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Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

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Computer Modeling in Engineering & sciences 2025年第1期142卷 609-633页

作者： Ghaliah Alhamzi Badr Saad TAlkahtani Ravi Shanker Dubey Mati ur Rahman Department of Mathematics and statistics College of ScienceImam Mohammad Ibn Saud Islamic University(IMSIU)Riyadh13318Saudi Arabia Department of Mathematics College of ScienceKing Saud UniversityRiyadh11989Saudi Arabia Department of Mathematics Amity School of Applied SciencesAmity University RajasthanJaipur302002India school of Mathematical sciences Jiangsu UniversityZhenjiang212013China Department of Computer Science and Mathematics Lebanese American UniversityBeirut13-5053Lebanon

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary *** HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered *** total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,*** proposed model is tested separately for unique solutions and existence on bi *** numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons *** proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler *** cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said *** study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered *** obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

关键词： HIV infection model qualitative scheme approximate solution piecewise global operator neural network

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Stabilities of delay stochastic McKean-Vlasov equations in the G-framework

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Science China(Information sciences) 2025年第1期68卷 255-277页

作者： Haiyan YUAN Quanxin ZHU Department of Mathematics Heilongjiang Institute of Technology Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) School of Mathematics and Statistics Hunan Normal University

This article focuses on a type of stochastic Mc Kean-Vlasov equation in the G-framework(G-SMVE) and addresses the stability issue for delay stochastic Mc Kean-Vlasov equations in the G-framework(G-SMVDEs). Distribution dependence and uncertainty prevent us from directly applying the stochastic analysis method for stochastic Mc Kean-Vlasov equations(SMVEs)to G-SMVEs directly. To overcome this difficulty, we introduce definitions, including the derivative of a function with a law under the G-expectation and the Lions derivatives. Then we construct a new G-It? formula for G-SMVEs according to the G-It? formula for stochastic differential equations in the G-framework(G-SDEs) and the It? formula for SMVEs. Using the new G-It? formula and the Lyapunov functional method, we investigate the moment exponential stability and almost sure asymptotic stability of G-SMVDEs. To overcome the difficulty in obtaining the distribution dependence of the exact solution to the G-SMVDE, we introduce the empirical measure and the corresponding interacting particle system, and then prove the stability equivalence between the underlying G-SMVDE and the corresponding interacting particle system. Two examples are used to confirm our theoretical results.

关键词： delay stochastic McKean-Vlasov equations Wasserstein distance G-Brownian motion Lions derivative stability

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CONTACT PROCESS ON HEXAGONAL LATTICE

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Acta Mathematica Scientia 2010年第3期30卷 769-790页

作者：姚强李群昌 Department of statistics and actuarial Science School of Finance and Statistics East China Normal University school of Mathematical sciences Peking University

In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

关键词： Hexagonal lattice contact process critical value complete convergence theorem rate of growth

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Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons

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Science China Mathematics 2025年第1期 223-252页

作者： Weidong Liu Dennis Leung Qi-Man Shao school of Mathematical sciences Shanghai Jiao Tong University school of Mathematics and statistics University of Melbourne Department of statistics and Data Science SICMSouthern University of Science and Technology

In a one-way analysis-of-variance(ANOVA) model,the number of pairwise comparisons can become large even with a moderate number of *** by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH) procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR) *** Tukey's perspective that the difference between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is sufficiently weak to establish the convergence result typically required for asymptotic FDR *** analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby offering a theoretical foundation for applications in more general settings.

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Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1281-1288页

作者： Jun Yi GUO Kam C.YUEN Ming ZHOU school of Mathematical sciences and LPMC Nankai University Department of statistics and actuarial Science The University of Hong Kong

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.

