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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.

Spectral anomalies and spectral switches of partially coherent and polychromatic light diffracted at an aperture

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Science china(physics,Mechanics & Astronomy) 2004年第1期47卷 24-35页

作者： Lü Baida1, 3 & PAN Liuzhan1, 2.1. Institute of Laser physics and Chemistry, Sichuan university, Chengdu 610064,{2. 2. department of physics, Luoyang normal College, Luoyang 47102.,{2. 3. State Key Laboratory of Laser Technology, Huazhong university of Science and Technology, Wuhan 430074,{2. Correspondence should be addressed to L Baida (email: badalu@***) Received July 10, 2.03 1. Institute of Laser physics and Chemistry Sichuan University 610064 Chengdu China 2. State Key Laboratory of Laser Technology Huazhong University of Science and Technology 430074 Wuhan China 3. department of physics Luoyang Normal College 471022 Luoyang China

Based on the propagation theory of partially coherent light in the space-frequency domain, the anomalous spectral behavior and spectral switches in the far field of partially coherent and polychromatic light diffracted at an aperture are studied. It is shown that, as compared with spatially fully coherent and polychromatic light whose spectral anomalies are induced only by aperture diffraction, the spectral anomalies and spectral switches of partially coherent and polychromatic light depend on the aperture diffraction, spatial correlationβ and bandwidth of the original spectrum. Detailed numerical calculations are made to illustrate the behavior of spectral switches of partially coherent and polychromatic light, and the results for spatially fully coherent and polychromatic light are treated as a special case ofβ=1 and included in our theory.

关键词： spectral anomaly spectral switch partially coherent and polychromatic light far field aperture diffraction

Non-universal Gauge Bosons Z'and the Process e~+e~- →f

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Communications in Theoretical physics 2004年第3期41卷 419-424页

作者： YUE Chong-Xing~1 WANG Shun-Zhi~2.1 department of physics,Liaoning{2. university,Dalian 11602.,china 2.College of physics and Information Engineering,Henan{2. university,Xinxiang 453002.china department of physics Liaoning Normal University Dalian 116029 College of physics and Information Engineering Henan Normal University Xinxiang 453002

Introduetion Altl、ough the standard model(SM)that bases on thega、lge gro、ip SU:(2.xU(1)has been sueeessful in de-seribing the Physies of eleetroweak interaetions,the meeh-anisn,of the eleetroweak symmetry breaking(... 详细信息

关键词： non-universal gauge bosons cross section TC2.models

Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

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Science china(physics,Mechanics & Astronomy) 2004年第1期47卷 8-16页

作者： TANG Zhilie1, XING Da2.& LIU Songhao2.1. department of physics, South{2. normal university, Guangzhou 510631,{2. 2. School for Information and Optoelectronic Science and Engineering, South{2. normal university, Guangzhou 510631,{2. Correspondence should be addressed to Tang Zhilie (email: tangzhl@***) Received April 2., 2.03 1. department of physics South China Normal University 510631 Guangzhou China 2. School for Information and Optoelectronic Science and Engineering South China Normal University 510631 Guangzhou China

The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single- and two-photon confocal microscopy.

关键词： second harmonic generation, third harmonic generation, confocal microscopy, three-dimensional point spread function.

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.

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.

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.

Different-Periodic Travelling Wave Solutions for Nonlinear Equations

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Communications in Theoretical physics 2004年第4期41卷 481-486页

作者： YE Li-Jun~1 LIN Ji~(1,2.1 department of physics,Zhejiang{2. university,Jinhua 32.004,china2.physics department,Shanghai Jiao Tong university,Shanghai 2.0030,china physics department Shanghai Jiao Tong University Shanghai 200030 China

Using Jacobi elliptic function linear superposition approach for the(1+1)-dimensional Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation and the(2.1)-dimensional Nizhnik-Novikov-Veselov(NNV)equation,many new periodic travelling wave solutions with different periods and velocities are obtained based on the knownperiodic *** procedure is crucially dependent on a sequence of cyclic identities involving Jacobi ellipticfunctions sn(ξ,m),cn(ξ,m),and dn(ξ,m).

关键词： linear superposition nonlinear equation travelling wave solution