فصلنامه مدل سازی پیشرفته ریاضی
سال یازدهم شماره 4 (زمستان 1400)

‎‎In this paper, parametric optimization problems are investigated. ‎In a‎ ‎parametric ‎optimization ‎problem ‎we ‎assume ‎‏‎$‎‎‎‎‎‏‎‎lambda‎in‎mathbb{R}^n‎$‎‎ ‎is ‎the ‎vector ‎of ‎the ‎parameters ‎and ‎‎$‎‎x^*$ ‎is ‎the ‎optimal ‎answer ‎corresponding ‎to ‎it. ‎The ‎purpose ‎of ‎this ‎paper ‎is ‎to ‎determine a‎ ‎function ‎such ‎as ‎‎$‎‎psi$ ‎so ‎that ‎we ‎have ‎‎$‎‎psi(‎lambda‎)=x^*$.‎ To do this, first for each ‎$‎‎‎lambda‎$‎, the corresponding optimal answer is calculated. In this way, a set of data bases consisting of parameters and the corresponding optimal values are obtained. A multilayer network of data base is trained to obtain the function ‎$‎‎psi$‎ in a domain. In fact, the function ‎$‎‎psi$‎ for each value of the parameter specifies the corresponding answer by the trained multilayer network.‎‎ Finally, we conduct several numerical examples to test our method.

Let p be a prime number and R_2 be the ring F_p^m + uF_p^m, where u^2 = 0. In this paper, we study the algebraic structure of F_p^m R_2-additive skew cyclic codes of length 2p^s and we determine a set of generator polynomials for this family of codes. These codes will be classified into seven distinct types of submodules. Finally, using a Gray map, we present some examples of F_p^m R_2-additive skew cyclic codes of length 2p^s.

One of the important aims in reliability engineering is to improve the performance and increasethe reliability of systems. Increasing the reliability of a system is possible by allocating redundancies components in the structure of the system. In this paper, we use the worked and functioning spares components in the structure of coherent systems to increase its performance. The stochastic comparisons between used redundant coherent systems and redundant coherent systems with used components done. A comparison of used redundant systems and redundant system with used components will the design engineers to build more reliable system out of the good components of a failed system. Using the distortion function, we obtain a mixture representation for the lifetime of the mentioned systems. Based on different random stochastic orders, we provide conditions on reliability functions that used redundant coherent systems work better (worse) than redundant coherent systems with used components.

‎In this paper‎, the existence of the solutions of a class of fractional integral equations inBanach algebra, are investigated. The main tools hereare the technique of the measure of noncompactness and the Petryshyn's fixed point theorem. ‎Also‎, ‎for the applicability of the obtained results‎, ‎some‎ examples are given‎.

In this article, we introduce OLG, CLG and LG maps in the context of LGT-spaces, show that they are generalizations of continuous function on LGT-spaces and some properties of them studied. Also, some generalized notions related to continuous functions as weak topology induced, quotient topology and decomposition topology are introduced and studied and is shown that each decomposition space is an LG-quotient space

Let G be a group, and let nse(G) be the set of the number of elements with the same order in group G. In this paper, we prove that if G is a group and Sz(2^9) is the Suzuki simple group such that nse(G) = nse(Sz(2^9)), then G is isomorphic to the Suzuki simple group Sz(2^9). In other words, we prove that the simple Suzuki group Sz(2^9) is uniquely determined by its set of the number of elements with the same order. Consequently, Thompson’s problem is true for the Suzuki simple group Sz(2^9 ).

Higher-order tensor structured data appear in many imaging scenarios, including hyperspectral imaging and colorful video. The recovery of a tensor from an incomplete set of its entries, known as tensor completion (TC), is significant in applications like compression. Moreover, in many illustrations, observations are not only incomplete but also highly quantized. Quantization is a critical step for high dimensional data transmission and storage in order to reduce storage requirements and power consumption, especially for energy-limited systems. In this paper, we propose a novel approach for the recovery of low-rank tensors from a small number of binary (1-bit) measurements. The proposed method called $1- bit$ Tensor Completion relies on the application of 1-bit matrix completion over different matricizations of the underlying tensor. Experimental results on hyperspectral images confirm that directly operating with the binary measurements, rather than treating them as real values, results in lower recovery error. Here a given third-order tensor with binary arrays is recovered. In practice, we open the tensor as a 3-matrix and apply the quantified tensor completion algorithm to all models of the matrix tensor. The data space here is distorted satellite spectral images for the purpose of image recovery.

In this paper, first, considering Fisher information of parametric type, we introduce a new informationmeasure based on Jensen inequality. Then, the Fisher information matrix and Jensen-Fisher are studiedor a finite mixture distribution of probability density functions. Further, another information criterion isintroduced as Jensen-χ2 based on a mixture of probability density functions. Generalizations of Jensen-Fisher and Jensen-χ2 information measures are presented based on m probability density functions and the relationship between these two new information criteria as well as the relationship between Jensen-Fisher information and some known information criteria such as Jensen-Shannon and Jeffreys informationmeasures are studied.

We carried out an analysis to investigate the effect of magnetic field on the pulsatile blood flow characteristics in a tapered artery. The main reason for considering the magnetic field in the presented model is that the blood flow conducts electricity and it is experimentally proved that the streaming of the blood flow can be affected significantly in the presence of the magnetic field. To simulate the realistic conditions of the human body, the artery wall has been assumed to be tapered and elastic with a combination of stenosis and aneurysm. The considered non-Newtonian model is characterized by the Cross fluid to describe the rheology of the blood flow. The governing PDE is solved numerically by utilizing the finite difference method. The effects of distinct parameters including aneurysm, stenosis, pulsatile nature of the blood flow and magnetic field on the blood flow velocity, volumetric flow rate and resistance impedance are presented by their representation graphs.

‎In this paper‎, ‎after calling a class of dependent random variables, APND, that contains some big classes of negatively dependent and some classes of positively dependent random variables‎, ‎the relationship of this class of random variables with well known classes of dependent variables are explained and some basic relations‎, ‎contain moment and maximal inequalities are proofed‎. ‎At the end‎, ‎the limiting behavior of an arbitrary array of random variables is studied‎.

In the present research, we were numerically solved nonlinear stochastic integral equation of the third kind by stochastic operational matrix based on Bernstein polynomials. For this aim, we were obtaining the Bernstein polynomials operation matrix and the stochastic operation matrix. Also we approximated all the functions in the Volterra integral equation of the third kind using the Bernstein polynomials series and then use the Bernstein polynomials operation matrix. By doing this, solving the third kind of stochastic Volterra integral equation turns into solving a system of algebraic equations, which could be a more suitable solution. Then we were analysed the convergence of the proposed method and provide several numerical examples to evaluate the accuracy and efficiency of this method. The current results were obtained by running a program written in Mathematica software.

The study of the function of vital organs of the body by mathematical models is one of the most important and interesting topics for researchers. In this work, we intend to study the mathematical model of human liver function using the fractional order derivative with Caputo approach. The Adomian Analytical Analysis (ADM) method will be used to solve the system of fractional-order differential equations obtained in the new model of the liver. We also provide a numerical simulation for the results obtained from the fractional order system and the integer order system using the available clinical data.