M. S.

The method of dimensional analysis has been used for almost a century with experimental methods to obtain, among other things, prediction equations in the physical sciences and engineering. Only recently has the method been considered in the statistical sense. A thorough literature research is presented, including history, method and theory, problems, and disadvantages of dimensional analysis. The dimensional analysis preliminary model is transformed into a multiple linear regression model and is compared to a quadratic regression model with respect to prediction of a single variable in some practical examples. Whereas dimensions are the main consideration in the dimensional analysis model, they are ignored in the quadratic regression model. Two sets of experimental data were used, each set on both models, and the respective residual sum of squares and multiple correlation coefficients compared. The results were similar in both cases. The correlation coefficients of the quadratic model were higher than those of the dimensional analysis model and the residual sum of squares were lower for the quadratic than for the dimensional analysis model. / M.S.

This investigation was undertaken to determine the effectiveness of ultrasonic energy in removing spray residue from collards, to determine its effect on the content of ascorbic acid and carotene levels in the treated tissues, and to investigate the influence of ultrasonic energy on the respiratory activity and the histological changes of the tissues involved. / Ph. D.

The previously unreported 3-methyltetrahydrothiophene I-oxide (<u>1</u>) and 3-methyl-2, 5-dihydrothiophene I-oxide (<u>2</u>) have been prepared by oxidation of the corresponding sulfides. The structure of these unsymmetric sulfoxides was established by chemical and physical methods. Nuclear magnetic resonance analyses have provided significant information concerning some stereochemical aspects of these molecules. In the case of <u>1</u>. which has four possible configurations, both <u>cis</u> and <u>trans</u> isomers were shown to exist in the synthetic material. A study on the temperature dependence of the nuclear magnetic resonance spectrum of <u>2</u> between -34° and 100°, suggested little or no association of a dimeric nature between molecules of this unsaturated sulfoxide. The rapid and clean reduction of <u>2</u> to the corresponding sulfide was carried out using hydriodic acid and detected by gas chromatographic analysis. The partial base catalyzed isomerization of <u>2</u> to 3-methyl-4, 5- dihydrothiophene 1-oxide (<u>13</u>) was carried out in sodium hydroxide solution and detected by gas chromatographic analysis of the reduced products. Maximum isomerization occurred after 96 hours when <u>2</u> and <u>13</u> were present in a ratio of 1.78:1 respectively. This finding is similar to the previously observed isomerization of the corresponding sulfone, but is in contrast to the lack of isomerization of the olefinic bond of the related 2, 5-dihydrothiophene l-oxide. A plausible mechanism has been proposed for this interesting isomerization of <u>2</u>. Sulfoxide <u>1</u> was reacted with various Grignard reagents and shown to undergo a substitution reaction at the α-carbon atoms. Predominant reaction occurred at position-5 of <u>1</u> and binary sulfide mixtures composed of 2-substituted-4-methyl- and 2-substituted-3-methyltetrahydrothiophenes were obtained in yields ranging from 17-31%. The ratio of isomeric sulfides ranged from 1.50:1, in the case of phenylmagnesium bromide, to 8.09:1 when using neopentylmagnesium chloride. The binary sulfide mixtures were desulfurized and the hydrocarbon products were identified. In this manner, the structure and composition of the components of the sulfide mixtures was established. Preparative-scale gas chromatography was used to separate two binary sulfide mixtures. Desulfurization of the individual sulfides led to the discovery of isomerization reactions which occurred during desulfurization. By-products of the Grignard reaction were identified as 3-methyltetrahydrothiophene, 3-methyl-2, 3- and 3-methyl-4, 5-dihydrothiophene, and, in some cases the alkene and alcohol derived from the Grignard reagent. A reaction pathway, by which these products and by-products may conceivably be formed has been proposed. Results of the reaction of the unsaturated sulfoxide <u>2</u> with Grignard reagents were quite different than with sulfoxide <u>1</u>. Sulfoxide <u>2</u> underwent reaction at the sulfur atom with a subsequent cleavage of the ring yielding single dienyl sulfides. These novel compounds were formed by a stereospecific ring cleavage of <u>2</u>, a reaction similar to that previously observed with the corresponding sulfone. The dienyl sulfides, 1-phenylthio- and 1-n-propylthio-2-methyl-1, 3-butadiene, were isolated in good yield and characterized by their spectral properties and by conversion to known compounds. The only detectable by-product of this reaction was a trace amount of 3-methyltetrahydrothiophene. A mechanism, consistant with the data obtained, has been suggested. / Ph. D.

