فصلنامه مدل سازی پیشرفته ریاضی
سال سیزدهم شماره 1 (بهار 1402)

In this paper, an iterative method for obtaining the numerical solutions of fractional partialdifferential equations (FPDEs) is introduced. This method is based on the combination of the differentialtransformation method (DTM) with fractional linear multistep methods (FLMM). The proposed methodhas a very low computational cost, with the help of which partial fractional differential equations areconverted into a system of ordinary differential equations. Then the resulting equations are solved with highaccuracy by applying fractional linear multi-step methods such as fractional Euler The series of solutionsobtained in the differential transformation method has a slow convergence speed in large regions. In thisstudy, by combining the mentioned method with linear multi-step methods, this shortcoming is solved.Numerical results show that the obtained solutions. They are in good agreement with the exact solution ofthe fractional differential equation. The obtained results confirm the proven stability and accuracy of themethod.

Researchers in different disciplines often face phenomena of random nature. Sometimes it is possible to use probability distributions to describe and predict such phenomena. Each distribution has a number of unknown parameters, whose values are estimated from data. In some problems, there are a few competing distributions for fitting to a data set. In this setup, selecting a suitable model based on some criteria is necessary. This article introduces facilities of R statistical software in performing the above steps. Application of the discussed methods is illustrated using a medical data set.

In this paper‎, ‎a numerical method is provided for solving multi-term time-fractional diffusion equations associated with a new fractional operator‎. ‎A semi-discrete scheme is obtained in temporal direction based on the finite difference method afterwards‎, ‎a Chebyshev-spectral method is used for spatial discretization‎. ‎Also‎, ‎the stability and error analysis are investigated‎. ‎Moreover‎, ‎the multi-term time-fractional diffusion equation is extended to a distributed order diffusion equation and numerical analysis has been done on it‎. ‎Finally‎, ‎the theoretical results are confirmed using some numerical examples.

Let $X=Y\cup \left\{\omega\right\}$ where $\omega \notin Y$, topologized by equipping $Y$ with the discrete topology, and by letting deleted neighborhoods of $\omega$ consist of complements of closed discrete subsets of $Y$ in its Riemann surface topology. Assume that $I$ is an ideal of $C^{*}(X)$ where $C^{*}(X)$ is the ring of all bounded real-valued continuous functions on $X$. A result of Adler and Williams showed that $I$ contains a regular element if and only if a set of regular elements generates $I$. In this note, we obtain some conditions on $X$ for which the rings of continuous functions on $X$ are Marot. Moreover, this paper gives a sufficient condition for a quasi-B\'ezout ring to be additively regular.

In recent years, pseudospectral methods have been used for solving many classes of differential and integral equations due to their high accuracy and rate of convergence. In this paper, we present an efficient Jacobi pseudospectral method for solving a class of fractional delay integral-differential equations. Then, by presenting several lemmas and theorems, we investigate the convergence of the method on space$ L ^ 2 _ {\ omega {alpha \ alpha, \ beta}} (I) $ and identify the error boundaries.

A square matrix $D$ is ​​called a ‎doubly‎ stochastic matrix if all its entries are non-negative and the sum of the entries of each row is equal to the sum of the entries of each column and is equal to one. For each linear and non-zero vector $x = (x_1, ‎‎\ldots, x_n)$, we define the degree of $x$ as the largest number ‎$‎i‎$‎ such that $x_i$ is non-zero and the degree of vector zero is zero. We say that a vector $x$ is degree majorized by $y$ and denote by $x\prec_{deg} y$ if the degree of $x$ is greater than or equal to the degree of $y$ and $x = yD$ for some doubly stochastic matrix $D$. ‎In this paper, we ‎obtain‎ the structure of all linear preservers of degree majorization on space ‎‎$‎‎\mathbb{R}^2‎$‎‎‏‎. Also, we find the structure of all strong linear preservers of degree majorization on real vector spaces $‎‎\mathbb{R}^‎n‎‎$.

