Relaxation properties of weakly coupled classical systems

The relaxation properties of a small classical system weakly coupled to a large classical system which acts as a heat bath are described using a generalized Fokker-Planck equation. The Fokker-Planck equation is derived in general using a modification of the elimination of fast variables techniques previously described. The specific example in which the small system is a harmonic oscillator linearly coupled to the heat bath is treated in detail and it is demonstrated that there is a dynamic frequency shift as well as a statistical shift of the oscillator frequency.     

Ultrasonic measurement of dental enamel demineralization

The DONAR (digital ultrasonic system) has been used to continuously measure the displacement, due to etching by hydrochloric acid, of the surface of bovine enamel and to monitor the development of a demineralized layer. Conventional pulse echoes are used to measure displacements of the order of micrometres with an uncertainty no greater than 0.1 μm. The demineralized zone in one instance attained a maximum thickness of 5 μm and was much less in other experiments.     

Decay of correlations. IV. Necessary and sufficient conditions for a rapid decay of correlations

We considerN-particle systems whose probability distributions obey the master equation. For these systems, we derive the necessary and sufficient conditions under which the reducedn-particle (n) probabilities also obey master equations and under which the Ursell functions decay to their equilibrium values faster than the probability distributions. These conditions impose restrictions on the form of the transition rate matrix and thus on the form of its eigenfunctions. We first consider systems in which the eigenfunctions of theN-particle transition rate matrix are completely factorized and demonstrate that for such systems, the reduced probabilities obey master equations and the Ursell functions decay rapidly if certain additional conditions are imposed. As an example of such a system, we discuss a random walk ofN pairwise interacting walkers. We then demonstrate that for systems whoseN-particle transition matrix can be written as a sum of one-particle, two-particle, etc. contributions, and for which the reduced probabilities obey master equations, the reduced master equations become, in the thermodynamic limit, those for independent particles, which have been discussed by us previously. As an example of suchN-particle systems, we discuss the relaxation of a gas of interacting harmonic oscillators.Supported in part (grants to D.B. and K.E.S.) by the Advanced Research Projects Agency of the Department of Defense as monitored by the U.S. Office of Naval Research under Contract N00014-69-A-0200-6018, and in part (grant to I.O.) by the National Science Foundation.     

Human pre-interleukin 1 alpha and beta: structural features revealed by limited proteolysis

Both pre-interleukin 1 alpha and beta (pre IL 1 alpha and beta) are proteolytically processed into extracellular mature forms of IL 1 alpha and beta. Since pre IL 1 alpha is shown to be biologically active, there may be other reasons for the proteolytic processing of IL 1 alpha and presumably, for IL 1 beta also. In order to examine the possibility that structural stabilization may be associated with the proteolytic processing of pre IL 1 alpha and beta, we investigated the structural features of pre IL 1 alpha and beta by the combination of limited proteolysis and immunoprecipitation with antibodies to the NH2-terminal halves or COOH-terminal halves of pre IL 1 alpha or beta. Both trypsin and V8 protease digested the NH2-terminal halves of pre IL 1 alpha and beta more easily than the COOH-terminal halves of pre IL 1 alpha and beta, yielding structurally stabilized "mature" forms of IL 1. Both trypsin and V8 protease yielded a fragment similar in size to mature IL 1 alpha from pre IL 1 alpha. In contrast, trypsin digested pre IL 1 beta into fragments smaller in size than mature IL 1 beta, while V8 protease yielded a fragment similar in size to mature IL 1 beta. Furthermore, mature IL 1 beta, once processed and released from cells, was resistant to trypsin.(ABSTRACT TRUNCATED AT 250 WORDS)     

Fluorocarbon derivatives of nitrogen. Part I. Some reactions of perfluoro-1-azacyclohexene

Controlled displacement of fluorine from perfluoro-1-azacyclo-hexene (I) by the nucleophilic reagents Me₂NH, Et₂NH, $\text{CH}{}_2\text{CH}{}_2\text{O(CH}{}_2\text{)}{}_2\text{N}$H, C₆Cl₅ONa, and (CF₃)₂NONa provides the derivatives (II) - (IV), respectively. The last of these can also be obtained by treatment of the parent compound (I) with mercury^II bistrifluoromethylnitroxide.