The application of dielectric analysis to drying latex films

Measurements of real and imaginary capacitance (C andC) have been made during the drying of a film-forming latex. In one experiment dielectric measurements at frequencies between 1 Hz and 100 kHz were made simultaneously with gravimetric measurements on a microbalance. It was found that both the rate of water evaporation and the a.c. conductance decrease sharply at high polymer volume fraction. These results are discussed qualitatively in terms of a model for the film-forming process. In another experimentC andC were recorded at 10 Hz along with automatic measurements of the build-up of the scratch resistance of the film. It was found that the mechanical response to film-formation appears significantly earlier than the dielectric response. This is also discussed qualitatively in terms of the model.The authors would like to thank Dr. I. Abrahams, Dr. S. Bell, and Dr. M. Reading for useful discussions regarding this work and M. Bahra for his help with the TFA measurements.     

A partially observed control problem for Markov chains

A finite state, continuous time Markov chain is considered and the solution to the filtering problem given when the observation process counts the total number of jumps. The Zakai equation for the unnormalized conditional distribution is obtained and the control problem discussed in separated form with this as the state. A new feature is that, because of the correlation between the state and observation process, the control parameter appears in the diffusion coefficient which multiplies the Poisson noise in the Zakai equation. By introducing a Gâteaux derivative the minimum principle, satisfied by an optimal control, is derived. If the optimal control is Markov, a stochastic integrand can be obtained more explicitly and new forward and backward equations satisfied by the adjoint process are obtained.This research was partially supported by NSERC Grant A7964, the Air Force Office of Scientific Research, United States Air Force, under Contract AFOSR-86-0332, and the U.S. Army Research Office under Contract DAAL03-87-0102.     

Analysis of the Thomas-Fermi-von Weizsäcker equation for an infinite atom without electron repulsion

The equation $$\left\{ { - \Delta + |\psi (x)|^{2p - 2} - |x|^{ - 1} } \right\}\psi (x) = 0$$ in three dimensions is investigated. Uniqueness and other properties of the positive solution are proved for 3/2<p<2. There are two physical interpretations of this equation forp=5/3: (i) As the TFW equation for an infinite atomwithout electron repulsion; (ii) The positive solution, ψ, suitably scaled, is asymptotically equal to the solution of the TFW equation for an atom or moleculewith electron repulsion in the regime where the nuclear charges are large andx is close to one of the nuclei.     

Bile acids LXIX. Selective K-Selectride reduction of 3,7-diketo steroids

The K-Selectride reduction at low temperature (-45°C) of 7-oxo-5α-holestan-3β-yl acetate and methyl 7-oxo-3α-hydroxy-5(β-cholanoate resulted in almost quantitative yield of the 7α-alcohol in the 5α-compound but only moderate yield of the 5β-analog. The simultaneous reduction of two carbonyl groups in the 3 and 7 positions afforded good to excellent yields of the diaxial diol in planar steroids (methyl 3,7-dioxo-5α-cholanoate, 3,7-dioxo-5α-cholestane and methyl 3,7-dioxo-5α-cholestan-27-oate) and only 14% of 3α,7α-(OH)₂ from methyl 3,7-dioxo-5β-cholanoate.     

The third law of thermodynamics and the degeneracy of the ground state for lattice systems

The third law of thermodynamics, in the sense that the entropy per unit volume goes to zero as the temperature goes to zero, is investigated within the framework of statistical mechanics for quantum and classical lattice models. We present two main results: (i) For all models the question of whether the third law is satisfied can be decided completely in terms of ground-state degeneracies alone, provided these are computed for all possible boundary conditions. In principle, there is no need to investigate possible entropy contributions from low-lying excited states, (ii) The third law is shown to hold for ferromagnetic models by an analysis of the ground states.Dedicated to Pierre Résibois. Work supported in part by NSF grant PHY-7825390 A01.