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101.
102.
D. B. McReynolds 《Geometriae Dedicata》2007,129(1):47-55
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat n-manifold M, we show that the set of similarity classes of flat metrics on M which occur as a cusp cross-section of a hyperbolic (n + 1)-orbifold is dense in the space of similarity classes of flat metrics on M. The set used for density is precisely the set of those classes which arise in arithmetic orbifolds.
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103.
Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-known assignment problem. 相似文献
104.
105.
Robert Young 《Geometriae Dedicata》2005,116(1):61-65
Let ρ
n
(V) be the number of complete hyperbolic manifolds of dimension n
with volume less than V . Burger et al [Geom. Funct. Anal. 12(6) (2002), 1161–1173.] showed that when n ≥ 4 there exist a, b > 0 depending on the dimension such that aV log V ≤ log ρ
n
(V) ≤ bV log V, for V ≫ 0. In this note, we use their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number grows double-exponentially with volume. Additionally, this bound holds in dimension 3. 相似文献
106.
本文利用群表示论研究李群以及紧致对称空间的热核,特征值与特征函数.特别讨论了复格拉斯曼流形以及流形Sp(n)/U(n)上特征值及特征函数。 相似文献
107.
We prove some sharp isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We also relate them to inequalities involving the higher order mean-curvature integrals. Applications include some sharp eigenvalue estimates, Pólya-Szegö inequality, Faber-Krahn inequality, Sobolev inequality and some sharp geometric inequalities in some warped product spaces. 相似文献
108.
109.
The phenomenon of the chaotic boundary crisis and the related concept of the chaotic destroyer saddle has become recently a new problem in the studies of the destruction of chaotic attractors in nonlinear oscillators. As it is known, in the case of regular boundary crisis, the homoclinic bifurcation of the destroyer saddle defines the parameters of the annihilation of the chaotic attractor. In contrast, at the chaotic boundary crisis, the outset of the destroyer saddle which branches away from the chaotic attractor is tangled prior to the crisis. In our paper, the main point of interest is the problem of a relation, if any, between the homoclinic tangling of the destroyer saddle and the other properties of the system which may accompany the chaotic as well as the regular boundary crisis. In particular, the question if the phenomena of fractal basin boundary, indeterminate outcome, and a period of the destroyer saddle, are directly implied by the structure of the destroyer saddle invariant manifolds, is examined for some examples of the boundary crisis that occur in the mathematical models of the twin-well and the single-well potential nonlinear oscillators. 相似文献
110.
Hans-Otto Walther 《Journal of Dynamics and Differential Equations》2007,19(3):593-622
Automatic soft landing is modeled by a differential equation with state-dependent delay. It is shown that in the model soft
landing occurs for an open set of initial data, which is determined by means of a smooth invariant manifold.
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