Showing papers on "Randomness published in 1968"

Vibrational Analysis of Random Polymers

Abstract: The frequency distributions of some isotopically random polymers are calculated by applying Dean's negative eigenvalue theorem. It is shown that the results of calculation are in good agreement with the infrared spectra of polymers of cis‐CHD = CHD and trans‐CHD = CHD, giving strong confirmation to the previous view that the polymerization by a Ziegler‐type catalyst occurs with the cis opening of the double bond. The spectra of copolymers of CH2 = CH2, CHD = CD2, and CD2 = CD2 are also discussed. The effects of randomness and deuterium content on the frequency distribution are studied.

Dependence of the Time‐Correlation Functions of Molecular Random Motions on the Intermolecular Potential

Abstract: A general theory on the time‐correlation function and the spectral density for the random motion in molecular system is presented. We study the dependence of these functions on the intermolecular potential and on the rate of fluctuation of the potential. It is shown that the fluctuating intermolecular interactions or potentials not only introduce the randomness to molecular motion but also characterize important details of the randomness. Here we assume that the fluctuation can be regarded as a Gaussian random process contributed from the perturbers around the molecule. Therefore, the theory may be applied to the molecular motions in the liquid state. As an example of application of the present theory we discuss the collapse of multiplet structure in magnetic resonance spectrum of two‐spin system; Anderson's results for the exchange narrowing of spectrum is derived as a special case of our formulation. The correlation functions and the spectral densities for the random reorientation of diatomic molecules ...

Individual consistencies in the random generation of choices.

Abstract: Snmmary.-Ss were instructed to generate random numbers while simultaneously listening to passages of varying degrees of approximation to English, under Recall and No-recall conditions. Randomness of choices was considered an index of attentional capacity and appeared to be a stable individual difference characteristic with a fair degree of generality across stimulus and instructional conditions. When Ss are asked to generate a sequence of random letters or single digits, the degree of randomness is a function of certain task parameters. For example, if Ss are simultaneously performing a second task which requires sorting cards into 1, 2, 4, or 8 piles, the degree of randomness varies inversely with the number of sorting alternatives (Baddeley, 1966). If a neutral story is heard while generating letters, the randomness score will be lower than when generating letters alone. When the story is emotionally charged, a further decrease in randomness will occur. These drops in randomness are associated with proportional increases in story recall (Spence & Greif"). If Ss are asked simply to generate letters without the instructions to be random, i.e., freely, the resiilting distribution of frequencies correlates from .70 to .83 with their distribution in the English language (Mayzner, Tresselt, Adler, & Schoenberg, 1964). These f~nd~ngs suggest that random sequences require a certain amount of attention and that the amount of attention demanded by a second task reduces the amount which can be given to generating random letters. S is less able to keep a running account of how often he has used each letter or number (Tune, 1964). Hence, the decrease in randomness. The letter or number generating task can then be thought of as a means of monitoring attentional capacity. Spence and Greif' reported a split-half reliability of .82 (p < .01), corrected for acteni~ation, for 12 Ss who generated letters for 6 min. in a no-distraction condition. The aim of the present study was to determine whether there are consistent individual differences in randomness across varying competing-task requirements and stimul~is conditions. The data for this study are based on a recent experiment by Spence, Wolitzky, and Pezenik:'.

The Influence of Random Filament Packing on the Elastic Properties of Composite Materials.

Abstract: : A new method of micromechanical analysis of composite materials (such as boron- or glass-fiber-reinforced aluminum or epoxy) that takes account of the randomness of arrangement of the reinforcing filaments. Previous analyses assumed a regular geometric array, in which case a physically unrealistic square array showed surprising agreement with experimental data. Since available computers cannot handle a completely random arrangement, a basic pattern was generated by random-number techniques and was then reflected to obtain symmetry; this unit was assumed to repeat itself throughout the material. Solutions for the modulus of elasticity were obtained for a 10-by-10 random array, for each of 20 random geometries using constituent stiffness ratios corresponding to boron/aluminum, glass/epoxy, and boron/epoxy composites, for filament volume contents of 39, 55, and 70 percent. The assumed symmetry permitted the use of standard boundary/value solution methods. When the assumed filament packing array is randomized, the more physically realistic 'hexagonal random array' is in better agreement with the data than the 'square random array.' Since the latter results in much higher local stress concentrations, use of the square array model could lead to unduly conservative analyses. (Author)

The non‐randomness of attempts at random responses: relationships with personality variables and psychiatric disorder

Abstract: Studies have shown that subjects are not random in their responses, even when attempting to achieve randomness. In this study, normal and schizophrenic subjects were asked to give numbers from one to nine at random and paced. They were given an interpolated task, and then retested. Some statistical tests of degree of randomness were devised and it was shown that no subject was random, but that stereotypy decreased within and over test—retest. The results are discussed in terms of learning and extinction of stereotypy. Differences between introverts and extraverts were almost significant in the opposite direction from that predicted. Schizophrenics were significantly more stereotyped than normals. Finally, it was shown that for a normal subject, his test could be identified from other subjects' tests on the basis of retest protocol, the test protocol providing a kind of psychological ‘fingerprint’.

A new method of estimating the weibull shape parameter

Abstract: : The method of random hazard functions is applied to the case of the Weibull distribution and the following results are obtained: It is well known that, in the case of a Weibull distribution with two parameters alpha and beta, there is no way of estimating and testing for the shape parameter beta without knowledge of the scale parameter alpha using the usual methods based on maximum likelihood. The method of random hazard functions is now used to obtain a consistent and asymptotically normal class of estimates for beta independent of any specification whatsoever on alpha. This result enables one to test for the randomness of the underlying failure phenomena under the Weibull set up. An illustrative example is given.