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Acta Mathematica Scientia 2005年第3期25卷 439-448页

作者：房艮孙叶培新 school of mathematical sciences Beijing Normal university school of mathematical sciences and LPMC Nankai university

The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.

关键词： worst (deterministic) case stochastic case average case setting bounded linear functional error estimate

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 205-212页

作者： Yi ZHOU school of mathematical sciences Fudan University Shanghai 200433 China

In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Und... 详细信息

关键词： Semilinear wave equation Critical exponent Cauchy problem Blow up

Simulating the Folding Pathway of RNA Secondary Structure Using the Modified Ant Colony Algorithm

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Journal of Bionic Engineering 2010年第4期7卷 382-389页

作者： Jun Yu~(1,2),Changhai Zhang~(1,2),Yuanning Liu~(1,2),Xin Li~(1,2) 1.College of Computer Science and Technology,jilin university,changchun 130012.P.R.china 2.Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education,china) jilin university,changchun 130012.P.R.china [a] College of Computer Science Technology Jilin University Changchun 130012 P. R. China [b] Key Laboratory of Symbolic Computation Knowledge Engineering (Ministry of Education China) Jilin University Changchun 130012 P. R. China

A new method for simulating the folding pathway of RNA secondary structure using the modified ant colony algorithmis *** a given RNA sequence,the set of all possible stems is obtained and the energy of each stem iscalculated and stored at the initial ***,a more realistic formula is used to compute the energy ofmulti-branch loop in the following *** a folding pathway is simulated,including such processes as constructionof the heuristic information,the rule of initializing the pheromone,the mechanism of choosing the initial andnext stem and the strategy of updating the pheromone between two different *** by testing RNA sequences withknown secondary structures from the public databases,we analyze the experimental data to select appropriate values *** measure indexes show that our procedure is more consistent with phylogenetically proven structures thansoftware RNAstructure sometimes and more effective than the standard Genetic Algorithm.

关键词： RNA secondary structure folding pathway ant colony algorithm

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

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Acta Mathematica Scientia 2006年第2期26卷 229-245页

作者：唐仲伟 school of mathematical sciences Beijing Normal university Beijing 100875China

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ（r）u^p-1, u 〉 0 in R^N, u ∈ D^1,2（R^N）, where N ≥ 3, x = （x^1,z） ∈ R^K×R^N-K,2 ≤ K ≤ N,r = ｜x′｜. It is proved that for 2（N-s）/（N-2）〈 p 〈 2^＊ = 2N/（N - 2）, 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^＊, the above equation does not have a ground state solution but a cylindrically ***, and when p close to 2^＊, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2＊, the ground state solution Up has a unique maximum point xp = （x′p, Zp） and as p → 2^＊, ｜x′p｜ → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^＊.

关键词： Cylindrical symmetry asymptotic behavior ground state solution

THE STABILITY AND CONVERGENCE OF COMPUTINGLONG-TIME BEHAVIOUR

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Journal of Computational Mathematics 1999年第4期17卷 397-418页

作者： HaI-jun Wu Rong-hua Li(Institute of Mathematics, jilin university, changchun 130023, china) 吉林大学数学系吉林长春 130023 吉林大学数学系吉林长春

The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].

关键词： stability compatibility covergence reaction-diffusion equation long-time error estimates

COMPARISON　THEOREMS　TO　BOUNDARY　VALUE　PROBLEMS　FOR　ORDINARY　DIFFERENTIAL　EQUATIONS

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 165-172页

作者： LI YONG WANG HUAIZHONG(Department of Matehematics,jilin university, changchun 130023, jilin, china) jilin UNIV DEPT MATHCHANGCHUN 130023PEOPLES R CHINA

A unified approach is given to several classes of nonlinear boundary value problems, and some previous existence theorems are extended.

关键词： Boundary value problem Existence theorem Brouwer degree,Schauder's fixed point theorem.

Birth-death processes on trees

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Science china Mathematics 2010年第11期53卷 2993-3004页

作者： MA YuTao school of mathematical sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal university, Beijing 100875, china 1. school of mathematical sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China

In this paper, we consider birth-death processes on a tree T and we are interested when it is regular, recurrent and ergodic (strongly, exponentially). By constructing two corresponding birth death processes on Z+, we obtain computable conditions sufficient or necessary for that (in many cases, these two conditions coincide). With the help of these constructions, we give explicit upper and lower bounds for the Dirichlet eigenvalue λ0. At last, some examples are investigated to justify our results.

关键词： birth-death process tree ergodicity Dirichlet eigenvalue

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

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Acta Mathematica Scientia 2011年第4期31卷 1494-1502页

作者：马宇韬 school of mathematical sciences Beijing Normal University

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequal... 详细信息

关键词： W 1 H inequality T p (C)-inequality weakly dependent sequences tensorization

A note on extremal quasi-conformal mappings

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Science china Mathematics 2010年第1期53卷 63-70页

作者： LI Zhongschool of mathematical sciences,Peking university,Beijing 100871,china 1. school of mathematical sciences Peking University Beijing 100871 China

An extremal quasi-conformal mapping f of a domain D is said to be of non-landslide type if the set Ef(δ):= {z∈D:|μf(z)|≤||μ|| ∞ -δ} has no interior points for any δ > 0. In this paper,we construct a quasi-conformal mapping f of the unit disc D such that its Teichmu¨ller equivalence class [f] contains infinitely many extremal mappings of non-landslide type. The relation between extremal mappings of non-landslide type and locally extremal mappings is also discussed.

关键词： quasi-conformal mappings extremal quasi-conformal mappings locally extremal quasi-conformal mappings

Progress in the bionic study on anti-adhesion and resistance reduction of terrain machines

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Science china(Technological sciences) 2009年第2期52卷 273-284页

作者： REN LuQuanKey Laboratory for Terrain-Machine Bionics Engineering of Ministry of Education, school for Biology and Agricultural Engineering, jilin university, changchun 130025, china 1. Key Laboratory for Terrain-Machine Bionics Engineering of Ministry of Education School for Biology and Agricultural Engineering Jilin University Changchun 130025 China

The theoretical studies of bionics of machinery have great scientific significance, and the development of bionic machines has large practical values in the field of engineering and technology. Through the rigorous selection process of evolution, the survived living organisms have successfully developed outstanding abilities to adapt to their surroundings and to reproduce their offspring. In this review,we interpreted the fundamental principles of anti-adhesion and anti-resistance of soil animals by reviewing the current status in this research field and summarizing the work of the research group at jilin university of china in the past decades. The principles and technologies used in morphology bionics,electric-osmosis bionics,flexibility bionics,configuration bionics and coupling bionics were ***,the applications of the engineering bionics and their extensive prospects were introduced.

关键词： terrain machines anti-adhesion and anti-resistance bionics non-smooth coupling