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non-isotropic weighted L^p estimates for the -equation on piecewise smooth strictly pseudoconvex domains

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Science China Mathematics 2008年第12期51卷 2161-2171页

作者： Heungju AHN Hong Rae CHO Jong-Do PARK Nims 3F TowerKoreana 628 Daeduk-Boulevard Yuseong-gu Department of Mathematics Pusan National University Department of Mathematics Seoul National University Department of Mathematics Pohang University of Science and Technology

In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversalit... 详细信息

关键词： non-isotropic norm Cauchy-Riemann equation piecewise strictly pseudoconvex domain

Spatial nonparametric Regression Estimation: non-isotropic Case

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 641-656页

作者： Zu-di Lu, Xing ChenInstitute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences. Beijing 100080, ChinaDepartment of Statistics, Yunnan University, Kunming 650091, China Institute of Systems Science Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing China Department of Statistics Yunnan University Kunming China

Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction are required.

关键词： Bandwidth kernel estimator mixing non-isotropic spatial data spatial conditional regression weak consistency and rates

Bubble Tree ConVergence for the Harmonic Sequence of Harmonic Surfaces in CP^n

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Acta Mathematica Sinica,English Series 2010年第7期26卷 1277-1286页

作者： Xiao Huan MO Fang SUN Key Laboratory of Pure and Applied Mathematics School of Mathematical Sciences Peking University Beijing 100871 P. R. China

We show that any harmonic sequence determined by a harmonic map from a compact Riemannian surface M to CP^n has a terminating holomorphic （or anti-holomorphic） map from M to CP^n, or a ＂bubble tree limit＂ consisti... 详细信息

关键词： bubble tree harmonic sequence non-isotropic energy identity

THE CHARACTERISTIC POLYNOMIAL OF A GEOMETRIC LATTICE IN SYMPLECTIC GEOMETRY OVER FINITE FIELDS

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Chinese Science Bulletin 1991年第12期36卷 974-978页

作者：陈冬生万哲先 Beijing Graduate School China University of Mining and Technology Beijing 100083 PRC Institute of Systems Science Academia Sinica Beijing 100080 PRC

Let F be a field and V= Vn（F）={（a1,…, an）|ai∈F} be the row vector space of finite dimension n over F. Let be a finite set ofsubspaces of Vsuch that U=（0）. And let L= L（（?）） be the set of intersections of dements of. Partial order L by reverse inclusion has V as its minimal element and as its set of atoms. We denote the partial order-

关键词： geometric lattice non-isotropic subspace characteristic polynomial.