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Science China(Information Sciences) 2025年第1期68卷 238-254页

作者： Guodong ZHANG Jinde CAO school of Mathematics and statistics South-Central Minzu University school of Mathematics Southeast University

This article concentrates on the fixed-time stabilization(FS) and fixed-time synchronization(FTS) of discontinuous inertial neural networks(DINNs) with distributed delays. Using mathematical induction to a new differential equality, a novel fixed-time stability lemma is constructed. Then, by designing an aperiodically semi-intermittent switching control and combining it with the theory of nonsmooth analysis, some novel criteria on the FS and FTS of DINNs are obtained. Unlike the methods used in most existing studies, the FS and FTS results are structured using the newly proposed fixed-time stability lemma and the nonreduced-order approach, resulting in broader practical applications and strengthening the scientific quality of the derived results. Lastly, numerical simulations and applications proffer the effectiveness of the established FS and FTS criteria.

关键词： inertial neural networks fixed-time synchronization semi-intermittent switching control nonreduced-order approach fixed-time stabilization

Escobar-Lichnerowicz-Reilly type eigenvalue estimate for the weighted p-Laplacian on manifolds with integral Ricci curvature

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Acta Mathematica Sinica,English Series 2025年

作者： Yong Tao LIU school of Mathematics and statistics Ningxia University

Under the assumption of integral m-Bakry-émery Ricci curvature, we give an Escobar-LichnerowiczReilly type eigenvalue estimate for the weighted p-Laplacian on compact smooth metric measure spaces with or without boundaries. This conclusion is a generalization and improvement of Wang-Li’s result in the case of integral Bakry-émery Ricci curvature, and of Seto-Wei’s one to the compact metric measure space setting. Our main tools are the weighted p-Bochner formula and the weighted p-Reilly formula.

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On construction of strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus

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Science China Mathematics 2025年

作者： Bochuan Jiang Yaping Wang Fasheng Sun school of Mathematics and statistics Beijing Jiaotong University Key Laboratory of Advanced Theory and Application in statistics and Data Science Ministry of EducationSchool of Statistics East China Normal University Key Laboratory for Applied statistics of Ministry of Education and school of Mathematics and statistics Northeast Normal University

Computer experiments require space-filling designs with good low-dimensional projection *** orthogonal arrays are a type of space-filling design that provides better stratifications in low dimensions than ordinary orthogonal arrays. In this paper, we address the problem of constructing strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus. Existing methods typically rely on regular designs or specific nonregular designs as base orthogonal arrays, limiting the sizes of the final ***, we propose two general methods that are easy to implement and applicable to a wide range of base orthogonal arrays. These methods produce space-filling designs that can accommodate a large number of factors,provide significant flexibility in terms of run sizes, and possess appealing low-dimensional projection ***, these designs are ideal for computer experiments.

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A General Association Test for High-Dimensional Random Vectors

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Acta Mathematica Sinica,English Series 2025年

作者： Yongshuai Chen Peng Lin Baoxue Zhang school of statistics Capital University of Economics and Business

Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications. In this paper, we propose a new test statistic based on the Frobenius norm and subtracting bias technique, which is generally applicable to high-dimensional data without restricting the distributional assumptions. The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation. Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions. To make the test statistic applicable, we introduce a wild bootstrap method and demonstrate its validity. The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests, even when the normal approximation is invalid. Real data analysis is devoted to illustrating the proposed test.

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Derivatives of local times and Hausdorff dimension of inverse images of space-time anisotropic Gaussian random fields

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Acta Mathematica Sinica,English Series 2025年

作者： Zhenlong Chen Peng Xu school of statistics and Mathematics Zhejiang Gongshang University

Let X={X（t）, t∈RN}be a centered space-time anisotropic Gaussian random field with values in Rd. Under some general conditions, the existence, joint continuity and H¨older conditions of higher-order derivative of local times of X are studied. Moreover, we obtain the uniform Hausdorff dimension of the inverse images of X. The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.

