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运用广义复变函数方法,通过构造适当的广义保角映射,研究了含有沿准周期方向穿透的半无限裂纹的一维正方准晶的反平面弹性问题,给出了在部分裂纹面上受均匀面外剪切时应力场和裂纹尖端应力强度因子的解析解.将此方法进一步推广到半无限裂纹垂直于一维正方准晶的准周期方向穿透的情形中,得到了相应的平面弹性问题的解析解.当准晶体的对称性增加时,还可以得出一维四方准晶相应问题的解析解. 相似文献
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本文根据微弹性结构线性理论研究了带空洞损伤的压力容器问题.解答是准静态的,其应力场为古典弹性力学关于球体对称压力容流问题应力解答,位移场和损伤场具有由于考虑损伤而表现出体积粘弹性特点. 相似文献
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在学习平面解析几何的“直线与圆”部分时,为了实现快速、简洁、准确解答“直线与圆”有关的问题,必须注意以下几个方面.1充分利用平面几何知识,实现问题快速解答很多直线与圆的问题,利用解析方法可以使问题得到解答,但若充分利用平面几何知识,则往往能使解法更加简捷.例1已知A 相似文献
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本文是著者在第一次全国微分方程学术会议上所作的综合性报告,经整理和补充而成.内容系介绍白尔氏的椭圆型偏微分方程的函数理论。白尔氏的理论的基础是准解析函数.本文分五段来进行:一,准解析函数;二,准解析函数与椭圆型偏微分方程理论;三,应用;四,准解析函数的起源与发展;五,与维库阿(N.H.Bekya)的工作的比较白尔氏以关系式: 相似文献
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基于现有空间曲线梁理论,考虑与扭转有关的翘曲变形和横向剪切变形的影响,建立了自然标架下空间曲线梁的内力和变形的解析解答.将该解答应用于受均布扭矩和竖向分布荷载的平面曲线梁的分析,将所得结果与Heins解答进行比较,证明了理论的正确.并应用该理论分析了解析式中翘曲和横向剪切变形项的影响. 相似文献
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关于概周期函数的准解析函数族的问题,已为李国平教授[1]—[3],Б.Левин教授[4]等所研究。本文,将应用[1]中关于整函数的一个结果,类似于[4]中的证明方法,得出一类概周期函数的准解析函数族。从[2]关于整函数的一个结果,直接推出下列引理: 相似文献
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Daniele C. Struppa 《Israel Journal of Mathematics》1986,54(1):60-70
We study spaces of “approximate solutions” to a given convolution equation. In particular we show how their quasianalyticity
can be reduced to the study of a suitably constructed Cauchy problem for related spaces. We give a unicity theorem for this
problem.
This paper is dedicated to the author’s son, Alessandro. The author has been partially supported by Ministero P.I., and G.N.S.A.G.A.
of Consiglio Nazionale delle Ricerche. 相似文献
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V. V. Napalkov K. V. Trunov R. S. Yulmukhametov 《Proceedings of the Steklov Institute of Mathematics》2006,253(1):115-122
We find conditions for the quasianalyticity at a boundary point of the Carleman function classes in a planar Jordan domain. 相似文献
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N. A. Shananin 《Mathematical Notes》2010,88(5-6):879-887
Known results about the unique continuation of solutions of anisotropic linear and weakly nonlinear differential equations and the extension of the invariance property of these solutions are applied to prove theorems about the fiberwise quasianalyticity and the fiber structure of sets of symmetry invariance of solutions to quasilinear equations. 相似文献
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V. V. Maimeskul 《Ukrainian Mathematical Journal》1993,45(7):1089-1100
Quasianalytic classes of functions in a Jordan domainG are defined. We consider classes of functions defined by conditions imposed on the decrease rate of the best uniform polynomial approximations and investigate the dependence of the quasianalyticity of these classes on the geometric structure of a domain.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 982–991, July, 1993. 相似文献
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《Expositiones Mathematicae》2022,40(3):679-757
We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney’s classical extension theorem, with special emphasis on the existence of continuous linear extension operators. The focus is on Denjoy–Carleman classes for which we develop the theory from scratch and discuss important related concepts such as (non-)quasianalyticity. It allows us to give an efficient and, to a fair extent, elementary introduction to Braun–Meise–Taylor classes based on their representation as intersections and unions of Denjoy–Carleman classes. 相似文献
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利用重排的方法找到了H~p空间的一类函数,这类函数的H~p范数和Lp范数是等价的(0p≤1).对于每一个f∈L~p(R~n),存在一个函数g∈H~p(R~n)满足其分布函数相等d_f=d_g,并且||g||Lp≤||g||H~p≤Cp||g||Lp.另外,还介绍了一种构造H~p空间的L~∞-原子的方法. 相似文献
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给定一个扩张矩阵A,得到了某些伴随于A的各向异性Hardy空间Hp(Rn)的分子特征刻画.作为其应用,还研究了与A相关的Calderón-Zygmund奇异积分算子和分数次积分算子在各向异性Hardy空间的有界性. 相似文献
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本文研究了二进求导极大算子的有界性.利用狄利克雷核的重要性质,构造了反例证明此极大算子在一维和二维情况下都不是从Hardy空间Hp到Hardy空间Hp有界的,其中0
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In this article we prove the property of unique continuation (also known for C∞ functions as quasianalyticity) for solutions of the differential inequality |Δu|?|Vu| for V from a wide class of potentials (including class) and u in a space of solutions YV containing all eigenfunctions of the corresponding self-adjoint Schrödinger operator. Motivating question: is it true that for potentials V, for which self-adjoint Schrödinger operator is well defined, the property of unique continuation holds? 相似文献