Recurrence spectra of He atoms in strong external fields

1 Introduction The photo-absorption phenomenon of high Rydberg atoms in strong external fields has attracted much attention in recent years. The semiclassical closed-orbit theory[1,2] developed by Du and Delos has been extensively used to explain this phenomenon. This theory has successfully calculated and interpreted the photo-absorption spectra of H- in various external fields[3,4] and has been applied to describe the photo-excitation, wave packet dynamics of some atoms and molecules such…     

Linear difference equations with transition points

Two linearly independent asymptotic solutions are constructed for the second-order linear difference equation

where and have power series expansions of the form

with . Our results hold uniformly for in an infinite interval containing the transition point given by . As an illustration, we present an asymptotic expansion for the monic polynomials which are orthogonal with respect to the modified Jacobi weight , , where , -1$"> and is real analytic and strictly positive on .

     

On the limit laws of the second order for additive functionals of Harris recurrent Markov chains

Let {X _n } _{n ≥0} be a Harris recurrent Markov chain with state space E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals of the form

一类递推关系式的解的计算公式

文献[1]给出了一个三项单指标的常系数齐次递推式的一般解公式。本文一类带双指标的变系数非齐次递推关系的解的结构。其结果，对双指标的相应递推关系式的解的求出，亦或在其有关理论的研究方面，皆有其作用。     

Random walks on a lattice

This paper discusses the mean-square displacement for a random walk on a two-dimensional lattice, whose transitions to nearest-neighbor sites are symmetric in the horizontal and vertical directions and depend on the column currently occupied. Under a uniform density condition for the step probabilities it is shown that the horizontal mean-square displacement aftern steps is asymptotically proportional ton, and independent of the particular column configuration. The model generalizes that of Seshadri, Lindenberg, and Shuler and the arguments are essentially probabilistic.     

Numerical solution of the abel integral equation

A numerical method for the solution of the Abel integral equation is presented. The known function is approximated by a sum of Chebyshev polynomials. The solution can then be expressed as a sum of generalized hypergeometric functions, which can easily be evaluated, using a simple recurrence relation.     

Discrete-Continuous Symmetrized Sobolev Inner Products

This paper deals with the bilinear symmetrization problem associated with Sobolev inner products. Let 007B;Q _n } _n=0 be the sequence of monic polynomials orthogonal with respect to a Sobolev inner product of order 1 when one of the measures is discrete and the other one is a nondiscrete positive Borel measure. Furthermore, assume that the supports of such measures are symmetric with respect to the origin so that the corresponding odd moments vanish. We consider the orthogonality properties of the sequences of monic polynomials 007B;P _n } _n=0 and {R _n } _n=0 such that Q _2n (x)=P _n (x ²), Q _2n+1(x)=xR _n (x ²). Moreover, recurrence relations for {P _n } _n=0 and {R _n } _n=0 are obtained as well as explicit algebraic relations between them.     

Asymptotics of recurrence coefficients for orthonormal polynomials on the line--Magnus's method revisited

We use Freud equations to obtain the main term in the asymptotic expansion of the recurrence coefficients associated with orthonormal polynomials for weights on the real line where is an even polynomial of fixed degree with nonnegative coefficients or where . Here for some real -1$">.

     

渐近幂级数的反演

讨论了渐近（广义）幂级数的反演这一级数的基本问题,从渐近级数乘幂的渐近展开出发,对渐近幂级数与渐近广义幂级数的反演给出了便于实际计算的纱数递推公式,并对展开式的渐近性予以证明,递推公式虽较繁杂,但却便于计算机进行大项数的计算。     

Solving Thue equations without the full unit group

The main problem when solving a Thue equation is the computation of the unit group of a certain number field. In this paper we show that the knowledge of a subgroup of finite index is actually sufficient. Two examples linked with the primitive divisor problem for Lucas and Lehmer sequences are given.