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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 {2. Hangzhou 3.002., china department of Mathematics, zhejiang normal university jinhua 3.1004, china 1. department of Mathematics Zhejiang University 310027 Hangzhou China 2. department of Mathematics Zhejiang Normal University 321004 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.

The maximal super-singular integral operators on product spaces

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Science china Mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2.3. 1department of Mathematics, Xidian university, Xi’an 710071, {2. 2.0} of Mathematics, zhejiang normal university, jinhua 3.1004, {2. 3.1} of Mathematics, zhejiang university, Hangzhou 3.002., {2. 1. department of Mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2.0｜∫｜u｜〉ε1,｜v｜〉ε2.b1（｜u｜）b2.｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2.∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

Superconductivity of small metal grains

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 431-441页

作者： ZHENG Renrong1 CHEN Zhiqian2.& ZHU Shunquan1,3.1. department of Physics, Shanghai normal {2., Shanghai 2.02.4, china 2. department of Physics, Southwest normal {2., Chongqing 400715, china 3. department of Computer and Electric Technology, Shanghai Business School, Shanghai 2.1400, china 1. department of Physics Shanghai Normal University 200234 Shanghai China 2. department of Physics Southwest Normal University 400715 Chongqing China 3. department of Computer and Electric Technology Shanghai Business School 201400 Shanghai China

The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关键词： size effect, superconductivity enhancements, small metallic grains.

A lower bound on the total signed domination numbers of graphs

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Science china Mathematics 2007年第8期50卷 1157-1162页

作者： Xin-zhong LU department of Mathematics,zhejiang {2. {3.,jinhua 3.1004,china department of Mathematics Zhejiang Normal University Jinhua 321004 China

Let G be a finite connected simple graph with a vertex set V (G) and an edge set E(G). A total signed domination function of G is a function f : V (G) ∪ E(G) → {?1, 1}. The weight of f is w(f) = Σ x∈V(G)∪E(G) f(x). For an element x ∈ V (G) ∪ E(G), we define $f[x] = \sum\nolimits_{y \in N_T [x]} {f(y)} $ . A total signed domination function of G is a function f : V (G) ∪ E(G) → {?1, 1} such that f[x] ? 1 for all x ∈ V (G) ∪ E(G). The total signed domination number γ s * (G) of G is the minimum weight of a total signed domination function on G.In this paper, we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values of γ s * (G) when G is C n and P n .

关键词： total signed domination function total signed domination number 2.A3.

Climate instability in the Yili region, Xinjiang during the last glaciation

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Chinese Science Bulletin 2000年第17期45卷 1604-1609页

作者： YE Wei, DONG Guangrong, YUAN Yujiang & MA Yingjie1. Xinjiang Institute of Ecology and geography, Chinese Academy of Sciences, Urumqi 83.011, china {2.,{3., jinhua 3.1004, china 3. Institute of Desert Research, Chinese Academy of Sciences, Lanzhou 73.000, china 4. Xinjiang Institute of Meteorological Research, Urumqi 83.002. china Xinjiang Institute of Ecology and geography Chinese Academy of Sciences Urumqi China department of geography Zhejiang Normal University Jinhua China Institute of Desert Research Chinese Academy of Sciences Lanzhou China Xinjiang Institute of Meteorological Research Urumqi China

The climate is influenced by westerlies year in year out and the aeolian loess is widespread in the Yili region, the Xinjiang Uygur Autonomous Region. Through the study of the loess section with a thickness of 2..5 m, much useful information about climatic change in this region during the last glaciation was gotten. Grain size analysis of loess samples in the section showed that the climatic change in the Yili region was of instability during the last glaciation and similar to those of the North Atlantic Ocean and Greenland. In correspondence with the Heinrich events, the percentage of the size fraction of loess with grain size less than 10 μm decreased in cold stadials in the Yili region. This result suggests that the westerly wind be strengthened during the cold periods. Compared with the stadials, the content of the loess with grain size less than 10 μm was increased in interstadials, which indicated that the strength of the westerly wind was weakened. It is obvious that the climate was instable

关键词： Yili region last glaciation climate instability.

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 {2. university,jinhua 3.1004,china 2.department of Mathematics,Tongji university,Shanghai 2.0092.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

Application test of matter element analysis in earthquake forecast

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Acta Seismologica Sinica(English Edition) 1998年第6期11卷 89-94页

作者： LI HUA FENG department of geography,{2., {3. 3.1004, china 1. department of geography Zhejiang Normal University 321004 Jinhua China

Calculation by means of the previous indices of the seismic activity can have the matter element analysis possess the forecast function. Readjusting repeatedly the grade limit value of every index can maximize the historical fitting ratio of the calculated and actual grade of the annual maximum magnitude, whose result is relatively ideal.

关键词： correlation function matter element analysis annual maximum magnitude earthquake forecast

Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science china Mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2.1 department of Mathematics, zhejiang normal university, {2. 3.1004, china 2.department of Mathematics, Kunming university of Science and Technology, Kunming 650093. china department of Mathematics Zhejiang Normal University Jinhua 321004 China department of Mathematics Kunming University of Science and Technology Kunming 650093 China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 3.C3. 3.C2. 74J3. 58Z05

Study on sea water intrusion into palaeochannels on south coastal plain of the Laizhou Bay by the Bohai Sea

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Acta Oceanologica Sinica 2003年第1期22卷 69-74页

作者： Han Mei geography department, Shandong {2. {3., Jinan 2.0014, china Shandong normal Univ Dept Geog Jinan 250014 Peoples R China

The palaeochannel evolution in the study region is divided into four stages by such methods as 14C dating. Sea water intrusion through palaeochannels has been studied as a focal point. Palaeochannels are the main passageways through which the sea water intrudes at a higher speed, through many means and in a changeable dynamic state.

关键词： Palaeochannel sea water intrusion south coastal plain of Laizhou Bay