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Recovering Unbounded Rough Surfaces with a Direct Imaging Method

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Acta Mathematicae Applicatae Sinica 2020年第1期36卷 119-133页

作者： Hai-wen ZHANG ncmis and Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China

In this paper,we consider the inverse acoustic scattering problem by an unbounded rough surface.A direct imaging method is proposed to reconstruct the rough surfaces from scattered-field data for incident plane waves and the performance analysis is also *** reconstruction method is very robust to noises of measured data and does’t need to know the type of the boundary conditions of the surfaces in ***,numerical examples are carried out to illustrate that our method is fast,accurate and stable even for the case of multiple-scale profiles.

关键词： direct imaging method inverse scattering problem unbounded rough surface incident plane wave near-field data

On orders in number fields: Picard groups, ring class fields and applications

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Science China Mathematics 2015年第8期58卷 1627-1638页

作者： LV Chang DENG YingPu Key Laboratory of Mathematics Mechanization NCMIS Academy of Mathematics and Systems ScienceChinese Academy of Sciences

We focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard *** an application, we give criteria of the integral solvability of the diophantine equation p = x2+ ny2 over a class of imaginary quadratic fields where p is a prime element.

关键词： Diophantine方程 d群环类应用数字域命令伽罗瓦群虚二次域

Analyzing Multiple Phenotypes Based on Principal Component Analysis

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 843-860页

作者： De-liang BU San-guo ZHANG Na LI School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of SciencesBeijing 100049China LSC NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Joint analysis of multiple phenotypes can have better interpretation of complex diseases and increase statistical power to detect more significant single nucleotide polymorphisms(SNPs)compare to traditional single phenotype analysis in genome-wide association *** component analysis(PCA),as a popular dimension reduction method,has been broadly used in the analysis of multiple *** PCA transforms the original phenotypes into principal components(PCs),it is natural to think that by analyzing these PCs,we can combine information across *** PCA-based methods can be divided into two categories,either selecting one particular PC manually or combining information from all *** this paper,we propose an adaptive principle component test(APCT)which selects and combines the PCs adaptively by using Cauchy combination *** proposed method can be seen as a generalization of traditional PCA based method since it contains two existing methods as special *** simulation shows that our method is robust and can generate powerful result in various *** real data analysis of stock mice data also demonstrate that our proposed APCT can identify significant SNPs that are missed by traditional methods.

关键词： multiple phenotypes principal component analysis cauchy combination method

Ciphertext-Only Attacks Against Compact-LWE Submitted to NIST PQC Project

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Journal of Systems Science & Complexity 2022年第3期35卷 1173-1190页

作者： LI Haoyu LIU Renzhang LIU Zhen PAN Yanbin XIE Tianyuan Key Laboratory of Mathematics Mechanization NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China State Key Laboratory of Cryptology Beijing 100878China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Westone Cryptologic Research Center Westone Information Industry INC.Beijing 100070China

As a candidate of the standard of post-quantum cryptography for NIST,Liu,et *** a new public-key encryption scheme Compact-LWE,whose structure is similar to LWE,but with different distribution of *** thought that the special error distribution would protect Compact-LWE from known lattice-based ***,they recommended a set of small parameters to improve the efficiency of Compact-LWE and claimed it can offer 192-bit ***,in this paper,the authors show that Compact-LWE is not secure under recommended parameters by presenting two ciphertext-only ***,the authors show that the message can be recovered efficiently from the *** the authors go further to recover an equivalent private key efficiently from the public key by exploiting the special structure of Compact-LWE.

关键词： Ciphertext-only attack Compact-LWE NIST post-quantum cryptography

Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions

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Science China Mathematics 2016年第11期59卷 2245-2264页

作者： MENG XiangYun YANG XueQin ZHANG Shuo School of Mathematical Sciences Peking University LSEC ICMSEC NCMIS Academy of Mathematics and Systems ScienceChinese Academy of Sciences

We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of O(h) order in energy norm and of O(h^2) order in L^2 norm on general d-rectangular triangulations. Moreover, when the triangulation is uniform, the convergence rate can be of O(h^2) order in energy norm, and the convergence rate in L^2 norm is still of O(h^2) order, which cannot be improved. Numerical examples are presented to demonstrate our theoretical results.

关键词： d-rectangular Morley element second order elliptic equation convergence analysis super convergence lower bound estimate

Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 92-103页

作者： Xia Ji Yingxia Xi Hehu Xie LSEC NCMISInstitute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper,we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding *** error estimates of the eigenvalue and eigenfunction approximation are given,***,... 详细信息

关键词： Transmission eigenvalue Morley element nonconforming finite element method

On extended state based Kalman filter design for a class of nonlinear time-varying uncertain systems

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Science China(Information Sciences) 2018年第4期61卷 118-133页

作者： Wenyan BAI Wenchao XUE Yi HUANG Haitao FANG Beijing Aerospace Automatic Control Institute LSC NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

This paper considers the filtering problem for a class of multi-input multi-output systems with nonlinear time-varying uncertain dynamics, random process and measurement noise. An extended state based Kalman filter, with the idea of timely estimating the unknown dynamics, is proposed for better robustness and higher estimation precision. The stability of the proposed filter is rigorously proved for nonlinear timevarying uncertain system with weaker stability condition than the extended Kalman filter, i.e., the initial estimation error, the uncertain dynamics and the noises are only required to be bounded rather than small enough. Moreover, quantitative precision of the proposed filter is theoretically evaluated. The proposed algorithm is proved to be the asymptotic unbiased minimum variance filter for constant uncertainty. The simulation results of some benchmark examples demonstrate the feasibility and effectiveness of the method.

关键词： Kalman filter extended state observer nonlinear time-varying uncertain system unbiased minimum variance filter active disturbance rejection control

RECURSIVE INTEGRAL METHOD FOR THE NONLINEAR NON-SELFADJOINT TRANSMISSION EIGENVALUE PROBLEM

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Journal of Computational Mathematics 2017年第6期35卷 828-838页

作者： Yingxia Xi Xia Ji LSEC NCMIS Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The transmission eigenvalue problem is an eigenvalue problem that arises in the scatter- ing of time-harmonic waves by an inhomogeneous medium of compact support. Based on a fourth order formulation, the transmission eigenvalue problem is discretized by the Mor- ley element. For the resulting quadratic eigenvalue problem, a recursive integral method is used to compute real and complex eigenvalues in prescribed regions in the complex plane. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

关键词： Transmission eigenvalue problem Nonlinear eigenvalue problem Contour integrals.

Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

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Computer Modeling in Engineering & Sciences 2019年第4期119卷 145-163页

作者： Philippe Devloo Wenchao Teng Chen-Song Zhang FEC Universidade Estadual de CampinasBrazil Tracy Energy Technologies BeijingChina ncmis&LSEC Academy of Mathematics and System SciencesCASBeijingChina

The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with *** two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite *** coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures *** issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator *** test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.

关键词： Fracture simulation discrete fracture model multiscale hybrid finite element mixed formulation