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Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem

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Acta Mathematica Sinica,English Series 2000年第4期16卷 579-592页

作者： Yiming Long nankai institute of mathematics. nankai University. Tianjin 300071. P. R. China Shiqing Zhang Department of Applied mathematics Chongqing University. Chongqing 40004, P.R. China nankai institute of mathematics Nankai University Tianjin 300071 P. R. China Department of Applied mathematics Chongqing 400044 P. R. China

In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R^3 or R^2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular rostricted 3-body problem in R^3 or R^2 are also planar equilateral triangle circular solutions.

关键词： 3-body problem Restricted 3-body problem Variational minimization Equilateral triangle circular solution

Quantum Deletion of Copies of Two Non-orthogonal Quantum States via Weak Measurement

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Chinese Physics Letters 2020年第5期37卷 5-9页

作者： Wei-Min Shang Jie Zhou Hui-Xian Meng Jing-Ling Chen Theoretical Physics Division Chern Institute of MathematicsNankai University School of mathematics and Physics North China Electric Power University

We propose a scenario to increase the probability of probabilistic quantum deletion and to enhance the fidelity of approximate quantum deletion for two non-orthogonal states via weak *** interestingly,by pretreating the given non-orthogonal states,the probability of probabilistic quantum deletion and fidelity of approximate quantum deletion can reach *** outcomes of the weak measurement that we required are probabilistic,we perform the subsequent deleting process only when the outcome of weak measurement is"yes"Remarkably,we find that our scenario has better performance in quantum information process;for example,it costs less quantum resources and time.

关键词： measurement. quantum probabilistic

Gray codes over certain run-length sequences for local rank modulation

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Science China(Information Sciences) 2018年第10期61卷 98-113页

作者： Xiang WANG Fang-Wei FU National Computer Network Emergency Response Technical Team The Chern institute of mathematics and LPMC Nankai University

In the local rank modulation(LRM) scheme, a sliding window produces a sequence of permutations by moving over a sequence of variables. LRM has been presented as a method of storing data in flash memory, which represents a natural generalization of the classical rank modulation scheme. In this paper, we present a study on Gray codes over certain run-length sequences for the(1, 2, n)-LRM scheme to simulate virtual multilevel flash memory cells while maintaining the advantages of LRM. Unlike previous studies on the LRM scheme, we present Gray codes over certain run-length sequences in the(1, 2, n)-LRM scheme. This class of Gray codes can overcome the drawback of the many distinct charge levels required in the rank modulation scheme and in certain Gray codes for LRM. Furthermore, we demonstrate that the proposed codes have an asymptotically optimal rate.

关键词： flash memory local rank modulation Gray codes rank modulation run-length sequences

INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS

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Acta Mathematica Scientia 2011年第5期31卷 1939-1944页

作者：臧丽丽孙文昌 Department of mathematics and LPMC Nankai University

In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is ... 详细信息

关键词： frames g-frames Riesz bases g-Riesz bases

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

Theoretical calculation and evaluation of n +^(240,242,244)Pu reactions

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Nuclear Science and Techniques 2019年第1期30卷 79-88页

作者： Hai-Rui Guo Yin-Lu Han Chong-Hai Cai institute of Applied Physics and Computational mathematics China institute of Atomic Energy Department of Physics Nankai University

The nuclear data of n+^(240;242;244)Pu reactions for incident energy below 200 MeV are calculated and evaluated to meet the requirement in the design of an accelerator-driven subcritical system. The optical model is used to calculate the total, nonelastic, shape elastic cross sections, shape elastic scattering angular distributions, and transmission coefficients. The distorted-wave Born approximation is applied to calculate the direct inelastic scatterings to the discrete excited states. The nuclear reaction statistical models and fission theory are applied to describe neutron, proton, deuteron, triton, helium-3, alpha and c emissions, and fission consistently. The results thus obtained are compared with experimental data and the evaluated data obtained from ENDF/B-VII.1 and JENDL-4.0.

关键词： n+240,242,244pu reactions Theoretical calculation of nuclear reaction Nuclear data for E≤200 MeV

Homogeneous Approximation Property for Wavelet Frames with Matrix Dilations,Ⅱ

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Acta Mathematica Sinica,English Series 2013年第1期29卷 183-192页

作者： Zhi Jing ZHAO Wen Chang SUN Department of mathematics and LPMC Nankai University

The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.

关键词： Wavelet frames homogeneous approximation property HAP matrix dilations

Braid Group and Quantum Group of Z(N)Model

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Chinese Science Bulletin 1993年第8期38卷 684-687页

作者：葛墨林刘广群赵宏康 Theoretical Physics Section Nankai Institute of Mathematics

HOFER-ZEHNDER CAPACITY AND ITS APPLICATION IN M×R^(2n)

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Science China mathematics 1992年第8期35卷 931-943页

作者：马仁义 nankai institute of mathematics Nankai University Tianjin 300071 PRC) Present address: Department of Applied Mathematics Tsinghua University Beijing 100084 PRC.

In this paper, we study the Hofer-Zehnder capacity and the Weinstein conjecture in symplectic manifold (M×R^(2n), ω(?)σ). Let us define l_1(M, ω)=inf{|>0, α∈π_2(M)}. Suppose l_1(M, ω)>O, O1, consider on Cp^(n-1) the standard symplectic form co such that ω[u]=n for a generator u of H_2(CP^(n-1). Suppose O<πr^2<2/1 n. ThenC_(HZ)(M×B(r))=C_(HZ)(M×Z(r))=πr^2.As an application, we claim that the Weinstein conjecture in M×Z(r) is proved correct.

关键词： symplectic capacity periodic solution pseudo-holomorphic curves Weinstein conjecture.