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The interchange of traffic density between lanes moving in the same direction is investigated on the basis of a simple mathematical model. Emphasis is placed on the question of stability, i.e., attenuation of disturbances from an “equilibrium density distribution.” A solution is obtained for a system of differential difference equations with a time lag corresponding to the interaction of two lanes. This solution is directly applicable to other problems described by similar equations, such as the follow-the-leader problem. The solution is generalized to n lanes, and it is found that the inherent instability is twice as great for n approaching infinity as it is for two lanes.

The stochastic theory of chromatographic kinetics is extended in two directions: (a) To include diffusion effects, and (b) to treat the n-site adsorption problem. In the first case we show that the solution to a first passage problem yields the moments of residence time in the mobile phase in a rather simple form. For the second problem we show that the central limit theorem allows us to deduce rather general results about the distribution of residence time.

This paper deals with a system capable of randomly attaining two states “on” and “off". For convenience this system is pictured as a pulse train. The question is, what is the expected amount of time that n n of such systems are in the same state simultaneously. The answer is shown to depend on the probability of a system being in a given state at a specified time. A formal solution for the Laplace transform of this probability is given.

THE NOISE GENERATED BY A STREAM OF TRAFFIC IS CONSIDERED USING AS A MODEL, A STREAM OF SIMPLE ACOUSTIC SOURCES. IN CONTRAST TO AN EARLIER ANALYSIS, THE POSSIBILITY OF A NEGATIVE EXPONENT HEADWAY DISTRIBUTION BETWEEN SUCCESSIVE CARS IS ALLOWED. THE MODEL IS SHOWN TO BE EQUIVALENT TO A SHOT PROCESS, AND THE CUMULANTS ARE READILY CALCULATED. IF TRAFFIC CONSISTS OF SEVERAL TYPES OF VEHICLES, EACH TYPE GENERATING NOISE OF A DIFFERENT INTENSITY, THEN IN THE LOW DENSITY REGIME THE TRAFFIC CAN BE REPRESENTED BY A SUPERPOSITION OF NONINTERACTING ACOUSTIC SOURCES. MODIFICATIONS OF THE SHOT NOISE MODEL CAN BE MADE TO TAKE INTO ACCOUNT SURFACE GRADIENTS OR SOUND-ABSORBING SURFACES BY A SUITABLE DISTRIBUTION OF ACOUSTIC SOURCES. /AUTHOR/

The general problem discussed is the optimal addition of an internal ring road to a circular city with a circumferential ring road. It is assumed that both the origins and destinations have circular symmetry, and that speed in any direction is a function of radial position only. Routes are chosen so as to minimize journey times. For plausible models of destination distributions and speed vs. radius relationship it is shown that optimal positioning of the internal ring road is insensitive to the ratio of speed at the city center to speed at a distance infinitely far from the city center. Furthermore, the benefit in improved journey time does not depend strongly on positioning of the internal ring road. /Author/

In this paper we present a method for the inversion of specific heat data to find the vibrational frequency spectrum of a solid. Our results are given in terms of a power series in UJ, the frequency. In this series the coefficients depend on C v (T) and its d~rivatives at T=O. The series thus derived is valid only in an asymptotic sense, but represents an improvement over inversions by Montroll and Kroll which require a knowledge of functions formed from the data, and the evaluation of double integrals over these functions, A method for forming the successive values of Cv(n) (0) from experimental data is also presented. One of the most frequently measured physical characteristics of a solid is the specific heat at constant volume Cv (T), where T is the temperature. The behavior of this function has quite accurately been predicted by various characterizations of a lattice of atoms which have harmonic interactions. If it is assumed that the specific heat can be attributed solely to harmonic effects, then it can be written as an integral over the vibrational frequency spectrum 1

This paper considers an infinitely long line of traffic moving on a highway without traffic lights or other inhomogeneities. It is assumed that each car travels at a constant speed which is a random variable. A further assumption is that when one car overtakes another, passing is always possible and occurs without change of speed. it is shown that any initial headway distribution must relax to a negative exponential distribution in the limit of t t becoming infinite. The statistics of passing events are examined, and it is shown that the probability of passing (or being passed by) n n cars In time t t is described by a Poisson distribution.

The response learning and associative hookup stages of paired-associate learning were studied in 8-year-old children as a function of intralist conceptual similarity. Response learning, as measured by response recall, was facilitated by the presence of similar items, while the associative stage, as measured by a matching test, was somewhat impeded by the use of category instances. These results are similar to those for young adults’ learning, and indicate the utility of the stage-analysis model in the study of paired-associate learning by children.

Summary A case of isoimmunization by the agglutinogen B as a result of a heterospecific pregnancy has been discussed in detail. A suggestion that Group O blood be given in similar cases is noted and advised. Included is a complete review of the literature.

We describe an extremely efficient and simple extraction procedure for ecdysones (moulting hormones) from plants. It is directly applicable to the crude ethanol extract of plants and can be readily scaled up to large scale extractions. The method is based on the principle of reversed-phase adsorption chromatography, and offers the advantage of versatility and economy in time and material.

The stereochemistry of theaspirone (9), blumenol A (5), and blumenol B (8) has been established; a stereospecific preparation of theaspirones is also described.