Considerable attention has been devoted to the rank correlation coefficients of Spearman and Kendall, denoted by r_S and r_K respectively. These coefficients were first proposed as measures of association between two groupings, requiring no assumptions on the parent distribution of the observations. Later work considered the distributions of r_S and r_K when the parent distribution is the bivariate normal. This study is an investigation of the moments and related properties of Spearman's r_S and Kendall's r_K when the underlying distribution is the singly truncated bivariate normal. / Ph. D.

The principal objective of th1s thesis has been accomplished. The technique for the analysis of a space frame has been developed and described. A computer program has been wr1tten and presented. A test frame was constructed, analyzed and tested and the results for deflections and rotations compared. / Master of Science

The effect of thyroid hormones on purine biosynthesis was studied in vitro. With 100,000 x g supernatant fraction of rat liver homogenate, the results suggested that thyroid hormones stimulated total purine synthesis from labeled glycine-1-¹⁴C. Further studies indicated that these hormones stimulated AMP synthesis but inhibited GMP synthesis. The stimulatory effect on AMP synthesis was found to be due to the stimulation of adenylosuccinate synthetase. Adenylosuccinate synthetase was isolated and purified from rat liver. The maximum stimulatory effect of these hormones occurred with 2.5 x 10⁻⁵ M thyroxine (T₄) and 2.5 x 10⁻⁹ M triiodo-L-thyronine (T₃). A slight increase or decrease in concentration of these hormones caused a drastic decrease in their stimulatory effect. Some analogues of T₄ were also studied and results of such experiments agreed qualitatively with their effects in vivo. Those which are physiologically active are capable of stimulating this enzyme and those which are physiologically inactive had little or no effect on this enzyme. Based on these results, a hypothesis, that thyroid hormones regulate the levels of AMP and GMP synthesis, was proposed. The significance of this preferential stimulatory effect on AMP synthesis was discussed. / Ph. D.

Pure cultures o! the yeast S. cerevisiae do not follow the classical continuous culture theory when tested in a variety or chemostats. Using a Coulter Counter, yeast populations were sized and enumerated electronically over a range or dilution rates. Total dry weight and Kjeldahl nitrogen per cell were determined for a variety or dilution rates. From these data it was shown that the yeast definitely increased in size as the dilution rate increased. Also, it appeared that the ratio of rate of synthesis of cell wall material to the synthesis of proteins decreased as the dilution rate increased. Step changes in various environmental factors (dilution rate, medium concentration, glucose concentration, ammonium sulfate, and temperature) indicated that yeast populations may not show a smooth transition from the initial to the final steady states. Decaying oscillations of the yeast population were observed in response to step changes in dilution rate and glucose concentrations. Step changes in ammonium sulfate or in total medium concentrations resulted in smooth responses to a new population level. To investigate the complex responses to dilution rate and glucose a frequency response analysis was employed. The growth of S. cerevisiae varied in a sinusoidal fashion in response to sinusoidal forcing of dilution rate and medium concentration. Bode diagrams were prepared for yeast response to dilution rate and medium concentration. Time constants were determined from the Bode diagrams. The time constants were in the order of several minutes and possible relations to growth control mechanisms can be postulated. The time constants probably pertain to accumulation of intracellular materials. A two-stage continuous culture system was built to investigate the interaction of E. coli and S. cerevisiae. By feeding a continuous pure yeast culture from the first stage into the mixed culture second stage it was found that the E. coli apparently produces a substance that inhibited the growth of yeast. / Doctor of Philosophy

The purpose of this investigation was to test the existing methods of correlating pipe-line data on dilatant fluids in a laminar flow, to gather pertinent physical properties of dilatant fluids, and to propose a theory for the mechanism of dilatancy. In order that the correlation for flow of dilatant fluids in conduits could be tested it was necessary to build a flow apparatus from which pressure drops and flow rates could be measured, to develop viscometric equipment such that flow curves could be determined at shearing conditions similar to those in the flow tests, and to uae the data from the two sources to calculate the variables of interest: the friction factor, f, and the modified Reynolds number, R'_e. A flow apparatus suitable for the purpose outlined was constructed from 1-1/4 inch, Schedule 40 galvanized pipe with motive power provided by a Moyno pump, was provided with temperature control and calming sections, and was provided with a ten foot test section. Flow curves were determined independently with a specially constructed cone and plate viscometer. Provisions were made to determine pressure drop over the fittings: coupling, glove valve, and 90 degree elbow. Dilatant fluids consisting of corn starch suspended in the liquids water, ethylene glycol, and glycerine with values of flow behavior index, n from 1.15-2.50 flowing in laminar flow between R’_e of 12-410 were studied. Results of the investigation showed that the Metzner-Reed correlation method could be used in correlating dilatant, laminar flow. Equivalent resistances of fittings, expressed as equivalent diameters of pipe, were found not to match those found in the literature for Newtonian fluids, except that for the case of couplings the value was negligible for both fluid types. Rather, much lower values were found for the case of flow through a globe valve, and the value found for the 90 degree elbow was strongly dependent on the flow rate. A cone and plate viscometer was used to study the dependency of the Power Law parameters on temperature for a starch suspension in glycerine and ethylene glycol. The parameter n was found to be independent of temperature over the 80-130° F range of temperature studied. Conversely, K varied with temperature in a manner described by an Arrhenius equation and its rate of change with temperature roughly paralleled that of the glycerine. A theory of the basic mechanism responsible for the phenomenon of dilatancy was presented and discussed, and its relation to the Power Law Model established. / Ph. D.

