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The best quadrature based on given Hermite information for the Sobolev class KW^r[a,b]

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Science china mathematics 2006年第8期49卷 1146-1152页

作者： wang Xinghua & YANG Shijun department of {2., Zhejiang university, Hangzhou 31002., china department of {2., Hangzhou normal College, Hangzhou 310036, china department of mathematics Zhejiang University Hangzhou 310028 China department of mathematics Hangzhou Normal College Hangzhou 310036 China

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given Hermite *** work reports the results on the best quadrature based on the given Hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

关键词： Sobolev class, Hermite information, perfect spline, optimal recovery, best quadrature.

On semisymmetric cubic graphs of order 6p^(2.

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Science china mathematics 2004年第1期47卷 1-17页

作者： LU Zaiping, wang Changqun & XU MingyaoLMAM, School of Mathematical Sciences, Peking university, {2. 100871, china department of mathematics, Zhengzhou university, Zhengzhou 450052. chinaPresent address: department of mathematics, Qufu normal university, Qufu 2.3165, china. 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China 3. department of mathematics Zhengzhou University 450052 Zhengzhou China

A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2.for an odd prime p.

关键词： (G-)semisymmetric graph, symmetric graph, bi-Cayley graph, regular covering, group action.

Approximation of functions on the Sobolev space with a Gaussian measure

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Science china mathematics 2010年第2期53卷 373-384页

作者： wang HePing 1, ZHANG YanWei 2.& ZHAI XueBo 1 1 School of Mathematical Sciences, Capital normal {2., beijing 100048, china 2.department of mathematics, Zaozhuang {2., Zaozhuang 2.7160, china 1. School of Mathematical Sciences Capital Normal University Beijing 100048 China2. Department of Mathematics Zaozhuang University Zaozhuang 277160 China

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

关键词： average width best approximation approximation by linear operators Sobolev space Gaussian measure

A Probabilistic Approach to the First Dirichlet Eigenvalue on Non-compact Riemannian Manifold

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Acta Mathematica Sinica,English Series 1997年第1期13卷 116-126页

作者： wang Fengyu (department of {2.,beijing normal university,beijing 100875,china) department of mathematics Beijing Normal University 100875 Beijing China

By using diffusion process with absorbing boundary,some lower bounds are obtained for the first Dirichlet eigenvalue of operator Δ+▽h on a non-compact complete Riemannian manifold. The resulting estimates contain McKean’s estimate for ▽h=***,the first Dirichlet eigen- value for elliptic operators on R^d and the first mixed eigenvalue are also *** examples show that our estimates can be sharp even for ▽h≠0.

关键词： Dirichlet eigenvalue Diffusion process Mixed eigenvalue

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science china mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua KONG~(1+) Ming-xin wang~(2.3) 1 department of Applied {2.,Dalian university of Technology,Dalian 11602.,china 2.department of {2.,Southeast university,Nanjing 2.0018,china 3 department of {2.,Xuzhou normal university,Xuzhou 2.1116,china 1. department of Applied mathematics Dalian University of Technology Dalian 116024 China 2. department of mathematics Southeast University Nanjing 210018 China 3. department of mathematics Xuzhou Normal University Xuzhou 221116 China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35K65

Extension of isometries on the unit sphere of l^p (Γ) space

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Science china mathematics 2010年第4期53卷 1085-1096页

作者： FANG XiNian 1,& wang JianHua 2.1 School of mathematics and Statistics,Nanjing Audit {2.,Nanjing 2.002.,china 2.department of mathematics,Anhui normal {2.,Wuhu 2.1000,china 1. School of mathematics and Statistics Nanjing Audit University Nanjing 210029 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto ... 详细信息

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

关键词： isometric extension l p (Γ) space isometry 1-Lipschitz mapping

Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2.& YAN LiTan 3 1 department of mathematics,East{2. university of Science and Technology,Shanghai 2.02.7,china 2.department of mathematics,Anhui normal university,Wuhu 2.1000,china 3 department of mathematics,Donghua university,Shanghai 2.162.,china 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2.be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and wang in 2.09, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2.2. 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2008年第2期26卷 123-148页

作者： Yuanming wang department of {2.,East china normal university,Shanghai 2.02.1,china Division of Computational Science,E-Institute of Shanghai Universities,Shanghai normal Benyu Guo department of {2.,Shanghai normal university,Shanghai 2.02.4,china Division of Computational Science,E-Institute of Shanghai Universities,Shanghai,china department of mathematics East China Normal University Shanghai 200241 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China department of mathematics Shanghai Normal University Shanghai 200234 China Division of Computational Science E-Institute of Shanghai Universities Shanghai China

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Electroluminescent properties of three ternary europium complexes with different phenanthroline derivatives

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Science china Chemistry 2004年第4期47卷 326-334页

作者： BIAN Zuqiang1,2. GAO Deqing1, GUAN Min1, XIN Hao1, LI Fuyou1, HUANG Chunhui1, wang Kezhi2.& JIN Linpei2.1. State Key Laboratory of Rare Earth Materials Chemistry and Applications, Peking university, {2. 100871, china 2. department of Chemistry, beijing normal university, {2. 100875, china 1. State Key Laboratory of Rare Earth Materials Chemistry and Applications Peking University 100871 Beijing China 2. department of Chemistry Beijing Normal University 100875 Beijing China

Three ternary Eu(III) complexes with general formula of Eu(DBM)3LN (DBM = dibenzoylmethanate, and LN (N = 1-3 ) stand for three different 1,10-phenanthroline derivatives) have been synthesized for vacuum deposition films-based electroluminescent devices. The complex Eu(DBM)3L3 (L3 = 2.phenyl-3-[3-(carbazol-9-yl)propyl]imidazo[4,5-f]1,10-phenan-throline) was designed with an effort to combine the electron-transporting phenanthroline platform and the hole-transporting carbazole group into one molecule expecting to improve both electron and hole transporting properties simultaneously. The results show that the variation of the neutral ligands in Eu(III) mixed ligand complexes is a simple and effective approach to the improvement in the thermal stability, PL and EL properties of materials. A double-layer device with the configuration of ITO/TPD (50 nm)/Eu(DBM)3L3 (50 nm)/Mg0.9Ag0.1 (2.0 nm)/Ag (100 nm) exhibited Eu(III)-based pure red emission with a maximum brightness of 561 cd/m2.at 16 V, and an onset driving voltage of 8 V. A device with the configuration of ITO/TPD (50 nm)/[Eu(DBM)3L3 (5 nm):BCP (5 nm)]4/BCP (2. nm)/AIQ (10 nm) Mg0.9Ag0.9 (110 nm)/Ag (100 nm) gave high efficient and pure red light emission with a luminance of 1419 cd/m2. Keywords dibenzoylmethane - electroluminescence - lanthanide - N ligands

关键词： dibenzoylmethane electroluminescence lanthanide N ligands