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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

Miyaoka-type inequalities for terminal threefolds with nef anti-canonical divisors

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Science China mathematics 2025年第1期68卷 1-18页

作者： Masataka Iwai Chen Jiang Haidong Liu Department of mathematics Graduate School of ScienceOsaka University Shanghai Center for Mathematical Sciences & school of Mathematical Sciences Fudan University Department of mathematics Sun Yat-sen University

In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical *** X be a terminal projective 3-fold such that-KXis *** show that if c1（X） · c2（X）≠0,then c1（X） · c2（X） ≥ 1/252;if further X is not rationally connected,then c1（X） · c2（X） ≥ 4/5 and this inequality is *** order to prove this,we give a partial classification of such varieties along with many *** also study the nonvanishing of c1（X）dim X-2· c2（X） for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.

关键词： terminal threefolds Miyaoka-type inequality boundedness

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1期68卷 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.

关键词： Boltzmann equation incompressible Euler equations hydrodynamic limit Hilbert expansion specular reflection boundary condition viscous boundary layer Knudsen boundary layer

Practical approach for detecting k-nonseparability of multipartite quantum states

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Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 32-48页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of mathematics Taiyuan University of Technology school of mathematics and Statistics Shanxi University Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi University

The instantaneous detection of entanglement in quantum states poses a significant challenge in the fields of quantum computation and quantum information, and there are no practical methods or tools to complete this task satisfactorily so far. We propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems, 2 ≤ k ≤ n. This criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipartite finite-dimensional systems. To exemplify the application of our scheme, we have developed a software tool that facilitates swift and precise identification of entanglement, k-nonseparability, and genuine entanglement within n-qubit systems, specifically tailored for systems with 2 ≤ n ≤ 4.

关键词： multipartite systems entanglement states entanglement witnesses ${\bm~k}$-nonseparability

Limit theorems of the 2D stochastic Navier-Stokes equation driven by a time-periodic force and a degenerate noise

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Science China mathematics 2025年

作者： Rongchang Liu Kening Lu Department of mathematics University of Arizona school of mathematics Sichuan University

The periodically forced 2D Navier-Stokes equation with a degenerate noise is studied. For the Markov chain obtained by restricting the solution process to the Poincarésection, we prove a quantitative version of the strong law of large numbers and the central limit theorem with explicit convergence rates. A law of the iterated logarithm is also obtained. The proof is based on a martingale approximation procedure.

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Holomorphic Koszul–Brylinski homologies of Poisson blow-ups

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Acta Mathematica Sinica,English Series 2025年

作者： Xiaojun CHEN Youming CHEN Song YANG Xiangdong YANG school of mathematics Sichuan University school of Science Chongqing University of Technology Center for Applied mathematics Tianjin University Department of mathematics Lanzhou University

We derive a blow-up formula for holomorphic Koszul–Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the E1-degeneracy of the Dolbeault–Koszul–Brylinski spectral sequence under Poisson blow-ups, and compute the holomorphic Koszul–Brylinski homology for del Pezzo surfaces and two complex nilmanifolds with holomorphic Poisson structures.

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New types of singular solutions of conformal Q-curvature equations

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Acta Mathematica Sinica,English Series 2025年

作者： Zongming Guo Zhongyuan Liu Fangshu Wan Department of mathematics Henan Normal University school of mathematics and Statistics Henan University school of Mathematical Sciences Anhui University

We construct radial and non-radial singular solutions u ∈ C4（B{0}） with a non-removable singular point x = 0 for the conformal Q-curvature equation:■where B = {x ∈ R4: |x| D0≥ 0, and satisfying ■Moreover, detailed asymptotic expansions near x = 0 of these radial and non-radial singular solutions can be established. As an application, we can also obtain the existence of two types of solutions u ∈ C4（R4■） to the problem ■ satisfying |x|-2u（x） →-D D0, and satisfying u（x） = o（|x|2） uniformly as |x| → ∞.

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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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Uniform measure attractors for non-autonomous stochastic evolution systems

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Acta Mathematica Sinica,English Series 2025年

作者： Dingshi Li Ran Li Tianhao Zeng school of mathematics Southwest Jiaotong University

This paper is concerned with uniform measure attractors for non-autonomous stochastic evolution systems. We first introduce the concept of uniform measure attractor and then provide a sufficient criterion for existence and uniqueness of such attractors. As an application, we prove the existence and uniqueness of uniform measure attractors for the stochastic Navier-Stokes equations with deterministic almost-periodic forcing and nonlinear diffusion terms.

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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