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51.
Frank Morgan 《Annals of Global Analysis and Geometry》2006,30(1):73-79
In a product M
1 × M
2 of Riemannian manifolds, the least perimeter required to enclose given volume among general regions is at least 1/√ 2 times that among regions of product form, assuming that the isoperimetric profiles of M
1 and M
2 are concave. This result sharpens earlier work of Grigor'yan, generalizes results of Bollobás and Leader and of Barthe, and yields a lower bound on the Cheeger isoperimetric constant of a product. 相似文献
52.
Boniface Nkemzi 《Mathematical Methods in the Applied Sciences》2006,29(9):1053-1080
This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
53.
We demonstrate the potential of femtosecond two-color pulse interferometry for in vitro optical glucose monitoring, by dispersion of the group refractive index in a glucose solution sample with respect to a red-color
light and a blue-color light. By comparison with femtosecond one-color pulse interferometry, the basic performance of the
present system with regard to sensitivity, quantitativeness, and tolerance to surrounding disturbances, is evaluated. The
resulting accuracy and precision of glucose determination are 77 and 118mg/dl for 10-mm-sample-thickness, respectively. This
near-common-path configuration of the two-color pulse light provides good stability to fluctuations of sample temperature,
which is important in clinical applications. Considering the performance of femtosecond two-color pulse interferometry as
an optical glucose sensor, a suitable measurement site for in vivo optical glucose monitoring is discussed. 相似文献
54.
Eckhard Steffen 《Discrete Mathematics》2004,280(1-3):191-214
Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let ck be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r3=|E|−c3 and
. We show that on one side r3 and r2 bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r3 and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr3. For k=2,3, let ζk denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other. 相似文献
55.
Pingan Zeng Jiaquan Liu Yuxia Guo 《Journal of Mathematical Analysis and Applications》2004,300(1):102-128
In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero. 相似文献
56.
岳华 《数学的实践与认识》2003,33(6):96-104
本文证明了可分无穷维 Hilbert空间上每个有界线性算子均可写成两个强不可约算子之和 .这回答了文献 [9]中提出一个公开问题 相似文献
57.
In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C1[0,1]∩C2(0,1) or C[0,1]∩C2(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed. 相似文献
58.
59.
60.
用迈克耳逊干涉仪测量气体折射率的误差的研究 总被引:1,自引:0,他引:1
研究在用迈克尔逊干涉仪测量气体折射率时存在的系统和方法误差,提出了误差修正方法。 相似文献