yes / Quantum systems with positions and momenta in Z(d) are described by the d zeros of analytic functions on a torus. The d paths of these zeros on the torus describe the time evolution of the system. A semi-analytic method for the calculation of these paths of the zeros is discussed. Detailed analysis of the paths for periodic systems is presented. A periodic system which has the displacement operator to a real power t, as time evolution operator, is studied. Several numerical examples, which elucidate these ideas, are presented.

toc / Chemistry / Master / Master of Science

Malonaldehyde, a very reactive member of the homologous series of dialdehydes, is associated with the autoxidative deterioration of lipids. Its measurement, in autoxidized lipid systems is an expression of the extent of oxidation, in lipids. Malonaldehyde lends itself well to such determinations because of the sensitivity and specificity of its quantification in complex lipid systems. Complete knowledge of the formation of malonaldehyde in autoxidized lipids. is lacking. Such knowledge would undoubtedly promote a better understanding of lipid autoxidation mechanisms. In this investigation, a method for detecting malonaldehyde through the use of its reaction with p-aminobenzoic acid was developed. This was adapted for use in measuring malonaldehyde in lipids and in tissue samples. The reaction between p-aminobenzoic acid and malonaldehyde was partially characterized, and a mechanism for the formation of the reaction product was postulated. The quantification of malonaldehyde in lipid systems by the use of p-aminobenzoic acid involves the use of a mild reducing agent such as stannous chloride to prevent interference from hyd roperoxides present in the system. The p-aminobenzoic acid reaction is highly specific for malonaldehyde and proceeds smoothly and rapidly at room temperature in a non-aqueous chloroform-methanol solvent system to yield a highly colored compound having a maximum absorbance at 406 mμ. and with a molar absorptivity of 73,500. The absorbance value may be converted directly to parts-per-million malonaldehyde through the use of a conversion factor in a simple equation. The limits of detectability of themethod are on the order of one ppm malonaldehyde. The measurement of malonaldehyde in the lipid fraction of tissue samples involves the prior extraction of the lipid with a non-aqueous chloroform-methanol solvent, by an extraction method which was developed for this purpose. The reaction of malonaldehyde with p-aminobenzoic acid involves the condensation of two molecules of p-aminobenzoic acid with one molecule of malonaldehyde. The reaction exhibits a rate maximum at a hydrogen ion concentrations of about 0.1 molar, and also exhibits rate dependencies upon the concentrations of both malonaldehyde and p-aminobenzoic acid. This strongly suggests that the reaction proceeds according to an S [subscript N] 2 mechanism. A postulated mechanism involves nucleophilic 1,4-addition of the amino nitrogen of p-aminobenzoic acid to the enol of malonaldehyde followed by-loss of water to form the enamine. The reaction with a second molecule of p-aminobenzoic acid involves nucleophilic substitution of the amino nitrogen at the carbonyl function of malonaldehyde followed by loss of water to form an imine linkage. / Graduation date: 1968

The rate of oxidation of copper metal to copper (I) by copper (II) in the presence of organic ligands has been determined for a variety of ligands using a flow injection analysis system to sample the reaction. The results obtained using the FIA sampling method compare favorably with those obtained in eariler work when allyl alcohol was used as the ligand. The mechanism proposed in that earlier work has been shown to be a general mechanism for the oxidation of copper metal in the presence of complexing ligands. It was found that some ligands increase the rate of the reaction beyond the ability of conventional FIA to sample many data points before the reaction reaches equilibrium. A method has been developed that allows for more rapid sampling of the reaction mixture by the FIA system, resulting in overlapping FIA peaks. These overlapping peaks can then be deconvolved by an iterative curve fitting/digital subtraction technique in which each peak in the FIA output is fitted to a model function and subtracted from the output, thus removing its effect on the peak height of subsequent peaks. The iodination of acetylacetone in acidic solution was also studied by the fast injection FIA technique. Iodine was generated coulometrically in the solution containing acetylacetone and hydrochloric acid. By this method, the keto-enol equilibrium constant of acetylacetone was determined over a range of pH's. They ranged from 2.3 x 10⁻⁵ at a pH of 2.63 to 1.8 x 10⁻⁴ at a pH of 4.03. It was also found that the reaction was first order with respect to the acetylacetone concentration.

The optimization of the competitive binding and sandwich immunoassays was investigated in order to examine some commonly encountered experimental aberrations. Experimental and theoretical results were integrated to provide a better understanding of the causes of the "hook" or "prozone" effect. The "hook" generates ambiguous results for the test sample in an immunoassay. The competitive binding assay manifests a low dose "hook" effect while the sandwich immunoassay demonstrates a high dose "hook" effect. Human growth hormone (hGH) having no repeating epitopes was examined as a model for the "hook" effect in the competitive binding assay. Three model analytes, hGH, the dimeric form of hGH (D-hGH, having a discrete number of repeating epitopes) and ferritin (multiple epitopes) with differing immunological properties were employed. To elucidate the low dose "hook" effects in the competitive binding assay the interaction of two different monoclonal antibodies with hGH was investigated. The individual monoclonal antibodies show normal behavior in a competitive binding assay, but mixtures of antibodies demonstrate a "hook" attributed to formation of multicomponent complexes in solution. Size exclusion chromatography was employed identify higher molecular weight complexes. The experimental data were supported by theoretical models assuming a circular tetrameric complex formation. The one-step sandwich immunoassay suffers from the "hook" effect irrespective of the analyte characteristics. Model analytes, hGH, D-hGH, and ferritin offer new insights into general guidelines for assay procedures allowing the analyst to quickly optimize assay conditions without a priori knowledge of the immunological characteristics of the antibody or the antigen. Experimental and theoretical data show that the high capacity solid-phase antibodies shifted the "hook" to relatively higher analyte concentrations. The effect of the concentration of labeled antibody on assay response was examined theoretically. The cause of the "hook" effect in two-step sandwich immunoassay is attributed to the desorption of the bound analyte most likely due to a conformational change after the labeled antibody interacts with the several epitopes of the analyte, hence the assay for hGH shows no "hook" effect. Two different protocols for D-hGH were implemented. These assays demonstrated a "hook" effect if the labeled antibody was allowed to interact with more than one epitope of the analyte. Multiple epitope interactions with the labeled antibody, as exemplified by ferritin, demonstrate the "hook" effect. The effect of the ferritin concentration, capture antibody and the labeled antibody was examined.

