نشریه پژوهشهای ریاضی
سال نهم شماره 4 (پیاپی 27، زمستان 1402)

Scheduling theory and permutation therein are two important subjects in discrete operation research. In this paper, a new heuristic algorithm is proposed for solving permutation flow shop problem by using regulations of columnar entries in the processing times matrix. There are  jobs to be processed on  machines with deterministic processing times and the object is obtaining the minimum of the total time to complete the schedule (makespan). This is not solvable in polynomial time. First, an initial suitable sequence of jobs is determined similar to many heuristics. For this, the matrix  is made such that every determines the measure of the fitness for the location of the th old row in the th new position. Thereafter, the Bellman Esogbue Nabeshima theorem is used. The presented algorithm is compared with the NEH (the best well-known existing method). This comparison is made by the Taillard’s standard test problems. Computational results demonstrate that the heuristic algorithm is better than some of the proposed heuristics known so far and it is superior with respect to others in a number of Taillard instances. As a result, it is almost as good as NEH and is very promising for the problem. On the basis of the structure of the proposed algorithm, it can perform a role as meta-heuristic.

The ability of insurers to pay claims is one of the most important issues in the management of insurance companies. In this paper, the collective risk model of insurance company with constant premium and compound Poisson process over a period of time is considered. For a general class of claim sizes with light tailed and heavy tailed distributions, a formula for computing the finite time ruin probability is obtained using the probability transformation, then the matrix form of the presented formula by the transformation matrix and continuous time Markov chain generating matrix is rewritten. Also, using simulation paths from the risk process for claim sizes with Exponential, Normal and Pareto distributions with different values of initial reserve at the different times, in addition to compute the finite time ruin probabilities and unbiased confidence intervals, their values estimated for transformation matrix and Markov chain generating matrix.

Redundancy allocation to the system is one way to improve the reliability and efficiency of the system. Adding a standby component to the system  is an important factor in improving system performance and usually will incur some costs to the system. In this paper, we investigate the stress-strength reliability of a k-out-of-n: G system in a Weibull-H model. Also, in order to increase the stress–strength reliability and decrease the costs simultaneously, we obtain the optimal time to activate  the standby component to the working state,in some cases related to the Weibull-H model.

Let G  be a finite group and let Irr(G)  be the set of irreducible characters of G . ‎We say that an element g  in G  is a vanishing element if there exists some χ∈ Irr(G)   such that χ(g)=0 ‎. In this paper, we provide a relatively short proof for the classification of finite groups whose set of vanishing elements is the :union: of exactly three conjugacy classes‎.

In this study, an efficient numerical method for solving the Fredholm integral equations of the second kind is presented. The proposed method is based on the Picard iteration method, the shifted Legendre polynomials, and the shifted Legendre-Gauss integration rule. According to the orthogonal property of Legendre polynomials, the proposed method uses an iterative scheme to update the coefficients of the series of approximate solution. Also, a vector-matrix structure is introduced to increase the efficiency and reduce the computational time. The numerical results clearly indicate the feasibility and the accuracy of the proposed technique.

All rings throughout this paper are commutative and Noetherian. Semidualizing modules were studied independently by Foxby [4], Golod [5], and Vasconcelos [11]. A finite R-module C is called semidualizing if the natural homothety map is an isomorphism and for all . If a semidualizing R-module has finite injective dimension, it is called dualizing and is denoted by D. The ring itself is an example of a semidualizing R-module. Many researchers, in particular Sather-Wagstaff [12], have studied the semidualizing modules. Let M be an R-module. The trace ideal of M, denoted by , is the sum of images of all homomorphisms from M to R. Trace ideals have attracted the attention of many researchers in recent years. In particular, Herzog et al. [6] and Dao et al. [3] studied the trace ideals of canonical modules. Also, the trace ideals of semidualizing modules were studied in [1].    In this paper, we study the trace ideals of tensor product of two arbitrary modules. We prove some known facts with a different approach via trace ideals. For example, let C and be two semidualizing R-modules. We show that is projective if and only if C and  are projective R-modules of rank 1. Also, we study the trace ideals of maximal Cohen-Macaulay modules over a Gorenstein local ring.

