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991.
Humberto Terrones Alan L. Mackay 《Progress in Crystal Growth and Characterization of Materials》1997,34(1-4):25-36
With the discovery of C60 or Buckminsterfullerene a new kind of materials with important applications has emerged. Orginary graphite is composed of flat hexagonal layers. If pentagons are introduced, the graphite sheets start to curve in such a way that 12 pentagons are needed to close the structure and form fullerenes. Starting from the properties of 2D manifolds or surfaces, we have found that by introducing rings with more than six carbon atoms, periodic structures with the same topology as triply periodic minimal surfaces, we have found that by introducing rings with more than six carbon atoms, periodic structures with the same topology as triply periodic minimal surfacds can be constructed. The D, G, P, H and I-WP type surfaces have been obtained from graphite-like sheets. In terms of the Gaussian curvature K, ordinary and cylindrical graphite have K=O, Fullerenes have K>O and triply periodic surfaces decorated with graphite have K60. Geometric and physical properties of hypothetical periodic graphite foams will be discussed. 相似文献
992.
We consider a family of phase-field models that couples a Cahn-Hilliard with several Allen-Cahn equations. We show that such family of phase-field models possesses a maximal attractor with finite fractal dimension. 相似文献
993.
The linearly independent and minimal conjugated (LM-conjugated) circuits of benzenoid hydrocarbons play the central role in the conjugated circuit model. For a general case, the enumeration of LM-conjugated circuits may be tedious as it requires construction of all Kekule structures. In our previous work, a recursive method for enumeration of LM-conjugated circuits of benzenoid hydrocarbons was established. In this paper, we further extend the recursive formulae for enumerations of LM-conjugated circuits for both catacondensed benzenoid hydrocarbons and some families of structurally related pericondensed benzenoid hydrocarbons. 相似文献
994.
In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make the estimates on its fractal dimension and exponential attraction. 相似文献
995.
996.
旋转对称的广义Lorenz奇怪吸引子 总被引:8,自引:1,他引:7
阐述了计算微分方程组最大Lyapunov指数的技术,介绍了由一维可观察量计算系统关联维数的方法.利用Lyapunov指数作判据,通过坐标变换,构造了具有旋转对称性的广义Lorenz奇怪吸引子,分析了奇怪吸引子的运动特征并计算了奇怪吸引子的关联维数. 相似文献
997.
We construct inertial manifolds for a class of random dynamical systems generated by retarded semilinear parabolic equations subjected to additive white noise. These inertial manifolds are finite-dimensional invariant surfaces, which attract exponentially all trajectories. We study the corresponding inertial forms, i.e., the restriction of the stochastic equation to the inertial manifold. These inertial forms are finite-dimensional Ito equations and they completely describe the long-time dynamics of the system under consideration. The existence of inertial manifolds and the properties of inertial forms allow us to show that under mild additional conditions the system has a global (random) attractor in the sense of the theory of random dynamical systems. 相似文献
998.
It is proved that any subset of an (m-1)-dimensional sphere of volume larger than l(m+ 1) of the volume of the entire sphere contains l+ 1 points forming a regular l-dimensional simplex. As a corollary, it is obtained that, if the exterior of a given m-dimensional filled ellipsoid contains no more than the 1/(m+ 1) fraction of some sphere, then the volume of the ellipsoid is no less than the volume of the corresponding ball. The existence of a pair of points a given spherical distance apart in a set of positive measure is examined. 相似文献
999.
Theodore P. Hill Victor Perez-Abreu 《Annals of the Institute of Statistical Mathematics》2001,53(3):543-551
A general goodness-of-fit test for scale-parameter families of distributions is introduced, which is based on quotients of expected sample minima. The test is independent of the mean of the distribution, and, in applications to testing for exponentiality of data, compares favorably to other goodness-of-fit tests for exponentiality based on the empirical distribution function, regression methods and correlation statistics. The new minimal-moment method uses ratios of easily-calculated, unbiased, strongly consistent U-statistics, and the general technique can be used to test many standard composite null hypotheses such as exponentiality, normality or uniformity (as well as simple null hypotheses). 相似文献
1000.