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Numerical simulation of shock wave phenomena in hydrodynamic model of semiconductor devices

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The Journal of China Universities of Posts and Telecommunications 2007年第1期14卷 71-76页

作者： XU Ning YANG geng College of Optical and Electric Engineering Nanjjing University of Posts and Telecommunications Nanjing 210003 China College of Mathematics and Physics Nanking University of Posts and Telecommunications Nanjing 210003 China

We propose a finite element method to investigate the phenomena of shock wave and to simulate the hydrodynamic model in semiconductor devices. An introduction of this model is discussed first. Then some scaling factors and a relationship between the changing variables are discussed. And then, we use a finite element method （P1-iso-P2 element） to discrete the equations. Some boundary conditions are also discussed. Finally, a sub-micron n%＋-n-n^＋ silicon diode and Si MESFET device are simulated and the results are analyzed. Numerical results show that electronic fluids are transonic under some conditions.

关键词： hydrodynamic model semiconductor devices finite element method shock wave

Convergence rate of Gibbs sampler and its application

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Science China Mathematics 2005年第10期48卷 1430-1439页

作者： LI Kaican geng Zhi Department of Mathematics Hubei Normal University Huangshi 435002 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Based on the convergence rate defined by the Pearson-χ~2 distance,this pa- per discusses properties of different Gibbs sampling *** a set of regularity conditions,it is proved in this paper that the rate of convergence on systematic scan Gibbs samplers is the norm of a forward *** also discuss that the collapsed Gibbs sam- pler has a faster convergence rate than the systematic scan Gibbs sampler as proposed by Liu et *** on the definition of convergence rate of the Pearson-χ~2 distance, this paper proved this result *** to Theorem 2,we also proved that the convergence rate defined with the spectral radius of matrix by Robert and Shau is equivalent to the corresponding radius of the forward operator.

关键词： compact operator Gibbs samplers Hilbert space transition function DOI:10. 1360/02ys0013

Point defects in 2-D liquid crystals with a singular potential:Profiles and stability

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Science China Mathematics 2024年第11期67卷 2515-2540页

作者： Zhiyuan geng Wei Wang Basque Center for Applied Mathematics Bilbao 48009Spain School of Mathematical Sciences Zhejiang UniversityHangzhou 310058China

We study radial symmetric point defects with degree k/2 in the 2-D disk or R^(2) in the Q-tensor framework with a singular bulk energy,which is defined by Bingham ***,we obtain the existence of solutions for the profiles of radial symmetric point defects with degree k/2 in the 2-D disk or R^(2).Then,we prove that the solution is stable for |k| = 1 and unstable for |k| > *** identities are derived and utilized throughout the proof of existence and stability/instability.

关键词： radial symmetric point defects singular bulk potential Bingham closure stability

An Improved Hyperplane Assisted Multiobjective Optimization for Distributed Hybrid Flow Shop Scheduling Problem in Glass Manufacturing Systems

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Computer Modeling in Engineering & Sciences 2023年第1期134卷 241-266页

作者： Yadian geng Junqing Li College of Computer Science Liaocheng UniversityLiaocheng252059China School of Information Science and Engineering Shandong Normal UniversityJinan25014China

To solve the distributed hybrid flow shop scheduling problem(DHFS)in raw glass manufacturing systems,we investigated an improved hyperplane assisted evolutionary algorithm(IhpaEA).Two objectives are simultaneously considered,namely,the maximum completion time and the total energy ***,each solution is encoded by a three-dimensional vector,i.e.,factory assignment,scheduling,and machine ***,an efficient initialization strategy embeds two heuristics are developed,which can increase the diversity of the ***,to improve the global search abilities,a Pareto-based crossover operator is designed to take more advantage of non-dominated ***,a local search heuristic based on three parts encoding is embedded to enhance the searching *** enhance the local search abilities,the cooperation of the search operator is designed to obtain better non-dominated ***,the experimental results demonstrate that the proposed algorithm is more efficient than the other three state-of-the-art *** results show that the Pareto optimal solution set obtained by the improved algorithm is superior to that of the traditional multiobjective algorithm in terms of diversity and convergence of the solution.

关键词： Distributed hybrid flow shop energy consumption hyperplane-assisted multi-objective algorithm glass manufacturing system

Exponentially convergent angular velocity estimator design for rigid body motion:a singular perturbation approach

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Science China(Information Sciences) 2020年第2期63卷 224-226页

作者： Xiuhui PENG Zhiyong geng State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering ScienceCollege of Engineering Peking University

Dear editor,The exponentially convergent angular velocity estimator on SO(3) is of great importance for the control of rigid body [1]. Based on the idea of adaptive technique, the angular velocity observer on SO(3) was firstly proposed in [2]. Refs.[3, 4]and references therein mainly focus on constructing different attitude error functions to improve convergence rate. In those studies, based on

关键词： Exponentially convergent angular velocity estimator design for rigid body motion:a singular perturbation approach Lyapunov

The Dimension Vectors of Indecomposable Modules of Cluster-tilted Algebras and the Fomin-Zelevinsky Denominators Conjecture

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Acta Mathematica Sinica,English Series 2012年第3期28卷 581-586页

作者： Shengfei geng Liangang PENG Department of Mathematics Sichuan University

The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.

关键词： Dimension vector cluster tilting object cluster-tilted algebra denominator

Municipal solid waste management in Dalian： practices and challenges

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Frontiers of Environmental Science & Engineering 2012年第4期6卷 540-548页

作者： Xinbei WANG Yong geng Institute of Applied Ecology Chinese Academy of ScienceShenyang 110016China

The fast growing of urban areas in developing countries has brought serious problems on municipal solid waste （MSW） management. It will be rational to adopt an integrated approach to deal with such a challenge so that the overall eco-efficiency of MSW management could be improved. To better examine how attributes of integrated MSW management are being interpreted and put into practice, and to explore what changes should be made to improve the application of integrated MSW management, we employ a case study method so that lessons learned could be used to inform initiatives in other cities and the potential solution may offer feasible strategies. The case study city is Dalian, a typical seaport city with fast growing rate in economy. The outcomes of this case study show us that fragmented management structure, ineffective and inefficient enforcement of relevant regulations, backward technologies, limited financial resources and lack of public participation are main barriers for the implementation of integrated MSW management. Consequently, in order to overcome these barriers, we propose an integrated management framework on MSW management, aiming to maximize the overall eco-efficiency of MSW management.

关键词： municipal solid waste (MSW) management 3R principles challenges eco-efficiency effective and efficient enforcement

Projection Improved SPAI Preconditioner for FGMRES

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Numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 1035-1052页

作者： Mingguang geng Shuli Sun LTCS Department of Mechanics and Engineering ScienceCollege of EngineeringPeking UniversityBeijing 100871China

Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all *** this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of *** proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the *** strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable *** paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different *** results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems.

关键词： Generalized minimal residual preconditioner sparse approximate inverse oblique projection orthogonal projection

THE VACUUM IN NONISENTROPIC GAS DYNAMICS

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Acta Mathematica Scientia 2012年第1期32卷 339-351页

作者： geng Chen Robin Young Department of Mathematics Pennsylvania State University University Park PA 16802 USA Department of Mathematics University of Massachusetts Amherst MA 01003 USA

We investigate the vacuum in nonisentropic gas dynamics in one space vari- able, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem. We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.

关键词： nonisentropic gas dynamics conservation laws vacuum large data Riemann problem