共查询到20条相似文献,搜索用时 125 毫秒
1.
张洪申 《数学物理学报(A辑)》2006,26(3):337-342
单位圆内充满圆序列是一个复杂的问题,该文改进了现有一些证法,使单位圆内充满圆证法类似于平面上充满圆证法.同时得到单位圆内K-拟亚纯映射涉及重值的充满圆序列及相应的奇异半径 相似文献
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初中数学当中,圆是最优美的图形.它内涵丰富、性质多样.圆的性质定理有:圆的基本性质、垂径定理、圆周角性质定理、圆的对称性、圆的切线的性质等.它们对应了圆中的条基本辅助线. 相似文献
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笔者对相交圆内接蝶形进行探究时,得到了两个有趣的等积性质.为了陈述方便,先给出如下定义:定义 两圆相交,若一个圆的圆弧含于另一个圆内,则称此段圆弧为该圆的内弧;若一个圆的圆弧不含于另一个圆内,则称此段圆弧为该圆的外弧.其中内弧和外弧均不包含两圆交点.如图1所示,(⌒)AGB为圆O2的内弧,(⌒)ACB为圆O1的外弧. 相似文献
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笔者对相交圆内接蝶形进行探究时,得到了两个有趣的等积性质.定义两圆相交,若一个圆的圆弧含于另一个圆内,则称此段圆弧为该圆的内弧;若一个圆的圆弧不含于另一个圆内,则称此段圆弧为该圆的外弧.其中内弧和外弧均不包含两圆交点.如图1所示,(AGB)为⊙O2的内弧,ACB为⊙O1的外弧. 相似文献
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初中教科书在介绍圆和圆的位置关系时,给出了两圆相切的判定方法,即:设两圆的半径分别为R和r,圆心距为d,若d=R+r,则两圆外切;若d=R-r(R>r),则两圆内切.本文不妨统称为"圆心距法".下面介绍另一种判定方法,这里统称为"公切线法".一、两圆相切的判定1.两圆外切的判定过两圆的公共点作 相似文献
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单位圆内亚纯函数的充满圆 总被引:6,自引:0,他引:6
张庆德 《数学年刊A辑(中文版)》1999,(4)
本文推广了Ahlfors不等式,给出了亚纯函数的充满圆的一个几何特征,从而证明了单位圆内亚纯函数的充满圆序列的存在性.此外还举例说明了这些结果就充满圆的指数而言是最好的. 相似文献
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<正>圆是常见的几何图形之一,是进一步学习数学以及其他学科的重要基础.小学阶段初步学习了圆的概念,初中阶段系统地学习圆的概念和性质,高中阶段将继续学习圆的方程.由此可见圆在几何学习中的重要性.圆的有关性质是进一步研究圆与其他图形关系的主要依据,是学习圆的基础.近年来,圆的基本性质成为了广东省中考选择题、填空题或是解答题第24题的高频考点,也成了日常教学的重难点.1 教学目标本节课的教学任务是巩固圆中弧与角的关系, 相似文献
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Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep
under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the
experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological
creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the
stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation
and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem
confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between
the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction
in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference
in their porosity.
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.)
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000. 相似文献
12.
K. Petras 《Constructive Approximation》1998,14(2):231-245
We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain
complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented.
This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error
constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas
and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively
for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally
symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the
optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the
constant weight function and arguments outside the interval of integration.
September 7, 1995. Date revised: October 25, 1996. 相似文献
13.
Leonid Tolmatz 《Journal of Mathematical Analysis and Applications》2005,304(2):668-682
The double Laplace transform of the distribution function of the integral of the positive part of the Brownian bridge was determined by M. Perman and J.A. Wellner, as well as the moments of this distribution. The purpose of the present paper is to determine the asymptotics of this distribution for large values of the argument, and the corresponding asymptotics of the moments. 相似文献
14.
Güngör Gündüz 《The Journal of mathematical sociology》2013,37(3):167-187
In this work, mathematical models for the growth of the Ottoman and Roman Empires are found. The time interval considered for both cases covers the time from the birth of the empire to the end of the fast expansion period. These empires are assumed to be nonlinearly growing and self-multiplying systems. This approach utilizes the concepts of chaos theory, and scaling. The area governed by the empire is taken as the measure of its growth. It was found that the expansion of each empire on lands, seas, and on both (i.e., lands+seas) can be expressed by power laws. In the Ottoman Empire, the nonlinear growth power of total area is approximately equal to the golden ratio, and the nonlinear growth power of the expansion on lands is approximately equal to the square root of 2. In the case of the Romans, some numbers associated with the golden ratio, or the square root of 2, appear as the power of the nonlinear growth term. The appearance of both the golden ratio and the square root of 2 show that both empires had intention on achieving stability during their growth. 相似文献
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C. E. Ferreira A. Martin C. C. de Souza R. Weismantel L. A. Wolsey 《Mathematical Programming》1996,74(3):247-266
We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights
in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the
partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present
alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen
to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts.
