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Incentive Feedback Stackelberg Strategy in Mean-Field Type Stochastic Difference Games

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Journal of Systems Science & Complexity 2024年第4期37卷 1425-1445页

作者： GAO Wenhui LIN Yaning ZHANG Weihai School of mathematics and Statistics Shandong University of Technology college of Electrical Engineering and Automation Shandong University of Science and Technology

This paper designs an incentive Stackelberg strategy for the discrete-time stochastic systems with mean-field terms. Sufficient conditions for the existence of such a design are suggested.Moreover, the incentive strategy is obtained as a feedback form including the deviation of the state and its mathematical expectation. Also, the stability analysis is involved. It is found that the stability can be guaranteed by the follower. In addition, the specific algorithm is proposed and its effectiveness is checked by two examples.

关键词： Discrete-time mean-field stochastic systems incentive strategy Stackelberg game teamoptimal solution

METRIZABILITY OF SPACES AND J.NAGATA'S PROBLEM

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Acta Mathematica Scientia 2006年第1期26卷 25-30页

作者：高智民 Department of mathematics college of Science Shenzhen University

In 1988, J.Nagata raised a problem about metrizability, The present article is an attempt to find a solution to the problem.

关键词： Metrizable space g-function weak g-function

THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS

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Acta Mathematica Scientia 2011年第5期31卷 1997-2006页

作者：白瑞蒲张杰 college of mathematics and Computer Science Hebei University

The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.

关键词： nilpotent Leibniz 3-algebra two-step nilpotent strong-nilpotent

CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

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Acta Mathematica Scientia 2024年第1期44卷 234-246页

作者：王晓慧 college of mathematics and Physics and Geomathematics Key Laboratory of Sichuan ProvinceChengdu University of TechnologyChengdu610059China

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provi... 详细信息

关键词： Euler system axisymmetric impinging jet incompressible free boundary convexity

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

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Computer Modeling in Engineering & Sciences 2024年第8期140卷 1619-1645页

作者： Nasser Sweilam Seham Al-Mekhlafi Aya Ahmed Ahoud Alsheri Emad Abo-Eldahab mathematics Department Faculty of ScienceCairo UniversityGiza12613Egypt mathematics Department Faculty of EducationSana’a UniversitySana’a1247Yemen mathematics Department Faculty of ScienceHelwan UniversityCairo11795Egypt Department of mathematics College of ScienceUniversity of BishaAl Namas67398-5644Saudi Arabia

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

关键词： Cancer diseases hybrid variable-order fractional derivatives adams bashfourth fifth step generalized fifth order Runge-Kutta method

ON THE GENERALIZED INVERSE NEVILLE-TYPE MATRIX-VALUED RATIONAL INTERPOLANTS

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Journal of Computational mathematics 2003年第2期21卷 157-166页

作者： Zhibing Chen9+(Department of mathematics, Normal college, Shenzhen University, Shenzhen 518060, China) Department of mathematics Normal College Shenzhen University Shenzhen 518060

A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

关键词： Generalized inverse for matrices Neville-type Rational interpolants.

Quasi-shadowing for Z^(d)-actions

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1563-1580页

作者： Juan PAN Xian Kun REN Yun Hua ZHOU School of mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067P.R.China college of mathematics and Statistics Chongqing UniversityChongqing 401331P.R.China

A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of th... 详细信息

关键词： Quasi-shadowing Z^(d)-action non-uniformly partially hyperbolic ergodic measure

INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON HEISENBERG GROUP

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Acta Mathematica Scientia 2010年第1期30卷 125-131页

作者：黄广月陈文艺 college of mathematics and Information Science Henan Normal University School of mathematics and Statistics Wuhan University

In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the （k ＋ 1）-th eigenvalue in terms of the first k eigenvalues independent of the domains.

关键词： eigenvalue universal bounds bi-Kohn Laplacian

Improved Data Stream Clustering Method: Incorporating KD-Tree for Typicality and Eccentricity-Based Approach

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Computers, Materials & Continua 2024年第2期78卷 2557-2573页

作者： Dayu Xu Jiaming Lu Xuyao Zhang Hongtao Zhang college of mathematics and Computer Science Zhejiang A&F UniversityHangzhou311300China college of Economics and Management Zhejiang A&F UniversityHangzhou311300China

Data stream clustering is integral to contemporary big data applications.However,addressing the ongoing influx of data streams efficiently and accurately remains a primary challenge in current research.This paper aims to elevate the efficiency and precision of data stream clustering,leveraging the TEDA(Typicality and Eccentricity Data Analysis)algorithm as a foundation,we introduce improvements by integrating a nearest neighbor search algorithm to enhance both the efficiency and accuracy of the algorithm.The original TEDA algorithm,grounded in the concept of“Typicality and Eccentricity Data Analytics”,represents an evolving and recursive method that requires no prior knowledge.While the algorithm autonomously creates and merges clusters as new data arrives,its efficiency is significantly hindered by the need to traverse all existing clusters upon the arrival of further data.This work presents the NS-TEDA(Neighbor Search Based Typicality and Eccentricity Data Analysis)algorithm by incorporating a KD-Tree(K-Dimensional Tree)algorithm integrated with the Scapegoat Tree.Upon arrival,this ensures that new data points interact solely with clusters in very close proximity.This significantly enhances algorithm efficiency while preventing a single data point from joining too many clusters and mitigating the merging of clusters with high overlap to some extent.We apply the NS-TEDA algorithm to several well-known datasets,comparing its performance with other data stream clustering algorithms and the original TEDA algorithm.The results demonstrate that the proposed algorithm achieves higher accuracy,and its runtime exhibits almost linear dependence on the volume of data,making it more suitable for large-scale data stream analysis research.

关键词： Data stream clustering TEDA KD-tree scapegoat tree