A theorem by Shah and Khatri [A.M.S. (1961) 321883-887] is extended to give the distribution of Q/X² , where Q is a positive definite quadratic form involving non-central normal variates and X² is an independently distributed chi-square variate. Conditions are given under which the distribution of this ratio reduces to that of non-central F. Kramer’s method for analysis of variance of a two-way classification with disproportionate subclass numbers is reviewed and shown to satisfy these conditions. Various functional forms of the non-centrality parameter for evaluating the power of his method are given. Additional algebraic and numerical results are obtained to compare the power of Kramer's method and the method of fitting constants (least squares) outlined by Yates [J.A.S.A. (1934) 24151-66]. A mnemonic rule, based on 310 randomly generated two-way classifications, is given for discriminating against use of Kramer’s method in situations where his method potentially may be very deficient in power as compared to the method of fitting constants. / Ph. D.

A formulation is presented which describes a new method of handling responses which are characteristically a function relating measurable random variables to mathematical variables. The formulation considers each response a random function which is called a functional observation. This statistical formulation results in each response being summarized in a convenient functional form which can be used to derive other functional relationships which describe the response. / Ph. D.

The interpretation of the data is done by two different methods. In method one each of the curves in Figure X is grouped separately with the curves of Figures VIII and IX to determine the matrix elements of the field gradient tensors, 1 since there are two different sites. / Ph. D.

A theory and method have been developed and design change drawn, for the estimation of certain stability derivatives for wings of arbitrary platform in subsonic flow. / Ph. D.

The state of polarization of neutrons emitted at an angle of 45° (Lab) from the D(d,n)He³ reaction has been determined by observing the asymmetry in scattering from carbon. Neutrons scattered at equal angles to the right and left were detected simultaneously by two cylindrical stilbene crystals, The neutrons were produced by bombarding a heavy ice target with an unanalyzed beam of deuterons from a Cockroft-Walton accelerator. The phase shifts of Meier, Scherrer, and Trumpy* were used to compute the induced polarization of carbon at an average neutron energy of 2.7 Mev. The observed asymmetries in scattering yielded neutron polarizations of 11.1 * 1.5%, 7.8 * 1.4%, and 6.0 * 1.8% at average deuteron energies of 99 Kev, 81.5 Kev, and 67.5 Kev respectively. Polarized neutrons (2.73 Mev) scattered from calcium indicated that the right-left asymmetry, P_nP_Ca changes sign in the interval 87.5° to 120° (CM). P_Ca ≤ 61.7% in the interval 0° to 180° (CM). * Meier, R. W., Scherrer, P., and Trumpy, G., "Elastische Streuung und Polarisationseffekte von D-D Neutronen an Kohlenstoff", Helv. Phys. Acta 27, 577 (1954). / Ph. D.

Propionyl-CoA carboxylase has been purified to a state of near nomogeniety, and some of its enzymatic properties relating to substrate binding and mechanism of action have been studied. The enzyme was not found to catalyze the incorporation of solvent tritium at the c-carbon of propionylâ CoA in the absence of ATP. Absolute stereospecificity was observed with regard to which a-hydrogen is replaced during the addition. / Ph. D.

The mitochondrial utilization of a-ketoglutaric and pyruvic acids have been found to be depressed in guinea pig and bovine ketosis. Addition of sodium acetoacetate to the reaction medium resulted in depressed oxidation of pyruvate and 1-ketoglutarate of isolated normal rat liver mitochondria. / Ph. D.

A method for determining the transient vibrational effects produced by application of a constant angular acceleration to a cantilever beam initially at rest was determined. This method is applicable to beams of uniform cross-sectional area vibrating in their planes of rotation. The governing differential equations include the effects of bending, shear deformation and rotary inertia. Coriolis' acceleration, however, is neglected. These governing equations were non-dimensionalized and solved by numerical means using a finite difference approach and dividing the beam's length into 12 sections, since their complexity made an exact solution appear impossible. This was done by the aid of a 1620 I.B.M. Computer. Application of this solution to an actual beam indicated that a wave propagation type of response becomes more clearly evident as the hub radius is increased. The numerical results also indicate that the initial displacements are a direct result of shear deformation. The effect of centrifugal force was also analyzed. At large values of time this force caused the beam to return to its undeformed axis. Solutions for a short time interval extending over 1100 steps, a large time interval extending over 275 steps, and another using the short time interval together with a reduced radius, 250 steps, were obtained. / Master of Science

The relationships between headspace gases in canned apple sauce and storage time and temperature, food pH and consistency, and headspace vacuum and volume were studied. The apple sauce processing method used essentially duplicated commercial procedures. Canned apple sauce was stored at l00°F for 7 or 10 months, and sampled for headspace gases with a modified Zahm air tester. Procedures were developed for sampling for chromatographic analysis gas from cans with high vacuum and small headspace, and for calculating gas volumes. A minimum headspaoe hydrogen was observed in samples within the pH range 3.45-3.75, in products of consistency within the range common to the Virginia commercial apple sauce, and in cans with higher vacuum. Maximum carbon dioxide content was noted in samples having a pH value of 3.45. Samples with more fluid consistency had more headspaoe carbon dioxide than those of higher consistency. Variations in headspaoe carbon dioxide content occurred in direct proportion to headspace size, and trends could not be associated with can vacuum. Oxygen was generally 1.2-1.9 percent of the headspace gas. Carbon monoxide was present in all samples in very small amounts. / Master of Science

The use of glass reinforcement in concrete was conceived over thirty years ago. However, it has been within the past ten years that the advantages of glass fiber over steel for use in prestressing have become known. Past research shows that, even though the physical properties of glass fiber in the form of laminated rods are desirable for prestressing concrete, the material presents several problems. The most difficult problem is that of gripping the fiber glass rods. Other problems are creep and developing adequate design criterion. The present investigation confirms many of the previous findings with respect to gripping devices and presents data on tensile tests performed on modified commercial grips. The Fanngrip is the most promising commercial grip investigated. Post-tensioned beams are designed and tested in flexure. The recorded test data is compared with the design data to verify existing design criterion. Present design formulas provide reliable results up to tho cracking load. Deflections are calculated with sufficient accuracy by empirical equations; however, a method of finding ultimate load remains to be found. / Master of Science