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Adaptive widths of the approximation functional on the Sobolev space W2~r with Gaussian measure

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Progress in Natural Science:Materials International 2002年第7期 28-33页

作者： fang gensun and YE Peixin(department of mathematics, beijing normal university, beijing 100875, china)

The tight orders for the Kolmogorov and adaptive ( n, ε, δ) -widths of the Sobolev spaces W2rrrrr equipped with a Gaussian measure in the Li-norm and Loo-norm are determined by the method of discretization, which is based on reducing the calculation of the ( n, ε, δ)-widths of the Sobolev space to the calculation of ( n, ε, δ)-widths of finite-dimensional set equipped with the Gaussian measure.

关键词： Kolmogorov (n eeeeeee 777777777)-widths non-adaptive and adaptive Gaussian measure.

Entropy number and non-linear approximations on multivariate Besov space by manifolds of finite pseudo-dimension

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Progress in Natural Science:Materials International 2006年第3期16卷 260-265页

作者： LONG Jingfan and fang gensun (School of Mathematical Sciences, beijing normal university, beijing 100875, china department of Computer Science, Information Technology Institute, beijing 100101, china) [a]School of Mathematical Sciences Beijing Normal University Beijing China [b]department of Computer Science Information Technology Institute Beijing China

We determine the asymptotic order of entropy number and optimal non -linear approximations of anisotropic periodic Besov class of Bpθr(Td') (1≤p≤∞,1≤0≤∞) by manifolds of finite pseudo-dimension in the metric Lq... 详细信息

关键词： Pseudo-dimension anisotropic Besov class of functions entropy number nonlinear width.

N-widths on the classes of multivariate bandlimited functions

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Progress in Natural Science:Materials International 2004年第10期14卷 23-26页

作者： fang gensun and LONG Jingfan (department of mathematics,beijing normal university,beijing100875,china) Received January30,2004 beijing normal Univ Dept Math Beijing 100875 Peoples R China

In this paper,the tight order on the n-widths of the classes of multivariate bandlimited functions in L p ( d ),1

关键词： n-width multivariate bandlimited function sampling theorem

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

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Acta Mathematica Scientia 2004年第2期24卷 228-234页

作者：马万房艮孙 departmentofmathematics BeijingNormalUniversityBeijing100875China

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So... 详细信息

关键词： Integral equations direct methods anisotropic sobolev classes

Exact n-width on the class of analytic functions in the space of continuous functions

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Progress in Natural Science:Materials International 2005年第8期15卷 761-764页

作者： fang gensun* and LI Xuehua(School of Mathematical Sciences, beijing normal university, beijing 100875, china) School of Mathematical Sciences Beijing Normal University Beijing 100875 China

Let ω(·) be a given concave modulus of continuity and ω(g,·) be the modulus of continuity of a function g∈C, where C is the space of 2π-periodic, continuous functions on with norm ‖f‖_C∶= maxt∈|f(t)|, r,ω__ ∞,β(r=0,1,2,…) denotes those 2π-periodic, real-valued functions f on that are analytic in the strip S_β∶=｛z∈:|Imz|0, and satisfy the restriction condition: ω(f (r),·)≤ω(·). In this paper, the exact n-width of the class of functions r,ω__ ∞,β in the space C is determined.

关键词： analytic function concave modulus of continuity n-width.

The ε-Complexity of the Approximate Solution of Integral Equations with Isotropic Kernels

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Acta Mathematica Sinica,English Series 2002年第4期18卷 679-686页

作者： Wan MA Gen Sun fang College of mathematics & Information Science of Wenzhou university, Wenzhou 325027, P. R. china department of mathematics, beijing normal university, beijing 100875, P. R. china College of mathematics & Information Science of Wenzhou university Wenzhou 325027 P. R. China department of mathematics Beijing Normal University Beijing 100875 P. R. China

The exact order of s-complexity is determined in L_p (2≤p≤∞) spaces for the second kind of Fredholm integral equations with kernels belonging to an isotropic Sobolev class.

关键词： Fredholm equation ε-complexity Sobolev classes

Particle tunnels across the horizon of Garfinkle-Horowitz-Strominger dilaton black hole

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Science china(Physics,Mechanics & Astronomy) 2007年第5期50卷 601-610页

作者： fang HengZhong1 & ZHAO Zheng2 1 department of Physics, china university of Petroleum, Dongying 257061, china 2 department of Physics, beijing normal university, beijing 100875, china department of Physics China University of Petroleum Dongying 257061 China department of Physics Beijing Normal University Beijing 100875 China

We promote the work of Parikh and Wilczek on the black hole radiation to the emission of massive and charged particles from Garfinkle-Horowitz-Strominger black hole. The energy and charge of the space-time are conservational during the course of the evaporation. The calculation shows that the emission spectrum is not precisely thermal, while has a correction, and the conclusion supports the view- point of information conservation.

关键词： Hawking radiation, black body spectrum, barrier, information loss, entropy of black hole, Komar energy

UNIQUENESS OF OPTIMAL QUADRATURE FORMULAS FOR W_1~m AND THE FUNDAMENTAL THEOREM OF ALGEBRA FOR PERIODIC MONOSPLINES

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Chinese Annals of mathematics,Series B 1990年第4期11卷 426-437页

作者：黄达人房艮孙 department of mathematics Zhejiang UniversityHangzhouZhejianghina. department of mathematics Beijing Normal UniversityBeijingChina.

This paper proves that the optimal quadrature formulas of type（r1,…rn） for Wm1 isunique,and the extremal function is characterized by its oscillatory *** theother hand,the fundamental theorem of algebra for periodi... 详细信息

关键词： quadrature oscillatory algebra formulas uniqueness whenever polynomial lemma 七势 isola

ONE-SIDED N-WIDTHS OF SOME CLASSES OF PERIODIC FUNCTIONS

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Analysis in Theory and Applications 1993年第4期9卷 21-36页

作者： fang gensun Zhang Jianhua beijing normal university,china 1. department of mathematics Beijing Normal University 100875 Beijing PRC

In this paper,we determine the exact estimation of one-sided n-widths d_n^+(w_q^r(p_r),L_1).q=1,∝, where W_q^r(P_r)is a class of differentiable 2π-periodic functions,and is determined by a differential opera- tor P_... 详细信息

关键词： Differential Operator Periodic Function Implicit Function Theorem Simple Zero Exact Estimation