In Part I the Maximum Likelihood/Entropy (ML/E) method of estimation of the cell probabilities for multinomial and contingency table problems is derived and discussed. This method is a generalization of the Maximum Likelihood estimator to situations when small probabilities are to be estimated and the standard Maximum Likelihood estimator is inadequate. In addition when no sample exists the technique gives meaningful results by reducing to the method of Maximum Entropy. The ML/E method is based on assuming an entropy prior on the cell probabilities and closely resembles the Pseudo-Bayes methods of Good, Fienberg, and Holland in which Dirichlet priors are assumed. Methods for calculating the ML/E estimates for varying circumstances including multidimensional tables are presented. Comparisons with other estimation methods are made and recommendations for selection of the more appropriate method in particular situations are given. In Part II we consider the Kolmogorov-Smirnov one-sample statistic. Various methods for calculating the Kolmogorov-Smirnov one-sample statistics have been developed in the literature. A transformation of an approximation method is here derived and some of its properties discussed. The main value of the new formulae is to obtain better convenient approximations in the lower tail than have been possible using other methods. The formulae are related to the theta functions. The relationships between various methods are given, as well as recommendations for each method of a usable range of the independent variable. An analysis is made-of the errors obtained by use of the approximation. / Ph. D.

Oidaematophorus monodactylus (L.) is a plume moth commonly found feeding on hedge bindweed (Convolvulus sepium L.) in southwestern Virginia. Females maintained at 23.9 + 1°C laid an average of 173 eggs, 61% viable, during a 10-day oviposition period. Average larval leaf consumption was 13 cm² at 18.3°C, increasing to 16 cm² at 29.4°C; over 60% was consumed by the last instar. Mean development period from egg to adult was 28.3 days at 23.9°C. O. monodactylus completely defoliated a hedge bindweed plant which was infested at the rate of 5 larvae per leaf in greenhouse cage experiments, and caused a significant decrease in the mean percentage of leaf and shoot production as well as total plant length with infestations of 3 larvae per leaf in field cages. This indicated that inundative releases of late instars in early June could reduce the growth rate and seed production of hedge bindweed plants. An estimate of the initial direct cost of rearing 10,000 third instars for a June release totaled a little less than $8,000; of which 30% are non-recurring costs. A second insect feeding on hedge bindweed is the leaf miner, Bedellia somnulentella (Zeller), which can be found in southwestern Virginia from September through October. Females maintained at 23.9 ± 2°C laid an average of 169 eggs, most of them within the first 8 days of oviposition. The highest rate of pupation was at 23.9°C (98.0), but only 4.6% pupated at 29.4°C. Less than 5% of field collected larvae were parasitized by Apanteles bedelliae Vier. / Master of Science

A comprehensive. qualitative and quantitative survey of parasites of 176 gray squirrels. Sciurus carolinensis pennsylvanicus, Ord. 1815, was conducted from September, 1966, to July, 1969, in southwestern Virginia. Most of the hosts came from Montgomery County, some being taken also from Giles and Craig counties. Of that total, 167 were examined for coccidia and intestinal flagellates; 84 were examined for blood parasites; 175 were examined for helminths and 106 for ectoparasitlc arthropods. The incidence of coccidiosis was 91% in which five species were described and identified with the genus, Eimerla. The sporozoan, Hepatozoon griseiscuri Clark. 1958, occurred In the blood as evidenced by a 58% incidence in stained blood smears and 79% in blood concentrates. Excysted gametes of this species were kept in vitro for four days without any apparent union or multiplication. The cysts of the flagellate, Giardi. sp., are reported for the first time in this host and occurred in 5% of those examined. Gray squirrels, hamsters, white mice, and a chipmunk were successfully infected with cysts obtained from a naturally infected squirrel. ln vitro cultivation of the trophozoites was partially successful. Cultures were maintained up to 21 days. In examinations for helminths, 3l of the hosts harbored adult cestodes of which two species were identified and 62% harbored nematodes of which 12 species were identified. From habitats designated "town, woodlot, forest fringes and remote forest," the highest incidence of nematode infestation occurred In the forest fringes sample. Nematodes were generally more prevalent among male squirrels than females and the average high incidence occurred during the spring. Numbers of worms per infection were generally higher in summer. The most common species were Citellinewa bifurcatum Hall, 1916. (45%), Strongyloides robustus Chandler, 1942, (28%), and Bohmiella wilsoni Lucker, 1943, (14%). The arthropod survey indicated 97% of the hosts were infested.Four species of lIce, two flies, one flea, one tick and six mites were reoovered. The greatest percentages of hosts infested, based on individual parasite species, were generally those collected during winter. The most common arthropods were Neohaematopinus sciuri Janoke, 1932, (81%). Orchopeas howardii (Baker, 1895), (74%) and Enderleinellus longiceps Kellogg and Ferris, 1915, (67%). Twenty-four adult squirrels (12 male. 12 female) were examined for total ectoparasites using a hair dissolving technique. Also the surface areas of those squirrels were calculated by body regions so that parasite densities could be determined. The results showed the highest densities generally occurred on the back, followed by legs, underparts, bead and tail. Parasite densities were generally greater on males. The preferences by the various species for certain body regions were determined from density data. A number of incidental arthropods were also encountered in these studies. Modified nest-funnels were constructed and placed in campus woodlots and monitored for a year. A list of the arthropod species occurring in these nests is given. Several new host records, a number of distributional records and one new species were evidenced in this study. / Ph. D.

