A framework for conceptualizing the development of individual differences in reading ability is presented that synthesizes a great deal of the research literature. The framework places special emph...

Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy.

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Analytic Combinatorics

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. 
In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.

/pdf/the-askey-scheme-of-hypergeometric-orthogonal-polynomials-46afheftah.pdf

The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Social preference of female gerbils (Meriones unguiculatus) as influenced by coat color of males.

We consider the solution of the Korteweg–de Vries (KdV) equation






with periodic initial value






where C, A, k, μ, and β are constants. The solution is shown to be uniformly bounded for all small ɛ, and a formal expansion is constructed for the solution via the method of multiple scales. By using the energy method, we show that for any given number T > 0, the difference between the true solution v(x, t; ɛ) and the Nth partial sum of the asymptotic series is bounded by ɛN+1 multiplied by a constant depending on T and N, for all −∞ < x < ∞, 0 ≤t≤T/ɛ, and 0 ≤ɛ≤ɛ0.

Asymptotic Analysis of a Perturbed Periodic Solution for the KdV Equation

Effects of diphenylhydantoin on saline intake of rats, gerbils, and hamsters

In this paper, we study the asymptotics of the Hahn polynomials Q_n(x; {\alpha}, {\beta}, N) as the degree n grows to infinity, when the parameters {\alpha} and {\beta} are fixed and the ratio of n/N = c is a constant in the interval (0, 1). Uniform asymptotic formulas in terms of Airy functions and elementary functions are obtained for z in three overlapping regions, which together cover the whole complex plane. Our method is based on a modified version of the Riemann-Hilbert approach introduced by Deift and Zhou.

Global Asymptotics of the Hahn Polynomials

We consider a pair of special functions, $u_\beta$ and $v_\beta$, defined respectively as the solutions to the integral equations \begin{equation*} u(x)=1+\int^\infty_0 \frac {K(t) u(t) dt}{t+x} ~~\mbox{and}~~v(x)=1-\int^\infty_0 \frac{ K(t) v(t) dt}{t+x},~~x\in [0, \infty), \end{equation*} where $K(t)= \frac {1} \pi \exp \left (- t^\beta \sin\frac {\pi\beta} 2\right )\sin \left ( t^\beta\cos\frac{\pi\beta} 2 \right )$ for $\beta\in (0, 1)$. In this note, we establish the existence and uniqueness of $u_\beta$ and $v_\beta$ which are bounded and continuous in $[0, +\infty)$. Also, we show that a solution to a model Riemann-Hilbert problem in Kriecherbauer and McLaughlin [Int. Math. Res. Not., 1999] can be constructed explicitly in terms of these functions. A preliminary asymptotic study is carried out on the Stokes phenomena of these functions by making use of their connection formulas. 
Several open questions are also proposed for a thorough investigation of the analytic and asymptotic properties of the functions $u_\beta$ and $v_\beta$, and a related new special function $G_\beta$.

Roderick Wong

Papers

Social preference of female gerbils (Meriones unguiculatus) as influenced by coat color of males.

Asymptotic Analysis of a Perturbed Periodic Solution for the KdV Equation

Effects of diphenylhydantoin on saline intake of rats, gerbils, and hamsters

Global Asymptotics of the Hahn Polynomials

Special functions, integral equations and Riemann-Hilbert problem