The analysis of the distortion which results when frequency-modulated waves are passed through linear networks is investigated by the Fourier method and the Quasi-steady-state method. The major enphasis is placed on the Fourier method, and extensive digital computer programs are developed to allow this method to be implemented on the modern, high-speed digital computer. In the Fourier method, the frequency-modulated wave which is applied to the input of a linear network is broken up into its Fourier spectrum. Each of the resulting ‘'sideband'' frequencies is then passed through the network and is subjected to alterations in amplitude and phase. The output wave is then synthesized by taking the vector sum of the "weighted" sideband components. In contrast to the single pair of sideband frequencies generated by amplitude modulation, the spectrum of a frequency-modulated wave contains an infinite number of sideband components. Fortunately, only a relatively small number of these sidebands have significant influence on the total makeup of the waveform. The number of significant sidebands is proportional to the value of modulation index. When the modulation index is high, the number of significant sidebands is very large and the number of computations required by the Fourier method becomes enormous. Previously considered to be completely impractical, the Fourier method was usually abandoned in favor of the Quasi-steady-state approach. However, the digital computer techniques developed in the course of this investigation allow for a fast, economical, and convenient analysis based on the Fourier method even when the modulation index is relatively high. Analyses were performed for values of modulation index up to 45 and techniques are discussed for increasing this range. The Quasi-steady-state method is based on the assumption that the frequency of the input wave is changing slowly enough that the frequency of the output wave at any instant is equal to the "instantaneous fregquency' of the input wave. This method is inherently in error since it neglects the transient terms generated by the changing frequency. To compensate for this error, it is the general practice to incorporate correction terms, usually in the form of an infinite series. The Quasi-steady-state method is more effective at low modulating frequencies (high modulation index). While the analysis contained in this paper considers in detail only a first-order correction, the application of higher-order correction terms is discussed. The results obtained from applying both analyses to a complex, multi-section filter indicate that the computer solution of the Fourier method is preferable for intermediate values of modulation index. Experimental verification of the Fourier method is obtained by simulating the system on an analog computer. The advantages of this rather novel approach are discussed in some detail. The agreement between the results predicted by the digital computer and those obtained experimentally leaves no doubt to the validity and accuracy of the analysis. Digital computer programs for analyzing the distortion using each of the above methods are given. Subprograms are also included, some of which can be used independently. Among these are a program that computes Bessel functions of the first kind for positive and negative orders and a program that computes the minimum phase shift of a network from its atténuation. All programs are written in the FORTRAN IV computer language and were executed on the IBM 7040/1401 system. / Ph. D.

The purpose of this study is to examine variances in the case of distributions obtained by truncating a given distribution at various points. In particular, the truncated distributions are restricted to nested increasing intervals, and the question is posed whether the variances of these distributions are monotonically increasing. The answer to this question is relevant to the use of conditional information for purposes of estimation and prediction. Several tables are presented in the thesis which provide evidence of the property of monotonic variance for nested increasing intervals of truncation in the case of univariate distributions., The Monte Carlo procedure is used to determine a table of standard deviations for the standard normal distribution with the same points of truncation reported by Clark(2). Clark's table is given intact, and it is used in comparison with the new table reported here as a check on the Monte Carlo procedure used in the present study. Distributions other than the standard normal distribution are examined as well, namely, a Pearson U-shaped distribution and a bimodal distribution consisting of a mixture or two Pearson distributions. Graphs of the U-shaped and bimodal distributions are given. A section is given in which dispersion for a bivariate case is examined in terms of the bivariate normal distribution. An interesting trend among the covariance matrices is observed in the data reported in that section. A separate computer program for each type of distribution was written and used to calculate the variances of the truncated distributions. FORTRAN programs and flow charts are presented in the Appendix. Explanation of the tables and procedures used to calculate the entries in the body of each table are given in each section as well as some discussion of the results presented. / Master of Science

