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121.
122.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
123.
提出一种采用Kohonen网络算法进行12电极电容CT系统的图像重建的方法.该网络由输入和输出两层神经元组成,输入为12电极电容CT系统测量所得的66个电容值,输出对应管道介质的空间分布模式.该网络采用竞争算法无监督学习,实验结果证明,该网络有较强的抗噪声能力,可重建出较精确的介质分布图像 相似文献
124.
Multi-separation, centrifugality and centripetality imply chaos 总被引:4,自引:0,他引:4
Jiehua Mai 《Transactions of the American Mathematical Society》1999,351(1):343-351
Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.
125.
Floris Takens 《Bulletin of the Brazilian Mathematical Society》1998,29(2):197-228
In this paper we first give an overview of the methods of analysis of time series in terms of correlation integrals, which were developed for time series generated by deterministic systems. From the extremal value theory one obtains asymptotic information on the behaviour of the correlation integrals of time series generated by non-deterministic (mixing) systems. This leads to an analysis in terms of correlation integrals which is complementary to the estimation of dimension and entropy.Dedicated to the memory of Ricardo Mañé 相似文献
126.
量子混沌在谱涨落统计特征上的表象 总被引:4,自引:0,他引:4
通过对Henon-Heiles模型、Barbanis模型和刚环转球模型这两类三种守恒体系之对应量子体系的研究,具体地剖析了本征值谱涨落统计特征与体系动力学行为的联系,说明了量子混沌现象的两种表现形式。同时,通过将本质上属于经典耗散系范畴的Lotka-Volterra模型之演化方程哈密顿化,发现其量子对应系本征值谱的涨落统计特征超出了Poisson-GOE(Wigner)或GUE框架。揭示出经典耗散 相似文献
127.
N. O. Weiss 《Journal of statistical physics》1985,39(5-6):477-491
Slowly rotating main-sequence stars with deep convective zones have activity cycles like the sun's. The solar cycle is aperiodic and modulated to give intervals of reduced activity. A simple sixth-order system, obtained by truncating the dynamo equations, has solutions that mimic this behavior. The transition to chaos is analyzed and the astrophysical significance of these results is discussed. 相似文献
128.
Generalized reduced-order synchronization of chaotic system based on fast slide mode 总被引:1,自引:0,他引:1
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A new kind of generalized reduced-order synchronization of different chaotic
systems is proposed in this paper. It is shown that dynamical evolution of
third-order oscillator can be synchronized with the canonical projection of
a fourth-order chaotic system generated through nonsingular states
transformation from a cell neural net chaotic system. In this sense, it is
said that generalized synchronization is achieved in reduced-order. The
synchronization discussed here expands the scope of reduced-order
synchronization studied in relevant literatures. In this way, we can achieve
generalized reduced-order synchronization between many famous chaotic
systems such as the second-order D\"{u}ffing system and the third-order
Lorenz system by designing a fast slide mode controller. Simulation results
are provided to verify the operation of the designed synchronization. 相似文献
129.
We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on
. We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10. 相似文献
130.
Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier
potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets result upon
passing through the multibarrier potential. 相似文献