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1.
The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance. 相似文献
2.
I. P. Kayumov 《Mathematical Notes》2005,78(3-4):498-502
In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z). 相似文献
3.
毛小兵 《南昌大学学报(理科版)》2003,27(1):23-25
对局部对称共形平坦黎曼流形中具有平坦法丛的极小子流形作了一些讨论,得到了极小子流形是全测地的两个充分条件。 相似文献
4.
The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions. 相似文献
5.
Cardy's formula for some dependent percolation models 总被引:2,自引:0,他引:2
F. Camia C. M. Newman V. Sidoravicius 《Bulletin of the Brazilian Mathematical Society》2002,33(2):147-156
We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton
corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice (with alternating
updates of two sublattices) [7]; it may also be realized on the triangular lattice 𝕋 with flips when a site disagrees with
six, five and sometimes four of its six neighbors.
Received: 24 December 2001 相似文献
6.
It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact
surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened
in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold
with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled
from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together
with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions.
Received: April 14, 2000; revised version: March 20, 2001 相似文献
7.
This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative. 相似文献
8.
Horst-Heino v. Borzeszkowski Hans-Jürgen Treder 《General Relativity and Gravitation》2002,34(11):1909-1918
The affine theory was conceived as a geometric model, wherein the connection field is the primary structure of the space-time. According to the program lying on the basis of this theory, metric and some sort of matter are somehow to be deduced from the connection field. In the present paper, we point out classical ways to a realization of this program. It is shown that, even in that case where the introduction of the metric seems to exclude the coupling of gravity to matter, the situation is not so hopeless as one may assume. In particular, for a symmetric Einstein tensor, it is answered the old question as to a self-consistent introduction of a metric and a metrical energy-momentum tensor controversially debated by Einstein, Eddington, and Weyl. 相似文献
9.
V. N. Dubinin 《Mathematical Notes》2006,80(1-2):31-35
It is shown that if P(z) = z n + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained. 相似文献
10.
Let
l
be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions 2=0.6240±0.0005±0.0011 and 3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions 2=5/8 and 3=35/24. 相似文献