Journal of Mathematical Modeling
Volume:9 Issue: 4, Autumn 2021

This paper deals with the existence and optimal harvesting of two competing species in a polluted environment under the influence of pollution reduction effort. We propose and analyze a nonlinear system wherein harvesting and pollution reduction activities, respectively, are incorporated into the resource and pollution dynamic equations. We investigate the coexistence, competitive exclusion, and extinction of both species in the system. Further, considering pollution-dependent revenues, we study an optimal harvest problem on an infinite horizon. The results indicate that the extinction of both species is inevitable when pollutant inflow is sufficiently large.  Otherwise, the proper effort allocation towards pollution reduction guarantees not only species coexistence but also improves the revenue. The significant outcomes of the study are verified by considering practical examples.

Pre-exposure prophylaxis (PrEP) has become a promising strategy used by uninfected individuals for the HIV prevention. The risk of infection with HIV after exposure to the virus can be understood through a stochastic framework. In this research we present a stochastic model for HIV/AIDS epidemic with the use of prophylaxis and we show that the model with random perturbation has a unique global positive solution. For a special case, we introduce an analogue, ${cal R}_{sigma}$, of the basic reproduction number. This invariant features in a theorem on almost sure exponential stability. Our results show that the disease goes extinct exponentially and almost surely whenever ${cal R}_{sigma}$ stays below unity. Simulations serve to illustrate various phenomena.

This paper presents a new heuristic algorithm for the following covering problem. For a set of $n$ demand points in continuous space, locate a given number of facilities or sensors anywhere on the plane in order to obtain maximum coverage. This means, in this problem an infinite set of potential locations in continuous space should be explored. We present a heuristic algorithm that finds a near-optimal solution for large-scale instances of this problem in a reasonable time. Moreover, we compare our results with previous algorithms on randomly generated datasets that vary in size and distribution. Our experiments show that in comparison to other methods in the literature, the proposed algorithm is scalable and can find solutions for large-scale instances very fast, when previous algorithms unable to handle these instances. Finally, some results of the tests performed on a real-world dataset are also presented.

In this paper, we study the bonus-malus model denoted by $BM_k (n)$. It is an irreducible and aperiodic finite Markov chain but it is not reversible in general. We show that if an irreducible, aperiodic finite Markov chain has a transition matrix whose secondary part is represented by a nonnegative, irreducible and periodic matrix, then we can estimate an explicit upper bound of the coefficient of the leading-order term of the convergence bound. We then show that the $BM_k (n)$ model has the above-mentioned periodicity property. We also determine the characteristic polynomial of its transition matrix. By combining these results with a previously studied one, we obtain essentially complete knowledge on the convergence of the $BM_k (n)$ model in terms of its stationary distribution, the order of convergence, and an upper bound of the coefficient of the convergence bound.

In this study, alpha power Maxwell (APM) distribution is obtained by applying alpha power transformation, a reparametrized version of the Exp-G family of distributions, to the Maxwell distribution. Some tractable properties of the APM distribution are provided as well. Parameters of the APM distribution are estimated by using the maximum likelihood method. The APM distribution is used to model a real data set and its modeling capability is compared with different distributions, which can be considered its strong alternatives.

In this article, we develop an iterative scheme based on the meshless methods to simulate the solution of one dimensional stochastic evolution equations using radial basis function (RBF) interpolation under the concept of Gaussian random field simulation. We use regularized Kansa collocation to approximate the mean solution at space and the time component is discretized by the global $ theta $-weighted method. Karhunen-lo`{e}ve expansion is employed for simulating the Gaussian random field. Statistical tools for numerical analysis are standard deviation, absolute error, and root mean square. In this work, we solve two major problems for showing the convergence, and stability of the presented method on two problems. The first problem is the semilinear stochastic evolution problem, and the second one is stochastic advection-diffusion model with different control values.

This paper deals with the mathematical modeling of the behavior of a reinforced rectangular thermo-elastic plate with a thin insulating stiffener. We use a variational asymptotic analysis, with respect to the thickness of the inserted body, in order to identify limit models that reflect its effect on the plate. We carry out a mathematical modeling for a stiffener of high rigidity and a stiffener of moderate rigidity.

A  singularly perturbed convection diffusion  equation with boundary  turning point  is considered in this paper. A higher order method on piecewise uniform Shishkin mesh is suggested to solve this problem. We  prove that this method is of  order $O(N^{-2}(ln N)^2)$. Numerical results are given which validate  the analytical results.

A fast and efficient Newton-Shultz-type iterative method  is presented to compute the inverse of an invertible tensor. Analysis of the convergence error shows that the proposed method has the sixth order convergence. It is shown that the proposed algorithm can be used for finding the Moore-Penrose inverse of tensors. Computational complexities of the algorithm is presented to support the theoretical aspects of the paper. Using the  new method, we obtain a new preconditioner to solve the multilinear  system $mathcal{A}ast_Nmathcal{X}=mathcal{B}$. The effectiveness and accuracy  of this method are re-verified by several numerical examples. Finally, some conclusions are given.

In this paper,  a new conjugate gradient-like algorithm is proposed to solve unconstrained optimization problems. The step directions generated by the new algorithm satisfy sufficient descent condition independent of the line search. The global convergence of the new algorithm, with the Armijo backtracking line search,  is proved.  Numerical experiments indicate the efficiency and robustness of the new algorithm.

Online Streaming Features (OSF) is a data streaming scenario, in which the number of instances is fixed while feature space grows with time. This paper presents a rough sets-based online feature selection algorithm for OSF.  The proposed method, which is called OSFS-NRFS, consists of two major steps: (1) online noise resistantly relevance analysis that discards irrelevant features and (2) online noise resistanlty redundancy analysis, which eliminates redundant features. To show the efficiency and accuracy of the proposed algorithm, it is compared with two state-of-the-art rough sets-based OSFS algorithms on eight high-dimensional data sets. The experiments demonstrate that the proposed algorithm is faster and achieves better classification results than the existing methods.

In this paper,  numerical solution of the singularly perturbed  differential equations with mixed parameters   are considered.  The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter,   $varepsilon$ and mesh size, $h$.   The numerical results are tabulated  and it is observed that the present method is more  accurate and $varepsilon$-uniformly convergent for $hgeqvarepsilon$,  where the classical numerical methods fails to give good result.