In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem
parameters change. 相似文献
16.
尽管PROMETHEE是当前最受欢迎的多准则决策方法之一,但在实践应用过程中,模型的应用范围与质量依然受制于指标权重问题。一些常用的赋权方法,不仅没有解决不确定权重问题,反而增加了决策风险。在偏序集相关定理的基础上,给出权重的定性信息即权重次序,由流出矩阵、流入矩阵和净流矩阵等定义,得到了PROMETHEE的偏序集表达形式。当流入和流出之和为常数时,证明了模型存在对偶性质。根据对偶性质,简化了PROMETHEE方法的分析步骤,删减模型冗余信息。应用偏序集表示的PROMETHEE,突破了模型没有具体权重便无法应用的思维定势,解决了模型赋权困难,增强了模型的鲁棒性,拓展了模型处理数据类型的范围。 相似文献
17.
Joydeep Dutta 《TOP》2005,13(2):185-279
During the early 1960’s there was a growing realization that a large number of optimization problems which appeared in applications
involved minimization of non-differentiable functions. One of the important areas where such problems appeared was optimal
control. The subject of nonsmooth analysis arose out of the need to develop a theory to deal with the minimization of nonsmooth
functions. The first impetus in this direction came with the publication of Rockafellar’s seminal work titledConvex Analysis which was published by the Princeton University Press in 1970. It would be impossible to overstate the impact of this book
on the development of the theory and methods of optimization. It is also important to note that a large part of convex analysis
was already developed by Werner Fenchel nearly twenty years earlier and was circulated through his mimeographed lecture notes
titledConvex Cones, Sets and Functions, Princeton University, 1951. In this article we trace the dramatic development of nonsmooth analysis and its applications
to optimization in finite dimensions. Beginning with the fundamentals of convex optimization we quickly move over to the path
breaking work of Clarke which extends the domain of nonsmooth analysis from convex to locally Lipschitz functions. Clarke
was the second doctoral student of R.T. Rockafellar. We discuss the notions of Clarke directional derivative and the Clarke
generalized gradient and also the relevant calculus rules and applications to optimization. While discussing locally Lipschitz
optimization we also try to blend in the computational aspects of the theory wherever possible. This is followed by a discussion
of the geometry of sets with nonsmooth boundaries. The approach to develop the notion of the normal cone to an arbitrary set
is sequential in nature. This approach does not rely on the standard techniques of convex analysis. The move away from convexity
was pioneered by Mordukhovich and later culminated in the monographVariational Analysis by Rockafellar and Wets. The approach of Mordukhovich relied on a nonconvex separation principle called theextremal principle while that of Rockafellar and Wets relied on various convergence notions developed to suit the needs of optimization. We
then move on to a parallel development in nonsmooth optimization due to Demyanov and Rubinov called Quasidifferentiable optimization.
They study the class of directionally differentiable functions whose directional derivatives can be represented as a difference
of two sublinear functions. On other hand the directional derivative of a convex function and also the Clarke directional
derivatives are sublinear functions of the directions.
Thus it was thought that the most useful generalizations of directional derivatives must be a sublinear function of the directions.
Thus Demyanov and Rubinov made a major conceptual change in nonsmooth optimization. In this section we define the notion of
a quasidifferential which is a pair of convex compact sets. We study some calculus rules and their applications to optimality
conditions. We also study the interesting notion of Demyanov difference between two sets and their applications to optimization.
In the last section of this paper we study some second-order tools used in nonsmooth analysis and try to see their relevance
in optimization. In fact it is important to note that unlike the classical case, the second-order theory of nonsmoothness
is quite complicated in the sense that there are many approaches to it. However we have chosen to describe those approaches
which can be developed from the first order nonsmooth tools discussed here. We shall present three different approaches, highlight
the second order calculus rules and their applications to optimization. 相似文献
18.
The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products. 相似文献
19.
V. P. Stavrov V. V. Stavrov N. V. Pankova K. Friedrich 《Mechanics of Composite Materials》2000,36(2):155-162
The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final
composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned
fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions
formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned
fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity
of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the
internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective
permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation.
Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000. 相似文献
20.
Luigi Ingaliso 《Historia Mathematica》2011,38(2):232-247
The contributions made by the Italian mathematician Mario Pieri (1860-1913) are well known in the field of geometry. Pieri was a member of the School of Peano at the University of Turin. There he became engaged both by the problems of logic and by the philosophical aspects of Peano’s epistemology. This article was motivated by Pieri’s address given at the University of Catania, at the inauguration of the 1906-1907 academic year. My aim is to identify Pieri’s philosophical premises as found in his works and to present them in the general framework of the historical development of the Peano School. 相似文献