Though some of the discrete distributions, for example the binomial, hypergeometric, Poisson, are well tabulated, often statisticians use the percentage points of approximating continuous distributions when analysing discrete data. In this thesis, the exact relationships between certain discrete and continuous distributions are established, and these relationships are used for setting confidence limits and significance testing of hypotheses. In Chapter 1, statements of all distributions and mathematical functions used in this thesis are made, and also some approximations are mentioned without proofs. In Chapter 2, exact relationships between discrete distributions (the binomial, negative-binomial, and Poisson) and continuous distributions (the F and χ²) are proved. In Chapter 3, use is made of the approximate and exact relationships between discrete and continuous distributions, for setting confidence limits on the parameters of the discrete distributions. Chapter 4 consists of the approximate and exact significance testing of hypotheses by using the approximate and exact relationships, given in Chapter 2. In Chapter 5, two-sample, exact and approximate, significance tests of hypotheses on the Poisson distribution are performed, in the case of fixed number of events experimentation and fixed time experimentation. / M.S.

The cost of handling and disposal of sewage sludge is a major expense in sewage treatment. Often half of the treatment plant expense is in the purchase and maintenance of sludge handling equipment. The sludge problem becomes particularly acute with activated sludge processes because of the large volumes of waste activated sludge produced and the nature of the activated sludge itself. The object of this investigation was to conduct laboratory scale investigations of the effects of aerobic digestion on activated sludge dewatering and to attempt to determine the chemical and biological mechanisms affecting sludge filterability. The results of this investigation showed that aerobic digestion can have a considerable effect on sludge filterability. The filterability of all sludges was improved with moderate aeration at 20° C. The degree of improvement depends on the nature of the fresh sludge, the rate of aeration during digestion, the temperature during digestion, and the time of digestion with the optimum time of digestion between four to six days. The mechanism of filtration improvement during aerobic digestion appears to be biological in nature. Biologically produced extracellular polymeric substances are secreted by or exposed on the surface of bacteria during the endogenous phase of metabolism. These polymers cause coagulation and bridging between sludge particles, thus affecting the filtering properties. This phenomenon occurs only when oxygen is present in the system. However, the organisms responsible can survive up to four days without the artificial addition of oxygen. A study of various operating parameters in aerobic digestion leads to some further conclusions regarding sludge filtration. Factors which have a detrimental effect on filtration are: lack of dissolved oxygen, excessive mixing, low temperature during digestion, and chlorination of sludge before filtering. Factors which do not appear to have a significant effect on filtration are: differences in dissolved oxygen concentrations above two mg per liter, and the maintenance of a neutral pH in the digester. / Ph. D.

A one-tenth scale model of a skewed reinforced concrete rigid frame bridge was constructed and tested both within the elastic range and to ultimate load. The model was fabricated of reinforced concrete using a 1: 3.8 : 0 mix and 1/8 inch deformed reinforcing bars. A total of 57 SR-4 type AR-7 rosette gages were used to measure the strains on the surface of the concrete at selected positions. An additional 108 SR-4 type AR-7 and AR-7-4 strain gages were fastened to the steel reinforcing. Deflections were measured at 11 points of the deck and supporting reactions determined by suitable dynamometers. The vast amount of strain data was presented in tables. Part of it was converted into stresses and these integrated to find the internal reactive forces and moments at selected sections. However, the unknown behavior of concrete in biaxial tension and difficulty in establishing the precise position of the neutral surface prevented as close a check of static equilibrium as would have been desirable. / Master of Science

