The method known in the literature as dynamical finite element analysis is investigated and applied to wave propagation problems occurring in membranes and thin shells of revolution. Both semi-infinite and finite versions of cylindrical and conical membrane shells are studied and a finite membrane shell having a meridional curve which is parabolic is solved. A thin cylindrical shell is also considered in order to determine the effect of including shear and rotary inertia. The source excitation is generally considered to be the constant velocity motion of one end, but the results for a stress pulse input to one end of a semi-infinite cylindrical membrane shell are also given. The thin cylindrical shell is considered as an initial value problem. The difference in the solutions resulting from prescribing an axial or tangential velocity excitation at the end of a semi-infinite conical membrane shell is presented. The method itself requires a careful ordering of the calculations and the principles for determining the correct order are discussed. The rules for handling the boundary conditions for finite shells are shown to follow logically from this ordering of the calculations. An energy balance check on the computations is shown to be an effective independent check on the correctness and stability of the solution, and a discussion of the conditions used to verify that the numerical results are the solutions is included. The results for the finite problems are new results and the semi-infinite problems are discussed with respect to previously published results. / Ph. D.

The capabilities of a biological waste treatment system designed to utilize filamentous microorganisms were defined in this study. Various chemical and physical tests such as pH, suspended solids, COD, BOD, sludge production, and oxygen utilization were used to determine the effects of parameters like flow rate, support media area, organic loading, pH, and the BOD-to-nitrogen ratio. Findings of the study indicated that the removal rate, suspended solids concentration in the effluent, and percent COD remaining in the final growth cell of the growth chamber increase as the dilution rate or flow rate increase. The study also showed that an organic waste can be effectively treated by a filamentous system over an influent pH range of 2.65 to 7.45 with an oxygen requirement similar to that found in other biological treatment systems. An increase in organic loading caused an increase in the suspended solids of the effluent with a decrease in COD removal efficiency. The removal rate was found to be directly proportional in influent COD concentration from a concentration of approximately zero to a concentration equal to 1200 milligrams per liter. A nitrogen deficient waste at both neutral and acid pH's was treated effectively by this system. For a pH range of 2.65 to 2.85, the critical BOD:N ratio was found to be greater than 45:1. A BOD:N ratio in excess of 90:1 was found to be critical for a waste with a pH range of 6. 6 to 7. 45. Recirculation of biological solids was not needed to retain sufficient culture in the growth chamber for efficient treatment of the waste. Sludge production values were found to be close to values for the activated sludge process treating organic wastes. The average value for "a" on a COD and total solids basis was found to equal 0.48 for most of the conditions studied. However, a tendency for sludge to build up for a period of time and then slough off was noted. The average value for "a" decreased significantly to 0.18 when the pH was lowered to a pH of 2.60 and increased significantly for BOD:N ratios above the critical ratios. / Ph. D.

A bitopological space (X,τ,μ) is a set X with two topologies. The study of bitopological spaces was initiated by J. C. Kelly. In this thesis, we study pairwise-separation axioms as defined by J. C. Kelly, C. W. Patty, and F. P. Lane. In addition, definitions for semi-compactness, semi-paracompactness, and bicontinuous functions are proposed and are related to the definitions of pairwise-separated spaces. Finally, quasi-pseudo-metric spaces are defined, and a number of quasi-pseudo-metrization theorems are summarized. / Master of Science

In an analysis of supply, Joan Robinson in her book, The Economics of Imperfect Competition, digresses first on the concept of rent to a heterogeneous resource, and secondly on the four cost curves of an industry. This study re-examines these digressions and seeks to provide the student of economics with a clearer understanding and appreciation of the tools Robinson uses, but at the same time it expands the analysis into additional situations faced by competitive firms. In the digression on rent, recognizing the use of marginal analysis in the application of a variable resource with a variable heterogeneous resource in the production of a product, this study finds that the price per efficiency unit of a quality is not limited by the price per efficiency unit of other qualities of the resource. It is the relative supply and demand for a quality that determines the price per efficiency unit of the quality and, therefore, the quality economic rent. In the digression on four cost curves, the cost curves of industries under conditions of scarcity and/or economies of large-scale industry are examined. Of the four cost curves the industry faces (i.e., average cost excluding rent, marginal cost excluding rent, average cost including rent, and marginal cost including rent), it is the long-run average cost including rent, as Robinson proposed, that represents the competitive industry's long-run supply curve. Economies and scarcity only serve to change the shape of this supply curve. / Master of Science