Several areas of the bionomics of Culicoides in Virginia were given preliminary investigation. These included surveys for larval habitats, colonization attempts with Culicoides guttipennis (Coq.), host preference studies and adult activity studies. Breeding sites of 22 species of Culicoides were located and briefly described. Samples of mud, debris, etc. from suspected breeding sites were brought into the laboratory and maintained at 70°F in food containers with screened tops. Most species were found to prefer a specific type of habitat (i. e. tree-holes, polluted areas, etc.) but exceptions were occasionally observed. Colonization attempts with C. guttipennis have resulted in the successful establishment of this species in the laboratory. The colony has been maintained for 12-15 generations and is currently producing over 1,000 adults per day and an excess of eggs. Techniques developed for larval and adult maintenance have proved to be highly successful in recent months. Adults were held in a constant temperature cabinet at 80°F ± 2° and 85% relative humidity ± 10% in semi-darkness (less than 1 ft-c ). Eggs were collected on moist filter paper exposed in shell vials. Fly eggs hatched in 3 days and the young larvae were introduced into aquaria containing leaf mold from hardwood forests and distilled water. Larvae pupated in about 12 days and adults emerged about 3 days later. The adult diet consisted of rabbit blood, raisins, sugar cubes, honey water and a 6:6:1:13 mixture of powdered milk, sugar, egg solids and water administered in capillary tubes. In host preference studies 15 species of Culicoides were collected on 1 or more of 14 different hosts used in animal-baited traps. Animals were restrained and exposed on a small platform. After 15 min the animals were covered with a collecting cage. Flies were aspirated from the traps and killed in 70% ethanol. Even though some preferences possibly were shown by some species, more data will be needed before definite conclusions can be drawn. In adult activity studies, most species appeared to be more abundant from 9 PM to 3 AM as indicated by light traps. This was especially noted in C. stellifer, C. haematopotus and C. venustus. The activity of C. haematopotus was fairly constant up to 3 AM and then decreased. C. stellifer and C. venustus activity decreased as the night progressed. / Doctor of Philosophy

The objectives of this study were: (1) to estimate the effects of certain non-genetic sources of variation in weight, gnde, and condition of beef cows; (2) to estimate the heritability of weight, grade. and condition of beef cows; and (3) to estimate the genetic, phenot;rpic, and environmental correlations between weight, grade, and condition of beef cows. Weights, grades., and condition scores taken on 1371 Angus cows were used to evaluate the genetic and environmental nature of these traits. This sample of cows represented 365 sire groups. Four models were used in this study: 1. Model A - Cow weight and grade were considered dependent variables; herds and sires within herds were considered random independent variables; and season, age, condition, nursing status, and their interactions were considered fixed independent variables. Least-squares procedures involving Henderson's (1953) Method II were used to adjust tor fixed effects and to obtain variance and covax-iance components. Heritability estimate and correlation coefficients were obtained by paternal half-sib analysis. 2. Model B differed from Model A in that condition 3 score was considered a dependent variable instead of an independent variable. 3. Model C was the same as Model A except that the coefficients (kₒ and k₂) for the within sire (σw²) component of variance included in the among sire and herd adjusted expected mean squares (EMS) were considered unity whereas as in Model A they were calculated according to Method II of Henderson. 4. Model D - Heritability estimates were computed by doubling the estimate of intra-sire regression of offspring on dam from 198 dam-daughter pairs representing 63 sire groups. The dam-daughter pairs were part of the group or 1371 cows. The results of this study indicated that season, age, condition score, nursing status, and age by nursing status remain significant when condition score was not considered as a fixed environmental effect (Model B). However, a comparison of the magnitude of the mean squares for these effects in Models A and B indicated that season, age, and nursing status are highly confounded with condition score. Season and flesh condition were found to have a significant effect on grade of beef cows when they were included in the same model (Model A). When condition score was not included (Model B) age had a significant effect on grade. Age, season, and nursing status were found to have a significant effect on flesh condition (Model B). Paternal half-sib heritability estimates for cow weight using Models A, B, and C were 0.38 ± 0.11, 0.29 ± 0.11, and 0.56.± 0.11, respectively. Estimates for grade from the same models were 0.49 ± 0.11, 0.43 ± 0.11, and 0.67 ±0.12, in that order. Estimates from Model A should be the most reliable. The differences in the estimates from Models A, B, and C, illustrate that variation in heritability estimates is not entirely due to genetic differences. Considerable variation can occur depending on how much adjustment has been made to fixed effects, and the methods used in estimating the variance and covariance components. The heritability estimates of cow weight and grade obtained by intra-sire regression of offspring on dam were 0.22 ± 0.14 and 0.10 ± 0.06, respectively. The paternal half-sib heritability estimate for condition score was 0.31 ± 0.11, which implies that adjusting cow weights and grades for condition may actually involve adjusting for genetic differences as well as differences due to environmental influences. The correlation between weight and grade or beef oowe was found to be largely genetic whereas the correlation between condition and cow weight or grade was primarily environmental. / Ph. D.