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The linear self-attracting diffusion driven by the weighted-fractional Brownian motion II: The parameter estimation

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Science China Mathematics 2025年

作者： Litan Yan Rui Guo Wenyi Pei Department of statistics College of Science Donghua University school of statistics and Mathematics Zhejiang Gongshang University

Let Ba,bbe a weighted-fractional Brownian motion with Hurst indexes a and b such that a>-1and 0≤b<1∧（1+a）.In this paper,we consider the linear self-attracting diffusion ■ interacting diffusion (see Cranston and Le Jan （1995）).Under the continuous observation,we study asymptotic ■ converges in distribution to the sum of the chi-square random variable with 1 degree of freedom and the random variable Z1a,b.

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Twist monomials of binary delta-matroids

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Acta Mathematica Sinica,English Series 2025年

作者： Qi YAN Xian'an JIN school of Mathematics and statistics Lanzhou University school of Mathematical Sciences Xiamen University

Recently, we introduced the twist polynomials of delta-matroids and gave a characterization of even normal binary delta-matroids whose twist polynomials have only one term and posed a problem:what would happen for odd binary delta-matroids? In this paper, we show that a normal binary deltamatroid whose twist polynomials have only one term if and only if each connected component of the intersection graph of the delta-matroid is either a complete graph of odd order or a single vertex with a loop.

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Dynamic behaviors of graphene platelets-reinforced metal foam piezoelectric beams with velocity feedback control

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Applied Mathematics and Mechanics(English Edition) 2025年第1期46卷 63-80页

作者： Jie CHEN Xinyue ZHANG Mingyang FAN school of Mathematics Statistics and Mechanics Beijing University of Technology College of Mechanical & Energy Engineering Beijing University of Technology

Graphene platelets(GPLs)-reinforced metal foam structures enhance the mechanical properties while maintaining the lightweight characteristics of metal foams. Further bonding piezoelectric actuator and sensor layers on the surfaces of GPLs-reinforced metal foam beams enables active vibration control, greatly expanding their applications in the aerospace industry. For the first time, this paper investigates the vibration characteristics and active vibration control of GPLs-reinforced metal foam beams with surfacebonded piezoelectric layers. The constant velocity feedback scheme is used to design the closed-loop controller including piezoelectric actuators and sensors. The effects of the GPLs on the linear and nonlinear free vibrations of the beams are numerically *** Newmark-β method combined with Newton's iteration technique is used to calculate the nonlinear responses of the beams under different load forms including harmonic loads,impact loads, and moving loads. Additionally, special attention is given to the vibration reduction performance of the velocity feedback control on the responses of the beam.

关键词： Piezoelectric actuators

High-dimensional large-scale mixed-type data imputation under missing at random

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Science China Mathematics 2025年

作者： Wei Liu Guizhen Li Ling Zhou Lan Luo school of Mathematics Sichuan University Center of Statistical Research and school of statistics Southwestern University of Finance and Economics Department of statistics and Actuarial Science University of Iowa

Missingness in mixed-type variables is commonly encountered in a variety of areas. The requirement of complete observations necessities data imputation when a moderate or large proportion of data is ***, inappropriate imputation would downgrade the performance of machine learning algorithms, leading to bad predictions and unreliable statistical inference. For high-dimensional large-scale mixed-type missing data, we develop a computationally efficient imputation method, missing value imputation via generalized factor models（MIG）, under missing at random. The proposed MIG method allows missing variables to be of different types,including continuous, binary, and count variables, and are scalable to both data size n and variable dimension p while existing imputation methods rely on restrictive assumptions such as the same type of missing variables,the low dimensionality of variables, and a limited sample size. We explicitly show that the imputation error of the proposed MIG method diminishes to zero with the rate Op(max{n-1/2, p-1/2}) as both n and p tend to infinity. Five real datasets demonstrate the superior empirical performance of the proposed MIG method over existing methods that the average normalized absolute imputation error is reduced by 5.3%–34.1%.

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Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential

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应用数学 2025年第1期38卷 14-29页

作者： LI Nan XU Liping school of Mathematics and statistics Henan University of Science and TechnologyLuoyang 471000China

In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant *** appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2... 详细信息

关键词： Nonlinear Choquard equation Potential function Variational method Normalized solution