فصلنامه مدل سازی پیشرفته ریاضی
سال یازدهم شماره 1 (بهار 1400)

For an infinite cardinal number λ , λ- semi compact spaces and λ-strongly compact spaces which are generalizations of semi-compact spaces and strongly compact spaces are introduced and studied. It is shown that for every infinite cardinal number λ , there exist non-discrete λ- semi compact spaces and non-discrete λ- strongly compact spaces. Basic properties of such spaces are investigated.

Freese and Cho have introduced the non-Archimedean 2-normed spaces and Eshaghi, et al. have introduced the Menger probabilistic non-Archimedean 2-normed spaces. In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of Euler-Lagrange type cubic functional equations in the non-Archimedean 2-normed spaces. Also, we prove the generalized Hyers-Ulam-Rassias stability for this system in the Menger probabilistic non–Archimedean 2–normed spaces.

In this paper, we will introduce a mathematical model, based on prey-predator models, to study reciprocal effects of water resources and population. First, we will construct the model and introduce the parameters and variables of the system. Next we will study local behaviors around inner equilibrium points and global behaviors in the admissible region of the system. Especially we will see that how changes of the parameters might cause simultaneous permanency/impermanency of population and water resources through local bifurcations and changes in the structure of solutions

In this article we investigate and study the ring LC(X) of all real-valued locally constant functions on a topological space X . We show that X is a connected space if and only if LC(X)=R. If X is a compeletly regular and Hausdorff space, we show that LC(X) is always Von Neumann regular ring and also we prove that LC(X)=∩{xin N}(R+Ox) which N is the set of all non-isolated points of X . Also we show that X is a P-space if and only if LC(X)=C(X), where C(X) denotes the ring of all real-valued continuous functions . It is also shown that X is a weakly pseudocompact space if and only if LC(X)=CF(X) , where CF(X) denotes the ring of all real-valued continuous functions with finite image. In case X is Lindel of, we prove that it is a CP-space if and only if LC(X)=CC(X), where CC(X) denotes the ring of all real-valued continuous functions with countable image. We introduce the concept of "oc-paracompact" and we observe that an oc-paracompact space is compact if and only if it is weakly pseudocompact. Finally, we show that if X is a zero dimensional and second countable space , then X is compact if and only if it is a weakly pseudocompact space.

‎In this paper, the dynamic behavior of a fractional-order predator-prey system based on the Mittag-Leffler function is investigated. First, we study the existence, uniqueness, non-negativity, and boundedness for the solution of this fractional-order system. Then, we show that this system has two different equilibrium points. Some sufficient conditions to ensure the global asymmetric stability of these points are also proposed by using the Lyapunov function. Finally, we present some numerical simulations to confirm the analytical results.

Application of fractional factorial design is common in experiments with a large number of factors. Choosing the appropriate fraction is an important issue in the fractional designs literature. There are different criteria based on different perspectives. In this paper, a criterion based on minimization of a weighted function of the mean squared error matrix of the least squares estimators of a pre-specified model is introduced. In two-level fractional designs, the criterion for the uniform weight function is calculated and shown to be equivalent to the well-known $ D $-optimal design. Finally, the method is described with examples.

An epidemic model is described and introduced in which a vaccination program has been included. The model considers disease-caused death in addition to natural death, and the total population size is variable. The equilibria of the model, the disease-free equilibrium and the endemic equilibrium, are obtained and the global dynamics of the model are stated via the basic reproduction number using proper Lyapunov functions. The disease-free equilibrium is asymptotically globally stable when this quantity is less than or equal to unity and when it is greater than unity, the endemic equilibrium is asymptotically globally stable.

This paper presents several sufficient conditions for the existence of at least one weak solution for the impulsive nonlinear fractional boundary value problem. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.

In this paper, the initial and boundary value problems which includes singular fractional integro-differential equations, are investigated. The fractional derivative which is considered in this article, is the Caputo fractional derivative. The integral equations which are discussed in this paper either without any singularity or contain singular kernels that can be weak or strong. In addition to, in this paper to check and study the singularity and regularity of this type of integral equations are paid. Also, the given integral equations are in the form of initial and boundary value problems, which are discussed in terms of the number and manner of boundary conditions. Finally, some examples are provided for the accuracy and efficiency of the method.

In this study, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature dependent thermal conductivity is revisited. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of different parameters on the thermal performance of the porous fin. Regarding the problem formulation, a novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing nonlinear differential equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Furthermore, the obtained results are more accurate than those reported in previous researches.

In this paper, a bi-objective closed-loop supply chain has been studied by Robust Possibilistic Programming (RPP) approach. This paper aims to minimize the cost and product shipping time (delivery) to the customers.  The KVSS and MK company are considered a case study of Iran’s vegetable oil industry. This paper addresses -and models- some challenges of this industry and provides the RPP solution approach with appropriate solutions. The main challenge of this industry is that the supply of raw materials and oilseeds is highly dependent on other countries. Accordingly, many other factors such as the exchange rate, sanctions, governmental rules and regulations, custom tariffs, and the supply and demand process, etc., have an impact on the definitive decision-making. Hence, the data are considered uncertain and the RPP approach is used to solve the model. The solving approach is also used to decide on the bi-objective function, in which managers can easily decide on the complex processes of this industry.  Finally, the results of the model and the sensitivity analysis are presented to validate the model. The validation process uses examples and practical analyses that have been localized based on Iran’s conditions.

Since volatility measurement plays an important role in risk assessment and uncertainty in financial markets, this study provides an appropriate method for predicting stock pricefluctuations using the GARCH and Bootstrap Garch method. And then compare the confidence intervals by the two methods. The research data were collected by reviewing the statistics of the companies listed in the list of the top 50 companies in the securities market. The results show that the confidence interval of the Bootstrap Garch method is shorter than the Garch method,so the Bootstrap Garch method provides a more accurate prediction than the GARCH method. In addition, it is usually expected to increase with the increase in horizons of prediction of variance, but this does not occur for the Garch (1.1) method; therefore, it seems that the prediction of the variance of the Bootstrap GARCH model has more compatibility with theoretical evidence.