On the limit behavior of recurrence coefficients for multiple orthogonal polynomials

In this paper we investigate general properties of the coefficients in the recurrence relation satisfied by multiple orthogonal polynomials. The results include as particular cases Angelesco and Nikishin systems.     

A note on the moments of order statistics from doubly truncated exponential distribution

Summary In a recent paper [2], the author has obtained some recurrence relations between the moments of order statitics from the exponential and right truncated exponential distributions. In this paper, similar relations are derived for a doubly truncated exponential distribution. It is shown that one can obtain all the moments by using these recurrence relations.     

Random walk versus random line

We consider random walks X_n in Z₊, obeying a detailed balance condition, with a weak drift towards the origin when X_n↗∞. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional Solid-On-Solid bridge with a corresponding Hamiltonian. Phase diagrams are discussed in terms of recurrence versus wetting. A drift of the random walk yields a Solid-On-Solid potential with an attractive well at the origin and a repulsive tail at infinity, showing complete wetting for δ≤1 and critical partial wetting for δ>1.     

On perturbations of strongly admissible prior distributions

Consider a parametric statistical model, P(dx|θ), and an improper prior distribution, ν(dθ), that together yield a (proper) formal posterior distribution, Q(dθ|x). The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of θ is admissible under squared error loss. Eaton [M.L. Eaton, A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains, Annals of Statistics 20 (1992) 1147–1179] used the Blyth–Stein Lemma to develop a sufficient condition, call it , for strong admissibility of ν. Our main result says that, under mild regularity conditions, if ν satisfies and g(θ) is a bounded, non-negative function, then the perturbed prior distribution g(θ)ν(dθ) also satisfies and is therefore strongly admissible. Our proof has three basic components: (i) Eaton's [M.L. Eaton, A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains, Annals of Statistics 20 (1992) 1147–1179] result that the condition is equivalent to the local recurrence of the Markov chain whose transition function is R(dθ|η)=∫Q(dθ|x)P(dx|η); (ii) a new result for general state space Markov chains giving conditions under which local recurrence is equivalent to recurrence; and (iii) a new generalization of Hobert and Robert's [J.P. Hobert, C.P. Robert, Eaton's Markov chain, its conjugate partner and -admissibility, Annals of Statistics 27 (1999) 361–373] result that says Eaton's Markov chain is recurrent if and only if the chain with transition function is recurrent. One important application of our results involves the construction of strongly admissible prior distributions for estimation problems with restricted parameter spaces.     

关于完全多部图的带宽和的一个注记

本文得到完全多部图的带宽和的一个递推方程；并由此给出带宽和的一些精确值．     

原子模型势中任意算符矩阵元的递推关系

运用升降算子和超维里定理计算出原子模型势中任意算符Af^U2(r)的矩阵元〈n′1l′1|Af^U2(r)|n1l1〉的递推关系.     

On the values of continued fractions: q-series

Using the Poincaré-Perron theorem on the asymptotics of the solutions of linear recurrences it is proved that for a class of q-continued fractions the value of the continued fraction is given by a quotient of the solution and its q-shifted value of the corresponding q-functional equation.     

Recurrence spectra of Li atom in strong external fields

Based upon our previous work [Commun. Theor. Phys.. 40,702 (2003)], we developed the closed orbit theory from two degrees of freedom to three non-separable degrees of freedom and calculated the recurrence spectra of Li Rydberg atom in strong perpendicular electric and magnetic fields. The Fourier transformed spectra of Li atom has allowed direct comparison between the resonance peaks and the scaled action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. The semiclassical result is in good agreement with the quantum one, which suggests that our calculation is correct.     

N维各向同性谐振子径向平均值的递推关系和解析表达式

推导出了用于N维各向同性谐振子径向平均值计算的二个递推关系,并在-3≤s≤3的条件下,给出了平均值〈n_rJ_N-2|r^2s|n_rJ_N-2〉的值.二维和三维各向同性谐振子的相关结果均作为特例包含在结论中.     

‘Classical’ convergence theorems for generalized continued fractions

In this paper the classical convergence theorems by Śleszyński-Pringsheim, Worpitzky and Van Vleck for ordinary continued fractions will be generalized to continued fractions generalizations (along the lines of the Jacobi–Perron algorithm) with four-term recurrence relations.