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On solving equations of algebraic sum of equal powers

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Science china mathematics 2006年第9期49卷 1153-1157页

It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.

关键词： algebraic sum of equal powers, Newton's identities, system of equations,roots of a polynomial.

Lp integrability of trigonometric series with special varying coefficients

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Applied mathematics:A Journal of Chinese Universities 2009年第4期24卷 402-410页

作者： WEI Bao-rong department of mathematics,hangzhou normal University,Zhejiang 310036,china department of mathematics Hangzhou Normal University Zhejiang China

Very recently,Yu,Le and Zhou introduced the so called Δ*B1 and Δ*B2 conditions,which are generalizations of the monotone *** applying these two new conditions,the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric *** fact,the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series,where coefficients may have diffierent signs.

关键词： Lp integrability trigonometric series special varying coefficients

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2(1. department of mathematics, hangzhou normal University, hangzhou 310036, china 2. department of Applied mathematics, School of Mathematical Sciences, South china University of Technology, Guangzhou 510640, china) department of mathematics Hangzhou Normal University Hangzhou 310036 China department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

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Chinese Annals of mathematics,Series B 2003年第2期24卷 249-260页

作者： WANG WENSHENG LIN ZHENGYAN department of mathematics, Zhejiang University, hangzhou 310028, china. department of mathematics, hangzhou Teacher’s college, hangzhou 310012, china. E-mail: wswang@*** department of mathematics, Zhejiang University, hangzhou 310028, china. department of mathematics Zhejiang University Hangzhou 310028 China department of mathematics Hangzhou Teacher's College Hangzhou 310012 China

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of th... 详细信息

关键词： Ornstein-Uhlenbeck processes Stationary Gaussian processes Modulus of continuity Law of the iterated logarithm

NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY L-LIPSCHITZIAN MAPPINGS

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Acta Mathematica Scientia 2011年第5期31卷 2058-2066页

作者：谷峰 Institute of Applied mathematics and department of mathematics hangzhou Teacher's college

The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Bana... 详细信息

关键词： asymptotically pseudo-contractive mapping uniformly L-Lipschitzian map- ping parallel iterative algorithm

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

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Chinese Annals of mathematics,Series B 2010年第2期31卷 201-210页

作者： Qingyan WU department of mathematics,Linyi normal University,Linyi 276005,Shandong,china department of mathematics,Zhejiang University,hangzhou 310027,china department of mathematics Linyi Normal University Linyi China department of mathematics Zhejiang University Hangzhou China

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al... 详细信息

关键词： Real-analytic infinitesimal CR automorphisms Rigid hypersurfaces Holomorphic automorphisms

Strong uniqueness of best approximations in spaces of bounded linear operators

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Science china mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics, Zhejiang University hangzhou 310027, china department of mathematics, Zhejiang normal University Jinhua 321004, china department of mathematics Zhejiang University Hangzhou China department of mathematics Zhejiang Normal University Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

Exact Rates of Convergence of Functional Limit Theorems for Csorgo-Revesz Increments of a Wiener Process

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Acta Mathematica Sinica,English Series 2002年第4期18卷 727-736页

作者： Wen Sheng WANG department of mathematics. Zhejiang University, hangzhou 310028, P. R. china department of mathematics. hangzhou Teacher’s college. hangzhou 310012. P. R. china department of mathematics Zhejiang University Hangzhou 310028

Let {W(t): t≥0} be a standard Wiener process and S be the Strassen set of functions. We investigate the exact rates of convergence to zero (as T→∞) of the variables sup_(0≤≤T-a_T inf_(f∈S sup_(0≤r≤1 |Y_t, T(x)-f(x)] and inf_(0≤t≤T-a_T sup_(0≤x≤1|Y_(t.T)(x)-f(x)| for any given f∈S, where Y_(t.T)(x)=(W(t+xa_T)-W(t))(2a_T(logTa_T^(-1)+log logT))^(-1/2). We establish a relation between how small the increments are and the functional limit results of Csrg-Revesz increments for a Wiener process. Similar results for partial sums of i.i.d, random variables are also given.

关键词： Wiener process Csorgo-Revesz increment Strassen's law of the iterated logarithm

L_p-mixed intersection bodies

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Science china mathematics 2008年第12期51卷 2172-2188页

作者： ZHAO ChangJian department of Information and mathematics Sciences, college of Science, china Jiliang University, hangzhou 310018, china department of Information and mathematics Sciences College of Science China Jiliang University Hangzhou China

In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.

关键词： L p -dual mixed volumes L p -intersection bodies L p -mixed intersection bodies 52A40