In the study of blast waves from a finite sphere, it has been observed that in addition to the primary strong shock wave ahead of the driving gas, a second shock also forms inside of this driving gas. This formation of the second shock will invalidate all the existing theories of blast waves in that an additional non-isentropic region actually exists inside of the interface between the driven and the driving gas. This thesis investigates the behavior of this second shock and the resultant flow patterns. / Ph. D.

This dissertation deals primarily with the development of the technique of orthogonal statistics and the use of this technique to investigate sampling properties of moment estimators of parameters of the negative binomial distribution. The general technique of orthogonal statistics which is based on the existence of an infinite set {q_r(x)} of orthogonal polynomials associated with a particular distribution, enables one to obtain expansions of sampling moments of statistics which are functions of say, the first k sample moments m₁, m₂,…, m_k. The thesis describes the technique in general, and gives tables which facilitate the expansion through terms in n⁻⁵ of sampling moments of statistics which are functions of any four sample moments. The need for the development of this technique resulted from an interest in the problem of investigating sampling properties of certain moment estimators for the case of the negative binomial distribution. Thus further work was done on the technique for this particular case. Tables are given in the thesis which simplify the procedure for moment statistics which result from a sample taken from this particular distribution. Sampling properties of moment estimators for the negative binomial distribution were investigated. The distribution forms considered in depth were due to Anscombe [Biometrika, 37 (1950}, pp. 358-362] with parameters λ and α, Evans [Biometrika, 40 (1953), pp. 186-211] with parameters m and a, and Fisher [Annals of Eugenics, 11 (1941), pp. 182-187] with parameters p and k. The purpose of this study was to obtain an insight into the behavior of expansions through high powers of 1/n (e.g., terms in n⁻⁴) of the bias, variance, and higher moments for these estimators. It was felt that the usual asymptotic properties described by the first term approximations might be misleading for practical cases (i.e., ordinary sample sizes). The results verified what was suspected. For the moment estimators of Ansaombe's form, when α > λ the sample sizes needed to make high order terms negligible for the expansion of the bias and variance were extremely large. (For one particular case, in order to use the usual asymptotic variance safely one would need an n of 2 million.) This then reveals the hazardous practice of using the first term approximation and resulting in a very serious under-assessment of the true variance of the estimate of α. Since for Fisher's form k̂ = α̂, the same applies. For Evans' form, the situation was in marked contrast. Higher order terms were "damped off" with much smaller sample sizes, and in most cases one is justified in using first term approximations. Studies for Evans' estimators were confined to the range λ > 1 and α > 1. The results for the estimators of Anscombe's form were compared with similar results for the maximum likelihood estimator of α, in order to ascertain the effect on efficiency of the chaotic nature of the n⁻³ term in the expansion of the covariance determinant of α̂. The maximum likelihood results were taken from Bowman [Thesis submitted for Ph.D. degree, Virginia Polytechnic Institute, Moments to Higher Orders for Maximum Likelihood Estimators with an Application to the Negative Binomial Distribution]. This study revealed that there is a striking similarity in the n⁻³ term in the covariance determinant for the two estimators. This made the "true" efficiency almost identical to the asymptotic efficiency in cases when sufficiently large sample sizes are used to "sink" terms beyond n⁻³. This statement cannot be generalized, however, to include any sample size, since for α > λ only relatively large sample sizes "damp off' further terms in the covariance determinants for both estimators. Hence one cannot be sure of the behavior of these determinants beyond n⁻³ unless these large sample sizes are used. Tables and charts are given which display the nature of the expansions given in the text. In particular, charts are given of minimum sample size needed in order that the expansions given can safely be used as approximations. / Ph. D.

The observations which have been noted and. discussed are consistent with the proposed hypothesis that molybdenum inhibits Some facet of protein Synthesis <u>in vivo</u>. The hypothesis warrants further investigation and with the rapid improvements in protein synthesis experimentation, definitive experiments should be possible. / Ph. D.

