非定常Navier-Stokes方程加罚形式的两重网格算法

A two-grid method (TGM) for the fully discrete unsteady NavierStokes (N-S) equations in a penalty form is discussed. An error estimate is given,and a numerical test is also given to verify the correctness of theoretical analysis.     

A construction of unitary linear systems

A construction is made of a unitary linear system whose transfer function is a given power seriesB(z) with operator coefficients such that multiplication byB(z) is an everywhere defined transformation in the space of square summable power series with vector coefficients. A condition is also given for the existence of an observable linear system with such a transfer function. For both constructions properties of the spaces are given which imply essential uniqueness of linear systems with given transfer functions. A canonical conjugate-isometric linear system is uniquely determined by its transfer function whenever the state space is a Pontryagin space.     

A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

A generalized Milne-Thomson theorem

Using analytic continuation theory, a new simple proof of a standard generalized circle theorem is given. Additionally, new cases involving complex coefficients in the boundary condition and allowing for an arbitrary singularity of a given complex potential at the interface are considered.     

A remark on analytic continuation

A simple example is given to show that the space of germs obtained by analytic continuation of a given germ need not be a covering space in the topological sense.

     

A collection formula

A table of partially ordered sets, corresponding to the basis commutators (in Hall's sense) of weight 9, is given. On the basis of this table, the exponents in the collection formula can be found by elementary combinatorial methods. An example is given.Translated from Zapiski Nauchnykh Seminarov Leningardskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 59–63, 1974.     

A new proof of Frobenius theorem and applications

A proof of Frobenius theorem on local integrability of a given distribution on a finite or infinite dimensional manifold under weak differentiability conditions is given using holonomy methods and the curvature two form of the associated connection. The local curvature two form, which measures the non-integrability of a given distribution, is studied and a variety of applications are given. The Inverse Problem in the Calculus of Variations appears as a particular case.     

微分代数问题的一类数值算法

其中y和f的维数为l,u和g的维数为m.假定函数f和g具有如下要求的连续导数且矩阵g_y(y)f_u(t,y,u)具有有界逆矩阵,即存在M>0,使‖(g_y(y)f_u(t,y,u))~(-1)‖≤M.     

含双参数半线性奇异摄动问题的L~1一致收敛差分格式

1连续问题 考虑如下半线性边值问题∈y~n-μ(a(x)y)~1-d(x·y)=0.0相似文献   

ON A LEMMA OF BOWEN

We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.     

A Theory of Dimension

In which a theory of dimension related to the Jonesindex and based on the notion of conjugation is developed. Anelementary proof of the additivity and multiplicativity of thedimension is given and there is an associated trace. Applicationsare given to a class of endomorphisms of factors and to the theoryof subfactors. An important role is played by a notion of amenability inspired by the work of Popa.     

A dynamical characterization of contact circles

A simple dynamical condition is given for line fields within a contact structure, which is satisfied exactly by those line fields which are common kernels of contact circles. Some convexity properties are established which are useful in the study of contact circles up to homotopy. A necessary condition for extending a contact form to a contact circle is given. Based on work of Lisca–Matić and Honda, concrete examples are given which show that the condition is not just homotopic but a geometric one. The paper ends with an open question. Dedicated to Fernando Varela, for many reasons.     

A higher rank Lefschetz formula

Since the early seventies flows with the Lefschetz property were studied by several authors. In this paper a Lefschetz formula is proved for the geodesic flow of a compact locally symmetric space. The flow is described in terms of actions of split tori of various dimensions and the geometric side of the Lefschetz formula is a sum over closed geodesics which correspond to a given torus. The cohomological side is given in terms of Lie algebra cohomology.     

A Probe Method of Gradient Projection Type

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ：（Ｐ）　　ｍｉｎｘ∈Ｘｆ（ｘ）（１）ｗｈｅｒｅＸ＝｛ｘ｜ｘ∈Ｅｎ,ｇｊ（ｘ）≤０,ｊ＝１,２,…,ｍ;ｇｊ（ｘ）＝０,ｊ＝ｍ＋１,…,ｍ＋ｌ｝,ｌｅｔＩ＝｛１,２,…,ｍ｝,Ｌ＝｛ｍ＋１,…,ｍ＋ｌ｝．Ｆｏｒｔｈｅｐｒｏｂｌｅｍ（Ｐ）ｗｉｔｈＬ＝,ｍａｎｙｅｆｆｉｃｉｅｎｔｐｒｏｊｅｃｔｉｏｎｔｙｐｅａｌｇｏｒｉｔｈｍｓ［１－１１］ｈａｖｅｂｅｅｎｐｒｏｐｏｓｅｄ．Ｉｎ［１２］,…     

一个新的时间序列的插值模型

在这篇文章里,通过使用二次B样条,给出了一个用于数据挖掘的新的插值法方法,给出了时间序列的局部插值模型,插值曲线是C1连续的,该方法具有不需要解线性方程组的优点,应用上海股票指数进行了数值实验,实验性结果表明方法是有效的.     

运输问题的模糊聚类分析求解

通过对传统模糊聚类经验公式的改进和对最后两类排序的确定,提出了一种基 于模糊聚类分析的运输问题简单快速的求解方法．编出了通用程序,并给除了实例和计算 结果．该算法既是模糊聚类分析应用的扩展,又是对运筹学知识的补充和完善．     

多元凸函数的一个定理

本文在［１］的基础上．给出了与多元函数中值定理结论类似的一个定理．     

一种新的测地块的构造

本文给出了一种新的测地块的构造方法，这种方法不同于已有的所有方法，它是由ＢＤ设计和某些已知的测地块来构造的。同时肯定地回答了Ｐｌｅｓｎｉｋ提出是否存在不同于ＷＰｄ和Ｋｎ＾（ｉ）的测地块的问题。     

A general multiplier rule

A general multiplier rule which is an extension of the multiplier rule given by Hestenes is proved. This multiplier rule is applied to obtain the necessary conditions given by Neustadt for a solution to a canonical optimization problem which includes many optimal control problems as special cases.This research is part of a dissertation submitted in partial satisfaction of the requirements for the Ph.D. degree in mathematics at the University of California, Los Angeles. The author would like to express his appreciation to Dr. M. R. Hestenes for his guidance.     

一个新的数值积分公式

本文主要构造了一个数值积分公式,进一步研究了数值积分公式中的中间点的渐进性,基于中间点的渐进性质,得到了该数值积分公式的校正公式,最后给出数值试验,数值试验表明该公式的精度非常高。