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41.
We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.) 相似文献
42.
L. Bartosch P. Kopietz 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(1):29-36
We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals
for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln2-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions
to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e
4 appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω
2 which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω
1)1/2exp(- Ω
1/|ω|) at T = 0, where Ω
1 is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance
that can be compared with experiments.
Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002 相似文献
43.
Andreas Rößler 《BIT Numerical Mathematics》2006,46(1):97-110
A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance. 相似文献
44.
Andreas Rößler 《BIT Numerical Mathematics》2007,47(3):657-680
The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main
novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due
to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with
order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly.
AMS subject classification (2000) 65C30, 65L06, 60H35, 60H10 相似文献
45.
We introduce some relative versions of star selection principles first considered in [5], [11]. Some of the work extends results
from [4], [5] and gives some examples.
相似文献
46.
It is well known that S 12 cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective (dual) weak pigeonhole principle in S 12 for provably weaker function classes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
47.
In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random
variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables
with respect to the distant past. The results contribute to the clarification of the central limit question for stationary
sequences.
Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the
NSA grant H98230-05-1-0066. 相似文献
48.
Morgan A. Hanson 《Journal of Global Optimization》1991,1(3):287-293
The van der Waerden permanent problem was solved using mainly algebraic methods. A much simpler analytic proof is given using a new concept in optimization theory which may be of importance in the general theory of mathematical programming. 相似文献
49.
为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性:同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。 相似文献
50.
本文利用势井理论讨论一类非线性波动方程的初边值问题 .我们构造其稳定集 W和不稳定集 V,证明了当初值属于 W时 ,对 β∈ R整体弱解存在并且利用乘子法得到当 β>0解的指数衰减估计 ;当初值属于 V时 ,而 β<0时 ,解将爆破 相似文献