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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,{2., 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))(2._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

Effects of Ca substitution and surface treatment on electrochemical performances of Ml_(1.0-x) Ca_xNi_(4.0) Co_(0.6) Al_(0.4) hydrogen storage alloy electrodes

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中国有色金属学会会刊：英文版 1999年第3期9卷 487-492页

作者： Chen Weixiang(陈卫祥) 1, Qi Jianqin(祁建琴) 1, Chen Changpin(陈长聘) 2.1. department of Physics 2. department of Materials Science and Engineering, {2. University, hangzhou 31002., P. R. china zhejiang Univ Dept Phys Hangzhou 310027 Peoples R China zhejiang Univ Dept Mat Sci & Engn Hangzhou 310027 Peoples R China

The influences of Ca substitution for Ml and surface treatment on electrochemical performances of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 hydrogen storage alloy electrode were investigated. Ca substitution with x 2.for Ml could improve its discharge capacity, but Ca substitution with x >0.2.could decrease the capacity. It was also found that Ca substitution deteriorates the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode. In order to improve these properties of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 alloy electrode, the alloy was treated in 6 mol/L KOH+0.02.mol/L KBH 4 solution. The results showed that the surface treatment improves the electrochemical performances such as the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode. :The influences of Ca substitution for Ml and surface treatment on electrochemical performances of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 hydrogen storage alloy electrode were investigated. Ca substitution with x 2.for Ml could improve its discharge capacity, but Ca substitution with x >0.2.could decrease the capacity. It was also found that Ca substitution deteriorates the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode. In order to improve these properties of Ml 1.0- x Ca x Ni 4.0 Co 0.6 Al 0.4 alloy electrode, the alloy was treated in 6 mol/L KOH+0.02.mol/L KBH 4 solution. The results showed that the surface treatment improves the electrochemical performances such as the electrocatalytic activity, high rate dischargeability and cycling durability of the alloy electrode.

关键词： hydrogen storage alloy electrode Ca substitution surface modification

The G Class of Functions and Its Applications

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Acta Mathematica Sinica,English Series 2000年第3期16卷 455-468页

作者： Shenghong Li department of mathematics,zhejiang University,{2.,31002.,P.R.chinaXiangao Liu department of mathematics,Fudan University,Shanghai,2.0433,P.R.china department of mathematics Zhejiang University Hangzhou 310027 P. R. China department of mathematics Fudan University Shanghai 200433 P. R. China

In this paper,we introduce the concept of the G class of functions of the parabolic class, and show the Hlder continuity of the G class of *** introduction *** concept contributes to the proof of the regularity and ex... 详细信息

关键词： Parabolic equation Regularity and existence G class of functions

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, china 2. department of mathematics, Yunnan University, Kunming 650091, china 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.

Piecewise-Koszul algebras

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Science china mathematics 2007年第12期50卷 1795-1804页

作者： Jia-feng L■~1 Ji-wei HE~2.Di-ming LU~(1+) ~1 department of mathematics,zhejiang University,{2. 31002.,china ~2.department of mathematics,Shaoxing College of Arts and Sciences,Shaoxing 312.00,china department of mathematics Zhejiang University Hangzhou 310027 China department of mathematics Shaoxing College of Arts Sciences Shaoxing 312000 China

It is a small step toward the Koszul-type *** piecewise-Koszul algebras are, in general,a new class of quadratic algebras but not the classical Koszul ones,simultaneously they agree with both the classical Koszul and higher Koszul algebras in special *** give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A),and show an A_∞-structure on E(A).Relations between Koszul algebras and piecewise-Koszul algebras are *** particular,our results are related to the third question of Green-Marcos.

关键词： (d-)Koszul algebras A_∞-algebras Yoneda-Ext algebras

Time-periodic solutions of the Einstein's field equations II:geometric singularities

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Science china mathematics 2010年第6期53卷 1507-1520页

作者： KONG DeXing1,LIU KeFeng2.& SHEN Ming3 1department of mathematics,zhejiang University,{2. 31002.,china 2.0},University of California at Los Angeles,CA 90095,USA 3Center of Mathematical Sciences,zhejiang University,{2. 31002.,china 1. department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China

In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,*** singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.

关键词： Einstein’s field equations time-periodic solution Riemann curvature tensor singularity event horizon

LIL and the Approximation of Rectangular Sums of B-valued Random Variables when Extreme Terms are Excluded

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Acta Mathematica Sinica,English Series 2002年第3期18卷 605-614页

作者： Li Xin ZHANG department of mathematics Xixi Campus. zhejiang University,{2., P. R. china department of mathematics Xixi Campus Zhejiang University Hangzhou P. R. China

Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r))S_=S_-(X_^((1))+…+X_^((r)). We approximate the trimmed sums ^((r))_n, by a Brownian sheet and obtain sufficient and necessary conditions for ^((r))S_ to satisfy the compact and functional laws of the iterated logarithm. These results improve the previous works by Morrow (1981), Li and Wu (1989) and Ledoux and Talagrand (1990).

关键词： Strong approximation Trimmed sums The law of iterated logarithm

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 32.004,{2. 2.department of mathematics,Tongji University,Shanghai 2.0092.{2. 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

Optimization of Approximate Solution of Integral Equations of Several Variables

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Acta Mathematica Sinica,English Series 2002年第3期18卷 455-462页

作者： Wan MA Xing Hua WANG department of mathematics, zhejiang University.{2., P. R. china atho.imed.uni-erlangen.de

In this paper, we consider the problem of optimization of adaptive direct methods of operator equations. Adaptivity of a direct method is understood in the sense that the subspace on the basis of which it is constructed is chosen depending on the operator of the concrete equation (otherwise, nonadaptive direct method is then concerned), which would essentially let us increase the precision. For some classes of the second kind of Fredhlom integral equations with anisotropic smooth kernels we determine the exact order of the error of adaptive direct methods, and we also give an optimal algorithm.

关键词： Integral equations Direct methods Anisotropic Sobolev classes