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1.
Michel Weber 《Transactions of the American Mathematical Society》2006,358(2):911-936
We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.
2.
陈创新 《中山大学学报(自然科学版)》2005,44(6):45-48
提出了一种新的线性混叠信号的盲分离算法,该算法利用信号相互独立时其协方差矩阵的对角化特征作为分离准则,采用最速下降法进行分离.该算法对源信号和混叠矩阵没有过多要求且计算量不大,理论分析与仿真结果表明:该算法具有很好的分离效果. 相似文献
3.
Shinji Takesue 《Journal of statistical physics》1989,56(3-4):371-402
This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems. 相似文献
4.
Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor 总被引:2,自引:0,他引:2
Y. Charles Li 《Proceedings of the American Mathematical Society》2005,133(9):2681-2687
Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.
5.
Rie Natsui 《Acta Mathematica Hungarica》2005,108(4):299-318
Summary Let Fq be a finite field with q elements. We consider formal Laurent series of Fq -coefficients with their continued fraction expansions by Fq -polynomials. We prove some arithmetic properties for almost every formal Laurent series with respect to the Haar measure. We construct a group extension of the non-archimedean continued fraction transformation and show its ergodicity. Then we get some results as an application of the individual ergodic theorem. We also discuss the convergence rate for limit behaviors. 相似文献
6.
The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound. 相似文献
7.
设(X,d)是一个可分的度量空间,Cu(X,d)是由全体一致连续函数所组成的C(X,d)的子空间,T是定义在X上的一致Lipschitz映射,那么对f∈Cu(X),1/n n∑k=1 Uk If在Cu(X)上收敛.从这个基本结果出发,利用Cu(X,d)的共扼空间的表示定理,得到了相空间的Yosida型遍历分解;利用空间的嵌入技术证明了非一致Lipschitz映射的大数法则. 相似文献
8.
Reaction diffusion systems on cylindrical domains with terms that vary rapidly and periodically in the unbounded direction can be analyzed by averaging techniques. Here, using iterated normal form transformations and Gevrey regularity of bounded solutions, we prove a result on exponential averaging for such systems, i.e., we show that traveling wave solutions can be described by a spatially homogenous equation and exponentially small remainders. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Let Ω be a region in ℝn and letp = Pi )
i
1m
, be a partition ofΩ into a finite number of closed subsets having piecewise C2 boundaries of finite(n - 1 )dimensional measure. Let τ:Ω→Ω be piecewise C2 onP where, τi = τ|pi is aC
2 diffeomorphism onto its image, and expanding in the sense that there exists α > 1 such that for anyi = 1, 2,...,m ‖Dτi
-1 ‖ < α-1, where Dτi
-1 is the derivative matrixτ
i
- 1 and |‖·‖ is the Euclidean matrix norm. By means of an example, we will show that the simple bound of one-dimensional dynamics
cannot be generalized to higher dimensions. In fact, we will construct a piecewise expanding C2 transformation on a fixed partition with a finite number of elements in ℝ2, but which has an arbitrarily large number of ergodic, absolutely continuous invariant measures 相似文献
10.
A generalized linear differential equation in a Banach space is studied. The construction of a phase space and solutions with the help of the spectral theory of linear operators, ergodic theorems, and degenerate semigroups of linear operators is carried out. 相似文献