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MORSE CONCAVITY FOR CLOSED GEODESICS

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Acta Mathematica Scientia 2009年第3期29卷 731-750页

作者：段华桂龙以明 School of mathematics Chern Institute of mathematics Key lab of Pure mathematics and Combinatorics of Ministry of Education Nankai UniversityTianjin 300071 China

In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.

关键词： closed geodesic concavity sypletic matrix Morse index

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2 1. mathematics lab, China University of Mining & Technology, Beijing 100083, China 2. Probability lab, Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, China mathematics lab China University of Mining & Technology Beijing China Probability lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

OPTIMAL CONDITIONS OF GLOBAL EXISTENCE AND BLOW-UP FOR A NONLINEAR PARABOLIC EQUATION

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Acta Mathematica Scientia 2016年第3期36卷 872-880页

作者：蒋毅罗川 VC/VR lab and Department of mathematics Sichuan Normal University

According to the variational analysis and the potential well argument, we get the optimal conditions of global existence and blow-up for a type of nonlinear parabolic equations. Furthermore, we give its application in... 详细信息

关键词： nonlinear parabolic equation variational analysis potential well argument global existence blow up

Pseudo-Randomness of Certain Sequences of k Symbols with Length pq

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Journal of Computer Science & Technology 2011年第2期26卷 276-282页

作者：陈智雄杜小妮吴晨煌 Department of mathematics Putian University State Key lab.of ISN Xidian University College of mathematics and Information Science Northwest Normal University

The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.

关键词： stream ciphers pseudo-random sequences well-distribution measure correlation measure discrete logarithm modulo pq residue class rings character sums

Construction of compressed sensing matrices based on affine symplectic space over finite fields

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The Journal of China Universities of Posts and Telecommunications 2018年第6期25卷 74-80页

作者： Wang Gang Niu Minyao Fu Fangwei Chern Institute of mathematics and lab of Pure mathematics and Combinatorics Nankai University College of Science Civil Aviation University of China

The compressed sensing matrices based on affine symplectic space are constructed. Meanwhile, a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. Moreover, we merge our binary matrices with other low coherence matrices such as Hadamard matrices and discrete fourier transform(DFT) matrices using the embedding operation. In the numerical simulations, our matrices and modified matrices are superior to Gaussian matrices and DeVore’s matrices in the performance of recovering original signals.

关键词： compressed sensing coherence sparsity affine symplectic space finite fields

Secretome of polarized macrophages:potential for targeting inflammatory dynamics in spinal cord injury

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Neural Regeneration Research 2025年第11期20卷 3231-3232页

作者： Andreia Monteiro Susana Monteiro Nuno A.Silva Life and Health Sciences Research Institute(ICVS) School of MedicineUniversity of MinhoBragaPortugal ICVS/3B’s Associate lab PT Government Associated LabBraga/GuimaraesPortugal

Spinal cord injury(SCI)involves an initial traumatic phase,followed by secondary events such as ischemia,increased blood-spinal cord barrier permeability,ionic disruption,glutamate excitotoxicity,and metabolic alterations.A pe rsistent and exagge rated inflammato ry response within the spinal cord accompanies these events(Lima et al.,2022).The complexity and interplay of these mechanisms exacerbate the initial injury,leading to a degenerative process at the injury *** the initial trauma is unavoidable,the secondary injury begins within minutes and can last for months,creating an optimal window for therapeutic intervention.

关键词： alterations injury companies

Survey on rain removal from videos or a single image

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Science China(Information Sciences) 2022年第1期65卷 72-94页

作者： Hong WANG Yichen WU Minghan LI Qian ZHAO Deyu MENG School of mathematics and Statistics Ministry of Education Key lab of Intelligent Networks and Network Security Xi'an Jiaotong University Pazhou lab

Rain can cause performance degradation of outdoor computer vision tasks. Thus, the exploration of rain removal from videos or a single image has drawn considerable attention in the field of image processing. Recently, various deraining methodologies have been proposed. However, no comprehensive survey work has yet been conducted to summarize existing deraining algorithms and quantitatively compare their generalization ability, and especially, no off-the-shelf toolkit exists for accumulating and categorizing recent representative methods for easy performance reproduction and deraining capability evaluation. In this regard, herein, we present a comprehensive overview of existing video and single image deraining methods as well as reproduce and evaluate current state-of-the-art deraining methods. In particular, these approaches are mainly classified into model-and deep-learning-based methods, and more elaborate branches of each method are presented. Inherent abilities, especially generalization performance, of the state-of-the-art methods have been both quantitatively and visually analyzed through thorough experiments conducted on synthetic and real benchmark datasets. Moreover, to facilitate the reproduction of existing deraining methods for general users, we present a comprehensive repository with detailed classification, including direct links to 85 deraining papers, 24 relevant project pages, source codes of 12 and 25 algorithms for video and single image deraining, respectively, 5 and 10 real and synthesized datasets, respectively, and 7 frequently used image quality evaluation metrics, along with the corresponding computation codes. Research limitations worthy of further exploration have also been discussed for future research along this direction.

关键词： rain removal maximum a posterior estimation deep learning generalization performance comprehensive repository

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Isotopic Meshing of a Real Algebraic Space Curve

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Journal of Systems Science & Complexity 2020年第4期33卷 1275-1296页

作者： JIN Kai CHENG Jinsan School of mathematics and Statistics Hubei University of Science and TechnologyXianning 437100China Key lab of mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

This paper presents a new algorithm for computing the topology of an algebraic space *** on an efficient weak generic position-checking method and a method for solving bivariate polynomial systems,the authors give a first deterministic and efficient algorithm to compute the topology of an algebraic space *** to extant methods,the new algorithm is efficient for two *** bit size of the coefficients appearing in the sheared polynomials are greatly *** other is that one projection is enough for most general cases in the new *** the topology of an algebraic space curve is given,the authors also provide an isotopic-meshing(approximation)of the space ***,an approximation of the algebraic space curve can be generated automatically if the approximations of two projected plane curves are first *** is also an advantage of our *** non-trivial experiments show the efficiency of the algorithm.

关键词： curve. method. algebraic

On the Topology and Isotopic Meshing of Plane Algebraic Curves

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Journal of Systems Science & Complexity 2020年第1期33卷 230-260页

This paper presents a symbolic algorithm to compute the topology of a plane *** is a full version of the authors’CASC15 *** algorithm mainly involves resultant computations and real root isolation for univariate *** to other symbolic methods based on elimination techniques,the novelty of the proposed method is that the authors use a technique of interval polynomials to solve the system f(α,y),?f/?y(α,y)and simultaneously obtain numerous simple roots of f(α,y)=0 on theα*** significantly improves the efficiency of the lifting step because the authors are no longer required to compute the simple roots of f(α,y)=*** the topology is computed,a revised Newton’s method is presented to compute an isotopic meshing of the plane algebraic *** the approximation method is numerical,the authors can ensure that the proposed method is a certified one,and the meshing is topologically *** nontrivial examples confirm that the proposed algorithm performs well.

关键词： Interval polynomial isotopic meshing plane curve topology