一类隐式偏微分方程的Dirichlet问题

给出了一类隐式偏微分方程的Dirichlet问题:g(x,Du(x))=0,a.e.x∈Ω,u(x)=φ(x),x∈ Ω,的弱解的存在性的充分条件.

一类隐式偏微分方程的边值问题

给出了一类具有线性约束的边值问题F(Du(x))=0, a.e. x∈Ω;L(D(x))=l, a.e. x∈Ω;u=, x∈ Ω的W1,∞(Ω,Rn)解的存在性的充分条件.

计算机对任意三维区域作正规网格剖分算法

详细介绍了一种三维复杂区域的正交差分网格的剖分方法。这种方法具有计算精度高、剖分速度快等特点。

数字照片修复

研究了照片修复问题,改进了纹理分析与合成、偏微分方程的照片修复的一般方法,编制了实验程序。

The Conformally Symmetric K-Contact Manifolds

In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.

Explicit Solutions for Generalized (2+1)-Dimensional Nonlinear Zakharov-Kuznetsov Equation

The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutionsof the Z-K equation are obtained.The methods used to solve the Z-K equation can be employed in further work toestablish new solutions for other nonlinear partial differential equations.

An effective quadrilateral mesh adaptation

Accuracy of a simulation strongly depends on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios and solution adaptive behaviour. It is not recommended to refine the parts of the domain where the solution shows little variation. It is desired to concentrate grid points and cells in the part of the domain where the solution shows strong gradients or variations. We present a simple, effective and com- putationally efficient approach for quadrilateral mesh adaptation. Several numerical examples are presented for supporting our claim.

A Power Penalty Approach to Numerical Solutions of Two-Asset American Options

This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.

Symbolic Computation of Extended Jacobian Elliptic Function Algorithm for Nonlinear Differential-Different Equations

The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.

量子論之今昔

此文初稿成於兩年以前,弃置箧衍,不復审视,所舉載籍,亦強半者作学生時所纂录。此间得书不易,雜誌尤尠,新知時論,寓目無多。改正時之所添附,殊嫌简略,亦有转录他书所引者,而尤以德文材料为最,然既以量子論之“今昔”名篇,亦欲留歷史意味之面目,故遂仍之。

基于U-Net卷积神经网络的纳米颗粒分割

为了准确测量纳米颗粒的尺寸,依据透射电子显微镜拍摄的纳米颗粒图像,提出了一种基于U-Net卷积神经网络的颗粒自动分割方法。将U-Net部分网络结构与批量归一化层相结合,减弱了网络对初始化的依赖,提升了训练速度。对纳米颗粒图像进行半隐式偏微分方程滤波以增强图像边缘信息,利用改进的U-Net网络训练纳米颗粒个体分割模型,得到了分割结果。研究结果表明,所提方法能准确分割出图像中的纳米颗粒,对边缘模糊和强度不均的纳米颗粒的分割效果提升显著。

人口指标的定量研究

《东北师大学报》(哲社版)1984年第5期载陈任昭的《我国人口指标的定量研究》一文中指出,近年来对人口问题的研究出现了人口发展过程的偏微分方程式。

Journal of Partial Differential Equations

Aims and Scope The Journal of Partial Differential Equations （JPDE） publishes research papers and short communications of high scientific quality in theory and applications including numerical analysis of partial differential equations. The main interest of the Journal is to encourage the research of partial differential equations, and to promote national and international exchange between partial differential equations, engineering, physics and different fields of mathematics.

威尔士斯旺西大学

英国威尔士斯旺西大学(University of Wales,Swansea)早在1920年就被英国皇家授权成立,历史悠久,是威尔士地区第二大传统大学。近几年来,西方就业市场正在进行一场对金融数学人才需求的革命。在伦敦、纽约、东京、新加坡、香港的金融市场,这一专业人才都急缺。斯旺西大学的金融数学是基于金融、数学和计算机三者的结合。目前,在英国只有极少的几个大学有金融数学硕士专业,而把金融、数学和计算机三者结合的授课式硕士点,全英只有斯旺西大学。本期将向读者重点介绍斯旺西大学的金融数学课程,为读者提供更多关于这一专业的信息。

Conformal vector fields on some Finsler manifolds

We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on R^n.

Talagrand's T_2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.

SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN R^n

This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.

Determinant Solutions to a (3+1)-Dimensional Generalized KP Equation with Variable Coefficients

1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.

DYNAMICS FOR VORTICES OF AN EVOLUTIONARY GINZBURG-LANDAU EQUATIONS IN 3 DIMENSIONS

This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away from the vortices, the author uses some measure theoretic arguments used by F. H. Lin in [16] to show the strong convergence of solutions.