Today, increases in expenditures are creating tremendous strains on the financial resources of state and local governments. As these demands for services increase, the state and local governments continuously find their financial resources incapable of bending to meet these needs. Currently state and local governments together combined spend twice as much as the federal government to provide public services to the citizens. Education, roads, welfare, public health, hospitals, police, sanitation are all state and local responsibilities with the cost of providing these services falling primarily upon state and local sources of revenue. Consequently, state and local taxes have been raised almost to the saturation point and the bases of old taxes have had to be enlarged. / Master of Arts

Cell structure was observed in polycrystalline alpha-titanium deformed up to 10% true strain at room temperature. These cells appeared to be slightly elongated rather than equiaxed. The cell boundaries were identified to be the {101̄0} type planes. Flow stress recovery of alpha titanium at 500 and 550ºC proceeded in two stages: (1) an initial rapid recovery during the first 6 hours and (2) a leveling off after 6 hours. Dislocation structure was studied by using transmission electron microscopy. During the first stage of recovery, significant rearrangement of dislocations took place. At this stage fairly regular dislocation loops appeared to surround the subgrains. The segments of the dislocation loop were found to lie along <101̄0> type directions on the (0001) plane, and [0001] type directions on the {112̄0} planes. In the second stage, continued rearrangement of dislocations formed low angle boundaries. The segments of dislocations lying along the <101̄0> type direction reacted to form networks on the basal plane, and those lying on the {112̄0} planes continued to remain aligned along [0001] direction. It was postulated that some of the subgrains formed as a result of rearrangement and interaction of dislocations developed twist networks on the (0001) planes and tilt boundaries on the {112̄0} type planes. An inverse relationship between the strength contributed by subgrain structure and the subboundary spacing predicted an increase in the subgrain size at the higher recovery temperature. The measured and the predicted value were in reasonably good agreement. / Master of Science

Triaxial tests under high loading rates and different confining pressures simulate the multi-pass effect of a tractor wheel loading on the soil. A volume measuring technique was developed to be used in triaxial tests conducted under high loading rates. A sandy clay agricultural soil was tested under predetermined conditions using an INSTRON loading frame, a differential pressure transducer and an APPLE Il + microcomputer. A preliminary analysis indicated that the measuring technique that was developed, was capable of recording volume changes under high loading rates. Stress-density plots were created using the obtained data and a mathematical model was developed relating stress to density. Stress-strain data was used to evaluate the soil parameters under the Mohr-Coulomb failure criteria. Furthermore, the influence of the initial soil density on the soil behavior was evaluated and subsequently compared to the results of a similar study conducted under a different initial density. / Master of Science

The amino acid requirement for milk protein synthesis was investigated in the rat mammary cells in tissue culture. Studies involved: 1) the amino acid reduction from a positive control (3X) back to a negative control (1X) for each of the essential amino acids that were present in the 1X-MEM (Omission Study) [X refers to the amino acid concentration of Eagle's minimal essential medium (MEM)], 2) the addition experiments which resulted in an inverse relation to those of the Omission studies, and 3) a three-dimensional central composite experiment with three variables (X₁ = lysine; X₂ = methionine, valine and arginine; X₃ = isoleucine, tryptophan, threonine, phenylalanine and histidine), embracing 15 treatment combinations. In addition, supplemental studies were conducted which determined: 1) the effect of varied labeled amino acid precursors (¹⁴C-U-lysine, phenylalanine and leucine) on the measured synthesis of milk protein, 2) the effect of varying cell density (6 x 10⁶ to 6 x 10⁷) on protein synthesis, and 3) the response to graded amino acid complement (1X through 5X) on milk protein synthesis. Supplemental studies indicated that: 1) synthesis of β-lactoglobulin and β-casein in response to the labeled amino acids were significant (P<.05), 2) cell numbers between 6 x 10⁶ to 6 x 10⁷ did not significantly (P>.05) alter the rates of the milk protein synthesis, and 3) the response of amino acid complement addition to the 1X-MEM was linear (P<.01) for β-lactoglobulin and β-casein synthesis. Data analysis from Omission and Addition experiments revealed that: 1) the first limiting amino acid was lysine, 2) the second limiting group of amino acids were methionine, valine and arginine, and 3) the least limiting amino acids were tyrosine, leucine and glutamine. The response surface study determined that the optimal combination of essential amino acids for the maximum milk protein synthesis were: 1) lysine = 15X, 2) methionine, valine and arginine = 4.5X, and 3) isoleucine, tryptophan, threonine, phenylalanine and histidine = 1. 5X elevation over that present in the 1X-MEM, and 4) leucine, tyrosine, cystine and glutamine = 1X. On the basis of these findings, it was possible to construct the optimal essential amino acid complement unique to the rat mammary cells in tissue culture for the maximum milk protein synthesis. / Ph. D.