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

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Science China Mathematics 2025年第01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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Multiplicative forms on Poisson groupoids

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Science China Mathematics 2025年第01期 169-206页

作者： Zhuo Chen Honglei Lang Zhangju Liu Department of mathematical Sciences Tsinghua University College of Science China Agricultural University school of Mathematics and statistics Henan University

First,we prove a decomposition formula for any multiplicative differential form on a Lie groupoid ***,we prove that if G is a Poisson Lie groupoid,then the space ?mult·（G） of multiplicative forms on G has a differential graded Lie algebra（DGLA） ***,when combined with ?·（M）,which is the space of forms on the base manifold M of G,?mult·（G） forms a canonical DGLA crossed *** supplements a previously known fact that multiplicative multi-vector fields on G form a DGLA crossed module with the Schouten algebra Γ（∧·A） stemming from the Lie algebroid A of G.

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Consistency of Chi-Squared Test with Varying Number of Classes

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Journal of Systems Science & Complexity 2015年第2期28卷 439-450页

作者： HUANG Rui CUI Hengjian College of Mathematic and statistics Jishou University school of mathematical Sciences Beijing Normal University Department of statistics School of Mathematical SciencesCapital Normal University

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null *** is well known that the number of classes varying with sample size in the test has attached more and more ***,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test *** paper proves the consistency of chi-squared test with varying number of classes under some ***,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random *** addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.

关键词： Consistency of chi-squared test goodness of fit test varying number of classes.

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BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2^(n-(n-k)) DESIGNS

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Acta Mathematica Scientia 2008年第4期28卷 949-954页

作者：赵胜利张润楚 school of mathematical Sciences Qufu Normal University LPMC and Department of statistics School of Mathematical SciencesNankai University

Clear effects criterion is an important criterion for selecting fractional factorial designs[1].Tang et al.[2]derived upper and lower bounds on the maximum number of clear two-factor interactions（2fi＇s）in 2^n-（n-k）designs of resolution Ⅲ and Ⅳ by constructing 2^n-（n-k）*** the method in[2]does not perform well sometimes when the resolution is Ⅲ.This article modifies the construction method for 2^n-（n-k） designs of resolution Ⅲ in[2].The modified method is a great improvement on that used in[2].

关键词： Random fractional design clear resolution

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The Hilbert expansion of the Boltzmann equation in the incompressible Euler level in a channel

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Science China Mathematics 2025年第01期 39-88页

作者： Feimin Huang Weiqiang Wang Yong Wang Feng Xiao Academy of Mathematics and Systems Science Chinese Academy of Sciences school of mathematical Sciences University of Chinese Academy of Sciences Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) School of Mathematics and StatisticsHunan Normal University

The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary *** this paper,the hydrodynamic limit from the Boltzmann equation with the specular reflection boundary condition to the incompressible Euler equations in a channel is *** on the multi-scaled Hilbert expansion,the equations with boundary conditions and compatibility conditions for interior solutions,and viscous and Knudsen boundary layers are derived under different scaling,***,some uniform estimates for the interior solutions,and viscous and Knudsen boundary layers are *** the help of the L2-L∞framework and the uniform estimates obtained above,the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales,and hence the hydrodynamic limit in the incompressible Euler level is justified.

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Stabilization of a Non-homogeneous Rotating Body-Beam System with the Torque and Nonlinear Distributed Controls

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Journal of Systems Science & Complexity 2017年第3期30卷 616-626页

作者： GUO Yaping WANG Junmin school of Mathematics and statistics Beijing Institute of Technology school of mathematical Sciences Shanxi University

This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively. As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite operator, the authors show that the torque and nonlinear distributed control laws suppress the system vibrations, in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.

关键词： Non-homogeneous nonlinear distributed control stabilization.

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Construction of Supersaturated Design with Large Number of Factors by the Complementary Design Method

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 253-262页

作者： Yan LIU Min-Qian LIU school of mathematical Sciences Tianjin Normal University Department of statistics School of Mathematical Sciences and LPMC Nankai University

Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.

关键词： balanced design coincidence number complementary design equidistant design weak equidistantdesign

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CONSTRUCTION OF OPTIMAL BLOCKING SCHEMES FOR ROBUST PARAMETER DESIGNS

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Acta Mathematica Scientia 2013年第5期33卷 1431-1438页

作者：杨建峰张润楚刘民千 Department of statistics School of Mathematical Sciences and LPMCNankai University

Robust parameter design （RPD） is an important issue in experimental designs. If all experimental runs cannot be performed under homogeneous conditions, blocking the units is effective. In this paper, we obtain the correspondence relation between fractional factorial RPDs and the blocking schemes for full factorial RPDs. In addition, we provide a construction of optimal blocking schemes that make all main effects and control-by-noise two-factor interactions estimable.

关键词： Alias blocking factorial design factorial effect robust parameter design

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Input-to-State Stability of Impulsive Switched Systems Involving Uncertain Impulse-Switching Moments

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1515-1517页

作者： Chang Liu Wenlu Liu Tengda Wei Xiaodi Li school of mathematical and statistics Shandong Normal UniversityJinan 250014China

Dear Editor,This letter studies the input-to-state stability(ISS)for a class of impulsive switched systems,where uncertain impulse-switching moments are *** robustness of ISS with respect to the perturbations of the occurrence time of impulse-switching moments is revealed by several less conservative dwell-time conditions for the uncertain impulse-switching moments combined with Lyapunov ***,the Lyapunov conditions have multiple coefficients at discrete time so as to handle the hybrid effect of impulse-switching moments,and the case that time derivative of Lyapunov function is indefinite is also taken into ***,a numerical example is proposed to illustrate the effectiveness of the theoretical results.

关键词： letter conservative derivative

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