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

This experiment was designed to determine the extent to which performance differences on learning tasks arising from infantile handling reflect learning or emotionality differences. Handled and nonhandled rats were trained and tested in a controlled operant situation where a response on every other trial yielded reinforcement. A key light was turned on for 10 sec during each trial and was off during the 10-sec intertrial interval. The reinforced (S+) trials alternated in a regular sequence with nonreinforced (S−) trials. The pattern of S+ and S− trials recycled continuously throughout the session of 160 trials. The handled rats emitted more responses during both S+ and S− trials than did the nonhandled rats. However, when they were compared on the percentage of emitted responses that were reinforced, there was no significant differences between the two groups. These results were interpreted to suggest that infantile handling does not directly facilitate associative learning in rats.

Early stimulation and patterned responding in rats

In memoriam Frank W. J. Olver (1924–2013)

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not yet been obtained previously. This particular formula involves a special function, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem, and which is asymptotically (as the polynomial degree $n$ tends to infinity) equal to the constant $"1"$ except at the origin. Numerical computation by using our formulas, and comparison with earlier results, are also given.

http://www.ucs.mun.ca/~xiangshengw/talks/slide200906-CityU.pdf

Uniform Asymptotics of the Meixner Polynomials

Instructors will appreciate the options this textbook provides for forming a course on brief introductions provided to key subjects in complex functions. 

More Explorations in Complex Functions

The trigonometric functions are the basic functions that are periodic with respect to a translation of the plane $\mathbb {C}$. An important class of complex functions is doubly periodic: periodic with respect to two sets of translations. This chapter presents the general theory of such functions, and Jacobi’s construction via theta functions. The following two chapters, which are independent of each other, present constructions due to Jacobi and to Weierstrass, respectively.

Roderick Wong

Papers

Early stimulation and patterned responding in rats

In memoriam Frank W. J. Olver (1924–2013)

Uniform Asymptotics of the Meixner Polynomials

More Explorations in Complex Functions

Elliptic functions and theta functions