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A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows

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Numerical Mathematics(Theory,Methods and Applications) 2022年第3期15卷 715-743页

作者： Meiyan Fu Tiao Lu School of Mathematical Sciences Peking UniversityBeijingChina Northwest Institute of Nuclear Technology Xi’anChina HEDPS&CAPT LMAM&School of Mathematical SciencesPeking UniversityBeijingChina

We propose a hybrid scheme combing the level set method and the multicomponent diffuse interface method to simulate complex multi-phase *** overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface,the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other *** exact Riemann solver,between the Euler equation and the six-equation model with highly nonlinear Mie-Gr¨uneisen equations of state,is developed to predict the interfacial states and compute the phase interface *** numerical examples,including shock tube problems,cavitation problems,air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

关键词： Multi-phase flow sharp interface diffuse interface level set six-equation model exact Riemann solver Mie-Gruneisen equation of state

On cutting sequences of the L-shaped translation surface tiled by three squares

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Science China Mathematics 2015年第6期58卷 1311-1326页

作者： WU ShengJian ZHONG YuMin lmam and School of Mathematical Sciences Peking University

We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.

关键词： affine shaped cutting labeled intersection letter infinite compatible saddle explicit

Cheeger's cut, maxcut and the spectral theory of1-Laplacian on graphs

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Science China Mathematics 2017年第11期60卷 1963-1980页

作者： CHANG KungChing SHAO SiHong ZHANG Dong lmam and School of Mathematical Sciences Peking University

This is primarily an expository paper surveying up-to-date known results on the spectral theory of1-Laplacian on graphs and its applications to the Cheeger cut, maxcut and multi-cut problems. The structure of eigenspa... 详细信息

关键词： spectral graph theory Laplacian graph cut optimization critical point theory

Schauder estimates for parabolic equation of bi-harmonic type

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Applied Mathematics and Mechanics(English Edition) 2007年第11期28卷 1503-1516页

作者：姚锋平周蜀林 lmam School of Mathematical SciencesPeking University

Global Schauder estimates for the initial-value parabolic problem of the hi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order case, first a formal expression of solutions by the Fourier transform is obtained, and then the regularity, uniqueness and existence of solutions using the potential theory and approximation argument are got. out approach is simple and straightforward.

关键词： bi-harmonic parabolic Schauder estimates existence uniqueness

Derived norms of finite groups

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Science China Mathematics 2022年第12期65卷 2493-2502页

作者： Zhencai Shen Shirong Li Jiping Zhang College of Science China Agricultural UniversityBeijing100183China Department of Mathematics Guangxi UniversityNanning 530004China lmam and School of Mathematical Sciences Peking UniversityBeijing 100871China

The intersection of particular subgroups is a kind of interesting substructure in group theory. Let G be a finite group and D(G) be the intersection of the normalizers of the derived subgroups of all the subgroups of G. A group G is called a D-group if G = D(G). In this paper, we determine the nilpotency class of the nilpotent residual G^(N) and investigate the structure of D(G) by a new concept called the IO-D-group. A non-D-group G is called an IO-D-group(inner-outer-D-group) if all of its proper subgroups and proper quotient groups are D-groups. The structure of IO-D-groups are described in detail in this paper. As an application of the classification of IO-D-groups, we prove that G is a D-group if and only if any subgroup of G generated by3 elements is a D-group.

关键词： derived subgroups D-groups nilpotent residuals IO-D-groups

Weakly repelling fixed points and multiply-connected wandering domains of meromorphic functions

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Science China Mathematics 2006年第2期49卷 267-276页

作者： QIU Ling WU Shengjian lmam School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

We consider the dynamics of a transcendental meromorphic function f(z) with only finitely many poles and prove that if / has only finitely many weakly repelling fixed points, then there is no multiply-connected wander... 详细信息

关键词： weakly repelling fixed point wandering domain.

Confidence limits for the mean of exponential distribution in any time-sequential samples

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Science China Mathematics 2005年第9期48卷 1182-1193页

作者： CHEN Jiading FANG Xiangzhong School of Mathematical Sciences LMAM Peking University Beijing 100871 China School of Mathematical Sciences LMAM Peking University Beijing 100871 China

We present the general results determining confidence limits for the mean of exponential distribution in any time-sequential samples, which are obtained in any sequential life tests with replacement or without replace... 详细信息

关键词： confidence limits, time-sequential samples, exponential distribution.

Generic regular decompositions for generic zero-dimensional systems

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Science China(Information Sciences) 2014年第9期57卷 5-18页

作者： TANG XiaoXian CHEN ZhengHong XIA BiCan lmam & School of Mathematical Sciences Peking University

Two new concepts,generic regular decomposition and regular-decomposition-unstable(RDU)variety for generic zero-dimensional systems,are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system *** solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU *** so called weakly relatively simplicial decomposition plays a crucial role in the algorithm,which is based on the theories of ***,the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU *** algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the *** results are also presented to show the good performance of the algorithm.

关键词： generic zero-dimensional system regular-decomposition-unstable variety parametric triangular decomposition generic regular decomposition

Regularity of Solutions to Elliptic Equations with VMO Coefficients

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1103-1118页

作者： Ye Min CHEN lmam School of Mathematical SciencePeking University

The aim of this paper is to study the regularity of solutions to the Dirichlet problems for general second-order elliptic equations in Lebesgue and Morrey *** consider both non- divergence and divergence forms and the... 详细信息

关键词： Regularity Elliptic equations VMO