Dielectric heating of quartz oscillating in several organic liquids

The dielectric heating in quartz has been measured by the substitution method and its dependence on the nature of the liquid in which the crystal oscillates has been examined.     

Unique eccentric point graphs

A graph G is defined to be a unique eccentric point graph (a u.e.p. graph) if each point of G has a unique maximum distance point. Here u.e.p. graphs which are self-centered are characterized. Two construction procedures are given for generating families of u.e.p. graphs from known u.e.p. graphs. Furthermore, some special classes of u.e.p. graphs are studied in detail.     

A study of the behaviour of solid-state membrane electrodes: Part III. A model for the response time

A model is proposed to explain the response time of solid-state membrane electrodes, in the range of potential—time curves corresponding to seconds or minutes. Several causes of slow response time are considered. In the range of milliseconds to seconds, diffusion seems to be the rate-determining factor, but for times exceeding about 10s, dissolution or crystallization and charge transfer at the membrane seem to be the predominant factors. A mathematical model is derived. The principle is applicable to any solid-state membrane electrode and takes into account the change in response time with changes in the nature or concentration of the test ion and in the surface electrochemical properties of the membrane.     

Ultrasonic absorption constant in liquids by an improved optical method

The optical diffraction set up as originally employed byDebye andSears andLucas andBiqdard has been used with various modifications to estimate the intensity of sound fields at two or more points along the axis of an ultrasonic beam travelling in a liquid and thereby to determine the absorption coefficient of the liquid medium. Almost all these methods involve a two step operation with the attendant possibility of errors due to variation in the conditions under which the two observations are made. In the method here reported two axially parallel beams of parallel monochromatic light are made to traverse the liquid normally to the direction of propagation of the sound beam and the resulting diffraction spectra are brought to focus on a common photographic plate. Sound intensities at two points separated by a known distance are thus measured simultaneously under identical conditions. Absorption coefficients calculated for half a dozen liquids by this method are reported. The values compare very favourably with those obtained by other precision methods.     

Probability distributions of the fractional differences of the structure amplitudes and intensities of two related crystals

The probability distributions of the fractional intensities and amplitudes of x-ray reflections from a pair of imperfectly related structures are derived when both the structures satisfy the requirements of a given type of basic Wilson distribution. These two distributions are used to obtain theoretical expressions for 2 new fractional type ofR-indices which are expected to be useful in the final stages of refinement. The theoretical distributions are also used to deduce some theoretical distributions which are useful as tests for centrosymmetry via the random permutation method. The theoretical values of the relevant semi-cumulative functions are also tabulated.     

Discounted,positive, and noncooperative stochastic games

In this paper, we consider the stochastic games ofShapley and prove under certain conditions the stochastic game has a value and both players have optimal strategies. We also prove a similar result for noncooperative stochastic games.