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Superprocesses arising from interactive stochastic flows

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Science China Mathematics 2006年第4期49卷 451-476页

作者： YAN Guojun & LI Zhanbing Medical School, Shantou University, Shantou 515063, China Department of Mathematics, Bejing Normal University, Beijing 100875, China Medical School Shantou University Shantou China Department of Mathematics Bejing Normal University Beijing China

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also g...

关键词： superprocess, interactive stochastic flows, martingale problem, dual processes.

Multiple solutions for a class of nonlinear elliptic equations on the Sierpinski gasket

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Science China Mathematics 2004年第5期47卷 772-786页

作者： HU Jiaxin Department of Mathematical Sciences Tsinghua University Beijing 100084 China

This paper investigates a class of nonlinear elliptic equations on a fractal domain. We establish a strong Sobolev-type inequality which leads to the existence of multiple non-trivial solutions of △u+ c(x)u = f(x, u), with zero Dirichlet boundary conditions on the Sierpihski gasket. Our existence results do not require any growth conditions of f(x,t) in t, in contrast to the classical theory of elliptic equations on smooth domains.

关键词： Sierpinski gasket, energy form, Laplacian operator, eigenvalue problem, genus, weak solution.

Binocular fusion in Panum's limiting case of stereopsis obeys the uniqueness constraint

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Science China(Life Sciences) 2001年第1期44卷 40-48页

作者：王志宏吴新年倪睿汪云九 Laboratory of Visual Information Processing Institute of Biophysics Beijing China Center for Brain and Mind Sciences Chinese Academy of Sciences Beijing China

In the information processing procedure of stereo vision, theuniqueness constraint has been used as one of the constraints to solve the "correspondence problem". While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum's limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum's limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum's limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum's limiting case and that the uniqueness constraint is still valid.

关键词： uniqueness constraint, Panum's limiting case, visual direction, orientation disparity, correspondence problem, psychophysics.

A new algorithm for pole assignment of single-input linear systems using state feedback

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Science China Mathematics 2005年第3期48卷 307-321页

作者： QIAN Jiang CHENG Mingsong XU Shufang LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

In this paper we present a new algorithm for the single-input pole assignment problem using state feedback. This algorithm is based on the Schur decomposition of the closed-loop system matrix, and the numerically stable unitary transformations are used whenever possible, and hence it is numerically *** good numerical behavior of this algorithm is also illustrated by numerical examples.

关键词： pole assignment problem, numerical method, Schur decomposition.

General inverse of Stokes, Vening-Meinesz and Molodensky formulae

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Science China Earth Sciences 2006年第5期49卷 499-504页

作者： CHENG Luying1,2 & XU Houze1 1. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China 2. Xi’an Research Institute of Surveying and Mapping, Xi’an 710054, China Institute of Geodesy and Geophysics Chinese Academy of Sciences Wuhan China Xi’an Research Institute of Surveying and Mapping Xi’an China

The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes’ formula, the general inverse Vening-Meinesz formula and the general Molodensky’s formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degen- erated into the classic ones.

关键词： spherical harmonics, boundary value problem, general inverse Stokes' formula, general inverse Vening-Meinesz formula, general Molodensky's formula.

Extremal problems on the Hua domain of the first type

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Science China Mathematics 2005年第Z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping Mathematics Department, Xuzhou Normal University, Xuzhou 221116, China Mathematics Department, Capital Normal University, Beijing 100037, China Mathematics Department Xuzhou Normal University Xuzhou China Mathematics Department Capital Normal University Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

Boundary value problems of discrete generalized Emden-Fowler equation

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Science China Mathematics 2006年第10期49卷 1303-1314页

作者： YU Jianshe GUO Zhiming College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China

By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.

关键词： discrete generalized Emden-Fowler equation, boundary value problem, Saddle Point Theorem, discrete variational theory.

CR Geometry in 3-D(Dedicated to Professor Haim Brezis with admiration)

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Chinese Annals of Mathematics,Series B 2017年第2期38卷 695-710页

作者： Paul C.YANG department of mathematics princeton universityFine HallW ashington RoadPrinceton NJ 08544 USA.

CR geometry studies the boundary of pseudo-convex manifolds. By concentrating on a choice of a contact form, the local geometry bears strong resemblence to conformal geometry. This paper deals with the role conformally invariant operators such as the Paneitz operator plays in the CR geometry in dimension three. While the sign of this operator is important in the embedding problem, the kernel of this operator is also closely connected with the stability of CR structures. The positivity of the CR-mass under the natural sign conditions of the Paneitz operator and the CR Yamabe operator is discussed. The CR positive mass theorem has a consequence for the existence of minimizer of the CR Yamabe problem. The pseudo-Einstein condition studied by Lee has a natural analogue in this dimension, and it is closely connected with the pluriharmonic *** author discusses the introduction of new conformally covariant operator P-prime and its associated Q-prime curvature and gives another natural way to find a canonical contact form among the class of pseudo-Einstein contact forms. Finally, an isoperimetric constant determined by the Q-prime curvature integral is discussed.

关键词： Paneitz operator, Embedding problem, Yamabe equation, Mass,P-prime, Q-prime curvature

Mathematical Model for the Continuous Vacuum Drying

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Journal of Donghua University(English Edition) 2002年第2期19卷 103-106页

作者：戴惠良 Coll. of Mech. Eng. Dong Hua Univ. Shanghai 200051 China

An improved mathematical model for the continuous vacuum drying of highly viscous and heatsensitive foodstuffs was proposed, The process of continuous vacuum drying was presented as a moving boundary problem of moisture evaporation in cylindrical coordinates. Boundary condition of the first kind for the known functional dependence of the drying body surface temperature on time was considered. Finally, the appropriate system of differential equations was solved numerically and the values of drying rate, integral moisture content of the material, moving boundary position as well as temperature in any point of the material and at any moment time were obtained. This procedure was applied to continuous vacuum drying of foods such as natural cheese and fresh meat paste.

关键词： Radioactive heat, conductive heat, heat-sensitive foods, moving boundary problem, theoretical analysis,experimental apparatus