. Therefore, choosing an appropriate method of imputation is an important part of a time series analysis. In this paper we introduce the new missing data imputation method from the singular spectrum analysis procedure, using the Kalman filter algorithm. Then other methods of imputation of missing values in univariate time series are introduced, and will be compared the mentioned methods using simulated data in structural models and real data. The results of the comparison based on the criteria of root mean square error and mean absolute deviations show that the method of imputation of missing values based on singular spectrum analysis approach using the Kalman filter algorithm has a better performance than the other imputation methods and the mode method is the worst.‎‎

‎In this paper, the concepts of shadowing, weak shadowing and expansiveness for finitely generated semigroup actions on non-compact metric spaces are introduced, which are dynamical properties and equivalent to their definitions on compact metric spaces. Also, the notion of topological stability for actions associated to finitely generated abelain semigroups is defined and a necessary and sufficient condition for the topological stability of finitely generated abelian semigroups on a locally compact metric space ‎is ‎provided.‎‎

In this study, we solve the nonlinear fractional differential equations with fractional integral boundary conditions. To solve the mentioned problems, we use an iterative method based on the reproducing kernel Hilbert spaces. In this method, the reproducing kernel of a finite-dimensional Hilbert space is constructed using Fibonacci polynomials. With the help of the obtained positive definite kernel, we produce bases that exactly satisfy the given integral boundary conditions. Then using the obtained bases, we construct fractional derivative operational matrices and obtain an approximation of the problem with the help of a simple iteration method. In fact, we construct an approximation of the solution in a finite-dimensional space. We have also shown the convergence of the method under certain conditions. To show the effectiveness of the proposed method, we have solved some examples, and the obtained results are ‎presented.‎

In this paper, we introduce an extension of the Hilfer fractional derivative, the "Hilfer fractional quantum derivative", and establish some of its properties. Then, we introduce and discuss initial and boundary value problems involving the Hilfer fractional quantum derivative. The existence of a unique solution of the considered problems is established via Banach's contraction mapping principle. Examples illustrating the obtained results are also presented.

In this paper, we define the concept of pseudo-irreducible elements in multiplicative lattices and examine its relationship with other important concepts of multiplicative lattices such as prime elements, primary elements, and maximum elements, and then with the help of this concept, we define and analyze the complete comaximal factorization in multiplicative lattices. In particular, we characterize multiplicative lattices whose every element can be written as a product of pseudo-irreducible and pairwise comaximal elements.

Tumor resistance to chemotherapy and targeted drugs is one of the main factors of treatment failure. Experimental evidence in recent years shows that the progression of cancer cells to drug resistance does not have to happen by chance, but may be caused by the treatment itself. In this regard, understanding the clinical consequences of resistance caused by treatment in the process of chemotherapy helps to develop appropriate solutions. In this paper, to investigate this issue, we first introduce the general mathematical model of drug resistance in the chemotherapy process in the form of a device of nonlinear ordinary differential equations. Then we perform the numerical simulation of the dynamic behavior of the model in three different cases using the least squares support vector machine approach. In this study, the effects of three drugs with different drug resistance induction coefficients are considered. Finally, we will examine the results of these simulations according to the type of drug prescribed in tumor growth control.

Ranking of decision making units (DMU) is an important issue in data envelopment analysis (DEA). When efficient DMUs have the same efficiency scores, traditional DEA models usually fail to rank efficient DMUs. In recent years, cooperative game theory has been used to compare and improve the discrimination power of efficient DMUs. In this research, a new method of cooperative game is proposed. The idea of this method is that first, by removing a certain subset of efficientDMUs from the set of units, the efficiency of all units is calculated, and then, using the Shepley value in cooperative game theory, the efficient units are ranked. A numerical example is presented to show the performance of the proposed method and its comparison with recent ranking methods. In the empirical study, the ranking of efficient DMUs is useful and reasonable.

Let R be a commutative ring with identity and let M be a unitary R-module.In this paper, the structure of completely irreducible submodules will be studied and it is proved that a submodule K has a comlpetely irreducible divisor if and only if Soc(M/K) is nontrivial which implies that a maximal ideal m is an strongly Bourbaki associated prime ideal of K if and only if K has an m-primal completely irrducible divisor. Submodules of M that are representable as an irredundant intersection of an overfamily of completely irreducible submodules are characterized. Then it will be shown that, if R is a Noetherian ring, then M is Artinian if and only if its zero submodule has a primary decomposition whose components are completely irreducible submodules. Finally, it is proved that M is distributive if and only if the set of its completely irreducible submodules is: { m(Rx)(m)</sub> | x ∈ M , m ∈ Max(R) ∩ Supp(Rx) }.

In this research work, a fifth-order well-balanced weighted essentially non-oscillatory scheme based on finite difference (FDWENO) was presented to solve a blood flow model in arteries. The FDWENO scheme preserves the balanced property for steady-state solutions while achieving fifth-order accuracy in smooth regions. Additionally, it does not exhibit spurious non-oscillatory behavior in discontinuous and shock areas. Several numerical examples were considered to investigate the balanced characteristic, fifth-order accuracy, and prevention of spurious oscillations. The results of these examples demonstrated the effectiveness of the newly developed scheme in this research.

In some medical studies, we may have several measurements on each patient. Sometimes these longitudinal data may be measured for several response variables, in this case, although the responses can be modeled separately, such an approach reduces the power and efficiency in estimating the effects of auxiliary variables on the response variable. In the analysis of such data, in addition to the analysis of the dependence between repeated measures related to each of the response variables, the dependence between the responses should also be considered. Among the methods used in recent years to model multivariate data is the copulafunction. One of the most important advantages of using the copula function compared to the longitudinal multivariate modeling of the data in the classic way is that, in addition to the normal distribution, any other distribution other than the normal can be considered as marginal distributions. Also, marginal distributions can even have different distributions. In situations where the data have a multivariate structure, one of the ways to form multivariate distributions is to use vine pair-copula function. In this study, we form a multivariate longitudinal structure by using the vine pair copula functions and compare these models with the model obtained from the fitting of the multivariate normal copula function. Then we will introduce the best model using the Akaike information criterion and at the end we will use the presented model on the data of the estimation of the effect of nutrition on growth.

The aim of this study is to investigate an eco-epidemiological model with a bilinear incidence rate and a square root functional response. First, we examine the equilibrium and stability points of the system for various parameter values. The main challenge in population models is finding a numerical method for approximating non-negative solutions. Some numerical methods, such as the Euler method, are inefficient as they sometimes fail to produce non-negative solutions. Non-negative approximations obtained from non-standard finite difference methods are also conditional. In this paper, we propose a numerical method that provides unconditional and acceptable solutions. We then discuss the compatibility of the proposed numerical method. Finally, we compare the efficiency of the proposed method with the Euler and non standard methods using numerical simulations. We also investigate the effect of the hunting behavior of the prey species on the population density and analyze the dynamic model for some numerical values of the parameters involved in the problem.

In this paper, we extend the collocation method for the numerical solution of two-dimensional Volterra integral equations. For this purpose, we first prove the existence and uniqueness of the solution of these types of equations and present a resolvent kernel representation for their solution. Then, we extend the collocation method using piecewise polynomials to solve the mentioned equations and obtain the corresponding algebraic system of equations and show that the system has a unique solution. We also prove the convergence of the method and obtain the order of convergence of the method by proving a theorem. Finally, we present some numerical examples to show the efficiency of the method and confirm the obtained theoretical results.