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Note on the number of integral ideals in Galois extensions

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Science china Mathematics 2010年第9期53卷 2417-2424页

作者： L GuangShi1,& WANG YongHui2.1school of Mathematics,Shandong university,Jinan 2.0100,{2. 2.epartment of Mathematics,capital normal university,Beijing 100048,{2. 1. school of Mathematics Shandong University Jinan 250100 China2. Department of Mathematics Capital Normal University Beijing 100048 China

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2.3,...).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

Modal identification of system driven by lévy random excitation based on continuous time AR model

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Science china(Technological sciences) 2009年第12期52卷 3649-3653页

作者： DU XiuLi 1,2.&WANG FengQuan 1 1 College of Civil Engineering,Southeast university,Nanjing 2.0096,china {2.,Nanjing normal university,Nanjing 2.0097,china College of Civil Engineering Southeast University Nanjing 210096 China school of mathematical {2. Nanjing Normal University Nanjing 210097 China

Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random *** structural dynamic equation is first transformed into the observation equation and the state equation(namely,stochastic differential equation).Based on the property of the strong solution of the stochastic differential equation,the uniformly modulated function is identified *** by virtue of the Girsanov theorem,we present the exact maximum likelihood estimators of ***,the modal parameters are identified by eigen *** results show that the method not only has high precision and robustness but also has very high computing efficiency.

关键词： modal identification uniformly modulated function CAR model lévy process exact maximum likelihood estimator

Integral spinor norms in dyadic local fields Ⅲ

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Science china Mathematics 2010年第9期53卷 2425-2446页

作者： L JianRui1 & XU Fei2.1Department of Mathematics,Jinan university,Guangzhou 510632.china 2.2. of Mathematics,capital normal university,Beijing 100048,china Department of Mathematics Jinan University Guangzhou China school of Mathematics Capital Normal University Beijing China

In this paper we give an alternative computation of integral spinor norms over dyadic local fields by using the Jordan decomposition of *** particular,we emphasize the striking similarity between the theory over dyadi... 详细信息

关键词： integral lattice spinor norm Jordan decomposition

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science china Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2.1 Department of mathematical sciences,Huzhou {2.,Huzhou 313000,china 2.school of mathematical sciences,Fudan {2.,Shanghai 2.0433,china 1. Department of mathematical sciences Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2.00）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

A note on periodic solutions for semi-ratio-dependent predator-prey systems

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 1-8页

作者： LIU Xiu-xiang school of mathematical {2., South china normal university, Guangdong 510631, china school of mathematical {2. South China Normal University Guangdong China

This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results.

关键词： Periodic solutions predator-prey system functional response.

A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching

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Science china Mathematics 2011年第3期54卷 603-610页

作者： WANG PeiHe1 & WEN YuLiang2.1school of mathematical {2., Qufu normal university, Qufu 2.3165, china 2.epartment of Mathematics, East china normal university, Shanghai 2.02.1, china 1. school of mathematical {2. Qufu Normal University Qufu 273165 China2. Department of Mathematics East China Normal University Shanghai 200241 China

Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2.4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.

关键词： k-th Ricci curvature Hausdorff convergence differentiable sphere theorem harmonic coordinate harmonic radius

Cu(Ⅱ) Potentiation of Alzheimer Aβ1-40 Cytotoxicity and Transition on its Secondary Structure

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Acta Biochimica et Biophysica Sinica 2006年第11期38卷 765-772页

作者： Xue-Ling DAI~1 Ya-Xuan SUN~2.Zhao-Feng JIANG~2. 1 College of Life Science,capital normal university,Beijing 100037,china 2.College of Applied {2. and Humanities,Beijing Union university,Beijing 100083,china College of Life Science Capital Normal UniversityBeijing 100037 China College of Applied sciences and Humanities Beijing Union UniversityBeijing 100083 China

Mounting evidence has shown that dyshomeostasis of the redox-active biometals such as Cuand Fe can lead to oxidative stress,which plays a key role in the neuropathology of Alzheimer's disease（AD）.Here we demonstrate that with the formation of Cu（Ⅱ）·Aβ1-40 complexes,copper markedly potentiatesthe neurotoxicity exhibited by β-amyloid peptide （Aβ）.A greater amount of hydrogen peroxide was releasedwhen Cu（Ⅱ）·Aβ1-40 complexes was added to the xanthine oxidase/xanthine system detected by potassiumiodide *** bound to Aβ1-40 was observed by electron paramagnetic resonance（EPR） *** dichroism （CD） studies indicated that copper chelation could cause a structuraltransition of Aβ.The addition of copper to Aβ introduced an increase on β-sheet as well as α-helix,whichmay be responsible for the aggregation of Aβ.We hypothesized that Aβ aggregation induced by copper maybe responsible for local injury in *** interaction between Cu2.and Aβ also provides a possible mechanismfor the enrichment of metal ions in amyloid plaques in the AD brain.

关键词： Alzheimer’s disease Cu(Ⅱ)·Aβ1-40 complex neuron injury Aβ secondary structure

Two applications of generalized Carleson measures to meromorphic Besov-type spaces

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Chinese Science Bulletin 1998年第15期43卷 1260-1264页

作者： TAN Haiou 1 and XIAO Jie 2.1. Department of Mathematics, Wuyi university, Jiangmen 52.02., china 2. {2. of mathematical sciences, Peking university, Beijing 100871, china Department of Mathematics Wuyi University Jiangmen China school of mathematical {2. Peking University Beijing China

The generalized Carleson measures are used to characterize the meromorphic Besov_type spaces and to explore some inclusions between these spaces.

关键词： generalized Carleson measures meromorphic Besov_type spaces.

Combined perturbation bounds:Ⅱ.Polar decompositions

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Science china Mathematics 2007年第9期50卷 1339-1346页

作者： Wen LI~(1+) Wei-wei SUN~2.1 school of mathematical {2.,South china normal university,Guangzhou 510631,china 2.Department of Mathematics,City university of Hong Kong,Hong Kong,china school of mathematical {2. South China Normal University Guangzhou China Department of Mathematics City University of Hong Kong Hong Kong China

In this paper,we study the perturbation bounds for the polar decomposition A=QH where Q is unitary and H is *** optimal (asymptotic) bounds obtained in previous works for the unitary factor,the Hermitian factor and singular values of A areσ_r^2.|ΔQ||_F^2.||ΔA||_F^2. 1/2.|ΔH||_F^2.||ΔA||_F^2.and ||Δ∑||_F^2.||ΔA||_F^2.respectively,where∑=diag(σ_1,σ_2....,σ_r,0,...,0) is the singular value matrix of A andσ_r denotes the smallest nonzero singular *** we present some new combined (asymptotic) perturbation boundsσ_r^2.|ΔQ||_F^2.1/2.|ΔH||_F^2.||ΔA||_F^2.andσ_r^2.|ΔQ||_F^2.||Δ∑||_F^2.||ΔA||_F^2.which are optimal for each *** corresponding absolute perturbation bounds are also given.

关键词： polar decomposition perturbation singular value