广义山路引理的一些应用

具有(CPS)型条件的Ghoussoub-Preiss广义山路引理是经典的AmbrosettiRabinowitz山路引理的一个推广,本文将应用它来研究给定能量的具有对称性或非对称性势能的二阶哈密尔顿系统周期解的存在性.     

Some generalizations of Ahlfors Lemma

One of the most influential versions of the classical Schwarz–Pick Lemma is probably that of Ahlfors. Pulling back a conformal semimetric on a Riemann surface under any holomorphic map from the open unit disk equipped with a Poincaré metric, the curvature of which is assumed to bound from above the curvature of the Riemann surface, he successfully showed that a conformal semimetric to be compared with the Poincaré metric is obtained. In the present paper, we give a comparison theorem between two conformal semimetrics of variable curvature in the same spirit. Our main theorem is a local one by its nature, but global results can be derived therefrom.     

一个嵌入引理及其应用

本文讨论单位球上涉临界Sobolev指标的椭圆方程正解问题.通过建立第一Sobolev空间上对称函数到加权L_p空间的嵌入定理,给出问题的径向及非径向解.     

Schwarz引理的推广及其应用

引入Schwarz引理的一个最常见的推广定理,并且作出了详细的证明.同时以引理形式介绍了一个实用的复数性质,并且利用这两个引理,给出了开圆盘内解析函数的的实部,虚部以及模的估计式.     

Zorn's Lemma on Quasi-ordering Sets and Applications

Itiswell-knownthatZorn'slemma,Brezis-Browderorderingprincipleanditsgeneralizationshavebeenwidelyusedinmanysciencefields(see[1-7]).Nevertheless,theorderingrelationsinthesetheoremsmustberequiredtosatisfyreflexivity(thatis,x≤xforanyxY),transitivity(thatis,x5yandy5zforx,y,zEYimplyx5z),anti-symmetry(thatis,x5yandy5xforx,yEYimplyx=y),wherewestillcallthisorderingrelationSasemi--order,andtermthepair(Y,5)asemi-ordersetinwhichSdenotesasemi-order.ButineconomictheorysuchaseconomicequilibriumandPareto…     

有限元Aubin-Nitsche技巧新认识及其应用

首先回顾有限元理论中经典的Aubin-Nitsche技巧,并给出一个基于多尺度空间意义下的认识.然后基于这个新认识,重新得到一些依赖Aubin-Nitsche技巧的算法,使得Aubin-Nitsche技巧可以多次使用.作为例子,我们具体给出了在非对称椭圆方程和椭圆特征值问题方面的应用.     

Pang-Zalcman Lemma of Several Complex Variables and Its Applications

The Pang-Zalcman lemma is an important tool to study normal families of meromorphic functions. In this paper, we extend Pang-Zalcman lemma to the case of holomorphic functions of several complex variables and establish some normality criteria as applications. © 2020, Chinese Academy of Sciences. All right reserved.     

A Lemma On C 0 -semigroups And Applications

In this note we characterize a large class of C ₀-semigroups which can be applied to prove the existence and the uniqueness of the solutions of many systems of partial differential equations. In fact, we apply our result to a strongly damped wave equation, damped vibration of a string equation and reaction diffusion systems. Finally, we formulate an open problem.     

多复变Pang-Zalcman引理及应用

单复变中的Pang-Zalcman引理是研究亚纯函数正规族问题的重要工具.本文将该引理推广至多复变全纯函数的情形.作为应用建立了多复变全纯函数族的正规定则,改进和推广了相关结果.     

Farkas引理的几个等价形式及其推广

本文考虑了Farkas引理,Gordan引理及其拓展形式之间的关系,从理论上证明了其等价性并说明了Farkas引理在各种等价形式中的重要地位,并指出了Gordan引理实际是叮看作是Farkas引理的弱形式,然后研究了Farkas引理及其它形式在锥线性不等式组中的推广.     

拟凸域上沿某些方向的边界 Schwarz 引理*

本文直接利用全纯映照的性质研究边界Schwarz引理,建立了拟凸域上沿某些满足正定条件的方向的边界Schwarz引理. 文章推广了强拟凸域情形的主要结果,但是证明的方法是不一样的.     

