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TWO DIMENSIONAL RIEMANN PROBLEM FOR GASDYNAMICS SYSTEM IN THREE PIECES

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Journal of Computational mathematics 1999年第3期17卷 327-336页

作者： Li, Jie-quan Yang, Shu-li Acad Sinica Inst Math Beijing 100080 Peoples R China Acad Sinica Inst Appl Math Beijing 100080 Peoples R China

The Riemann problem for two-dimensional flow of polytropic gas with three constant initial data is considered. Under the assumption that each interface of initial data outside of the origin projects exactly one planar wave of shock, rarefaction wave or contact discontinuity, it is proved that only two kinds of combinations, JRS and Js, are reasonable. Numerical solutions are obtained by using a nonsplitting second order accurate MmB Scheme, and they efficiently reflect the complicated configurations and the geometric structure of solutions of gas dynamics system. (Author abstract) 10 Refs.

关键词： two-dimensional Riemann problem MmB scheme gas dynamics

OPTIMAL INTERIOR AND LOCAL ERROR ESTIMATES OF A RECOVERED GRADIENT OF LINEAR ELEMENTS ON NONUNIFORM TRIANGULATIONS

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Journal of Computational mathematics 1996年第4期14卷 345-362页

作者： I. Hlavacek M. Krizek(mathematical institute, Zitna 25, CZ-11567, Prague 1, Czech Republic) inst math CZ-11567 PRAGUE 1CZECH REPUBLIC

We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we derive an interior superconvergencefor the averaged gradient over quasiuniform triangulations. Local error estimatesup to a regular part of the boundary and the effect of numerical integration arealso investigated.

关键词： math Pro OPTIMAL INTERIOR AND LOCAL ERROR ESTIMATES OF A RECOVERED GRADIENT OF LINEAR ELEMENTS ON NONUNIFORM TRIANGULATIONS

UNIQUENESS OF GENERALIZED SOLUTION FOR THE CAUCHY PROBLEM OF TRANSPORTATTION EQUATIONS

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Acta mathematica Scientia 1997年第3期17卷 341-352页

作者：王振丁夏畦 ACAD SINICA INST MATH PHYSYOUNG SCIENTIST LAB MATH PHYSWUHAN 430071PEOPLES R CHINA SHANTOU UNIV MATH INSTSHANTOU 515063PEOPLES R CHINA ACAD SINICA INST APPL MATHBEIJING 100080PEOPLES R CHINA

In this paper, we prove the uniqueness of generalized solution defined by Lebesgue-Stieltjes integral for the Cauchy problem of transportation equations. Our results are based on the discussions for linear system with... 详细信息

关键词： hyperbolic system generalized solution Lebesgue-Stieltjes integral generalized potential

Recent Advances in Artificial Sensory Neurons: Biological Fundamentals, Devices, Applications, and Challenges

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NANO-MICRO LETTERS 2025年第1期17卷 1-49页

作者： Zhong, Shuai Su, Lirou Xu, Mingkun Loke, Desmond Yu, Bin Zhang, Yishu Zhao, Rong Guangdong inst Intelligence Sci & Technol Zhuhai 519031 Hengqin Peoples R China Zhejiang Univ Coll Integrated Circuits Hangzhou 3112000 Peoples R China ZJU Hangzhou Global Sci & Technol Innovat Ctr Hangzhou 310027 Peoples R China Singapore Univ Technol & Design Dept Sci Math & Technol Singapore 487372 Singapore Tsinghua Univ Dept Precis Instruments Beijing 100084 Peoples R China Tsinghua Univ Ctr Brain Inspired Comp Res Beijing 100084 Peoples R China Tsinghua Univ IDG McGovern Inst Brain Res Beijing 100084 Peoples R China

