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Birth-death processes on trees

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Science china Mathematics 2010年第11期53卷 2993-3004页

作者： MA YuTao school of mathematical sciences & Laboratory of Mathematics and Complex Systems, beijing normal university, beijing 100875, china 1. school of mathematical sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China

In this paper, we consider birth-death processes on a tree T and we are interested when it is regular, recurrent and ergodic (strongly, exponentially). By constructing two corresponding birth death processes on Z+, we obtain computable conditions sufficient or necessary for that (in many cases, these two conditions coincide). With the help of these constructions, we give explicit upper and lower bounds for the Dirichlet eigenvalue λ0. At last, some examples are investigated to justify our results.

关键词： birth-death process tree ergodicity Dirichlet eigenvalue

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 sciences, South china normal university, Guangdong 510631, china school of mathematical sciences 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.

Power functions with low uniformity on odd characteristic finite fields

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Science china Mathematics 2010年第8期53卷 1931-1940页

作者： ZHA ZhengBang 1,3 & WANG XueLi 2 1 school of mathematical sciences,Luoyang normal university,Luoyang 471022,china 2.school of mathematical sciences,South china normal university,Guangzhou 510631,china 3 State Key Laboratory of Information Security,Graduate university of Chinese Academy of sciences,beijing 100049,china 1. school of mathematical sciences Luoyang Normal University Luoyang 471022 China3. State Key Laboratory of Information Security Graduate University of Chinese Academy of Sciences Beijing 100049 China2. School of Mathematical Sciences South China Normal University Guangzhou 510631 China

In this paper,we give some new low differential uniformity of some power functions defined on finite fields with odd *** corollaries of the uniformity,we obtain two families of almost perfect nonlinear functions in GF... 详细信息

关键词： almost perfect nonlinear function differential uniform function finite field

On Riemann-Finsler geometry

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Chinese Science Bulletin 1998年第6期43卷 447-450页

作者： MO Xiaohuan school of mathematical sciences, Peking university, beijing 100871, china school of mathematical sciences Peking University Beijing China

The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.

关键词： Finsler space Chern connection Hilbert form Minkowski potential projective sphere bundle.

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 2school 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

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 250100,china 2Department of Mathematics,capital normal university,beijing 100048,china 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

Hausdorff dimension of Julia set of a polynomial with a Siegel disk

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Science china Mathematics 2006年第9期49卷 1284-1296页

作者： SHEN Liang LMAM, school of mathematical sciences, Peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let f(z) = e2πiθz(1+z/d)d,θ∈R\Q be a polynomial. Ifθis an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension o... 详细信息

关键词： Hausdorff dimension Siegel disk porous set

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 sciences 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

DISCRIMINANT ANALYSIS BASED ON STATISTICAL DEPTH

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Journal of Systems Science & Complexity 2010年第2期23卷 362-371页

作者： Jiao JIN·Hengjian CUI school of mathematical sciences,Key Laboratory of Mathematics and Complex Systems,Ministry of Education, beijing normal university,beijing 100875,china. school of mathematical sciences Key Laboratory of Mathematics and Complex Systems Ministry of Education

In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been *** this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is *** aclassification rule based on the depth function family is *** classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.

关键词： Depth discriminant analysis location parameter MVE scatter matrix.