Journal of Applied Mathematics and Computing最新文献

The main objective of this article is to study the effectiveness of wearing masks and implementing active screening and testing to contain the spread of COVID-19 during stages when the disease has already started to spread. This work innovates by focusing on the basic measures of mask use and active screening and testing, which are frequently overlooked in the literature in favor of more expensive interventions like travel bans and vaccinations. We study their effectiveness and determine the optimal way to implement them. To achieve this goal, we develop a stochastic SEIR model that includes four populations: susceptible, exposed, infected, and recovered individuals. We integrate two control functions into the model to represent mask-wearing and active screening and testing interventions. Using an adapted formulation of Pontryagin’s maximum principle suitable for the stochastic context, we aim to find the optimal approach to implementing these controls. We combine the Forward-Backward Sweep Method (FBSM) with a special Runge–Kutta scheme for stochastic differential equations to solve the optimality system for our stochastic optimal control problem. Our study demonstrates that even when the disease has begun to spread, using both mask-wearing and active screening and testing can lead to significant reductions in the numbers of exposed and infected individuals, offering a cost-effective strategy for countries with limited resources.

In this paper, an anti-periodic boundary value problem for a class of higher order nonlinear time scale systems is studied. Based on the method of mathematical analysis and some inequality techniques, we construct a new Lyapunov-type inequality. Finally, we give some applications to illustrate the importance of our results.

In this paper, an operational method based on Chelyshkov polynomials is used for solving a class of two dimensional optimal control problem for fractional order differential system involving fractal-fractional derivatives. The operational matrix of the corresponding fractional integration operator is calculated. First, the control signal and the differential of the state signals are approximated with unknown coefficients by orthogonal basis. Next, by replacing the approximate signals in objective functions, using two dimensional Gauss–Legendre quadrature rule and necessary optimal conditions the main problem is converted to a system of algebraic equations, which can be solved easily. Theoretically, the convergence analysis of the proposed method is stated. Moreover, to demonstrate the efficiency of the method, three test problems solved.

The objective of this article is to develop and analyze a parameter uniform numerical method for solving 2D singularly perturbed elliptic convection-diffusion differential-difference equations. The previous studies in this area have mainly focused on cases involving small shifts, but practical scenarios may involve shifts of arbitrary sizes, both larger and smaller. Despite this, the 2D singularly perturbed elliptic differential-difference equations involving shifts of arbitrary sizes have remained unsolved. To address this challenge, a fitted operator finite difference method is developed on a special equidistant mesh that ensures the nodal point coincides with the shifts after discretization.. The scheme is rigorously analyzed to prove parameter uniform a priori error estimate in (L_{infty }) norm. To illustrate the theoretical findings, we provide numerical results and implement numerical experiments to investigate the effect of shifts on the solution.

The topological index is a useful tool in mathematical chemistry that connects a numerical value to a network structure. The Sombor index is well-known for establishing such connections. This work presents the generalization of the Sombor index from a fuzzy point of view. We introduce the Sombor index for fuzzy graphs ((SO(FG))). Some crucial bounds of (SO(FG)) are established for numerous graph operations, including Cartesian product, composition, join, and union. In addition, we find the relationship between the Sombor index and other topological indices. Moreover, we present an application of the Sombor index for fuzzy graphs to identify the most alarming type of cancer in India, which clearly justifies the generalization of the Sombor index.

Abstract

The Topological index serves as a powerful mathematical descriptor, capturing the intricate structural features of molecules and providing insightful analysis in the field of chemical sciences. This communication studies the higher-order Neighborhood Harmonic index ((NH_{alpha })) and presents an alternative perspective on the correlation of the second-order Neighborhood Harmonic index ((NH_{2})) with the normal boiling point of straight-chain Alkanes and Octane Isomers. Based on the findings of this study, it can be observed that with an increase in the molecular weight of an straight-chain alkane, there is a concurrent elevation in both the normal boiling point and the collective involvement of (NH_{2}) along all conceivable internal C–C–C routes. As all the isomers of Octane possess the same molecular weights, we first categorize the isomers into distinct groups and then establish a meaningful connection with their respective normal boiling points. In case of normal boiling point (computed using modified Frost-Kalkwarf equation), it is found that, the proposed index i.e., Second-Order Neighborhood Harmonic index has good predictive ability with a probability of (90%) for absolute relative errors of less than (6.29%). Further, some important mathematical properties of the ((NH_{2})) are also presented in the paper.

Graphical abstract

This paper investigates the single machine group scheduling with unrestricted (different) due date assignments and resource allocations (controllable processing times). The resource allocations mean that the actual job processing times are convex decreasing function of their consumption of resources. To solve the general problem of minimizing the weighted sum of earliness, tardiness, due date assignment cost and resource consumption cost (the weights are job-dependent weights), we propose lower and upper bounds to speed up the search process of the branch-and-bound algorithm. To solve this problem quickly and accurately, we also propose a heuristic algorithm. Computational results are tested to evaluate the performance of the algorithms.

The first point of this research is to develop several representations for the weighted m-weak group inverse. Secondly, we consider the minimization problem (min Vert W(AW)^{m+1}X-(WA)^mBVert _F), (mge 1) in the Frobenius norm, subject to constraint (mathcal{R}(X)subseteq mathcal{R}((AW)^k)), where the exponent k is defined as the maximum between indices of AW and WA. The solution is expressed in terms of weighted m-weak group inverse. Particular settings of obtained results recover several known results in the literature. A representation in the form of an appropriate outer inverse of WAW with given image and kernel is obtained.

Alliances and conflicts in social, political and economic relations can be represented by positive and negative edges in signed networks. A cycle is said to be positive if the product of its edge signs is positive, otherwise it is negative. Then, a signed network is balanced if and only if all its cycles are positive. An index characterizing how much a signed network deviates from being balanced is known as a global balance index. Here we give a step forward in the characterization of signed networks by defining a local balance index, which characterizes how much a given vertex of a signed network contributes to its global balance. We analyze the mathematical foundations and unique structural properties of this index. Then, we apply this index to the study of the evolution of international relations in the globe for the period 1816–2014. In this way we detect and categorize major historic events based on balance fluctuations, helping our understanding towards new mixed approaches to history based on network theory.

An m-polar fuzzy set model is a mathematical tool for dealing with uncertainty in multipolar data. This paper extensively investigates the use of the eigenvalue-eigenvector approach to solve nth order differential equations with distinctive m-polar fuzzy initial conditions. It digs further into three different eigenvalue scenarios using this strategy. Given that we are working with m-polar fuzzy numbers, the solution is a fuzzy number encompassing each component. Furthermore, the methodology is explained through a variety of examples to aid readers in understanding the principles. Moreover, the graphical presentation of the solution is also provided.