فصلنامه مدل سازی پیشرفته ریاضی
سال دوازدهم شماره 2 (تابستان 1401)

‎In this paper‎, ‎estimating the mean problem of the population when the sampling data have measurement errors has been studied via a new efficient estimator‎. ‎We also investigate the efficiency of this estimator compared to other available estimators‎. ‎And finally‎, ‎we use these results for real data‎. ‎We show that the proposed estimator is more efficient than other existing estimators‎.

Boolean networks are one of the models for studying complex dynamic behaviors in biological systems. The analysis of attractors of these networks is very important .But the exponential dependence of the state transition graph of these models with the number of network nodes is a major problem for large-scale systems analysis. Therefore, it is necessary to use network reduction methods. In these methods, the size of the networks is reduced, while the dynamic properties are preserved, but the reduction methods are not minimal. In this paper, while the two biological networks "abscisic acid" and "breast cancer" have been reduced, also the sensitivity analysis of the nodes of the reduced networks has been performed. The results show that reduced network nodes are important components in the main network dynamics because most of them have zero opposite sensitivity. Also, zero sensitivity nodes in reduced networks can be removed under certain conditions, using From the reduction method and the concept of sensitivity, our proposed method is able to modify the Saadatpour reduction method. Using the proposed method, we obtained reduced networks with fewer nodes that maintain the main network dynamics and have a smaller state space. These nodes are also important in both structural and dynamic aspects of biological networks.

Let $EuScript{H}$ be a Complex Hilbert space and $EuScript{B(H)}$ be the algebra of allbounded linear operators on $EuScript{H}$. The non-commuting graph of $EuScript{B(H)}$, denoted by $mathnormal{Gamma}(EuScript{B(H)})$ is a graph whose vertices are non-scalar bounded operators and two distinct vertices $A$ and $B$ are adjacent if and only if $AB neq BA$. In this paper, we prove the connectivity of $mathnormal{Gamma}(EuScript{B(H)})$ for separable and non-separable complex Hilbert spaces. Also we show that the noncommuting graphs of the set of all finite rank operators on $EuScript{H}$, the set of all compact operators on $EuScript{H}$, the set of all non-invertible operators on $EuScript{H}$ and the set of all Fredholm operators on $EuScript{H}$ are connected graphs.

A proper unital subring of a ring R is called a maximal subring, if it is maximal with inclusion between proper subrings of R. In this paper we present conditions under which a Pr"{u}ferr domain has a maximal subring. We study the Pr"{u}fer and B'{e}zout properties which are shared between an integral domain and its maximal subrings too.

In this paper, the optimal control of delay systems with piecewise constant delay function is investigated. Using Chebyshev hybrid functions, an approximate method is proposed to obtain the optimal solution to the control problem of linear delay systems. In order to present an approximate method, integral, product of multiplication and delay operational matrices of the hybrid functions have been introduced and used to solve the problem. The optimal control problem is transformed into an optimization problem with the help of the operational matrices and then solving it, an approximate solution to the original problem is obtained. Efficiency and accuracy of the proposed method are illustrated with two examples of the optimal control problem. ‎‎

In this paper, we investigate the completeness of cones in the symmetric topology ‎induced ‎the ‎sublinear ‎quasi-metrics‎ and prove that in the symmetric complete cone the symmetric neighborhoods are of the second category. Then we present an extension of the Baire category theorem for the symmetric topology of locally convex quasi-metric cones.

‎In this paper‎, ‎we provide a new difference scheme on a graded mesh for solving the time-space fractional diffusion problem‎. ‎In ‎this ‎equation ‎the ‎time ‎derivative ‎is ‎the ‎Caputo ‎of ‎order ‎‎$‎‎gammain(0,1)$ ‎and ‎the ‎space ‎derivative ‎is ‎the ‎Riesz ‎of ‎order ‎‎$‎‎alphain(1,2]$.‎ ‎The stability and convergence of the difference scheme are discussed which provides the theoretical basis of the proposed‎ ‎schemes‎. W‎e prove that the new difference scheme is unconditionally stable‎. Also, ‎we find that the difference scheme is convergent with order $min{2-gamma,rgamma}$ in time for all $gammain (0,1)$ and $alpha in (1,2]$‎. ‎A test example is given to verify the efficiency and accuracy of the difference scheme‎.

The present study is devoted to finding the approximate solutions of a new design of a second-order nonlinear functional system of Lane-Emden differential equation with boundary conditions. Our proposed matrix technique is based on the Chelyshkov functions together with collocation points to transform the nonlinear system into an algebraic fundamental matrix equation. The convergence of the spectral Chelyshkov approach is also proved. To show the efficiency and the accuracy of the presented technique, three test examples are solved numerically. Also, comparisons with the exact solutions and with an available method in the literature are performed.

In this paper, we approximate the solution of fractionalBagley–Torvik equation by using the non-polynomial spline function andthe shifted Gr"{u}nwald difference operator. The proposed methodsreduce to the system of algebraic equations. The convergenceanalysis of the methods has been discussed. The numerical examplesare presented to illustrate the applications of the methods and tocompare the computed results with the other methods.

In this paper, a sliding mode control for systems that are nonlinear, having fractional order, andinvolve delay is used. The aim of this paper is to design a sliding mode controller, such that the closed looped nonlinear system becomes asymptotically stable and its trajectory can be driven onto the slidingsurface in finite time. By using the fractional Razumikhin theorem for the stability of fractional ordersystems including delay and a linear matrix inequality, necessary conditions on asymptotic stabilizationare obtained. Some numerical examples are given to illustrate the effectiveness of the proposed results.

‎The aim of this work is to provide a specific process for solving a reaction-diffusion partial differential equation with boundary conditions ‎(‎RPDEs)‎‎. ‎We first convert this ‎R‎PDE problem to Volterra-Fredholm integral equation (VFIE)‎, ‎because of the good numerical stability properties of integral operators in compare to differential operator‎, ‎then apply the numerical Tau method to solve the obtained integral equation‎. ‎‎‎‎We present the convergence analysis and error estimation of the Tau method based on the proposed process‎. ‎Applying the Tau method yields a system of the ordinary differential equation such that this system is solved by piecewise polynomial collocation methods‎. ‎Intended to show advantages of converting ‎RPD‎E to an integral equation‎, ‎we consider two cases to solve the proposed examples‎. ‎In the first case‎, ‎we apply the Tau method to solve the ‎converted ‎‎R‎PDE problem ‎(‎integral ‎form‎‎‎) and in the second case‎, ‎we solve ‎the ‎R‎PDE ‎problem‎ ‎directly ‎(direct ‎form‎‎)‎ by Tau method‎. ‎Comparing the numerical results‎, ‎we observe that the results obtained from the ‎integral ‎form‎ ‎ are higher than which obtained from the ‎direct ‎form‎‎‎‎.

Ideals of points are considered as a significant and efficient tools in modeling and computingscience, which is why algorithms computing these types of ideals are of crucial importance. This paperproposes an algorithm to compute order ideals for ideals of points. Then those order ideals are used formodeling gene regulatory networks.