In this thesis we investigate the properties of M-spaces and M*-spaces, which are generalized metric spaces. Chapter II is devoted to preliminary results, and in Chapter III we prove the characterization for M-spaces theorem of K. Morita [12]. This theorem states that a space X is an M-space if and only if there exists a quasi-perfect map from X onto a metrizable space T. Chapter IV is concerned with the relationships between M-spaces and M*-spaces. We first prove an M-space is an expandable, M*'-space and then show that every normal, expandable, M*-space is an M-space. Using Katetov's Theorem, we show that in a collectionwise normal space, X is an M-space if and only if it is an M*-space. We conclude by generalizing this to the following. In a normal space X, X is an M-space if and only if it is an M*-space. Chapter V is concerned with the study of M-spaces and M*-spaces under quasi-perfect maps. We also prove the Closed Subspace Theorem for M-spaces and M*-spaces and establish the Locally Finite Sum Theorem for M-spaces and M*-spaces. In Chapter VI, we give an example of a T₂, locally compact M-space X, which is not normal and therefore not metrizable. We also give an example of a T₂, locally compact M*-space Y, which is not an M-space, but is however the image of X under a quasi-perfect mapping. / Master of Science

Aspartate transcarbamylase (carbamoyl phosphate: Laspartate carbamoyltransferase, E.C. 2.1.3.2.) activity from a thermophilic strain 7-11-05 of Chlorella pyrenoidosa appears to be stabilized during and after (NH₄)₂SO₄ precipitation of the enzyme by at least two factors, one having a molecular weight greater than 10,000 and the other having a molecular weight less than 10,000. The high molecular weight factor(s) appears to be an albumin-like protein which is important in stabilizing the activity of the reconstituted enzyme during storage in buffer. The low molecular weight factor(s) is necessary for stabilization of enzyme activity both during and after (NH₄)₂SO₄ precipitation, and it appears to be organic in nature. Stabilization of enzyme activity in whole son1cates during aging appears to be dependent on a heat-stable factor(s) which has a molecular weight of less than 1,000. Aspartate transcarbamylase activity can be stabilized and modulated in vitro by a number of different compounds such as carbamoyl phosphate, UMP, uridine, and cytidine. This low molecular weight stabilizing factor(s) is suggested to be similar to the low molecular weight factor(s) necessary for stabilization of the enzyme during and after (NH₄)₂SO₄ precipitation. The decay of enzyme activity during aging in vitro is proposed to be due to a breakdown of a polymeric form of aspartate transcarbamylase into subunits which have greater catalytic activity than the native enzyme and which are labile 1n the absence of a stabilizing factor(s). An active breakdown of a stabilizing factor(s) could not be observed in whole sonicates, and proof of an active breakdown of the enzyme itself must await further experimentation. / Master of Science

