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November 29, 2006

Sobolev in English

A new book set promises to expand access to the works of Sergei Lvovich Sobolev. The first volume out covers equations of mathematical physics, computational mathematics, and cubature formulas.

The preface notes that "the first three works are practically unknown to readers because they were published in sources which are difficult to access," viz., the 1932-1933 Trudy Seismologicheskii institut (Akademiia nauk SSSR). In the first of these, "Sobolev solves the classical problem posed in the famous article by H. Lamb (1904) on propagation of elastic vibrations in a half-plane and a half-space."

For many of the papers, this book also provides their first appearance in English. Dr. V. V. Fokin is credited for "his huge work in the translation of this book into English," from the 2003 Russian edition. Not that the original language of all the papers was Russian; for example, the fourth article, "On vibrations of a half plane and a layer with arbitrary initial conditions," originally appeared in French (Mat. Sb. 40 (1933), 236--266), although a Russian translation was published decades later (Uspehi Mat. Nauk 23 1968 no. 5 (143), 143--176). I wonder which source was used for the English version?

Selected Works of S.L. Sobolev, edited by G.V. Demidenko, and V. L. Vaskevich. New York: Springer, 2006. Mathematics Library QA401 S6313 2006 Link to MnCat Record

November 17, 2006

Smallpox math

"Smallpox and anthrax are two of the most likely biological agents to be used in a deliberate release since they are easily aerosolized and support high case fatality rates. The earliest mathematical smallpox epidemic model is attributed to Daniel Bernoulli. His goal was to calculate the adjusted life table when smallpox was eliminated as a cause of death. Interest on homeland security issues have resulted in the development of a series of models geared towards the exploration of the consequences of the use of smallpox as a biological agent. . . .Deterministic epidemic models can indeed incorporate dynamic network structures that account for changes in population size and behavior modification in a tractable manner while network epidemic models are extremely useful in identifying in a probabilistic sense the role of divergent contact structures on disease patterns--including the final epidemic size."

from "Mathematical applications associated with the deliberate release of infectious agents," by Gerardo Chowell et al., in Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges: AMS-IMS-SIAM Joint Summer Research on Modeling the Dynamics of Human Diseases, July 17-21, 2005, Snowbird, Utah. Abba Gumel, editor-in-chief; Carlos Castillo-Chavez, Ronald E. Mickens, Dominic P. Clemence, editors. Contemporary Mathematics v. 410. Providence, R.I.: American Mathematical Society, 2006, pp. 51-71. Mathematics Library RA652.2.M3 A54 2005 Link to MnCat Record

November 10, 2006

Monstrous Moonshine

A very tidy abstract:
"Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms, and vertex operator algebras. Moonshine beyond the Monster, the first book of its kind, describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between modern mathematics and mathematical physics."

conceals a very inquisitive approach, concluding
"So, has Monstrous Moonshine been explained? According to most of the fathers of the subject, it hasn't. . . .We are entering a consolidation phase, tidying up, generalising, simplifying, clarifying, working out more examples, climbing a few metres higher. Important and interesting discoveries will be made in the next few years, and yes, there still is mystery. . ."

Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics, by Terry Gannon. Cambridge, UK; New York: Cambridge University Press, 2006. Link to MnCat Record