The general problem considered in this thesis is to determine an optimum strategy for deciding how to allocate the observations in each stage of a multi-stage experimental procedure between two binomial populations (e.g., the numbers of successes for two drugs) on the basis of the results of previous stages. After all of the stages of the experiment have been performed, one must make the terminal decision of which of the two populations has the higher probability of success. The optimum strategy is to be optimum relative to a given loss function; and a prior distribution, or weighting function, for the probabilities of success for the two populations is assumed. Two general classes of loss functions are considered, and it is assumed that the total number of observations in each stage is fixed prior to the experiment. In order to find the optimum strategy a method of analysis called extensive-form analysis is used. This is essentially a method for enumerating all the possible outcomes and corresponding strategies and choosing the optimum strategy for a given outcome. However, it is found that this method of analysis is much too long for all but small examples even when a digital computer is used. Because of this difficulty two alternative procedures, which are approximations to extensive-form analysis, are proposed. In the stage-by-stage procedure one assumes that at each stage he is at the last stage of his multi-stage procedure and allocates his observations to each of the two populations accordingly. It is shown that this is equivalent to assuming at each stage one has a one stage procedure. In the approximate procedure one (approximately) minimizes the posterior variance of the difference of the probabilities of success for the two populations at each stage. The computations for this procedure are quite simple to perform. The stage-by-stage procedure for the case that the two populations are normal with known variance rather than binomial is considered. It is then shown that the approximate procedure can be derived as an approximation to the stage-by- stage procedure when normal approximations to binomial distributions are used. The three procedures are compared with each other and with equal division of the observations in several examples by the computation of the probability of making the correct terminal decision for various values of the population parameters (the probabilities of success}. It is assumed in these computations that the prior distributions of the population parameters are rectangular distributions and that the loss functions are symmetric} i.e., the losses are as great for one wrong terminal decision as they are for the other. These computations show that, for the examples studied, there is relatively little loss in using the stage-by-stage procedure rather than extensive-form analysis and relatively little gain in using the approximate procedure instead of equal division of the observations. However, there is a relatively large loss in using the approximate procedure rather than the stage-by-stage procedure when the population parameters are close to 0 or 1. At first it is assumed there are a fixed number of stages in the experiment, but later in the thesis this restriction is weakened to the restriction that only the maximum number of stages possible in the experiment is fixed and the experiment can be stopped at any stage before the last possible stage is reached. Stopping rules for the stage-by- stage and the approximate procedures are then derived. / Ph. D.

Dried rumen microblota were isolated from fistulated steers. Proximate analyses were conducted and the amino acid composition and B-vitamin content were determined. Protein quality tests were carried out using the Bender-Miller method. The data obtained from the investigation indicated that the protein quality of dried rumen microbiota is comparable with that of dried defatted egg, dried milk, fish meal and meat meal, but it is better than that of a soy protein and wheat gluten. No amino acid deficiency appeared in the feeding trials even though the amino acid composition showed that the dried rumen microbiota might be deficient in sulfur-containing amino acids. / Master of Science

The solution to the problem of a satellite with a small constant thrust and under the influence of a central force field presents difficulties due to equations non-linearity. An investigation was made to determine what range of values of the thrust parameter could be utilized to obtain a valid approximate solution for the case of tangential thrusting. The investigation was accomplished by developing programs for the 1620 High Speed Digital Computer, since the solution to the exact and approximate equations would otherwise be exceedingly laborious. Under the assumption of no atmosphere, and neglecting the earth's oblateness, the study showed that the validity of the Kryloff and Bogoliuboff method was dependent on both the specific thrust aud the vehicle speed. For a Speed corresponding to an orbit of smaller eccentricity it was determined that the method of Kryloff and Bogoliuboff remained valid for larger values of W than when V was a velocity corresponding to an orbit with a greater eccentricity. The method of Kryloff and Bogoliuboff represents a practical approach to the solution of satellite motion both from the aspect of ease of application and reasonable calculation times. / Master of Science

