Thesis (Ph. D.)--University of Wisconsin--Madison, 1963. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 151-153).

Thesis (M.S.)--University of Wisconsin--Madison, 1970. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--Catholic University of America, 1931. / Vita.

We present PTIME language-preserving techniques for the reduction of non-deterministic tree automata, both for the case of finite trees and for infinite trees. Our techniques are based on new transition removing and state merging results, which rely on binary relations that compare the downward and upward behaviours of states in the automaton. We use downward/upward simulation preorders and the more general but EXPTIME-complete trace inclusion relations, for which we introduce good under-approximations computable in polynomial time. We provide a complete picture of combinations of downward and upward simulation/trace inclusions which can be used in our reduction techniques. We define an algorithm that puts together all the reduction results found for finite trees, and implemented it under the name minotaut, a tool built on top of the well-known tree automata library libvata. We tested minotaut on large collections of automata from program verification provenience, as well as on different classes of randomly generated automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances. Taking reduction of automata on finite trees one step further, we then introduce saturation, a technique that consists of adding new transitions to an automaton while preserving its language. We implemented this technique on minotaut and we show how it can make subsequent state-merge and transition-removal operations more effective. Thus we obtain a PTIME algorithm that reduces the number of states of tree automata even more than before. Additionally, we explore how minotaut alone can play an important role when performing hard operations like complementation, allowing to obtain smaller complement automata and at lower computation times overall. We then show how saturation can extend this contribution even further. An overview of the tool, highlighting some of its implementation features, is presented as well.

A new technique for tube sinking has been developed which should, in a number of ways, help to solve the problems associated with conventional tube sinking processes, eg die wear and the need for a swaged down leading end for easy insertion through the die. The conventional reduction die is altogether replaced by a die-less reduction unit of stepped bore configuration. The deformation is induced by means of hydrodynamic pressure and drag force generated in the unit due to the motion of the tube through the viscous fluid medium (polymer melt). The dimensions of the die-less reduction unit are such that the smallest bore size is dimensionally greater than the nominal diameter of the undeformed tube, thus metal to metal contact and hence wear, should no longer be a problem. As no conventional reduction die is used, the need for a reduced diameter leading end is also eliminated. Experimental results show that greater reduction in tube diameter and the coating thickness were obtained at slower drawing speeds (about 0.1 m/s). The maximum reduction in diameter noted was about 7 per cent. Analytical models have been developed, assuming with Newtonian and non-Newtonian characteristics of the pressure medium, which enabled prediction of the length of the deformation zone, percentage reduction in diameter and drawing stress. In the non-Newtonian analysis account was taken of the pressure coefficient of viscosity, derived from the available data; the limiting shear stress, which manifests itself as slip in the polymer melt and the strain hardening and the strain rate sensitivity of the tube material. The percentage reduction in diameter predicted using the Newtonian analyses appear to differ considerably from the experimental results both in trend and magnitude. Non-Newtonian analysis predicted theoretical results which are much closer to the ones observed experimentally.

The environmental problem of carbon dioxide pollution has caused considerable interest over recent years. Much work has concentrated on catalysts for the reduction of carbon dioxide. There are two main methods for the reduction, electrochemical and photochemical reduction. There are several catalysts reported in the literature but the most selective and efficient one for the electrochemical reduction of carbon dioxide to carbon monoxide is nickel(II) 1,4,8,11-tetraazacyclodecane perchlorate (more commonly known as [Ni(cyclam)]2+(ClO4)2). In order to understand how this catalysis occurs the complex was investigated using a variety of electrodes and solvents in order to determine the best system for catalysis to occur. The best system is an aqueous solution of the complex with sodium perchlorate as the supporting electrolyte and with a mercury working electrode. The effect of macrocycle ring size was investigated using [n]aneN4 complexes, n = 13 - 16. The highest current produced under carbon dioxide was for the n = 14 ring. Subsequent complexes investigated have a [14]-membered backbone. The other important effect in the macrocyclic structure is the nature of the conformation of the complex. Cyclam itself exists as five conformations, three of which are readily accessible. The other conformations do not reduce carbon dioxide to the same extent as the original [Ni(cyclam)]2+. The origin of this difference was shown to be related to the extent of adsorption of each conformer. Also, if the chelate sequence of the cyclam is changed from cyclam to isocyclam the catalytic efficiency is lowered but the potential at which the reduction occurs is more positive. Rotating disc electrochemistry was attempted in order to find a method for comparing the catalytic efficiency of different complexes. A mercury plated copper electrode was used but unfortunately the mercury deteriorated and left behind bare copper. Copper itself showed current plateaux for reduction under carbon dioxide; these current plateaux varied linearly with (rotation rate)1/2. On closer examination the current plateaux were due to the Ni(II/I) reduction and not carbon dioxide reduction. The adsorption of the catalyst onto the mercury is important as it is this adsorbed species that is catalytically active. To determine the nature of the catalytic species various electrochemical techniques such as chronocoulometry and a.c. impedance were employed to measure the extent of the adsorption. Chronocoulometry showed that adsorption occurred on the mercury, but adsorption onto the copper surface was inhibited in the presence of carbon dioxide. A.C. impedance spectroscopy showed that adsorption occurred at -1.20 V which is considerably more positive than the redox potential of the complex. A variety of unsaturated macrocycles were also investigated for catalytic behaviour. As the unsaturated macrocycles have lower redox potentials than the corresponding saturated macrocycle, the result should be that the potential for the reduction becomes more positive. However with these macrocycles no reduction of carbon dioxide is observed under the same conditions as [Ni(cyclam)]2+, A series of new catalysts has been identified. These complexes have the ability to reduce carbon dioxide at more positive potentials with a greater current efficiency, than [Ni(cyclam)] 2+. The new catalysts are based on a [14aneN6 backbone. The extra nitrogen atoms appear to stabilise the intermediate hydrogen bonded NiI-CO2 adduct.

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