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Characteristic finite element scheme and analysis the three-dimensional two-phase displacement semi-definite problem

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Chinese Science Bulletin 1997年第1期42卷 17-22页

作者： YUAN YirangInstitute of mathematics, shandong university, jinan 2.0100, china Institute of mathematics Shandong University Jinan China

NUMERICAL simulation of the two-phase (oil and water) displacement problem is the mathematical basis of energy sources. For two-dimensional positive problem, Douglas et al. put forward the well-known characteristic finite difference method and characteristic finite element method. However, for numerical analysis there exist some difficulties. They assumed that the problem is periodic and the diffusion matrix of the concentration equation is positive difinite

关键词： two-phase displacement three-dimensional semi-definite characteristic finite element convergence.

Existence and uniqueness for BSDE with stopping time

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Chinese Science Bulletin 1998年第2期43卷 96-99页

作者： CHEN Zengjing Department of mathematics, shandong university, jinan 2.0100, china Department of mathematics Shandong University Jinan China

The existence and uniqueness of the solutions for a class of backward stochastic differential equations (BSDEs for short) in a random interval are discussed.

关键词： BSDE stopping time adapted solution.

Almost every graph has a fixed edge

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Chinese Science Bulletin 1998年第2期43卷 99-101页

作者： FAN Hongbing Department of mathematics, shandong university, jinan 2.0100, china Department of mathematics Shandong University Jinan China

An edge e of a graph G is called a fixed edge if G-e+e′ G implies e′=e, and an isomorphic fixed edge if G-e+e′ G implies that there exists an automorphism of G-e, which maps the ends of e to the ends of e′. It is proved that almost every graph is with all its edges as fixed edges and isomorphic fixed edges, and it is conjectured that all graphs contain isomorphic fixed edges.

关键词： graph isomorphism automorphism group fixed edge.

THE GOLDBACH-VINOGRDOV THEOREM WITH THREE PRIMES IN A THIN SUBSET

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Chinese Annals of mathematics,Series B 1998年第4期19卷 479-488页

作者： LIU JIANYA (Department of mathematics, shandong university, jinan 2.0100, china.) 山东大学数学系山东济南

It is proved constructively that there exists a thin subset S of primes, satisfying for some absolute constant c＞0, such that every sufficiently large odd integer N can beLet r be prime, and hi positive integers with (bj, r) = 1,j = 1, 2, 3. It is also proved that, for almost all prime moduli r＜ log- N, every sufficiently large odd integer N = b1 + b2 +ba(modr) can be represented as where c ＞ 0 is an absolute constant.

关键词： Goldbach-Vinogradov theorem Exponential sum Primes Arithmetic progression Mean-value theorem

LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

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Journal of Computational mathematics 2002年第2期20卷 153-164页

作者： Dan-ping Yang (School of mathematics and System Science, shandong university, jinan 2.0100, china) School of mathematics and System Science Shandong University Jinan 250100

Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio... 详细信息

关键词： least-squares algorithm mixed finite element nonlinear parabolic problems convergence analysis

The extension of the first main theorem for π-blocks

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Science china mathematics 2006年第5期49卷 620-625页

作者： HAI Jinke Department of mathematics, Qingdao university, Qingdao 266071, china College of mathematics ,shandong university, jinan 2.0100, china Department of mathematics Qingdao University Qingdao China College of mathematics Shandong University Jian China

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

关键词： π-block, π-separable group, π-regular classes, defect group.

MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROL SYSTEM WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE

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Journal of Systems Science & Complexity 2010年第2期23卷 219-231页

作者： Jingtao SHI·Zhen WU School of mathematics,shandong university,jinan 2.0100,china. School of mathematics Shandong University Jinan China

Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are *** control variableis allowed to enter both diffusion and jump *** result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization *** expressionof the optimal portfolio selection strategy is obtained in the state feedback form.

关键词： Forward-backward stochastic control system maximum principle Poisson random measure recursive utility stochastic optimal control.

Adaptive bidirectional diffusion for image restoration

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Science china(Information Sciences) 2010年第12期53卷 2452-2460页

作者： FU ShuJun 1,2 & ZHANG CaiMing 1 1 School of Computer Science and Technology, shandong university, jinan 250101, china 2 School of mathematics, shandong university, jinan 2.0100, china School of Computer Science and Technology Shandong University Jinan China School of mathematics Shandong University Jinan China

A large number of applications in image processing and computer vision depend on image quality. In this paper, combining the forward diffusion with the backward diffusion by different weights, we present an adaptive bidirectional diffusion method for image denoising and deblurring simultaneously. Further, we introduce a gradient factor into the data fidelity term, which forms a spatially varying constraint and allows a better restoration of image edges and fine details. In order to obtain a stable solution, we develop a numerically stable scheme and give its theoretical analysis. Finally, we show advantages of this method in deblurring edges, denoising and restoring fine details of image compared with other related methods in experiments.

关键词： image restoration bidirectional diffusion inverse diffusion anisotropic diffusion stabilizing scheme spatially varying constraint

Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations

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Science china mathematics 2009年第7期52卷 1391-1411页

作者： PENG ShiGe Institute of mathematics,shandong university,jinan 2.0100,china Institute of mathematics Shandong University Jinan China

This is a survey on normal distributions and the related central limit theorem under sublinear *** also present Brownian motion under sublinear expectations and the related stochastic calculus of It's *** results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.

关键词： probability and distribution uncertainty normal distribution Brownian motion central limit theorem 60H10 60H05 60H30 60E05 60E07 62C05 62D05