Master Equation and Fokker–Planck Equation: Comparison of Entropy and of Rate Constants

A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.     

Experimental mathematics. I. Computational study on the limit cycle behavior of a two-dimensional chemical oscillator

A computational procedure, developed from the power series method, is used to investigate oscillating systems. In addition to its great accuracy and reduced computer time, the method is very easily programmable since the algorithm is provided by the reaction mechanism itself.     

Entropy of transfer of n-nitroalkanes from n-octane to water at 25°C

Entropy of transfer of nitromethane, nitroethane, 1-nitrobutane, 1-nitropentane, and 1-nitrohexane from n-octane to water at 25°C is calculated using an electrostatic model. The calculations indicate that the electrostatic transfer entropy depends primarily on the dipole moment and the size of the-C–NO₂ group, showing a trend which is similar to that previously found for the transfer free energy of the same process.     

A control-theoretic approach to the plasma confinement problem

The problem of confining a collisionless plasma by means of external electromagnetic fields is formulated as an optimal control or variational problem. The paper begins with a formal development of the equations governing the plasma motion. Then, various mathematical formulations of the confinement problem are discussed. Specific results are obtained for the simplified case where confinement is achieved by means of a spatially uniform, time-varying magnetic field. Physical interpretations of these results are also given.This work was supported by the Office of Scientific Research of the United States Air Force under Grant No. AFOSR-68-1547.     

Notiz zur Synthese des Nonactins

With (?)-nonactic acid and the 8-epitosylate of benzyl (+)-nonactate usingWalden inversion (?)-nonactyl-(+)-nonactic acid is constructed. The latter forms by way of its imidazolide or its α-mercaptopyridyl ester the macrotetrolide nonactine in poor yield.     

Transmission measurements of soft X-ray absorption fine structure in solids by a new scintillation technique

Transmission measurements of the extended X-ray absorption fine structure above the oxygen K-edge have been made by using a new scintillation detection technique. The absorption spectrum is in close resemblance with the total electron yield spectrum recorded at the same time. This new technique is of interest for studies of soft X-ray absorption spectroscopy for thin films of solid materials.     

Inventory control with fixed cost and price optimization in continuous time

We continue to study the problem of inventory control, with simultaneous pricing optimization in continuous time. In our previous paper [8], we considered the case without set up cost, and established the optimality of the base stock-list price (BSLP) policy. In this paper we consider the situation of fixed price. We prove that the discrete time optimal strategy (see [11]), i.e., the (s, S, p) policy can be extended to the continuous time case using the framework of quasi-variational inequalities (QVIs) involving the value function. In the process we show that an associated second order, nonlinear two-point boundary value problem for the value function has a unique solution yielding the triplet (s, S, p). For application purposes the explicit knowledge of this solution is needed to specify the optimal inventory and pricing strategy. Se- lecting a particular demand function we are able to formulate and implement a numerical algorithm to obtain good approximations for the optimal strategy.