Cayley graphs generated by small degree polynomials over finite fields

We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields

Extension of a theorem of Duffin and Schaeffer

Let $r_1,\ldots,r_s:\mathbb{Z}_{n\geqslant 0}\to\mathbb{C}$ be linearly recurrent sequences whose associated eigenvalues have arguments in $\pi\mathbb{Q}$ and let $F(z):=\sum_{n\geqslant 0}f(n)z^n$, where $f(n)\in\{r_1(n),\ldots,$ $r_s(n)\}$ for each $n\geqslant 0$. We prove that if $F(z)$ is bounded in a sector of its disk of convergence, it is a rational function. This extends a very recent result of Tang and Wang, who gave the analogous result when the sequence $f(n)$ takes on values of finitely many polynomials.Comment: 2 page

Expertise effects in memory recall: A reply to Vicente and Wang

This article may not exactly replicate the final version published in the APA journal. It is not the copy of record.In the January 1998 Psychological Review, Vicente and Wang propose a "constraint attunement hypothesis" to explain the large effects of domain expertise upon memory recall observed in a number of task domains. They claim to find serious defects in alternative explanations of these effects which their theory overcomes. Re-examination of the evidence shows that their theory is not novel, but has been anticipated by those they criticize, and that other current published theories of the phenomena do not have the defects Vicente and Wang attribute to them. Vicente and Wang's views reflect underlying differences (a) about emphasis upon performance versus process in psychology, and (b) about how theories and empirical knowledge interact and progress with the development of a science