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排序方式: 共有223条查询结果,搜索用时 15 毫秒
1.
Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples. 相似文献
2.
Francesca Aicardi 《Functional Analysis and Other Mathematics》2006,1(2):93-109
We give a recursive method for building X
p
(a,b) for each prime p. Arnold’s triangle is composed of positive integers: for a>1 and 0<b<a, X
p
(a,b) is the degree of the highest power of p dividing the difference of the binomial coefficients C
pa
pb
−C
a
b
.
相似文献
3.
设M=(m_(ij))是一个b×b阶矩阵且m_(ij)∈{0,1},∑_(M)是矩阵M=(m_(ij))诱导产生的有限型,σ是其上左推移算子.本文主要研究的是有限型动力系统(∑_(M),σ)上的首次返回速度问题.令τ_(k)(x)是点x∈∑_(M)首次返回到包含x的k阶柱集时间,且E_(α,β)={x∈∑_(M):lim inf_(k→∞)(logτ_(k)(x))/k=α,lim sup_(k→∞)(logτ_(k)(x))/k=β}.我们证明了:当M是不可约矩阵时,对任意0≤α≤β≤+∞,集合E_(α,β)的Markov测度要么等于0要么等于1并且具有满的Hausdorff维数. 相似文献
4.
Patterns were generated inside a horizontal cylinder rotating at low speeds. The cylinder was filled with a very low volume liquid fraction of 1.8% of Newtonian fluid and the rotation speed ranged between 0.08 and 5.2 s−1. A novel laser-plane technique was utilized to obtain time series from each pattern. This enabled the characterization of fluid patterns using Fourier spectral (FS) and dynamical-systems (chaotic) techniques such as the recurrence map, correlation dimension (D2) and Hurst exponent (H). Four patterns were found (fingers, furrows, waterfall and smooth tooth) before annular flow was reached. The results indicate that the FS technique not is suitable for flow pattern characterization; and H only has the ability to indicate a possible pattern change. The best tool for indicating the pattern transitions and the inner coat liquid evolution was found to be recurrence maps and D2. 相似文献
5.
Khalfa Douak 《Journal of Computational and Applied Mathematics》1996,70(2):279-295
We are dealing with the concept of d-dimensional orthogonal (abbreviated d-orthogonal) polynomials, that is to say polynomials verifying one standard recurrence relation of order d + 1. Among the d-orthogonal polynomials one singles out the natural generalizations of certain classical orthogonal polynomials. In particular, we are concerned, in the present paper, with the solution of the following problem (P): Find all polynomial sequences which are at the same time Appell polynomials and d-orthogonal. The resulting polynomials are a natural extension of the Hermite polynomials.
A sequence of these polynomials is obtained. All the elements of its (d + 1)-order recurrence are explicitly determined. A generating function, a (d + 1)-order differential equation satisfied by each polynomial and a characterization of this sequence through a vectorial functional equation are also given. Among such polynomials one singles out the d-symmetrical ones (Definition 1.7) which are the d-orthogonal polynomials analogous to the Hermite classical ones. When d = 1 (ordinary orthogonality), we meet again the classical orthogonal polynomials of Hermite. 相似文献
6.
A new method is introduced for the computation of hyperterminants. It is based on recurrence relations, and can also be used to compute the parameter derivatives of the hyperterminants. These parameter derivatives are needed in hyperasymptotic expansions in exceptional cases. Numerical illustrations and an application are included. 相似文献
7.
Antonia M. Delgado Jeffrey S. Geronimo Plamen Iliev Yuan Xu 《Constructive Approximation》2009,30(1):71-91
The one-variable Bernstein–Szegő theory for orthogonal polynomials on the real line is extended to a class of two-variable
measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their
recurrence coefficients discussed.
相似文献
8.
It is shown that the Positivity Problem for a sequence satisfying a third order linear recurrence with integer coefficients, i.e., the problem whether each element of this sequence is nonnegative, is decidable. 相似文献
9.
Dong Han Kim Kyewon Koh Park 《Proceedings of the American Mathematical Society》2008,136(11):3941-3951
If an ergodic system has positive entropy, then the Shannon-McMillan-Breiman theorem provides a relationship between the entropy and the size of an atom of the iterated partition. The system also has Ornstein-Weiss' first return time property, which offers a method of computing the entropy via an orbit. We consider irrational rotations which are the simplest model of zero entropy. We prove that almost every irrational rotation has the analogous properties if properly normalized. However there are some irrational rotations that exhibit different behavior.
10.
Yevgeniy Kovchegov 《Journal of Theoretical Probability》2008,21(2):437-448
We consider a multi-particle generalization of linear edge-reinforced random walk (ERRW). We observe that in absence of exchangeability,
new techniques are needed in order to study the multi-particle model. We describe an unusual coupling construction associated
with the two-point edge-reinforced process on ℤ and prove a form of recurrence: the two particles meet infinitely often a.s.
This research was supported in part by NSF VIGRE Grant DMS 9983726 at UCLA. 相似文献