If X is a complex with a triangulation and if P is a homeomorph of a polyhedron in X with respect to this triangulation, then P is tame in X if there is a homeomorphism h of X onto itself and another triangulation of X in which h(P) is a polyhedron. A function from one complex X into a complex is called tame and is said to preserve tame sets if for each tame set PcX, f(P) is tame. Tame local homeomorphisms from triangulated n-manifolds into triangulated n-manifolds and tame light open maps of 2-manifolds into themselves are homeomorphisms. Connected complexes are compact if and only if every tame map of the complex into itself has a polyhedral image. Tame linear maps of Euclidean spaces and tame simplicial maps on triangulated n-manifolds with boundaries are homeomorphisms if their images are of dimension greater than one. Functions from polyhedra into topological spaces which take tame arcs onto sets consisting of finite number of components have images of, at most, a finite number of components. If the function and its inverse takes tame sets onto tame sets then the image is connected, provided its image is in a complex. If the function is from a topological space into a polyhedron, then it is continuous if and only if its inverse takes tame arcs onto closed sets. Finally a function from a complex to a complex is continuous if its inverse takes tame sets onto tame sets. A function from an n-manifold into an n-manifold which has an image of dimension greater than one and which takes arcs onto arcs or points is a homeomorphism. A function from a compact triangulated n-manifold into a topological space which takes tame arcs onto arcs or points and whose image is not an arc or point is a homeomorphism. A function from a triangulated n-manifold into an n-manifold which takes tame arcs onto arcs or points and whose image is of dimension greater than one is a homeomorphism. A function from a triangulated n-manifold into a triangulated n-manifold which takes tame arcs onto connected tame sets such that the image of no tame arc contains a triod is a homeomorphism if its image set is not a point, arc or simple closed curve. Finally there are tame maps which raise the dimension of sets. And there are 1:1 maps which do not preserve tame sets. A K-R manifold is a n-manifold with boundary whose interior is Eⁿ and whose boundary is Eⁿ⁻¹. A 1:1 map of a 2-dimensional K-R manifold onto a 2-dimensional K-R manifold is a homeomorphism. / Doctor of Philosophy

This paper provides a systematic study of order statistics drawn from discrete parent distributions. New procedures are followed for the derivation of the distribution of the r^th order statistic x_(r) and of the joint distribution of x_(r), x_(s) (s > r), that is, we first derive the cumulative probability distribution, from which the probability distribution comes directly. This approach is easier than the usual method, moreover the formulae for the c.d.f. derived in this way can be easily computed. To get the moments of X_(r), we use convenient formulae involving the tails of the c.d.f. of X_(r) rather than the p.d.f. of X_(r). The moments are then readily derived from general results for discrete distributions. We show the analogy between the results in the continuous and discrete cases. Applications to three discrete distributions are given. We consider some results on uncorrelated statistics which were established in the continuous case and show that the same results hold also for the discrete case. Many recurrence relations between moments of order statistics are derived in the discrete case yielding the same results as previously given by Govindarajulu (1963) and Sillitto (1951, 1964) in the continuous case. / M.S.

In order to optimally design and utilize any system or process, it is necessary to know the parameters within which the process must function. This thesis developed some of the more important organizational parameters affecting the capital expenditure process. A primary objective that has operational significance for capital expenditure decision-making purposes was developed. The primary objective was formulated in a framework of uncertainty utilizing the basic characteristics of a closed-loop information-feedback system. Since it was formulated in a framework of uncertainty, it allowed for variation; therefore, the limits of this objective were established. The enterprise damps oscillations in its complex interconnected system of objectives to assure relative stability within the limits of the developed primary objective. The damping methods employed by the enterprise place parameters on the capital expenditure process. The important parameters that were discussed are: 1. The common and unique characteristics that evolve from the pattern in which an enterprise increases in magnitude. 2. The organizational structure that evolves in an effort to plan, coordinate, and control all activities of the enterprise. 3. The administrative processes utilized within the framework of the primary objective and the organizational structure to perform all activities relative to the capital expenditure process. Although detailed design considerations were beyond the scope of this thesis, it was emphasized that an awareness on the part of the decision-maker that these parameters exist and have an impact on decision-making can contribute to improved capital expenditure decisions within an existing capital expenditure process. In the design or redesign of a capital expenditure process, it appears essential that they be considered. / Master of Science

The aim of the study was to determine the differences between inbred and linecross litters in litter size and litter weight at birth, 21 and 56 days of age. The effect of line of dam, age of dam and year of birth on each of the production traits was also studied. Data comprising 556 litters (229 inbred and 327 linecross) from seven inbred lines developed by the U.S.D.A. at Beltsville were analyzed by the method of least squares. There were no differences between the inbred and linecross litters for number farrowed, but highly significant differences (P<0.01) were observed for all other traits. The lines of dam differed considerably in performance; the L-LB line gave the largest and heaviest litters and the L-CW line the smallest and lightest litters at each of the three ages. Age of dam at farrowing was the most important single factor affecting both litter size and weight. It accounted for 70 percent of the variation in both traits at birth and about 50 percent at weaning. Sows weaned litters, which were 2.4 pigs larger and 119 pounds heavier than those weaned by gilts farrowing under one year of age. / Master of Science

In this paper, the application of the diffusion equation to the problem of moisture movement below the fiber saturation point is investigated. The general diffusion equation was solved by numerical methods for the case of a concentration-dependent coefficient and a boundary condition of a specified concentration variation. Experimental concentration-distance curves were generated from the drying of yellow poplar. Solutions to the diffusion equation using coefficients from the literature were then compared with the experimental data. The diffusion coefficient of yellow poplar was determined directly from the concentration-distance curves by the method of Matano. On the basis of the above information, a diffusion coefficient was determined which accurately describes the drying of yellow poplar between 61 and 181 moisture content. / Master of Science