Rubel's problem on bounded analytic functions

The paper shows that for any $G_\delta$ set $F$ of Lebesgue measure zero on the unit circle $T$ there exists a function $f \in H^{\infty}$ such that the radial limits of $f$ exist at each point of $T$ and vanish precisely on $F$. This solves a problem proposed by Lee Rubel in 1973

COLLECTION 0100: Thomas Lee Osborn Collection, 1956-1991

The Osborn collection consists of audio and video tapes recording the messages and lessons of T. L. and Daisy Osborn and their daughter LaDonna Osborn. Also included are Manuals for the Life Discovery Bible Institute Bible Study Course. Titles include Creation Realities by Daisy Osborn, Winning Our World by T.L. Osborn and Redemption by LaDonna Osborn

Book Reviews

Reviews of Experiencia misionera en la Florida (siglos XVI y XVII). By P. G. J. Keegan and L. Tormo Sanz. Instituto Santo Toribio de Mogrovejo. Consejo Superior de Investigaciones Cientificas. Biblioteca “Missionalica Hispanica,” Series B. Vol. VII. (Madrid, Talleres Graficos Jura, 1957. 404 pp.); The Story of Southwestern Florida, By James W. Covington. (New York, Lewis Historical Publishing Company, 1957. 2 vols. Maps, illustrations, index. $48.50.); Ante Bellum Alabama Town and Country. By Weymouth T. Jordan. Florida State University Studies, No. 27. (Tallahassee, Florida State University, 1957. viii, 172 pp. Bibliography.$3.00.); Lee Chronicle; Studies of the Early Generations of the Lees of Virginia. By Cazenove Gardner Lee, Jr. Compiled and edited by Dorothy Mills Parker. (New York, New York University Press, 1957. 411 pp. Illustrations, maps, genealogical tables, index. $6.50.); The South in Northern Eyes, 1831-1861. By Howard R. Floan. (Austin, University of Texas Press, 1958. xi, 198 pp.$3.95.

Preaching Fools: The Gospel as a Rhetoric of Folly

Preaching fools: the Gospel as a rhetoric of folly. Author: Charles L Campbell; Johan Cilliers. Publisher: Waco, Tex. : Baylor University Press, ©2012. ISBN: 978160258367

Phase transitions with four-spin interactions

Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition(and spontaneous magnetization) if, and only if, the external field $h=0$ (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are shown to hold for a larger class of multi-spin interactions

[Review of] Ambrose Y.C. King and Rance P.L. Lee, eds. Social Life and Development in Hong Kong

This book is a collection of research papers on the political and social conditions of Hong Kong sponsored by the Social Research Centre of The Chinese University of Hong Kong. The collection is not a comprehensive coverage of such conditions in Hong Kong. I t is a selective report with the purpose of updating existing information. The new information will provide a better understanding of Hong Kong\u27s problems and serve as a resource in coping with these problems

Persistence in systems with algebraic interaction

Persistence in coarsening 1D spin systems with a power law interaction $r^{-1-\sigma}$ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent $\sigma$ ($\sigma\geq 1/2$ in our simulations), persistence decays as an algebraic function of the length scale $L$, $P(L)\sim L^{-\theta}$. The Persistence exponent $\theta$ is found to be independent on the force exponent $\sigma$ and close to its value for the extremal ($\sigma \to \infty$) model, $\bar\theta=0.17507588...$. For smaller values of the force exponent ($\sigma< 1/2$), finite size effects prevent the system from reaching the asymptotic regime. Scaling arguments suggest that in order to avoid significant boundary effects for small $\sigma$, the system size should grow as ${[{\cal O}(1/\sigma)]}^{1/\sigma}$.Comment: 4 pages 4 figure