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341.
We study analytically and numerically the propagation of spatial solitons in a two-dimensional strongly nonlocal nonlinear medium. Exact analytical solutions in the form of self-similar spatial solitons are obtained involving higher-order Hermite-Gaussian functions. Our theoretical predictions provide new insights into the low-energy spatial soliton transmission with high fidelity. 相似文献
342.
A. Hof 《Journal of statistical physics》1993,72(5-6):1353-1374
We consider Schrödinger operators onl
2(
) with deterministic aperiodic potential and Schrödinger operators on the l2-space of the set of vertices of Penrose tilings and other aperiodic self-similar tilings. The operators onl
2(
) fit into the formalism of ergodic random Schrödinger operators. Hence, their Lyapunov exponent, integrated density of states, and spectrum are almost-surely constant. We show that they are actually constant: the Lyapunov exponent for one-dimensional Schrödinger operators with potential defined by a primitive substitution, the integrated density of states, and the spectrum in arbitrary dimension if the system is strictly ergodic. We give examples of strictly ergodic Schrödinger operators that include several kinds of almost-periodic operators that have been studied in the literature. For Schrödinger operators on Penrose tilings we prove that the integrated density of states exists and is independent of boundary conditions and the particular Penrose tiling under consideration. 相似文献
343.
344.
We study various dimensions of spaces with nonpositive curvature in the A. D. Alexandrov sense, in particular, of ?-trees. We find some conditions necessary and sufficient for the metric space to be an ?-tree and clarify relations between the topological, Hausdorff, entropy, and rough dimensions. We build the examples of ?-trees and CAT(0)-spaces in which strict inequalities between the topological, Hausdorff, and entropy dimensions hold; we also show that the Hausdorff and entropy dimensions can be arbitrarily large while the topological dimension remains fixed. 相似文献
345.
Toshiro Watanabe 《Journal of Theoretical Probability》2002,15(3):631-665
Natural examples of increasing shift self-similar additive random sequences are constructed, which are associated with supercritical branching processes. The rate of growth and the distributional properties of them are studied in terms of the offspring distributions of the supercritical branching processes. The results are applied to two types of laws of the iterated logarithm for a Brownian motion on the unbounded Sierpinski gasket. An extension of the Bingham–Doney–de Meyer theorem on the limits of supercritical branching processes is also proved. 相似文献
346.
我们提出了二维自相似变换理论,以聚焦的(2+1)维NLS方程(数学称为抛物型的非线性微分方程)为模型,构建了它被转变为聚焦的(1+1)维NLS方程的二维自相似变换,深入研究了它的空间怪波激发,发现除了(1+1)维NLS方程的Peregrine孤子、高阶怪波和多怪波诱导的线怪波所具有的短寿命特征外,由Akhmediev呼吸子(AB)和Kuznetsov-Ma孤子(KMS)诱导的线怪波也具有这种短寿命特征.这与由亮孤子(包括多孤子)诱导的空间相干结构保持形状和幅值不变的演化特征完全不同.通过图示展现了本文例举的各类线怪波的演化规律.本文揭示的线怪波激发新机制,有助于提升对高维非线性波动模型的相干结构的新认识. 相似文献
347.
An integrated-wavelet-transform (IWT) approach is proposed for the study of scattering from slightly rough surfaces that manifest scaling properties over a finite domain of correlation lengths. Instead of collecting angle-resolved intensities, values of the irradiance integrated over increasing areas are used to enhance the contributions of small irradiances at large scattering angles and to reduce the coherent noise. In the case of self-similar surfaces, the scaling behavior of IWT allows investigation of the surface roughness at various length scales. For the realistic case of self-affine surfaces, IWT permits the evaluation of the scaling exponent of the autocorrelation and also offers a direct way to evaluate the necessary length scale of the surface profile. 相似文献
348.
Multifractal Decomposition of Statistically Self-Similar Sets 总被引:1,自引:0,他引:1
Let K be a statistically self-similar set defined by Graf. In this paper, we construct a random measure ρ which is supported by
K and study the multifractal decomposition for K with ρ. Under such a decomposition, we obtain the expression of the spectrum function ƒ(α).
Received July 18, 1997, Accepted October 13, 2000 相似文献
349.
构造了随机自相似分形及其上的记忆函数,并得出了有关结论,在此基础上,我们可以定义一个随机概率测度dΦn(τ)=Kn(τ)dτ,Φn(τ)弱收敛于Φ,进一步可得到强测度序列Ψn(.)=EΦn(.),则{Ψn}弱收敛于Ψ=EΦ. 相似文献
350.
Summary This paper introduces a novel idea: the concept of an image transformation. We also introduce the closely related concept
of a quasi-homomorphism, and study the properties of these mathematical objects, and give several examples. In particular
we investigate iterated systems of image transformations, which we believe give a more realistic approach to the study of
so called self-similar structures in nature than what is obtained by iterated function systems. 相似文献