For lunar satellites within a few hundred miles of the lunar surface the primary cause of disturbance from pure Keplerian motion is the disturbing force due to the moon's noncentral gravitational field which, unlike the earth's field, is unsymmetrical and rotating. This thesis presents a first-order approximation to the motion of lunar satellites under the forces resulting from this field. The results are a set of equations which give the short period, long period and secular variations of a slightly modified set of Delauney elements. A typical set of orbital characteristics are utilized to obtain an estimate of the order of magnitude of the variations in the various elements. / Master of Science

The purpose of this investigation was to test three insecticides on all the life stages of the alfalfa weevil. The objectives were to obtain information on the toxicity of certain insecticides on the alfalfa weevil in the laboratory, to establish standard susceptibility curves of the life stages of the alfalfa weevil to the insecticides tested, to establish a basis for insect resistance, to compare the speed of action of certain classes of insecticides and to observe the effects of certain insecticides on molting, feeding and other processes that may be affected. Dibrom, heptachlor epoxide, and Indian were tested against various life stages of the alfalfa weevil. These three insecticides were chosen because of the differences in their chemistry and activity. Dibrom, a volatile organophosphate, could be expected to act fast but have relatively limited residual life.Heptachlor epoxide as a cyclodiene compound should have exhibited the characteristic latent period of from two to six hours before symptoms of its activity appeared. The residual activity should be great. Indian, a more stable organophosphate than Dibrom, would be expected to be somewhat intermediate between the other two in speed of action and residual activity. Each insecticide was impregnated in filter paper at the dosage of 100 micrograms per square centimeter of filter paper surface. The insects were introduced on to the filter paper for continuous exposure to the insecticide residue. Mortality and certain other effects were recorded according to time of exposure. In general, responses of the alfalfa weevil to the three insecticides were comparable. One insecticide may have been quicker acting than the other two against a particular life stage, but the differences in the effects of the insecticides were not great. In every case, the three insecticides inhibited feeding, molting, or maturation to another life stage. / Master of Science

Two age factors were studied: the age of the roach at the time of testing, and the age of the female parent at the time reproduction occurred. Age groups from 1-3 days to 25-28 days were used to test the first factor and the first three egg eases were used to test the latter. Age was found to be a statistically significant factor when malathion, aldrin, and DDT were tested on both sexes of the normal strain. However, because of inconsistencies and a lack of differences of any great magnitude, it is believed that the differences in all but the aldrin tests were of no biological significance. In the aldrin tests it appeared that as the age of the roach increased, susceptibIlity gradually increased. The tests using aldrin on the Aldrin-resistant strain were significant for the females. Resistance in this strain appeared to increase from the 1-3 day age group until it reached a peak in the 10-12 day age group, then decreased to a level equal to or lower than that of the younger age groups. Statistical significance was found for the parental age factor in about one-half of the tests. However, it was of little biological significance because the variations were of a small magnitude and inconsistencies between the males and females occurred of ten. / Master of Science

The objective of this thesis investigation was to design an experiment to investigate superheat effect on gate velocities pressurized and unpressurized gating system each having two gates, and to analyze statistically any interrelationship between these variables in CO₂ molds. A discussion on metal flow through different parts of a gating system, with a minimum of turbulence and gas aspiration, and a discussion of hydrodynamic principles relating to gating systems were given. The realization of these conditions is desirable because it results in improved casting, fewer rejects, and greater economy in a casting production. This was followed by a discussion on metal flow variables. Principle and use of instrumentation used in the experiment was discussed. Split-split-plot type of statistical design was used. Statistical analysis of results were made. The author concluded that, the type of gating system (pressurized or unpressurized) and individual gate location have significant effect, whereas superheat (100-300°F.) has no significant effect on gate velocities of aluminum - 12 percent silicon in CO₂ molds. Also, all the there variables are independent of each other. / Master of Science