In this research, an efficient numerical method is presented for solving a class of nonlinear delay fractional optimal control problems with inequality constraints on the state and control variables. The proposed approach is based on the hybrid of block-pulse functions and fractional-order Legendre functions. By using the operational matrices of delay and derivative associated with the hybrid functions, the original optimal control problem is transformed into a parameter optimization one. The numerical results, demonstrate the accuracy and validity of the suggested method.

Solidification processes are present in a wide range of manufacturing methods and applications, from metallurgy to food processing. In recent years, Phase-Field models have been increasingly used to simulate and predict the formation and evolution of material microstructure and phase change interfacial kinetics. In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys based on the kobayashi model. At first, the kobayashi  phase-field model, which describes the solidification of a pure material from an undercooled melt, is introduced in detail. In discretization process of this model, the time derivatives are approximated via finite difference method.   Then the local meshless moving Kriging method is applied for discretization of the model in space direction. The moving Kriging method is a truly meshless method in which the unknown function can be approximated locally, and this leads to the sparsity of the coefficient matrix. As the shape functions possess the Kronecker delta function property, boundary conditions can be implemented without any difficulties. The model is simulated for various values of it’s parameters.  Numerical simulations illustrate the applicability and effectiveness of the proposed method. As a consequence, it is found that the method is very efficient and accurate for phase-field models compared with those of other conventional methods. Therefore, this method can be considered as an attractive alternative to existing mesh-based methods in solving phase-field models.

A Banach algebra A is called contractible if for any Banach A-bimodule E, every continuous derivation from A into E is inner. One of the oldest unconfirmed conjectures in amenability  says that every contractible Banach algebra is finite dimensional. It is well-known that a Banach algebra A is contractible if and only if its unital and has a diagonal, that is a member M in the Banach algebra A⊗πA such that satisfies in ∆(M)=1 and a⊗1M=M(1⊗a) for every a in A. In this note we show that any diagonal of a contractible Banach algebra of operators on an infinite dimensional Banach space has a specific null property.

In this paper, using a new method based on the generalized hat functions, we solve a class of fractional delay differential equations in which the fractional derivative is considered in the sense of Caputo. First, we introduce the generalized hat functions and their corresponding operational matrices. Then, in order to solve the considered problem, the existing functions are approximated using the basis functions. By employing the properties of generalized hat functions, the Caputo fractional derivative and the Riemann-Liouville fractional integral, a system of algebraic equations is obtained which by solving it, the unknown coefficients are determined. By substituting the resulting values, an approximation of the solution of the problem is obtained. In addition, the computational complexity of the resulting system is investigated. In continue, an error analysis of the method is given. Finally, the accuracy and efficiency of the proposed method are shown by presenting two examples.

In this paper, using the concept of measure of noncompactness, we introduce a new extended contraction of operators on a Banach space and obtain some generalizations of Darbo’s fixed-point theorem. In the following, as an application of the obtained results, we deal with the solvability of a system of integral equations of Stochastic type in Banach space. Our results generalize and extend a lot of comparable results in the literature. Finally, a concrete example is also included, which demonstrates the applicability of the obtained results.

In this article, a linear inverse problem for approximating the right hand side of a fourth order parabolic equation is studied. In this problem, it is assumed that the homogeneous boundary conditions along with an integral condition on the time domain and a local condition at a point of the space domain are known. In the first step, we show that this problem has a unique classical solution. Then, we convert the initial problem into a new problem by using suitable transformations, in which the time-dependent unknown function is transferred to the boundary conditions, and then we provide a spectral approximation based on the Ritz method to detect the unknown functions. The discretization of the problem using the presented technique leads to a system of linear algebraic equations which is solved by employing the Tikhonov's regularization method. The numerical simulation results confirm the acceptable accuracy and stability of the approximate solution.

In this paper, by using the concept of Cartan curvature,  the  Douglas metric reduce to  constant R.I   Landsberg metric  and if it's bounded, to  Riemannian one. Finally, it is shown that with a condition on Cartan curvature, Landsberg, weakly Landsberg and generalized Landsberg  metrics are equivalent.