University of GuilanJournal of Mathematical Modeling2345-394X9420211201Existence and optimal harvesting of two competing species in a polluted environment with pollution reduction effect517536461310.22124/jmm.2021.18266.1573ENSimon DerkeeZawkaDepartment of Mathematics, College of Natural and Computational Sciences, Arba Minch University, Ethiopia0000-0002-8814-5516Diwakara Narasimha SrinivasuPichikaSri Sathya Sai University for Human Excellence, Gulbarga, IndiaJournal Article20201205This 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.https://jmm.guilan.ac.ir/article_4613_6bd094a03843ce20f528f44d13a32575.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201A stochastic model for HIV with the use of PrEP537553462710.22124/jmm.2021.16870.1461ENMozart Umba NsuamiNsuamiDepartment of Mathematics and Applied Mathematics,
University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa0000-0002-0917-0271Peter JosephWitbooiDepartment of Mathematics and Applied Mathematics,
University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South AfricaJournal Article20200620Pre-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.https://jmm.guilan.ac.ir/article_4627_c0c66263d87aa9523fb2fa05bfdb0163.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201A practical heuristic for maximum coverage in large-scale continuous location problem555572463510.22124/jmm.2021.18624.1594ENMahdiImanparastDepartment of Computer Science, University of Bojnord, Bojnord, IranVahidKianiDepartment of Computer Engineering, University of Bojnord, Bojnord, IranJournal Article20210113This 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.https://jmm.guilan.ac.ir/article_4635_43dd386994d4999be00212ee5bcfe838.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201On the spectral properties and convergence of the bonus-malus Markov chain model573583468310.22124/jmm.2021.18991.1625ENKenichiHirose10-17 Moto-machi, Ono City, Fukui 912-0081, JapanJournal Article20210222In 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.<br /><br />https://jmm.guilan.ac.ir/article_4683_f88575afeb1b588add985c55d0b88c1d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201Alpha power Maxwell distribution: Properties and application585598468410.22124/jmm.2021.17987.1553ENNecatiErdoganDepartment of Econometrics, Van Yuzuncu Yil University, 65080 Van, Turkey.KubraBagciDepartment of Econometrics, Van Yuzuncu Yil University, 65080 Van, Turkey.TalhaArslanDepartment of Econometrics, Van Yuzuncu Yıl University, 65080 Van, Turkey.H. ErayCelikDepartment of Econometrics, Van Yuzuncu Yil University, 65080 Van, Turkey.Journal Article20201020In 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.https://jmm.guilan.ac.ir/article_4684_3af33833a88dd74f31789c9d0dced22f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201The approximate solution of one dimensional stochastic evolution equations by meshless methods599609468710.22124/jmm.2021.18683.1598ENMahdiJaliliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, IranRezvanSalehiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, IranJournal Article20210119In 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.https://jmm.guilan.ac.ir/article_4687_bf6a9185228471f4c586859c2261fc55.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201Mathematical modeling of the effect of an insulating stiffener on a nonlinear thermo-elastic plate611631475110.22124/jmm.2021.18895.1616ENHanifaMokhtariLaboratoire de mathematiques pures et appliquees (LMPA), Mouloud Mammeri University of Tizi-Ouzou, AlgeriaLeilaRahmaniLaboratoire de mathematiques pures et appliquees (LMPA), Mouloud Mammeri University of Tizi-Ouzou, AlgeriaJournal Article20210213This 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.https://jmm.guilan.ac.ir/article_4751_c4b85d696a199b76eb81b7a500665eca.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201Second order difference scheme for singularly perturbed boundary turning point problems633643475810.22124/jmm.2021.18771.1606ENGovindarajan JananiJayalakshmiDepartment of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, IndiaAyyaduraiTamilselvanDepartment of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, IndiaJournal Article20210130A 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.https://jmm.guilan.ac.ir/article_4758_8e7f2014d3bcedb899496b890f1c3f01.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201A fast and efficient Newton-Shultz-type iterative method for computing inverse and Moore-Penrose inverse of tensors645664475910.22124/jmm.2021.19005.1627ENEisaKhosravi DehdeziDepartment of Mathematics, Persian Gulf University, Bushehr, Iran0000-0002-1106-4451SaeedKarimiDepartment of Mathematics, Persian Gulf University, Bushehr, IranJournal Article20210223A 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 $\mathcal{A}\ast_N\mathcal{X}=\mathcal{B}$. The effectiveness and accuracy of this method are re-verified by several numerical examples. Finally, some conclusions are given.https://jmm.guilan.ac.ir/article_4759_0b3014f3bc2edf1193959cb9c4437a11.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201A globally convergent gradient-like method based on the Armijo line search665676476010.22124/jmm.2021.18854.1612ENAhmadKamandiDepartment of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran0000-0002-7489-2342KeyvanAminiDepartment of Mathematics, Razi university, Kermanshah, Iran0000-0002-9264-3091Journal Article20210208In 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.https://jmm.guilan.ac.ir/article_4760_88d9189d3ca6cd0475a3ea442cb33ae8.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201Streamwise feature selection on big data using noise resistant rough functional dependency677690476110.22124/jmm.2021.18707.1603ENSadeghEskandariDepartment of Computer Science, University of Guilan, Rasht, Iran0000-0002-3007-2369Journal Article20210123Online 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.https://jmm.guilan.ac.ir/article_4761_c204ce401f0f2c234d97a750061b4a66.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9420211201Numerical solution of singularly perturbed differential difference equations with mixed parameters691705476210.22124/jmm.2021.18365.1576ENGemechis FileDuressaDepartment of Mathematics, College of Natural Sciences,Jimma University, Ethiopia0000-0003-1889-4690Habtamu GaromaDebelaDepartment of Mathematics, College of Natural Sciences,Jimma University, Ethiopia0000-0003-1033-3602Journal Article20201207In 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 $h\geq\varepsilon$, where the classical numerical methods fails to give good result.https://jmm.guilan.ac.ir/article_4762_9d9efc5b184ebed8c1128998fdb26503.pdf