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A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2, R)

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Chinese Annals of mathematics,Series B 1996年第1期17卷 81-88页

作者： XIAO CHANGBAI ZHENG WEIXING SU WEIYI (department of mathematics, nanjing university nanjing 210093, china.) nanjing UNIV DEPT MATHNANJING 210093PEOPLES R CHINA

A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal *** use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.

关键词： Inversion formula Zonal function Approximation kernel

Global dimension and left derived functors of Hom

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Science china mathematics 2007年第6期50卷 887-898页

作者： Li-xin MAO & Nan-qing DING Institute of mathematics, nanjing Institute of Technology, nanjing 211167, china department of mathematics, nanjing university, nanjing 210093, china 1. Institute of mathematics Nanjing Institute of Technology Nanjing 211167 China 2. department of mathematics Nanjing University Nanjing 210093 China

It is well known that the right global dimension of a ring R is usually computed by the right derived functors of Hom and the left projective resolutions of right R-modules. In this paper, for a left coherent and right perfect ring R, we characterize the right global dimension of R, from another point of view, using the left derived functors of Hom and the right projective resolutions of right R-modules. It is shown that rD(R) ? n (n ? 2) if and only if the gl right Proj-dim M R ? n?2 if and only if Ext n?1(N,M) = 0 for all right R-modules N and M if and only if every (n?2)th Projcosyzygy of a right R-module has a projective envelope with the unique mapping property. It is also proved that rD(R) ? n (n ? 1) if and only if every (n?1)th Proj-cosyzygy of a right R-module has an epic projective envelope if and only if every nth Proj-cosyzygy of a right R-module is projective. As corollaries, the right hereditary rings and the rings R with rD(R) ? 2 are characterized.

关键词： global dimension projective resolution envelope 16E10 16E30 16E05

Wavelet estimation of the diffusion coefficient in time dependent diffusion models

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Science china mathematics 2007年第11期50卷 1597-1610页

作者： Ping CHEN~(1,2+) Jin-de WANG~1 1 department of mathematics,nanjing university,nanjing 210093,china 2 School of Science,nanjing university of Science and Technology,nanjing 210094,china department of mathematics Nanjing University Nanjing 210093 China School of Science Nanjing University of Science Technology Nanjing 210094 China

The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time *** is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the *** paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz *** the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the Lr convergence rate.A strong consistency of the estimate is *** this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability *** example,in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.

关键词： wavelet estimation time-dependent diffusion coefficient linear growth condition strong consistency

HUBER'S M-ESTIMATOR ON UNDERDETERMINED PROBLEMS

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Journal of Computational mathematics 1995年第2期13卷 130-143页

作者： Wang Jia-song Tang Sheng-rong (department of mathematics, nanjing university, nanjing, china) 南京大学数学系江苏南京

After surveying the theoretical aspects of Huber's M-estimator on underdeter-mined problems, two finite algorithms are presented. Both proceed in a construc-tive manner by moving from one partition to an adjacent one. One of the algorithm,which uses the tuning constant as a continuation parameter, also has the facility to simultaneously estimate the tuning constant and scaling factor. Stable and efficient implementation of the algorithms is presented together with numerical results. The L1-norm problem is mentioned as a special case.

关键词： Za Pro HUBER’S M-ESTIMATOR ON UNDERDETERMINED PROBLEMS

On the Conditions of a Center and General Integrals of Quadratic Differential Systems

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Acta Mathematica Sinica,English Series 2001年第2期17卷 229-236页

作者： Wei Yin YE department of mathematics. nanjing Normal university. nanjing 210097, P. R. china Yan Qian YE department of mathematics. nanjing university, nanjing 210093, P. R. china department of mathematics Nanjing Normal University Nanjing 210097 P. R. China department of mathematics Nanjing University Nanjing 210093 P. R. China

We give the general integral of quadratic differential system with center in two cases under the Chinese classification.

关键词： Quadratic differential system Center General integral

A LINEARIZED DIFFERENCE SCHEME FOR THE KURAMOTO-TSUZUKI EQUATION

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Journal of Computational mathematics 1996年第1期14卷 1-7页

作者： Z.Z. Sun(department of mathematics and Mechanics, Southeast university, nanjing, china) SOUTHEAST UNIV DEPT MATH & MECHNANJINGPEOPLES R CHINA

In this paper, a linearized three-level difference scheme is derived for the mixed boundary value problem of Kuramoto-Tsuzuki equation, which can be solved by double-sweep method. It is proved that the scheme is uniqu... 详细信息

关键词： parabolic Southeast instead conduction derivative

Asymptotic bound on binary self-orthogonal codes

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Science china mathematics 2009年第4期52卷 631-638页

作者： DING Yang department of mathematics, Southeast university, nanjing 210096, china 1. department of mathematics Southeast University Nanjing 210096 China

We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the in-formation rate R = 1/2, by our constructive lower bound, the relative minimum distance δ≈ 0.0595 (for GV bound, δ≈ 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound.

关键词： algebraic geometry codes concatenated codes Gilbert-Varshamov bound Reed-Muller codes self-dual basis self-orthogonal codes 11T71

ABSOLUTELY E-PURE MODULES AND E-PURE SPLIT MODULES

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Acta Mathematica Scientia 2011年第1期31卷 207-220页

作者：阎舫宇 department of mathematics Nanjing University department of Basic Courses China Pharmaceutical University

We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.

关键词： Absolutely E-pure module E-pure split module IF ring copure flat module

ω-Gorenstein injective modules and dimensions

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Science china mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2 & DING NanQing3 1department of mathematics, Zhejiang university, Zhejiang 310027, china 2department of mathematics, Zhejiang university of Technology, Zhejiang 310023, china 3department of mathematics, nanjing university, nanjing 210093, china 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module