This research presents an analytical investigation of the buckling of eccentrically stiffened orthotropic cylinders and includes the influence of prebuckling deformations. Nonlinear equilibrium equations and boundary conditions are derived by using energy principles. The stiffened cylinder consists of a cylindrical shell made of a homogeneous orthotropic material with eccentric stiffeners on its surface. The rings, or circumferential stiffeners, are considered to be located discretely on circumferential lines along the length of the cylinder and the stringers, or longitudinal stiffeners, are considered to be closely spaced so that their properties can be averaged (smeared out) over the stringer spacing. The stiffeners are considered to be beam elements, to be equally spaced, and to have the stiffener twisting accounted for in an approximate manner. Non-linear Donnell type strain-displacement relations for the shell and the stiffeners are defined and the strain energy of the stiffener-cylinder system is formulated. The governing nonlinear equilibrium equations and boundary conditions are then obtained by the principle of minimum potential energy and the fundamental lemma of calculus of variations. The discrete ring terms are included in the nonlinear equilibrium equations by use of a Dirac delta function. By a perturbation of the nonlinear equilibrium equations and boundary conditions, a set of nonlinear prebuckling equations and boundary conditions and linear buckling equations and boundary conditions are obtained which govern the prebuckling deformations and stresses and buckling of a stiffened orthotropic cylinder with discrete rings. Solutions of the prebuckling and buckling equations are obtained for classical simple support boundary conditions and for loadings of axial compression, lateral pressure, and combinations of axial compression and external or internal pressure. The solutions are obtained by the method of finite differences in which the governing equations and boundary conditions are changed to a system of second order differential equations which are then written in terms of finite differences at stations along the length of the cylinder. The difference equations are formulated in terms of a matrix equation which is solved by a modified G~ussian elimination technique. Solutions of the prebuckling and buckling equations for the case where the rings are considered to be smeared out are presented for comparison with the discrete case. A Galerkin solution of the buckling equations for discrete rings assuming classical prebuckling deformations is also presented in the Appendix. Computed results for two types of contemporary stiffened cylinders are presented in order to study and illustrate the importance of prebuckling deformations, discrete rings, and eccentrically applied compressive loads. The results show that the predicted buckling loads for stiffened cylinders may be substantially affected by using an analysis which takes into account prebuckling deformations. / Doctor of Philosophy

This study was undertaken as a beginning of an analysis of "zoning in action." Henrico County, Virginia, has had a rural zoning ordinance in force for over a third of a century. During this period, the County was transformed from a rural locality to an urban-suburban one. The study had as one of its objectives the tracing of rural zoning in response to population growth in Henrico County. The study sought to probe the types of requests sought, the manner in which they were sought, and whether or not they were granted. The consequences of zoning on real estate values were also probed. The study has shown how the initial, rather broad Ordinance has evolved in 35 years into a complex, quite restrictive ordinance. In 1933, there were four use districts. Today there are 16. Building regulations have been strengthened by the "beefing up” of older regulations and the addition of many new ones. As new problem uses have appeared, they have been incorporated into the Ordinance. Population pressures and the advent of unforeseen situations were responsible for most changes. Variance requests have been similar since the inception of the Ordinance. Sideyard and setback requests have predominated. As the Ordinance has become more restrictive, other requests have become more frequent. The vast majority of requests continue to be granted. Public interest in variance requests is for the most part dormant. The granting of variance requests affect assessed real estate values significantly only if the variance renders the property useful, where previously it was not. Zoning requests, over time, have changed markedly, however. Prior to urbanization of the County, most zoning requests were from an agricultural designation. Today agricultural requests trail business and residential requests in number. Most importantly, the ratio between zoning changes recommended by the advisory board and granted by the Board of Supervisors has changed. As requests have increased in size and in value, and as opposition has become more prevalent, professionals have dominated the presentation of requests. Rezoning of a tract to a more intensive use usually results in a doubling of its assessed value. / Master of Science