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Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2. WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing University, Nanjing 2.0093,{2. 2. department of mathematics, henan University, kaifeng 475001,{2. 3. department of Applied mathematics, Southeast University, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

On the Exceptional Set for the Equation n=p+k^2

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Acta Mathematica Sinica,English Series 1995年第2期11卷 156-167页

作者： Wang Tianze department of mathematics {2. University kaifeng, 475001 china lay.psych.mun.ca

Denote by E（X） the number of integers n≤X which are not a sum of a prime and a square. Set θ=1-0.99442.b, where b≤min（0.9365/c3, 0.02.78/c4）, c3, c4 being given in Lemma 8. The result E（x） xθ is proved in th... 详细信息

关键词： Lemma Square Denote Prime sums Integer Equation

Surface-induced interaction of colloidal particles in isotropic liquid crystals

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Communications in Theoretical Physics 2024年第7期76卷 114-122页

作者： Hualing Zhang kaifeng Weng Rui Ma department of Physics College of Physical Science and TechnologyXiamen UniversityXiamen 361005China Fujian Provincial Key Laboratory for Soft Functional Materials Research Research Institute for Biomimetics and Soft MatterXiamen UniversityXiamen 361005China

In this work,we study the interaction between two colloidal particles in a liquid crystal that is in the isotropic *** interaction is caused by surface-induced polarization of the liquid crystal molecules in the vicinity of the *** find that the interaction is short-ranged in both 2. and 3D *** symmetric homeotropic anchoring conditions,the interaction is *** under anti-symmetric homeotropic anchoring conditions,the interaction is repulsive at short distances but attractive at intermediate *** particle size has a strong impact on the effective interaction force.

关键词： surface-induced interaction colloidal particles liquid crystals

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of mathematics, Beijing Normal University, Beijing 100875,{2. 2. department of mathematics, Neijiang Teacher's College, Neijiang 641112.{2.) Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Automorphisms with order three of affine Lie algebras

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Chinese Science Bulletin 1998年第21期43卷 1793-1798页

作者： JIN Quanqin 1,2.and HOU Zixin 2.1. department of mathematics, Hebei University, Baoding 071002.{2. 2. department of mathematics, Nankai University, Tianjin 300071,{2. department of mathematics Hebei University Baoding China department of mathematics Nankai University Tianjin China

Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two... 详细信息

关键词： affine Lie algebra automorphism of order three first (second) kind of automorphism.

Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2.1. department of mathematics, Shanghai University, Shanghai 2.1800,{2. 2. department of mathematics, Zhongshan University, Guangzhou 5102.5,{2. department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Perturbations of the radical of nest algebras

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Chinese Science Bulletin 1998年第7期43卷 556-560页

作者： LU Fangyan 1 and LU Shijie 2.1. department of mathematics, Suzhou University, Suzhou 2.5006,{2. 2. department of mathematics, Zhejiang University, Hangzhou 31002.,{2. department of mathematics Suzhou University Suzhou China department of mathematics Zhejiang University Hangzhou China

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.

关键词： nest algebras radical perturbation.

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2.GUO Yuqi 2.and CEN Jiaping (Shum Kar-ping) 31. department of mathematics, Xi’an University of Architecture & Technology, Xi’an 710055,{2. 2. department of mathematics, Yunnan University, Kunming 650091,{2. 3. department of department of mathematics Xi’an University of Architecture & Technology Xi’an China department of mathematics Yunnan University Kunming China department of mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. department of mathematics,Inner Mongolia Normal University, Huhhot 01002.,{2. 2. department of mathematics, Harbin Institute of Technology, Harbin 150006,{2. department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.