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排序方式: 共有115条查询结果,搜索用时 15 毫秒
1.
We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system
of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping
infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran
to compute the Hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausforff
dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated
function system. Our methods are applicable to some iterated function systems that do not satisfy the finite type condition
recently introduced by Ngai and Wang.
相似文献
2.
It is proposed a class of statistical estimators H =(H_1,…,H_d) for the Hurst parameters H =(H_1,…,H_d) of fractional Brownian field via multi-dimensional wavelet analysis and least squares,which are asymptotically normal.These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals,which is important in texture classification and improvement of diffusion tensor imaging(DTI) of nuclear magnetic resonance(NMR).Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators.We find that when H_i ≥ 1/2,the estimators are accurate,and when H_i 1/2,there are some bias. 相似文献
3.
Summary Nonstationary regimes of the wave turbulence evolution are considered in the framework of isotropic kinetic equation. It is
predicted analytically and confirmed by numerical experiment that there is a class of wave systems in which any initial distribution
of the turbulence energy ink-space comes into a universal, Kolmogorovtype spectrum in a finite time. Before and after the formation of the Kolmogorov
spectrum, two different self-similar regimes of evolution occur: the first one is responsible for explosively forming the
universal spectrum and the second one determines energy dissipation. 相似文献
4.
Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths 总被引:1,自引:0,他引:1
This paper develops a class of consistent estimators of the parameters of a fractional Brownian motion based on the asymptotic
behavior of the k-th absolute moment of discrete variations of its sampled paths over a discrete grid of the interval [0,1]. We derive explicit
convergence rates for these types of estimators, valid through the whole range 0 < H < 1 of the self-similarity parameter. We also establish the asymptotic normality of our estimators. The effectiveness of
our procedure is investigated in a simulation study.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed. 相似文献
6.
Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR+, and its (2k+l)th-order extensions are studied. Such a refined scattering is based on a "Hermitian" spectral theory for a pair {B,B*} of non self-adjoint rescaled operators 相似文献
7.
张连增 《应用数学学报(英文版)》1999,15(3):240-248
1.IntroductionMotiffedbysomelargedeviationresultsforbranchingparticlesystem,thelargedeviationresultsforsuperprocesseshavebeeninvestigatedrecently.CoxandGffeathll]startedtheinvestigationofthelargedevistionforcriticalbranchingBrochanmotion.IscoeIZIcarr... 相似文献
8.
A. A. Osiptsov 《Fluid Dynamics》2004,39(1):47-60
Within the framework of the asymptotic thin-film equations for a highly viscous heavy Newtonian fluid, a hydrodynamic model of non-axisymmetric lava dome growth on a conical surface is constructed. A new class of self-similar solutions describing the flow on a conical surface with finite inclination to the horizontal and a point mass supply at the apex is found analytically for power-law or exponential growth of the liquid volume with time. For a conical surface with a small inclination to the horizontal, the free-surface shape is found numerically. The asymptotics of this solution are compared with the solutions describing the flow on a horizontal plane and a conical surface with finite inclination to the horizontal. 相似文献
9.
Michele Ciavarella Marco Paggi 《Journal of the mechanics and physics of solids》2008,56(12):3416-3432
Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m=2-5 in metals and m=10-50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review. 相似文献
10.
Marta L. Suleiman Juliana C. Precioso Andréa C. Prokopczyk 《Mathematical Methods in the Applied Sciences》2020,43(9):6103-6116
In this work, we present conditions to obtain a global-in-time existence of solutions to a class of nonlinear viscous transport equations describing aggregation phenomena in biology with sufficiently small initial data in Besov-Morrey spaces and gradient potential as a Radon measure. We also study the self-similarity and asymptotic stability of solutions at large times. 相似文献