Capillary Zone Electrophoresis (CZE) is an important analytical technique used to analyze the chemical makeup of small samples with volumes on the order of picoliters. However, in the quest for smaller sample volumes, smaller capillaries are used. This research has focussed on analyzing the optical properties of these small capillaries to determine if and how they affect the fluorescence spectrum of the molecules inside the capillary. In the course of this research we have determined that for fluorescent liquids, there is no evidence of angular dependencies in the fluorescent emissions for the total intensity or the linear polarization components of the total intensity. This angular isotropy does not show any noticeable temperature dependence. We have also determined that the fluorescence spectrum from these molecules is not smooth. Even with weak reflections from the capillary inner walls, enough feedback exists to superimpose resonances on the otherwise smooth spectrum. If the reflectivity is high enough, typically when the core index of refraction is higher than the capillary's index, it is possible to cause some materials to lase. This lasing has been shown in a variety of systems by several researchers. However, total internal reflection is not required for resonances, although weak, to be present. Resonances between the cavity dimensions and the incident laser light are also responsible for a nonlinearity in fluorescence intensity normalized to volume. This normalized intensity nonlinearity may also be due partially to photoinduced decay processes that were observed. In any event, some care is required in the selection of capillary size for CZE in order to maximize fluorescence intensity per unit volume from the capillary. The use of small capillaries exposes the experimenter to a wide variety of physical phenomena which make their use and appropriate interpretation of the data somewhat complex, although manageable.

The use of scientifically operated charge-transfer device array detectors are investigated for several spatial and spectroscopic optical imaging applications in chemical analysis and are described in this dissertation. The improved optical detection capabilities of this class of solid state detectors, made up of both charge-injection and charge-coupled device (CCD) detectors, offers a number of significant advantages over previous optical detection technologies utilized for these applications. The results obtained from the investigation of the use of a scientifically operated charge-injection device based echelle spectrograph system for the on-line monitoring of heteropoly acids, after chromatographic separation, for the indirect determination of phosphate, silicate and arsenate are presented. The obtained results represent an improvement over direct aspiration into an emission source for these nonmetals, showing excellent linearity over three orders of magnitude. Results from the evaluation of a scientific CCD detector based technique for the luminescence imaging of latent fingerprint residues on glass and paper, after chemical treatment with fluorescence enhancement agents, is presented. The use of a scientific CCD for fingerprint imaging is demonstrated to be a viable alternative to those methodologies requiring the use of high power laser excitation sources and photographic film imaging. Results of the use of a scientific CCD for the spectroscopic determination of seawater pH are also presented. Discussion is given to general system design, detector characteristics and modes of operation which will result in a ship board instrument capable of making both sensitive fluorometric and precise absorbance measurements. Additional investigations presented include the use of a scientific CCD for the in situ detection of DNA fragments separated in agarose electrophoretic slab gels and aflatoxins separated on thin-layer chromatographic plates. Scientific CCD detection, in contrast to previous optical detection techniques, is demonstrated here to provide for a competitive means of component detection in these media, offering significant advantages in speed, precision and ease of analysis.

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The aim of this thesis is to explain some basic facts, examples, ideas and results in Tate’s theory and its applications. / In the first chapter, we will introduce some preliminaries of Banach algebras over k. The Tate algebra (resp. affinoid algebra) is analogous to the power series defined on the unit disc (resp. analytic set of unit disc). There are some properties of its algebraic structure. / In the second chapter we will construct the rigid analytic variety X, the topology on it, and the structure sheaf Oₓ. Tate found an interesting property, now called Tate’ Acyclicity Theorem, which makes analytic continuation stand. Moreover, by using G-topology, we define rigid analytic spaces, and we are able to paste them. The Tate curve is a good example. / In the last chapter, we introduce Schottky group and Mumford curve. A Mumford curve is obtained from P¹ discarding a compact set quotient by a group action, and it can be characterized as an algebraic curve with totally split reduction. The converse is also true. / 這篇文章的目的是闡釋Tate理論中的一些基本事實、例子、想法和結果，以及一些應用。 / 在第一章中，我們會介紹一些關於k上的Banach代數的初等事實。Tate代數（affinoid代數）類似於定義在單位圓（單位圓的解析集）上的冪級數。關於它的代數結構有一些結論。 / 在第二章中，我們會構造剛性解析簇，它的拓撲，以及它的層結構。Tate發現了一個它的有趣的性質，現在被稱為Tate Acyclicity Theorem；這個性質使得我們可以做解析延拓。此外，通過使用G-拓撲，我們構造剛性解析空間，並且我們可以將幾塊剛性解析空間“粘”起來。Tate曲線是它的一個很好的應用。 / 在第三章中，我們將介紹Schottky群和Mumford曲線。一條Mumford曲線是P¹挖掉一個緊集后除掉一個群作用而得到的，並且可以被表徵為擁有totally split reduction的代數曲線。反之亦然。 / Yuan, Zhiri. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaf 65 ). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

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