Negative exterior curvature foliations on compact Riemannian manifolds

The topological structure of compact Riemannian manifolds that admit hyperbolic foliations is studied. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 673–676, November, 1997. Translated by S. S. Anisov     

Radiation damping in closed expanding universes

The dynamics of a coupled model (harmonic oscillator-relativistic scalar field) in Conformal Robertson-Walker (k = +1) spacetimes is investigated. The exact radiation-reaction equation of the source-including the retarded radiation terms due to the closed space geometry – is obtained and analyzed. A suitable family of Lyapunov functions is constructed to show that, if the spacetime expands monotonely, then the source's energy damps. A numerical simulation of this equation for expanding Universes, with and without Future Event Horizon, is performed.     

弹性波方程有限元模拟的曲边地表处理

本文对比研究了关于弹性波模拟中的曲边地表形状处理的两种方法,一种是用给定的实际介质数值划定的地表形状,另一种是用样条插值逼近地表形状.本文采用有限元方法进行弹性波数值模拟,给出了基于这两种方法计算的数值例子,并对结果进行了分析比较.结果表明使用后一种方法对地表进行处理时,地表人工离散产生的干扰明显减少,优于前一种方法.     

Analysis and design of mechanical crack arrestors for gas pipeline

Mechanical arrestors are frequently used in gas transmission pipelines to prevent the possibility of long running cracks. These arrestors have the effect of reducing the pipe from opening as the crack passes. This decreases the available crack driving force and, as a result, crack arrest may take place. This essentially is a second line of defence against catastrophic failure in the event crack initiation cannot always be prevented. A novel analyzing method presented in this paper has been developed to investigate the suitability of these crack arrestors. This is based on a fluid/structure/fracture interaction package, PFRAC. A dynamic finite element approach has been developed for a three dimension curved beam with initial plane curvature, which has been implemented in PFRAC to simulate the behaviour of the arrestor. The contact conditions between the pipe wall and the arrestor, along with the various computational procedures, are described. Several numerical results for a cracked pipe with arrestors are presented and compared with those for pipes without arrestors.     

Arithmetic cusp shapes are dense

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.      

Some Global Optimization Problems on Stiefel Manifolds

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.     

黎曼流形上不变集的分形维数估计

本文利用整体Lyapunov指数给出了光滑黎曼流形上C1-映射不变集的分形维数的上界.     

Counting Hyperbolic Manifolds with Bounded Diameter

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.     

紧致对称空间的热核、特征值和特征函数

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。