Journal of Mathematics Research最新文献

An Optimal Multiquadric Variable Shape Parameter for Boundary Value Problems Using Particle Swarm Optimization 利用粒子群优化法优化边界值问题的多四方变量形状参数

Journal of Mathematics Research Pub Date : 2024-05-02 DOI: 10.5539/jmr.v16n2p108

Abdou Bacar, Said Charriffaini Rawhoudine

{"title":"An Optimal Multiquadric Variable Shape Parameter for Boundary Value Problems Using Particle Swarm Optimization","authors":"Abdou Bacar, Said Charriffaini Rawhoudine","doi":"10.5539/jmr.v16n2p108","DOIUrl":"https://doi.org/10.5539/jmr.v16n2p108","url":null,"abstract":"The multiquadric radial basis function method has been widely used to solve partial differential equations-based problems regarding its flexibility and meshfree characteristics. The accuracy and stability of this method are derived and based on the use of a free-shape parameter that sensibly controls the comportment of the technique. Significant improvements have already been reported and show that variable shape parameters conduct the method to handle problems with striking results compared to global-based techniques. Nevertheless, choosing a suitable set of shape parameters is still an open topic because of the complexity of the method when the number of collocation points increases. The current work proposes a variant particle swarm optimization based on local displacement with attractors to determine the multi-quadratic function's ``best'' optimal variable shape parameter in solving boundary value problems. Based on an initially random set of variable shape parameters, the proposed algorithm first performs and evaluates the errors between the expected exact solution and the approximate solution thoroughly. In the first stage, the particle swarm algorithm search for an optimal set of shape parameters that minimize the error and the conditioning number of the radial basis system matrix. In the second stage, the obtained optimal set of shape parameters is applied to solve the considered problem. In this way, when the number of collocation points increases, the first stage based on particle swarm optimization stabilizes the strategy. It proposes an ``acceptable'' set of shape parameters for the given problem. The proposed method is applied to a set of well-known boundary value problems in one and two-dimensional spaces and compared to other techniques published in the literature. The results show that the proposed method achieves more accurate solutions than recently proposed in the literature.","PeriodicalId":512715,"journal":{"name":"Journal of Mathematics Research","volume":"38 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141021609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 16, No. 2 数学研究》杂志第 16 卷第 2 期审稿人致谢

Journal of Mathematics Research Pub Date : 2024-05-02 DOI: 10.5539/jmr.v16n2p132

Sophia Wang

引用次数: 0

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 16, No. 1 数学研究杂志》第 16 卷第 1 期审稿人致谢

Journal of Mathematics Research Pub Date : 2024-01-31 DOI: 10.5539/jmr.v16n1p66

Sophia Wang

引用次数: 0

Exponential Stability of Non-uniform Timoshenko Beam With Indefinite Damping Under Boundary Control 边界控制下具有无限阻尼的非均匀季莫申科梁的指数稳定性

Journal of Mathematics Research Pub Date : 2024-01-30 DOI: 10.5539/jmr.v16n1p54

Kouassi Ayo Ayébié Hermith, Diop Fatou N., T. K. Augustin

引用次数: 0

The Upwind Finite Volume Element Method for Two-Dimensional Time Fractional Coupled Burgers’ Equation 二维时间分数耦合布尔格斯方程的上风有限体积元素法

Journal of Mathematics Research Pub Date : 2024-01-26 DOI: 10.5539/jmr.v16n1p31

Zechao Lv, Qing Yang

引用次数: 0

A Proof of a Gantmacher’s Result on Nonnegative Square Matrices by Means of M-matrices 用 M 矩阵证明甘特马赫关于非负平方矩阵的结果

Journal of Mathematics Research Pub Date : 2024-01-26 DOI: 10.5539/jmr.v16n1p46

Giorgio Giorgi

引用次数: 0

Stochastic SIR Epidemiological Model With Two Levels of Severity 两级严重程度的随机 SIR 流行病学模型

Journal of Mathematics Research Pub Date : 2024-01-25 DOI: 10.5539/jmr.v16n1p16

Gérard Kanga, Jacques Tano

{"title":"Stochastic SIR Epidemiological Model With Two Levels of Severity","authors":"Gérard Kanga, Jacques Tano","doi":"10.5539/jmr.v16n1p16","DOIUrl":"https://doi.org/10.5539/jmr.v16n1p16","url":null,"abstract":"In this paper, we develop an epidemic model to analyze the spread of an infectious disease with two levels of severity within a population of varying size. Additionally, we examine the stability of the disease-free equilibrium. \u0000Such a model is suitable for the dynamics of COVID-19 disease spread. If the two types of infected individuals have different recovery rates, then there is no endemic equilibrium; only the disease-free equilibrium will be the subject of our study. We then study both the deterministic model and a stochastic version. The stochastic model is obtained by perturbing the contact rate using white noise. For the deterministic model, we have shown that if the basic reproduction number R_0 < 1, then the equilibrium state is globally asymptotically stable by using Lyapunov function. This implies that the disease will disappear, and the entire population will become susceptible. For the stochastic version, we demonstrate that the system admits a unique positive global solution that exists within a positively invariant domain. Under suitable conditions on the intensity of the white noise perturbations, we prove that the number of infectious individuals converge almost surely exponentially to zero and the disease-free equilibrium of system is stochastically asymptotically stable in the large provided. Finally, we give some numerical simulations to illustrate our theoretical results.","PeriodicalId":512715,"journal":{"name":"Journal of Mathematics Research","volume":"36 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139597233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Improved Method to Estimating Parameters of a Poisson Hidden Markov Model Using Bayesian Approach 利用贝叶斯方法估算泊松隐马尔可夫模型参数的改进方法

Journal of Mathematics Research Pub Date : 2024-01-22 DOI: 10.5539/jmr.v16n1p1

Johnson Joseph Kwabina Arhinful, Okyere Gabriel Asare, Adebanji Atinuke Olusola, Owusu -Ansah Emmanuel Degraft Johnson, Burnett Tetteh Accam

{"title":"Improved Method to Estimating Parameters of a Poisson Hidden Markov Model Using Bayesian Approach","authors":"Johnson Joseph Kwabina Arhinful, Okyere Gabriel Asare, Adebanji Atinuke Olusola, Owusu -Ansah Emmanuel Degraft Johnson, Burnett Tetteh Accam","doi":"10.5539/jmr.v16n1p1","DOIUrl":"https://doi.org/10.5539/jmr.v16n1p1","url":null,"abstract":"Expectation-Maximization (EM) is a popular method for estimating parameters of the Poisson-Hidden Markov Model (P-HMM). However, over-dispersion in comparison to the Poisson distribution remains a concern. This study developed a Bayesian method to Poisson count models. The study compares the Mean Square Errors and sufficiency of the EM to the Gibbs sampler technique using Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion as model selectors. The Maximum Likelihood Estimates and Maximum a textit{posteriori} were calculated using both simulated and real data in this case. The study's findings indicate that using any of the two approaches depends on the data type and the sample size. Whereas the Poisson Hidden Markov model, which uses the EM algorithm is preferred when using Zero-inflated data with a sample size n ≤ 20 , the Bayesian Poisson-Hidden Markov Model, which uses a Gibbs sampler is better used for Heavy and Mixture data types irrespective of the sample size. The model predicted parameters of simulated data with remarkable accuracy and produced some unique statistical property results. This method is applicable to Poisson-hidden Markov models with homogeneous time series.","PeriodicalId":512715,"journal":{"name":"Journal of Mathematics Research","volume":"89 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139606317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0