梯度投影算子的广义陡度引理及其应用

在一般闭凸集上建立了梯度投影算子的广义陡度引理,利用它证明了几种松 弛搜索下梯度投影算法的全局收敛性、强收敛性以及若干良好的收敛性质.     

Poincaré's Lemma on Some Non-Euclidean Structures

The author proves the Poincar′e lemma on some(n + 1)-dimensional corank1 sub-Riemannian structures, formulating the(n-1)n(n~2+3 -2)/8 necessarily and sufficient y "curl-vanishing" compatibility conditions. In particular, this result solves partially an open problem formulated by Calin and Chang. The proof in this paper is based on a Poincar′e lemma stated on Riemannian manifolds and a suitable Ces`aro-Volterra path integral formula established in local coordinates. As a byproduct, a Saint-Venant lemma is also provided on generic Riemannian manifolds. Some examples are presented on the hyperbolic space and Carnot/Heisenberg groups.     

拉格朗日反演的q模拟与Bailey引理的注记

本文主要揭示了Gessel Ira.等给出的拉格朗日反演的q—模拟形式与An-drews G.E.的Bailey引理之间的相互转化的联系,做为例证,给出了利用这些关系得到的古典超几何级数(hypergeometric series)变换和求和公式的新证明,同时得到了模5、7、9、27四个新的Roger’s-Ramanujan类型的恒等式,其具有十分重要的组合意义。     

A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization

Random sampling is an efficient method to deal with constrained optimization problems in computational geometry. In a first step, one finds the optimal solution subject to a random subset of the constraints; in many cases, the expected number of constraints still violated by that solution is then significantly smaller than the overall number of constraints that remain. This phenomenon can be exploited in several ways, and typically results in simple and asymptotically fast algorithms. Very often the analysis of random sampling in this context boils down to a simple identity (the sampling lemma ) which holds in a general framework, yet has not been stated explicitly in the literature. In the more restricted but still general setting of LP-type problems , we prove tail estimates for the sampling lemma, giving Chernoff-type bounds for the number of constraints violated by the solution of a random subset. As an application, we provide the first theoretical analysis of multiple pricing , a heuristic used in the simplex method for linear programming in order to reduce a large problem to few small ones. This follows from our analysis of a reduction scheme for general LP-type problems, which can be considered as a simplification of an algorithm due to Clarkson. The simplified version needs less random resources and allows a Chernoff-type tail estimate. Received June 8, 2000, and in revised form September 10, 2000. Online publication March 26, 2001.     

The Lovász Local Lemma and Its Applications to some Combinatorial Arrays

The Lovász Local Lemma is a useful tool in the “probabilistic method” that has found many applications in combinatorics. In this paper, we discuss applications of the Lovász Local Lemma to some combinatorial set systems and arrays, including perfect hash families, separating hash families, ?-free systems, splitting systems, and generalized cover-free families. We obtain improved bounds for some of these set sytems. Also, we compare some of the bounds obtained from the local lemma to those using the basic probabilistic method as well as the well-known “expurgation” method. Finally, we briefly consider a “high probability” variation of the method, wherein a desired object is obtained with high probability in a suitable space.     

Bishop's Lemma

Bishop's Lemma is a centrepiece in the development of constructive analysis. We show that

• 1. its proof requires some form of the axiom of choice; and that
• 2. the completeness requirement in Bishop's Lemma can be weakened and that there is a vast class of non‐complete spaces that Bishop's Lemma applies to.

     

Blow-up Lemma

Regular pairs behave like complete bipartite graphs from the point of view of bounded degree subgraphs.     

Weight Lemma

In the paper, we give the first complete presentation of author’s proof of the Weight Lemma, which lies at the basis of the proof of Cartan’s conjecture from the theory of meromorphic curves.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 115–124.Original Russian Text Copyright © 2005 by E. I. Nochka.     

E小波乘子的某些应用

Let E=(1 1 1 -1) or (0 1 2 0). A measurable function v is called an E-waveletmultiplier if (rψ)v is an E-wavelet whenever ψ is an E-wavelet. Some characterizations and applications of E-wavelet multiplier were considered in [1]. In this paper, we give some other applications of E-wavelet multiplier, and prove that the set of all MRA E-wavelets is arcwise connected.