The influence of DMSO (dimethyl sulfoxide) on foliar absorption and translocation of herbicides and plant membrane permeability was investigated. Primary leaves of bean (<i>Phaseolus vulgaris</i> L., var. Black Valentine) were treated with ¹⁴C-labeled DMSO, 3,6-dicholoro-<u>o</u>-anisic acid (dicamba), 1,1′-dimethyl-4,4′-bipyridinium salt (paraquat) and 2-choloro-4(ethylamino)-6-(isopropylamino)-<u>s</u>-triazine (atrazine). DMSO at concentrations of 25% or more caused by varying degrees of acute toxicity. However, ¹⁴C was generally distributed throughout the plant 5 days after application of DMSO-¹⁴C, as determined by autoradiography and counting. DMSO, 30%, was not as effective as 0.25% Tween 80 (non-ionic surfactant containing polyoxyethylene sorbitan monooleate) in enhancing the absorption and translocation of dicamba, a phloem-mobile herbicide. Tween 80 was more effective than DMSO in enhancing the foliar uptake of atrazine and distributing it within the treated leaves. The contact toxicity and apoplastic movement of paraquat was increased with DMSO. Spectrophotometric studies revealed the absorption spectrum of paraquat was shifted by addition of DMSO. Root uptake of KH₂³²PO₄ by corn (<i>Zea mays</i> L., var. VPI 646) was inhibited by 3% or higher DMSO. Treatments of DMSO reduced oxygen uptake in corn roots. DMSO failed to increase diffusion of labeled solutes through isolated plant cuticular membranes. In <i>Beta vulgaris</i> L. (beet) permeability studies, DMSO increased efflux of betanin from root cells. Combining atrazine with DMSO resulted in a greater increase in membrane permeability. Membrane permeability of corn mitochondria as determined by characteristic swelling and shrinkage was unaffected by DMSO. / M.S.

This is an exploratory thesis. The objective of this thesis is to isolate human measurement error in a physical measuring environment. A secondary objective is to evaluate this measurement error, if successfully isolated, with respect to its effect of biasing statistical quality control tests that describe a manufacturing process. The author of this report designed a specialized measurement jig that was used to isolate human measurement error. Specifically, the tests involved seven human inspectors making micrometer measurements of the diameters of cylindrical brass pieces. Several physical factors were rigidly held in control or eliminated by the design of the jig and the experimental process. This was necessary to obtain as accurate an estimate as possible of the human error. The human measurement error in this experiment was successfully isolated. Further analysis of this measurement error led to the hypothesis that it probably can bias statistical quality control tests that describe a manufacturing process. This bias is reasoned to have a greater effect on statistics that describe processes with very close physical tolerances. / Master of Science

Using Richard Krutchkoff and Stephen Custer's stochastic model for pollution in estuaries, a Stochastic Simulation study of random inputs of pollution particles in estuaries was made. This study investigated four types of input in each of twelve estuarial situations and examined the resulting average distributions of both the biochemical . oxygen demand and the oxygen deficit. For two types of input, the number of input particles ranged from zero to ten and was chosen randomly from a binomial distribution and a uniform distribution. Another type of entry used an input of zero or ten particles, each with probability of .5. These three situations were compared with a constant input of five particles, which was the mean number of input particles for each of the probability-input cases. Graphs were plotted using all four types of input for each estuarial situation. On the basis of these graphs, the study indicates that the average distributions of both pollution particles and oxygen deficit particles which result from using random inputs do not differ significantly from each other and from the average distributions obtained by using the mean input. / Master of Science

Previous discrete analysis techniques applied to shear walls with openings have utilized finite elements with linear displacement fields. These elements require relatively fine meshes in order to correctly describe the reverse bending behavior of the connecting beams and to avoid an idealization for the shear wall which is too stiff. This study presents the use of finite elements which have additional degrees of freedom and allow curved deformation patterns to exist. These refined elements are also combined with plane frame beam elements which are used to idealize slender connecting beams in pierced shear walls. This combination of elements is also applied to analysis of the interaction of shear walls with their surrounding frames in plane frame shear wall combinations. A computer program is developed and presented which is capable of handling a wide range of general shear wall configurations. Only the geometry, loading conditions, and elastic properties are used as input to the program. The output consists of the input data, as a check, then the displacements and stresses at each node as well as member and actions for the beam elements if they are used. Several refined finite element solutions are compared with experimental results for pierced shear wall problems of varying story heights and beam to shear wall stiffness ratios as well as frame and shear wall configurations. These comparisons provide initial guidelines for the efficient use of this refined element in the analysis of general shear wall configurations. / Master of Science