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Optimal Error Estimation of the Modified Ghost Fluid Method

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Communications in Computational Physics 2010年第7期8卷 403-426页

作者： Liang Xu Tiegang Liu lmib and school of mathematics and systems science Beijing University of Aeronautics and AstronauticsBeijing 100191China

The modified ghost fluid method(MGFM)has been shown to be robust and efficient when being applied to multi-medium compressible *** this paper,we rigorously analyze the optimal error estimation of the MGFM when it is applied to the multi-fluid Riemann *** analyzing the properties of the MGFM and the approximate Riemann problem solver(ARPS),we show that the interfacial status provided by the MGFM can achieve“third-order accuracy”in the sense of comparing to the exact solution of the Riemann problem,regardless of the solution *** addition,our analysis further reveals that the ARPS based on a doubled shock structure in the MGFM is suitable for almost any conditions for predicting the interfacial status,and that the“natural”approach of“third-order accuracy”is practically less *** examples are presented to validate the conclusions made.

关键词： Modified ghost fluid method Riemann problem approximate Riemann problem solver

Characteristic Decomposition: From Regular Sets to Normal Sets

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Journal of systems science & Complexity 2019年第1期32卷 37-46页

作者： MOU Chenqi WANG Dongming lmib–school of mathematics and systems science/Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University lmib–SKLSDE–school of mathematics and systems science/Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Centre National de la Recherche Scientifique

In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.

关键词： Characteristic decomposition characteristic pair normal set regular set W-characteristic set

Study of the interactive effect of prey toxin and optimal foraging strategy on a predator-prey model

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International Journal of Biomathematics 2018年第4期11卷 95-110页

作者： Ya Li school of mathematics and systems science & lmib Beijing 100191 P. R. China

The optimal foraging theory predicts that predators choose prey with more net rate of energy intake and less energy costs if there are multiple food sources available. Toxins are found in many species in nature. Those toxins may be produced by prey as self- protection from predatory animals, or come from other sources such as pesticide residue. Therefore, it requires a balance between energy intake and toxicity damage. In order to study the interactive effect of prey toxin and optimal foraging strategy, we construct a predator-prey model with toxin-induced functional response and optimal foraging property. Dynamical analysis shows that the optimal strategy system presents more complex dynamical behavior than the fixed preference system. We conclude that optimal foraging strategy might play a key role in stabilizing or destabilizing the coexistence states of the species in the system, depending on the level of prey toxins.

关键词： Predator-prey model toxicity optimal foraging stability bifurcation.

A BINARY INFINITESIMAL FORM OF TEICHMLLER METRIC AND ANGLES IN AN ASYMPTOTIC TEICHMLLER SPACE

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Acta Mathematica Scientia 2016年第2期36卷 334-344页

作者：吴艳漆毅 lmib and school of mathematics and systems science Beihang University lmib and school of Mathematical science and systems science Beihang University

The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT（X） is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller space AT（X） is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT（X） is obtained.

关键词： Angles of asymptotic Teichmiiller space geodesic segment Finsler structure Boundary dilatation

On the Phase Transitions of (k,q)-SAT

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 605-610页

作者： Jun LIU Zong-sheng GAO Ke XU State Key Laboratory of Software Development Environment Beihang University lmib and school of mathematics and systems science Beihang University

Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk（V） denote the set of all 2^kn^k possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in Tk（V） independently with probability p, and let Q be a given set of q ＂bad＂ tuple assignments. An instance I = （C, Q） is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tupie assignment in Q. Suppose that θ, q 〉 0 are fixed and ε=ε（n）〉 0 be such in 2 that ε Inn/ In Inn → ∞. Let k ≥ （1 ＋ θ） log2 n and let p0 = ln2/qn^k-1. We prove thatlim∞ P[I issatisfiable] ={1,p≤（1-ε）p0, 0,p≥（1＋ε）p0.

关键词： constraint satisfaction phase transition the second moment method

A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes

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Communications in Computational Physics 2014年第9期16卷 1116-1134页

作者： Jian Cheng Tiegang Liu lmib School of Mathematics and Systems ScienceBeihang UniversityBeijing 100191P.R.China.

In[SIAM ***.,35(2)(2013),A1049–A1072],a class of multi-domain hybrid DG and WENO methods for conservation laws was *** applications of this method showed that numerical instability may encounter if the DG flux with Lagrangian interpolation is applied as the interface flux during the moment of conservative *** this continuation paper,we present a more robust approach in the construction of DG flux at the coupling interface by using WENO procedures of *** on this approach,such numerical instability is overcome very *** addition,the procedure of coupling a DG method with a WENO-FD scheme on hybrid meshes is disclosed in *** testing cases are employed to demonstrate the accuracy of this approach and the stability underthe flexibility of using either WENO-FD flux or DG flux at the moment of requiring conservative coupling.

关键词： Discontinuous Galerkin method weighted essentially nonoscillatory scheme hybrid method conservation laws.

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2019年第4期39卷 1173-1184页

作者： Minfeng CHEN Zongsheng GAO Jilong ZHANG school of mathematics and Statistics Guangdong University of Foreign Studies Guangzhou 510006 China lmib and school of mathematics and systems science Beihang University Beijing 100191 China

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

关键词： Non-linear difference equation meromorphic solution rational solution value dist ribution

Interpolation of Lorentz martingale spaces

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science China mathematics 2012年第9期55卷 1951-1959页

作者： REN YanBo GUO TieXin school of mathematics and Statistics Henan University of Science and Technology Luoyang 471003 China lmib and school of mathematics and systems science Beihang University Beijing 100191 China

In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale *** new interpolation theorems concerning Lorentz martingale spaces are *** results that we obtain generaliz... 详细信息

关键词： martingale Lorentz space interpolation function parameter

Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems

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Acta Mathematica Sinica,English Series 2011年第9期27卷 1803-1812页

作者： Yong XIA lmib of the Ministry of Education school of mathematics and systems science Beihang University Beijing 100191 P. R. China

In this paper we study a Class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.

关键词： Nonconvex programming quadratically constrained quadratic programming quadratic assignment problem polynomial solvability strong duality