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A hybrid mean value related to the Dedekind sums and Kloosterman sums

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Science china mathematics 2010年第9期53卷 2543-2550页

作者： ZHANG WenPeng & LIU YanNi department of mathematics,northwest {2.,xi’an 71012.,china 1. department of mathematics Northwest University Xi’an 710127 China

The main purpose of this paper is using the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums,and give some interesting mean val... 详细信息

关键词： Dedekind sum Kloosterman sums Hybrid mean value asymptotic formula identity

Potential energy surfaces for low-lying electronic states of SO_2

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Science china Chemistry 2006年第4期49卷 289-295页

作者： LI Anyang1, SUO Bing2. WEN Zhenyi2.& WANG Yubin2.1. Shanxi Key Laboratory of Physico-inorganic Chemistry, department of Chemistry,{2., xi’an 710069, china 2. Institute of Modern Physics,{2., xi’an 710069, china 1. Shanxi Key Laboratory of Physico-inorganic Chemistry Department of Chemistry Northwest University Xi’an 710069 China 2. Institute of Modern Physics Northwest University Xi’an 710069 China

The potential energy surfaces for the nine low-lying electronic states of SO2.have been constructed by using the multi-reference second order perturbation theory (MRPT2. with the basis set cc-pVTZ. The optimized geometries and the adiabatic excitation energies of these states are in good agreement with experiments and previous calculations. The crossings and avoided crossings dis- played in the potential energy surfaces are expounded.

关键词： cross of PES, MRPT2. SO2 (sulfur dioxide).

Invariant sets and solutions to the generalized thin film equation

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Science china mathematics 2007年第6期50卷 875-886页

作者： Chang-zheng QU & Chun-rong ZHU Center for Nonlinear Studies, northwest university, xi’an 710069,{2. department of mathematics, northwest university, xi’an 710069,{2. department of mathematics, Anhui Normal university, Wuhu 2.1000,{2. 1. Center for Nonlinear Studies Northwest University Xi’an 710069 China 2. department of mathematics Northwest University Xi’an 710069 China 3. department of mathematics Anhui Normal University Wuhu 241000 China

The invariant sets and the solutions of the 1+2.dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set $$E_0 = \{ u:u_x = v_x F(u),u_y = v_y F(u)\} ,$$ where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2.01) and for the 1+1-dimensional nonlinear evolution equations.

关键词： thin film equation invariant set invariant solution rotation group scaling group 35K55 35K40 82.2.

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 {2., Shanghai 2.1800, china 2. department of mathematics, Zhongshan {2., 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,{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.

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. department of mathematics, Sichuan university, Chengdu 610064,{2. 2. department of mathematics, Shaanxi Normal university, xi’an 710062.{2. department of mathematics Sichuan University Chengdu China department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

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 {2., Baoding 071002. china 2. department of mathematics, Nankai {2., 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.

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.,{2. 2. department of mathematics, Zhejiang university of Technology, Hangzhou 310032.{2.) 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.

On the Mean Value Formula of Dedekind Sums

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Acta Mathematica Sinica,English Series 1999年第2期15卷 245-254页

作者： xiali He Wenpeng Zhang, department of mathematics,{2., xi’an 710069, P. R. china department of mathematics Northwest University Xi’an P. R. China

The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula.

关键词： Dedekind sums Distribution of the mean value Asymptotic formula