Precise large deviation estimates for a one-dimensional random walk in a random environment

ω_x } (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X _k } (called a RWRE) which, when at x, moves one step to the right with probability ω _x , and one step to the left with probability 1 −ωx. Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlier work by Greven and den Hollander (1994) on the quenched case, have computed rough tail asymptotics for the empirical mean of the annealed RWRE. They conjectured the form of the rate function in a full LDP. We prove in this paper their conjecture. The proof is based on a “coarse graining scheme” together with comparison techniques. Received: 22 July 1997/Revised version: 15 June 1998     

Composition of cementite in the dependence on the temperature. In situ neutron diffraction study and Ab initio calculations

The structure state of carbon eutectoid steel has been studied by the in situ neutron diffraction method in the temperature range from room temperature to 800°C. It has been shown that an increase in the temperature is accompanied by a decrease in the concentration of carbon in cementite, whereas its weight fraction and the parameters of the orthorhombic lattice change slightly. The ab initio calculations of the nonstoichiometric carbides Fe₃C _x (0 < x < 1) indicate that the structure of cementite remains stable upon the appearance of vacancies in the carbon sublattice with a relatively low formation energy. Thus, cementite should be considered as an interstitial phase Fe₃C _x with a wide homogeneity range.     

Fractals Everywhere

Abstract

Like every other component of government these days, the U.S. federal statistical system is being reinvented, reengineered, and downsized. At this writing, several bills are before the U.S. Congress to restructure the system, relocate key agencies, and reallocate programs and budgets. Janet L. Norwood, Senior Fellow with The Urban Institute and former Commissioner of Labor Statistics, offers a trenchant commentary on the situation. Norwood identifies serious problems with the U.S. federal statistical system, as it is currently organized, that need to be addressed. At the same time, she notes the grave danger that solutions attempted by the U.S. Congress may make matters worse. She ends with a call to action for those who “care about data quality and who understand the important uses of the government's statistical output.”     

Toward a versatile allylation reagent: practical,enantioselective allylation of acylhydrazones using strained silacycles

A highly practical method for the enantioselective allylation of acylhydrazones has been developed. The previously reported strained silacycle reagent 1 reacts with a wide variety of acylhydrazones to give the hydrazide products with good enantioselectivity (83-89% ee, typically). It has been demonstrated that the products may be isolated without chromatography by recrystallization in >/=98% ee.