用条件(PW)刻画的幺半群

本文引入了条件(PW),讨论了条件(PW)与条件(P)、条件(PE)之间的关系,刻画了幺半群上S-系的平坦性.     

有限Boole语义中公式的条件随机真度

基于条件概率的思想,利用赋值集的随机化方法,在有限Boole语义中引入公式的条件随机真度,证明了条件随机真度的MP规则和HS规则。引入公式间的条件相似度和条件伪距离,建立了条件随机逻辑度量空间,证明了条件随机逻辑度量空间中逻辑运算的连续性,并初步研究了给定条件下的近似推理理论。     

关于一致半格的注记

首先证明了满足极大条件的无限链一定是一致半格.其次,通过探究一致半格与极大条件之间的关系,给出了一致半格为满足极大条件的无限链的充分必要条件.最后,讨论了一致半格与极小条件以及反一致半格与极大条件之间的内在关系,并且给出了相应的例子.     

L-矩阵的多参数预条件AOR迭代法

最近王广彬等人讨论了在预条件因子P=I+S′作用下的预条件AOR方法,推广了他们的预条件因子,提出了一个多参数的预条件因子P_α=I+S_α,并建立了新的预条件AOR迭代法与经典的AOR迭代法的比较定理.     

已有降维方法的推广

SAVE,PHD和SIRⅡ已被证明是有效的降维方法,这些方法基于下面的两个假设1线性条件和常数方差条件.但是,常数方差条件非常强.当常数方差不成立时,即使线性条件成立,SAVE,PHD和SIRⅡ经常会找到中心空间之外的方向.通过去掉了常数方差条件,在较弱条件下推广了SAVE,PHD和SIRⅡ从而使得在较弱的条件下,能得到中心空间的正确估计.     

模糊选择函数拟传递合理性的研究

本文在Georgescu模糊选择函数意义下,研究了一些模糊合理性条件之间的关系及模糊选择函数的拟传递合理性。首先,给出了模糊选择函数合理性条件FA1,条件FA2与条件Fγ的定义,研究了模糊选择函数G-合理性与条件FA1之间的关系。其次对合理性条件FA2,条件FPI及条件Fδ之间的关系进行了详细的讨论。最后得出了模糊选择函数拟传递合理的三个充分条件。     

全概率公式的推广

首先给出了普通事件在普通条件和Fuzzy条件下的Fuzzy条件概率及Fuzzy事件在普通条件和Fuzzy条件下的Fuzzy条件概率公式,并通过对普通事件的全概率公式进行推广,得到普通事件和Fuzzy事件分别在普通划分和Fuzzy划分下的全概率公式     

常型Sturm-Liouville问题的左定边值条件

本文刻画了常型Sturm-Liouville问题的左定边值条件．通过Sturm-Liouville微分算式的系数、区间端点以及边值条件给出了其左定性的充要条件．应用自伴边值条件分类,确切地给出了所有可能的左定边值条件．     

矩条件下的任意随机变量序列的一类强极限定理

本文利用随机变量的截尾方法和条件三级数定理,研究了任意随机变量序列在矩条件下的一类强极限定理,改进了与此相应的一些结果的条件.     

模糊选择函数拟传递合理性的研究

本文在Georgescu模糊选择函数意义下,对模糊合理性条件及拟传递合理性进行了深入研究。首先给出了模糊选择函数合理性条件FC1、条件FC2、条件FC3、条件FC4及条件FC5的定义并且重新定义了条件Fδ;其次讨论了它们与拟传递合理之间的关系;最后得出了模糊选择函数拟传递合理的一些充分条件及一个充要条件。     

Signature invariants of covering links

We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.

     

NUMERICAL SOLUTIONS OF PARABOLIC PROBLEMS ON UNBOUNDED 3-D SPATIAL DOMAIN

In this paper,the numerical solutions of heat equation on 3-D unbounded spatial do-main are considered. n artificial boundary Γ is introduced to finite the computationaldomain.On the artificial boundary Γ,the exact boundary condition and a series of approx-imating boundary conditions are derived,which are called artificial boundary conditions.By the exact or approximating boundary condition on the artificial boundary,the originalproblem is reduced to an initial-boundary value problem on the bounded computationaldomain,which is equivalent or approximating to the original problem.The finite differencemethod and finite element method are used to solve the reduced problems on the finitecomputational domain.The numerical results demonstrate that the method given in thispaper is effective and feasible.     

