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Multiplicative forms on Poisson groupoids

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Science China Mathematics 2025年第1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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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

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.

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

THE OPIAL INEQUALITY IN R^N

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Acta Mathematica Scientia 2001年第4期21卷 572-576页

作者：邓引斌 college of mathematical and statistics Science Wuhan University Wuhan 430072 China

This paper discusses the minimal eigenvalue lambda (1)(p,q,Omega) and its best estimate of the following nonlinear eigenvalue problem -Delta (p)u = lambda \u \ (q-2)u, u \ (partial derivative Omega) = 0. Where Omega is a bounded smooth domain in R-N, Delta (p) is the p-laplace operator, p greater than or equal to 2, q is an element of [p, Np/N-p). [p, NP). By this result, the famous Opial inequality in R-N are deduced.

关键词： Opial inequality eigenvalue p-laplace

AN EXTENDED BLOCK RESTRICTED ISOMETRY PROPERTY FOR SPARSE RECOVERY WITH NON-GAUSSIAN NOISE

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Journal of Computational Mathematics 2020年第6期38卷 827-838页

作者： Klara Leffler Zhiyong Zhou Jun Yu Department of Mathematics and mathematical statistics Umea UniversityUmeaSweden. Department of statistics Zhejiang University City CollegeHangzhou 310015China Department of Mathematics and mathematical statistics Umea UniversityUmeaSweden

We study the recovery conditions of weighted mixedl2/lp minimization for block sparse signal reconstruction from compressed measurements when partial block support information is *** show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of anlq norm of the residual error,thus establishing a setting wherein we are not restricted to Gaussian measurement *** illustrate the results with a series of numerical experiments.

关键词： Compressed sensing Block sparsity Partial support information Signal reconstruction Convex optimization

A new mixed scheme based on variation of constants for Sobolev equation with nonlinear convection term

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Applied Mathematics(A Journal of Chinese Universities) 2013年第2期28卷 158-172页

作者： LIU Yang LI Hong HE Siriguleng GAO Wei MU Sen School of mathematical Sciences Inner Mongolia University college of Finance and statistics Hunan University

A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.

关键词： Sobolev equation nonlinear convection term variation of constants H1-Galerkin mixed method,optimal error estimate.

Positivity of Toeplitz Operators on Harmonic Bergman Space

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Acta Mathematica Sinica,English Series 2016年第2期32卷 175-186页

作者： Yong Lu SHU Xian Feng ZHAO college of Mathematics and statistics Chongqing University Shanghai Center for mathematical Sciences Fudan University

In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.

关键词： Positive Toeplitz operators harmonic Bergman space Berezin transform

Kinematic Formulas of Total Mean Curvatures for Hypersurfaces

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Chinese Annals of Mathematics,Series B 2016年第1期37卷 137-148页

作者： Ming LI Jiazu ZHOU School of Mathematics and statistics Chongqing University of Technology School of Mathematics and statistics Southwest University college of mathematical Science Kaili University

kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space

关键词： Kinematic formula Total mean curvature Hypersurface