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On Hua-Tuan's conjecture

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Science china mathematics 2009年第2期52卷 389-393页

作者： ZHANG QinHai & QU Haipeng School of mathematics and Computer Sciences, shanxi Normal university, Linfen 041004, china 1. School of mathematics and Computer Sciences Shanxi Normal University Linfen 041004 China

Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1 + p, 1 + p + p2 or 1 + p + 2p2 (mod p3). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold.

关键词： Hua-Tuan’s conjecture metacyclic p-groups abelian p-groups inner abelian p- groups superspecial p-groups

Incoherent control of two classes of finite-level quantum systems

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Journal of Systems Engineering and Electronics 2011年第4期22卷 679-683页

作者： Chunlin Chen 1,2 and Zhenquan Qin 3,1.department of Control and System Engineering,Nanjing university,Nanjing 210093,p.r.china 2.State Key Laboratory for Novel Software Technology,Nanjing university,Nanjing 210093,p.r.china 3.School of Software,Dalian university of Technology,Dalian 116620,p.r.china department of Control and System Engineering Nanjing University Nanjing 210093 P. R. China State Key Laboratory for Novel Software Technology Nanjing University Nanjing 210093 P. R. China School of Software Dalian University of Technology Dalian 116620 P. R. China

The incoherent control of finite-level quantum systems is investigated. Following a brief introduction to coherent control paradigms in quantum control, a control problem that can not be accomplished using only coherent control is presented. For such a control problem, it is proved that it can be accomplished using incoherent control based on projective measurement and coherent control for two classes of finite-level quantum systems, i.e., eigenstate controllable quantum systems and wavefunction controllable quantum systems.

关键词： quantum control eigenstate controllability wavefunction controllability coherent control incoherent control.

Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3 1 department of mathematics,East china university of Science and Technology,Shanghai 200237,china 2.department of mathematics,Anhui Normal university,Wuhu 241000,china 3 department of mathematics,Donghua university,Shanghai 201620,china 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

Comparability and s-Comparability of Modules over Exchange rings

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Acta Mathematica Sinica,English Series 2001年第3期17卷 481-488页

作者： Huan Yin CHEN department of mathematics,Hunan Normal university,Changsha 410006 p.r.china E-mail:chyzxl@sparc2.hunnu.edu.cnFu An LI Institute of mathematics,Academy of mathematics and System Sciences Chinese Academy of Sciences,Beijing 100080,p.r.china E-mail:fal@*** department of mathematics Human Normal University Changsha 410006 P. R. China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy Sciences Beijing 100080 P. R. China

In this paper,we investigate the comparability structure over exchange *** is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the *** provides a new class of exchange rings satisfying the ***,we investigate the s-comparability over exchange *** generalizes the corresponding results of Goodearl and Chen.

关键词： Exchange ring Comparability s-comparability

Schwarz-pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science china mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 department of mathematics,Zhejiang Normal university,Jinhua 321004,china 2.department of mathematics,Tongji university,Shanghai 200092,china 1. department of mathematics Zhejiang Normal University Jinhua 321004 China2. Department of Mathematics Tongji University Shanghai 200092 China

We give higher order derivatives Schwarz-pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-pick estimate holomorphic function Taylor expansion

p-th moment exponential stability of stochastic differential equations with impulse effect

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Science china(Information Sciences) 2011年第8期54卷 1702-1711页

作者： SHEN LiJuan 1,2 & SUN JiTao 11 department of mathematics, Tongji university,Shanghai 200092,china 2.department of mathematics,Luoyang Normal university, Luoyang 471022,china 1. department of mathematics Tongji University Shanghai 200092 China2. Department of Mathematics Luoyang Normal University Luoyang 471022 China

The p-th moment exponential stability of stochastic differential equations with impulse effect is *** employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are *** addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential *** examples are also discussed to illustrate the effectiremess of the results obtained.

关键词： stochastic differential equations impulse p-th moment exponential stability vector Lyapunov functions

EXISTENCE AND NONEXISTENCE OF GLOBAL pOSITIVE SOLUTIONS FOr DEGENErATE pArABOLIC EQUATIONS IN EXTErIOr DOMAINS

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Acta Mathematica Scientia 2010年第3期30卷 713-725页

作者：曾宪忠刘振海 department of mathematics and Computational Science Hunan University of Science and Technology department of mathematics Central South University

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

关键词： Degenerate parabolic equations exterior domains -inhomogeneous dirichlet boundary conditions critical exponent blow-up global existence

Howe duality in Dunkl superspace

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Science china mathematics 2010年第12期53卷 3153-3162页

作者： rEN GuangBin 1,2 1 department of mathematics, university of Science and Technology of china, Hefei 230026, china 2.department of mathematics, university of Aveiro, Aveiro 3810-193, portugal 1. department of mathematics University of Science and Technology of China Hefei 230026 China2. Department of Mathematics University of Aveiro Aveiro 3810-193 Portugal

In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.

关键词： Dunkl operators superspace Fischer decomposition Dirac operator

NONOSCILLATION rESULTS FOr A CLASS OF THIrD OrDEr NONLINEAr DIFFErENTIAL EQUATIONS

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Applied mathematics and Mechanics(English Edition) 2002年第10期23卷 1170-1175页

作者： pakize Temtek 1, Aydn Tiryaki 2 (1 department of mathematics, Faculty of Arts and Science, Erciyes university, 38039, Kayseri, Turkey 2.department of mathematics, Faculty of Arts and Science, Gazi university, Teknikokullar 06500 Ankara, Turke department of mathematics Faculty of Arts and Science Erciyes University 38039 Kayseri Turkey department of mathematics Faculty of Arts and Science Gazi University Teknikokullar 06500 Ankara Turkey

Sufficient conditions for the nonoscillatory solutions of a class of third order nonlinear differential equations are presented. The results obtained generalize some criteria given by parhi. In some special cases, som... 详细信息

关键词： differential equation nonlinear nonoscillatory solution parhi criteria