Biological fundamentals and recent progress of artificial sensory neurons are systematically *** device, performance metrics, and potential applications of artificial sensory neurons are *** for the future development of artificial sensory neurons are discussed. Spike-based neural networks, which use spikes or action potentials to represent information, have gained a lot of attention because of their high energy efficiency and low power consumption. To fully leverage its advantages, converting the external analog signals to spikes is an essential prerequisite. Conventional approaches including analog-to-digital converters or ring oscillators, and sensors suffer from high power and area costs. Recent efforts are devoted to constructing artificial sensory neurons based on emerging devices inspired by the biological sensory system. They can simultaneously perform sensing and spike conversion, overcoming the deficiencies of traditional sensory systems. This review summarizes and benchmarks the recent progress of artificial sensory neurons. It starts with the presentation of various mechanisms of biological signal transduction, followed by the systematic introduction of the emerging devices employed for artificial sensory neurons. Furthermore, the implementations with different perceptual capabilities are briefly outlined and the key metrics and potential applications are also provided. Finally, we highlight the challenges and perspectives for the future development of artificial sensory neurons.

关键词： Artificial intelligence Emerging devices Artificial sensory neurons Spiking neural networks Neuromorphic sensing

GENERALIZED DIFFERENCE METHODS ON ARBITRARYQUADRILATERAL NETWORKS

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Journal of Computational mathematics 1999年第6期17卷 653-672页

作者： Yong-hai Li Rong-hua Li(institute of mathematics, Jinn University, Changchun 130023, China) Jilin Univ Math Inst Changchun 130023 Peoples R China

This paper considers the generalized difference methods on arbitrary networks for Poisson equations. Convergence order estimates are proved based on some a priori estimates. A supporting numerical example is provided.

关键词： quadrilateral elements dual grids bilinear functions generalized difference methods priori estimates error estimates

ANTIPERIODIC WAVELETS

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Journal of Computational mathematics 1996年第1期14卷 32-39页

作者： H.L. Chen(institute of mathematics, Academia Sinica, Beijing) ACAD SINICA INST MATHBEIJING 100080PEOPLES R CHINA

In this paper, we construct the orthogonal wavelet basis in the space of antiperiodic functions by appealing the spline methods. Differing from other results in papers([1,2,3,6,8]), here we derive the 3-scale equation, by using this equation we construct some basic functions, those functions can be used to construct different orthonormal basis in some spline function spaces.

关键词： math ANTIPERIODIC WAVELETS Pro

BOUNDARY LAYER ESTIMATION OF THE QUASILINEAR STOKES EQUATIONS

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Acta mathematica Scientia 1997年第4期17卷 413-428页

作者：何成 Shantou Univ Inst Math Guangdong 515063 Peoples R China Acad Sinica Inst Appl Math Beijing 100080 Peoples R China

We first prove the existence and uniqueness of solution of quasilinear Stokes equations. Then it is shown when the viscosity vanishes, the solution of the quasilinear Stokes equations tends to the solution of the degenerate equations, in which the viscous term is omitted from the quasilinear Stokes equations and the boundary condition is weakened. In the end, we obtain the boundary layer estimation, Our result shows that the thickness of the boundary layer is proportional to epsilon(1/4).

关键词： quasilinear Stokes equations degenerate equations boundary layer

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

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Journal of Computational mathematics 1999年第1期17卷 73-88页

作者： Lung-an Ying(Research institute for mathematical Sciences, Kyoto University, Japan Department of mathematics, Peking University, Beijing 100871, China) Peking Univ Dept Math Beijing 100871 Peoples R China Kyoto Univ Math Sci Res Inst Kyoto Japan

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half pl... 详细信息

关键词： Navier Stokes equation vortex method fractional step method convergence

COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY

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Journal of Computational mathematics 1998年第5期16卷 403-416页

作者： Bai－sheng Wu (Department of mathematics,Jilin University, Changchun 130023, China)Tassilo Kupper (institute of mathematics, University of Cologne, D-50931 Koln, Germany) Jilin Univ Dept Math Changchun 130023 Peoples R China Univ Cologne Inst Math D-50931 Cologne Germany

This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the *** standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is ***: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system

关键词： Hopf/pitchfork point Z_2-symmetry Hopf point bifurcation Extended system