关键词： Cox risk model ruin probability Markov process infinitesimal generator

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Impact of Pollutant Concentration and Particle Deposition on the Radiative Flow of Casson-Micropolar Fluid between Parallel Plates

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Computer Modeling in Engineering & sciences 2025年第1期142卷 665-690页

作者： Ghaliah Alhamzi Badr Saad T.Alkahtani Ravi Shanker Dubey Vinutha Kalleshachar Neelima Nizampatnam Department of Mathematics and statistics College of ScienceImam Mohammad Ibn Saud Islamic University(IMSIU)Riyadh11564Saudi Arabia Department of Mathematics College of ScienceKing Saud UniversityRiyadh11989Saudi Arabia Department of Mathematics Amity School of Applied SciencesAmity University RajasthanJaipur302002RajasthanIndia Department of Studies in Mathematics Davangere UniversityDavangere577002India Department of Electronics and Communication Engineering Amrita School of EngineeringAmrita Vishwa VidyapeethamBengaluru560035India

Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental *** the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge *** waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution *** study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle *** explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are *** governing equations are transformed into ordinary differential equations with the help of suitable similarity *** Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary *** integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of *** outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current *** reveal that concentration upsurges as the micropolar parameter *** concentration reduces with an upsurge in the thermophoretic *** upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass *** surface drag force declines for improved values of porosity and micropolar parameters.

关键词： Micropolar fluid thermal radiation porous medium thermophoretic particle deposition waste discharge concentration

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Alternative Approach to the Optimality of the Threshold Strategy for Spectrally Negative Lvy Processes

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Acta Mathematicae Applicatae Sinica 2013年第4期29卷 705-716页

作者： Ying SHEN Chuan-cun YIN Kam Chuen YUEN school of Mathematical sciences Qufu Normal UniversityChina Department of statistics and actuarial Science The University of Hong Kong

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy （also called refraction strategy） forms an optimal strategy under the condition that the Levy measure has a completely monotone density.

关键词： Spectrally negative Levy process optimal dividend problem scale function complete monotonic-ity threshold strategy

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VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES

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Acta Mathematica Scientia 2013年第5期33卷 1387-1397页

作者： N.B.OKELO J.O.AGURE P.O.OLECHE school of Mathematics and actuarial Science Jaramogi Oginga Odinga University of Science and Technology school of Mathematics Statistics and Actuarial Science Maseno University

In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kern... 详细信息

关键词： orthogonality normed space elementary operator

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Asymptotics of the goodness-of-fit test for a partial linear model with randomly censored data

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Science China Mathematics 2003年第2期46卷 145-158页

作者：陈敏 Kam C.YUEN 朱力行 Academy of Mathematics and System sciences Chinese Academy of Sciences Department of statistics and actuarial Science the University of Hong Kong Department of statistics and actuarial Science the University of Hong Kong Hong Kong China

In this paper, we discuss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals,is proposed. The asymptotic distributions of the test statistic under null hypothesis and the local alternativehypothesis are given. The number simulation shows that the test is available.

关键词： partial linear regression random censoring empirical process model checking

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Optimal Investment and Premium Control in a Nonlinear Diffusion Model

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Acta Mathematicae Applicatae Sinica 2017年第4期33卷 945-958页

作者： Ming ZHOU Kam Chuen YUEN Chuan-cun YIN China Institute for actuarial Science Central University of Finance and Economics Department of statistics and actuarial Science the University of Hong Kong school of statistics Qufu Normal University

This paper considers the optimal investment and premium control problem in a diffusion approxi- mation to a non-homogeneous compound Poisson process. In the nonlinear diffusion model, it is assumed that there is an unspecified monotone function describing the relationship between the safety loading of premium and the time-varying claim arrival rate. Hence, in addition to the investment control, the premium rate can be served as a control variable in the optimization problem. Specifically, the problem is investigated in two cases：（i） maximizing the expected utility of terminal wealth, and （ii） minimizing the probability of ruin respectively. In both cases, some properties of the value functions are derived, and closed-form expressions for the optimal policies and the value functions are obtained. The results show that the optimal investment policy and the optimal premium control policy are dependent on each other. Most interestingly, as an example, we show that the nonlinear diffusion model reduces to a diffusion model with a quadratic drift coefficient when the function associated with the premium rate and the claim arrival rate takes a special form. This example shows that the model of study represents a class of nonlinear stochastic control risk model.

关键词： CARA utility dependent control policies Hamilton-Jacobi-Bellman (HJB) equation investment premium control

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