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On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3 1. department of Applied mathematics, Beijing Institute of Technology, Beijing 100081, China {2., yunnan University, kunming 650091, China 3. Institute of Applied mathematics, C department of Applied mathematics Beijing Institute of Technology Beijing China department of mathematics Yunnan University Kunming China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

Exponential attractors of the nonlinear wave equations

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Chinese Science Bulletin 1998年第16期43卷 1331-1335页

作者： DAI Zhengde 1 and MA Dacai 2.1. department of mathematics, {2. University, kunming 650031, China 2. department of mathematics, Shangrao Teachers College, Shangrao 334000, China department of mathematics Yunnan University Kunming China department of mathematics Shangrao Teachers College Shangrao China

The (E, E)-type exponential attractors for the nonlinear wave equation were obtained by using the decomposition of operators and finite covering *** results solves the open problem of Eden et al.

关键词： nonlinearity wave equations exponential attractors.

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, China {2., Neijiang Teacher's College, Neijiang 641112. China) 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. China {2., Nankai University, Tianjin 300071, China 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.

Response to“Discussion on the systematic position of the Early Cambrian priapulomorph worms”

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Science Bulletin 2006年第2期51卷 250-256页

作者： HAN Jian1 & HU Shixue2.1. department of Geology and Key Laboratory for Continental Dynam- ics of the Education Ministry, Northwest University, Xi’an 710069, China 2. yunnan Geological Institute, {2. 650011, China department of Geology and Key Laboratory for Continental Dynamics of the Education Ministry Northwest University Xi’an China yunnan Geological Institute Kunming China

Due to the combination of complex states of preservation and taphonomies inChengjiang fossils, Huang et al.) expressed different opinions to those of Han et al.) on themorphology and systematic position of the fossil priapulomorph worms (Priapulomorpha) based on theiradditional materials. These diverse opinions are critical in any investigation of the diversity ofthe Introverta in the Cambrian explosion. However, some of their ideas need to be discussed infurther detail.

关键词： Response to Discussion on the systematic position of the Early Cambrian priapulomorph worms

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, China {2., Zhongshan University, Guangzhou 5102.5, China 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, China {2., Zhejiang University, Hangzhou 31002., China 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.

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., China {2., Harbin Institute of Technology, Harbin 150006, China 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.

Shape blending of artistic brushstroke represented by disk B-spline curves

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Progress in Natural Science:Materials International 2007年第12期17卷 1501-1507页

作者： Cheng Min1,2.and Wang Guojin1(1. department of mathematics, Zhejiang University, Hangzhou 31002., China {2., Zhejiang University of Technology, Hangzhou 310032. China) department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Zhejiang University of Technology Hangzhou 310032 China

This paper presents an algorithm for automatically generating in-between frames of two artistic brushstrokes. The basic idea of the algorithm is to represent the two key frames of artistic brushstrokes in disk B-spline curves, and then make blending of their geometric intrinsic variables. Given two key frames of artistic brushstrokes, the skeleton curves can be obtained by certain skeleton-based techniques. After disk B-spline representation of the key frames is generated, interpolation of the intrinsic variables of the initial and the target disk B-spline curves is carried out. Examples show that this method can efficiently create in-between frames of artistic brushstrokes.

关键词： computer aided calligraphy shape blending brushstroke disk B-spline curve skeleton.