In this article, we study the linear inverse problem for approximating a timewise-dependentfunction in the second-order hyperbolic equation. To solve the problem, information such as Neumannboundary conditions along with an integral condition and initial conditions at the initial moment and thefinal instant have been provided. In the first step, we show that this problem has a unique solution. Then,we change the main problem into a new one and then we present the spectral approximation based onthe Ritz-collocation method to recover the unknown functions. Discretization of the problem by usingthe presented technique leads to a linear system of algebraic equations, which Tikhonov’s regularizationmethod is used to obtain stable solutions. The results of the numerical simulation confirm the high accuracyand stability of the approximate solution.

Blackford (2008) [1] introduced the concept of negacyclic duadic codes over the field Fq, andclassified all self-dual negacyclic codes over Fq. In this paper, we define negacyclic duadic codes overring Fq +vFq and by using a Gray map on these codes, we get self-dual and self-orthogonal codes on thefield Fq. Also, we introduce some extensions of negacyclic duadic codes over ring Fq + vFq and presenttheir properties. Finally, we present some examples of negacyclic duadic codes over this ring and self-dualand self-orthogonal codes on the field Fq.

Let 𝑋 be a graph and G ≤ 𝐴𝑢𝑡(𝑋). the graph 𝑋 is called 𝐺 -symmetric if 𝐺 acts transitively on its arcs. The covering technique has long been known as a powerful tool in topology and graph theory. In this paper, by using the concepts of linear algebra and covering techniques, we will classify the symmetric elementary abelian covers of the Nauru graph for one of its symmetric subgroups

Public health and most economic activities have been affected by the coronavirus pandemic. This has caused a lot of difficulties for the public and the governance. A suitable solution that balances public health and economic activities is essential. In this paper, we provide a game-theoretic approach to find this balance, given a desired priority ratio between the two. We propose a Stackelberg game where Corona National Headquarters is the leader, and the people are the followers. We find an optimal solution to the proposed game for different color zones based on the number of patients in a given region. We also find the mixed Nash equilibria of the proposed game and explain the effects of different model parameters on the equilibria. We introduce the optimal mix strategies for each player to control the outbreak. We illustrate the performance of the proposed model for different color zones at different stages of the total deaths curve of the outbreak. Finally, we incorporate the possibility of having inaccurate decisions in the model for real world applications. The proposed strategy could also be used to control other possible respiratory pandemics that spread through close human contacts.

In this paper, we presented an optimal control problem for the least myofibroblast diffusionin order to prevent the formation of fibrotic tissue in the repair process in lung tissue. Since transforminggrowth factor-beta causes the proliferation and activation of myofibroblast, we considered this factor asthe control function of the optimal control problem. By presenting a theorem, the optimal control of theabove issue is guaranteed. In order to solve the problem of optimal control, there is a need to convertan equation with partial derivatives into a system of linear ordinary differential equations. Therefore,we solved this problem by using the central finite difference method. Then, using two methods of themaximum principle (Hamiltonian equations ) and the calculus of variations (Euler–Lagrange equation) inoptimal linear regulator problem, we controlled the most important factor, i.e. transforming growth factor-beta, which is common to all fibrotic tissues. In a theorem, we prove that the solution of the optimal linearregulator problem is the same for both methods. Finally, we compared the calculation results with the twopresented methods.

One of the most common causes of death during the birth of babies is heart failure. Diagnosis of this disease requires observation of heart activity. Since the electrical signals recorded in the mother’s abdomen contain a lot of information such as: mother’s heart signal, mother’s and fetus’s muscle activity, fetus’s brain activity and environmental noises, researchers are looking for ways to separate the fetus’s heart signals from the mother’s are. The proposed method has super-linear convergence, which provides global convergence results and an exact solution to solve the sub-problem. The performance of the proposed method is compared with the best existing methods and the results show that the proposed method has the lowest error rate and the highest speed in separating fetal heart signals from the mother compared to other methods.