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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

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.

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THE SPECTRAL RADIUS OF UNIFORM HYPERGRAPH DETERMINED BY THE SIGNLESS LAPLACIAN MATRIX

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数学杂志 2025年第1期45卷 1-12页

作者： HE Fang-guo College of mathematics and statistics Huanggang Normal UniversityHuBei 438000

This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian *** upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic *** spectral radius of the graph is generalized.

关键词： spectral radius uniform hypergraph Signless Laplasian matrix

Sharp Bounds for Upper and Bottom Spectrum of Hermitizable Tridiagonal Matrices

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Journal of Mathematical Research with Applications 2025年第1期 125-132页

作者： Yueshuang LI Lingdi WANG School of statistics Capital University of Economics and Business School of mathematics and statistics Henan University

We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix. The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector) of tridiagonal matrices, isospectral transforms and sharp bounds for speed stability of birth-death processes.

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Extensions and Deformations of 3-Lie Algebras with Higher Derivations

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Journal of Mathematical Research with Applications 2025年第1期 20-32页

作者： Shuangjian GUO School of mathematics and statistics Guizhou University of Finance and Economics

In this paper, we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair. We introduce a cohomology theory of 3-LieHDer pairs. Next, we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions. Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.

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Aperiodically semi-intermittent-based fixed-time stabilization and synchronization of delayed discontinuous inertial neural networks

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Science China(Information Sciences) 2025年第1期 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.

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A Remark on Strong Law of Large Numbers for Weighted U-statistics

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1595-1605页

作者： Hyung-Tae HA Mei Ling HUANG Department of Applied statistics Gachon University Department of mathematics and statistics Brock University

Let （X, Xn; n≥ 1} be a sequence of i.i.d, random variables with values in a measurable space （S,8） such that E｜h（X1, X2,..., Xm）｜〈 ∞, where h is a measurable symmetric function from Sm into R = （-∞, ∞）. Let {wn,i1,i2 im ; 1 ≤ i1 〈 i2 〈 …… 〈im 〈 n, n ≥ m} be a matrix array of real numbers. Motivated by a result of Choi and Sung （1987）, in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m. We show that whenever SUP n≥m max1〈i1〈i2〈…〈im≤｜wn i1,i2 i,im｜〈∞, where 0 = Eh（X1, X2,..., Xm）. The proof of this result is based on a new general result on complete convergence, which is a fundamental tool, for array of real-valued random variables under some mild conditions.

关键词： Strong law of large numbers weighted U-statistics complete convergence

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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 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.

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WELL-POSEDNESS AND PEAKON SOLUTIONS FOR A HIGHER ORDER CAMASSA-HOLM TYPE EQUATION

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数学杂志 2025年第1期45卷 57-71页

作者： CHEN shuang School of mathematics and statistics Ningbo UniversityNingbo 315211China

In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>*** addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.

关键词： Generalized higher order Camassa-Holm type equation Local well-posedness Peakon

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