Analysis of artificial boundary conditions for exterior boundary value problems in three dimensions

Summary. Simple boundary conditions on an artificial boundary are discussed, then an exact boundary condition on the artificial boundary is obtained. Approximation to this boundary condition with high accuracy is given, and the error estimates are obtained. A numerical example is presented, and the numerical results are compared with the exact solution. Received January 27, 1997 / Revised version received May 14, 1999 / Published online February 17, 2000     

On viscous incompressible flows of nonsymmetric fluids with mixed boundary conditions

In this paper we are concerned with the initial boundary value problem for the micropolar fluid system in nonsmooth domains with mixed boundary conditions. The considered boundary conditions are of two types: Navier’s slip conditions on solid surfaces and Neumann-type boundary conditions on free surfaces. The Dirichlet boundary condition for the microrotation of the fluid is commonly used in practice. However, the well-posedness of problems with different types of boundary conditions for microrotation are completely unexplored. The present paper is devoted to the proof of the existence, regularity and uniqueness of the solution in distribution spaces.     

Solution for a problem of linear plane elasticity with mixed boundary conditions on an ellipse by the method of boundary integrals

A numerical boundary integral scheme is proposed for the solution of the system of field equations of plane, linear elasticity in stresses for homogeneous, isotropic media in the domain bounded by an ellipse under mixed boundary conditions. The stresses are prescribed on one half of the ellipse, while the displacements are given on the other half. The method relies on previous analytical work within the Boundary Integral Method [1], [2].The considered problem with mixed boundary conditions is replaced by two subproblems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way and the problem at this stage is reduced to the solution of a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution inside the domain, and the unknown boundary values of stresses or displacements on proper parts of the boundary.On the basis of the obtained results, it is inferred that the tangential stress component on the fixed part of the boundary has a singularity at each of the two separation points, thought to be of logarithmic type. A tentative form for the singular solution is proposed to calculate the full solution in bulk directly from the given boundary conditions using the well-known Boundary Collocation Method. It is shown that this addition substantially decreases the error in satisfying the boundary conditions on some interval not containing the singular points.The obtained results are discussed and boundary curves for unknown functions are provided, as well as three-dimensional plots for quantities of practical interest. The efficiency of the used numerical schemes is discussed, in what concerns the number of boundary nodes needed to calculate the approximate solution.     

Duffing型方程组的边界值问题的解的存在性

给出了带Dirichlet边界条件、Neumann边界条件和周期边界条件的Duffing型方程组的两点边界值问题的解的几个存在性定理。     

An Algorithm of Linear Combinations: Thermal Conduction

This paper presents computational algorithms that make it possible to overcome some difficulties in the numerical solving boundary value problems of thermal conduction when the solution domain has a complex form or the boundary conditions differ from the standard ones. The boundary contours are assumed to be broken lines (the 2D case) or triangles (the 3D case). The boundary conditions and calculation results are presented as discrete functions whose values or averaged values are given at the geometric centers of the boundary elements. The boundary conditions can be imposed on the heat flows through the boundary elements as well as on the temperature, a linear combination of the temperature and the heat flow intensity both at the boundary of the solution domain and inside it. The solution to the boundary value problem is presented in the form of a linear combination of fundamental solutions of the Laplace equation and their partial derivatives, as well as any solutions of these equations that are regular in the solution domain, and the values of functions which can be calculated at the points of the boundary of the solution domain and at its internal points. If a solution included in the linear combination has a singularity at a boundary element, its average value over this boundary element is considered.     

一类非线性奇摄动方程解的渐近表示

应用匹配渐近方法讨论一类非线性奇异摄动方程的边值问题解的渐近表示,得到了边界层或冲击层解的刻画,阐述了边界参数对边界层或冲击层位置的影响.     

Absorbing boundary conditions for electromagnetic wave propagation

In this paper, the theoretical perfectly absorbing boundary condition on the boundary of a half-space domain is developed for the Maxwell system by considering the system as a whole instead of considering each component of the electromagnetic fields individually. This boundary condition allows any wave motion generated within the domain to pass through the boundary of the domain without generating any reflections back into the interior. By approximating this theoretical boundary condition a class of local absorbing boundary conditions for the Maxwell system can be constructed. Well-posedness in the sense of Kreiss of the Maxwell system with each of these local absorbing boundary conditions is established, and the reflection coefficients are computed as a plane wave strikes the artificial boundary. Numerical experiments are also provided to show the performance of these local absorbing boundary conditions

     

Improved boundary treatment for the smoothed particle hydrodynamics method using implicit surfaces

The boundary treatment for modeling complex geometries in smoothed particle hydrodynamics (SPH) methods is always challenging, especially for objects with sharp corners. In this paper, we propose an improved boundary treatment technique to handle boundary conditions in the SPH method where objects are represented as implicit surfaces. The improved boundary treatment technique provides a full treatment for complicated geometries and can handle sharp edges without any special treatment. The boundary particles are uniformly distributed in compliance with the curvature of the objects, therefore taking into consideration the effect of the boundary. Several simulations are presented to validate and demonstrate the applicability and versatility of the proposed technique.