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ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of Computational mathematics 2000年第6期18卷 561-566页

作者： Lie-heng Wang (State key laboratory of Scientific and Engineering Computing, Institute of Computational mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, beijing 100080, China) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

Recommendation Method for Contrastive Enhancement of Neighborhood Information

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Computers, Materials & Continua 2024年第1期78卷 453-472页

作者： Hairong Wang beijing Zhou Lisi Zhang He Ma School of Computer Science and Engineering North Minzu UniversityNingxia750021China

Knowledge graph can assist in improving recommendation performance and is widely applied in various person-alized recommendation ***,existing knowledge-aware recommendation methods face challenges such as weak user-item interaction supervisory signals and noise in the knowledge *** tackle these issues,this paper proposes a neighbor information contrast-enhanced recommendation method by adding subtle noise to construct contrast views and employing contrastive learning to strengthen supervisory signals and reduce knowledge ***,first,this paper adopts heterogeneous propagation and knowledge-aware attention networks to obtain multi-order neighbor embedding of users and items,mining the high-order neighbor informa-tion of users and ***,in the neighbor information,this paper introduces weak noise following a uniform distribution to construct neighbor contrast views,effectively reducing the time overhead of view *** paper then performs contrastive learning between neighbor views to promote the uniformity of view information,adjusting the neighbor structure,and achieving the goal of reducing the knowledge noise in the knowledge ***,this paper introduces multi-task learning to mitigate the problem of weak supervisory *** validate the effectiveness of our method,experiments are conducted on theMovieLens-1M,MovieLens-20M,Book-Crossing,and Last-FM *** results showthat compared to the best baselines,our method shows significant improvements in AUC and F1.

关键词： Contrastive learning knowledge graph recommendation method

Numerical simulation of Richtmyer-Meshkov instability

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Science China mathematics 2004年第Z1期47卷 234-244页

作者： FU Dexun, MA Yanwen, ZHANG Linbo & TIAN BaolinState key laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, beijing 100080, China State key laboratory of Scientific and Engineering Computing, Institute of Computational mathematics, Chinese Academy of Sciences, beijing 100080, China State key laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing China State key laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Chinese Academy of Sciences Beijing China

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

关键词： R-M instability, direct numerical simulation, shock-interface interaction.

A CRITERION FOR THE SIMILARITY OF LENGTH-TWO ELEMENTS IN A NONCOMMUTATIVE PID

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Journal of Systems Science & Complexity 2011年第3期24卷 580-592页

作者： Ziming LI Huaifu WANG key laboratory of mathematics and mechanization Academy of Mathematics and Systems Science Beijing 100190 China

This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are similar, where A1, A2, B1, B2 are first-order differential （difference） operators. The main step in the algorithm is to find a rational solution of a parametric differential （difference） Risch＇s equation, which has been well-studied in symbolic integration （summation）.

关键词： Completely reducible elements irreducible elements Ore polynomials Risch's equations similarity.

Symbolic Computation Study of (2+1)-Dimensional Dispersive Long Wave Equations

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Communications in Theoretical Physics 2006年第8期46卷 199-202页

作者： LU Zhuo-Sheng~(1,2,+) and XIE Fu-Ding~(2,3) ~1School of Science, beijing University of Post and Telecommunications, beijing 100876, China ~2key laboratory of mathematics mechanization, Academy of mathematics and System Sciences, the Chinese Academy of Sciences, beijing 100080, China ~3Department of Computer Science, Liaoning Normal University, Dalian 116029, China School of Science Beijing University of Post and Telecommunications Beijing 100876 China key laboratory of mathematics mechanization Academy of Mathematics and System Sciences the Chinese Academy of Sciences Beijing 100080 China Department of Computer Science Liaoning Normal University Dalian 116029 China

Seeking exact analytical solutions of nonlinear evolution equations is of fundamental importance in mathematical physics. In this paper, based on a constructive algorithm and symbolic computation, abundant new exact solutions of the (2+1)-dimensional dispersive long wave equations are obtained, among which there are soliton-like solutions, mult-soliton-like solutions and formal periodic solutions, etc. Certain special solutions are considered and some interesting localized structures are revealed.

关键词： dispersive long wave equations symbolic computation exact solution localized structure

PARALLEL CHAOTIC MULTISPLITTING ITERATIVE METHODS FOR THE LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEM

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Journal of Computational mathematics 2001年第3期19卷 281-292页

作者： Zhong-zhi Bai (State key laboratory of Scientific/Engineering Competing Institute of Computational mathematics and Scientific/Engineering Computing, Academy of mathematics and Systems Sciences, Chinese Academy of Sciences, beijing 100080, China) 中科院计算数学与工程计算数学所科学与工程计算国家重点实验室北京 100080

Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting met... 详细信息

关键词： linear complementarity problem matrix multisplitting chaotic iteration relaxed method convergence property

A CRITERION FOR TESTING WHETHER A DIFFERENCE IDEAL IS PRIME

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Journal of Systems Science & Complexity 2009年第4期22卷 627-635页

作者： Chunming YUAN Xiao-Shan GAO key laboratory of mathematics mechanization,Institute of Systems Science Academy of mathematics and Systems Science,Chinese Academy of Sciences,beijing 100190,China. key laboratory of mathematics mechanization Institute of Systems Science Beijing China Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension *** this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.

关键词： Characteristic set difference prime ideal irreducibility strong irreducibility.

ON THE EXPLICIT COMPACT SCHEMES II: EXTENSION OF THE STCE/CE METHOD ON NONSTAGGERED GRIDS ON THE EXPLICIT COMPACT SCHEMES II: EXTENSION OF THE STCE/CE METHOD ON NONSTAGGERED GRIDS

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Journal of Computational mathematics 2000年第5期18卷 467-480页

作者： Hua-zhong Tang , Hua-mu Wu (State key laboratory of Scientific and Engineering Computing, Institute of Computational mathematics, Chinese Academy of Sciences, beijing 100080, China) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

This paper continues to construct and study the explicit compact (EC) schemes for conservation laws. First, we axtend STCE/SE method on non-staggered grid, which has same well resolution as one in [1], and just requires half of the computational works. Then, we consider some constructions of the EC schemes for two-dimensional conservation laws, and some 1D and 2D numerical experiments are also given.

关键词： Conservation laws Compact scheme Shock-Capturing method Euler equations.

CORRECTION METHODS FOR STEADY INCOMPRESSIBLE FLOWS

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Journal of Computational mathematics 1999年第4期17卷 419-424页

作者： Jian Li(State key laboratory of Scientific and Engineering Computing, ICMSEC, Chinese Academy of Sciences, beijing 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京

Correction methods for the steady semi-periodic motion of incompressible fluid are investigated. The idea is similar to the influence matrix to solve the lack of vorticity boundary conditions. For any given boundary condition of the vorticity, the coupled vorticity-stream function formulation is solved. Then solve the governing equations with the correction boundary conditions to improve the solution. These equations are numerically solved by Fourier series truncation and finite difference method. The two numerical techniques are employed to treat the non-linear terms. The first method for small Reynolds number R equals 0-50 has the same results as that in M. Anwar and S.C.R. Dennis' report. The second one for R greater than 50 obtains the reliable results. (Author abstract) 4 Refs.

关键词： incompressible flow vorticity stream function numerical solution