The work reported here is concerned with the measurement of the spin-lattice relaxation of protons in water, acetone, a D₂O - acetone mixture and various aqueous solutions of acetone. The theory to account for the decay rates has been outlined for a general case and has been applied in particular to acetone-water mixtures. The NMR technique has been described briefly. Temperature dependences of T₁ for all solutions have been investigated. It has been found that the relaxation in mixtures are slower than predicted by the theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Sapote gum polysaccharide was examined for homogeneity by ion-exchange chromatography on diethylaminoethyl (DEAE)-cellulose and by fractional precipitation of its propionate derivative. The polysaccharide showed essential homogeneity and was therefore suitable for structural analysis. The polysaccharide showed a low negative specific rotation and contained residues of L-arabinose, D-xylose, D-glucuronic and 4-O-methyl-D-glucuronic acids. A new method was developed for the simultaneous estimation of 4-O-methyl-D-glucuronic acid and other uronic acids by gas-liquid chromatography. Uronic acids in polysaccharides may be reduced by reaction with lithium borohydride in tetrahydrofuran. After hydrolysis and reduction of the monosaccharides the acetylated alditols may be separated by gas-liquid chromatography on a column of butanediol succinate. The method permits the simultaneous estimation of 4-O-methyl-D-glucuronic acid, D-glucuronic acid and D-galacturonic acids. It was found by this method that L-arabinose, D-xylose, D-glucuronic and 4-O-methyl-D-glucuronic acids were present in the ratio of 1:2.8:0.48:0.52. An examination of the O-methyl-derivative of the gum yielded 2,3,5- (+++) and 2,3,4- (+)- tri-O-methyl-L-arabinose, 2,3,4- (+)- tri-O-, 2,3- (+)- di-O-, 3-0- (+++)-methyl-D-xylose, 3,4- (++)- di-O-methyl-D-glucuronic and 2,3,4— (++)- tri-O-methyl-D-glucuronic acid. The methylation data indicates the high degree of branching in the polysaccharide. The presence of 3,4-di-O-methyl-D-glucuronic acid also indicates that a part of the total uronic acids is branched at C-2. Autohydrolysis of the gum yielded a series of oligouronic acids and a lesser branched polysaccharide. The polysaccharide after methylation, reduction and hydrolysis afforded 2,3,4-tri-O-methyl, 2,3-di-0-methyl, 3-O-methyl-D-xylose and 2,3,4~tri-O-methyl-D-glucose in a molar ratio of 2: 1.3: 1: 2 indicating that the degraded polysaccharide has a xylose backbone. Sapote gum polysaccharide after successive periodate oxidation, borohydride reduction and mild acid hydrolysis yielded a series of homologous glycosides, (xylosyl) n=1,2,3 glycerol, which were fully identified by methylation and periodate oxidation. The occurrence of these glycosides signifies a random branching in the polysaccharide. Periodate oxidation and subsequent complete acid hydrolysis of the carboxyl reduced polysaccharide afforded ethylene glycol, glycerol, 2-O-methyl-D-erythritol, D-xylose and 4-O-methyl-D-glucose whose molar ratios were determined by gas-liquid chromatography (g.l.c.). The presence of 4-O-methyl-D-glucose indicates that a major part.of 4-O- methyl-D-glucuronic acid is branched at C-2 (a conclusion supported by the methylation data) and 2-O-methyl-D-erythritol arises from a minor part of 4-O-methyl-D-glucuronic acid with no substituent at C-2. Partial acetolysis of the carboxyl-reduced polysaccharide afforded a new series of oligosaccharides [formula omitted] and [formula omitted]. The results confirm the presence of the oligouronic acids in the polysaccharide. A new method for the selective cleavage of glycosiduronic acids, Hofmann. degradation, was applied to sapote gum in order to study the resulting degraded polysaccharide and to find out the nature of the substituent on 4-O-methyl-D-glucuronic acid. The degraded polysaccharide after methylation and hydrolysis afforded 2,3,4-tri-O-methyl-, 2,3-di-O-methyl-, and mono-O-methyl-D-xylose in a molar ratio of 3: 11: 2. An oligosaccharide originally attached at C-2 of 4-O-methyl-D-glucuronic acid was isolated. Digestion of the polysaccharide with arabinofuranosidase yielded free arabinose indicating that a major part of the terminal non-reducing arabinose units are in the furanose form and linked with xylose in [symbol omitted] configuration. Some enzymes with known ‘xylanase’ activity did not degrade the gum because of the high degree of branching of the polysaccharide. The structural evidence suggests that sapote gum polysaccharide possesses a highly branched xylan framework to which are attached L-arabinose units, D-glucuronic acid and 4-O-methyl-D-glucuronic acid containing side chains. / Science, Faculty of / Chemistry, Department of / Graduate

This thesis describes an implementation of abstract interpretation and its application to strictness analysis and termination analysis. The abstract interpretation is performed based on a lattice-theoretical model of abstraction, or translation, of functions expressed in a lambda-calculus notation and defined over a concrete domain into functions defined over a user-specified, application-dependent, abstract domain. The functions thus obtained are then analyzed in order to find their least fixed-points in the lattice which is the abstract domain, using a method which is a simplification of the frontiers algorithm of Chris Clack and Simon Peyton Jones. In order to achieve the required efficiency, this method is implemented using lattice annotation, along with constraints upon the annotations. The implementation is then applied to the problems of strictness analysis and termination analysis, deriving useful pre-compilation information for many functions. The concrete domains over which the functions are defined may or may not include lists. / Science, Faculty of / Computer Science, Department of / Graduate

Lattices of hereditary properties of nite graphs have been extensively studied. We investigate the lattice L of induced-hereditary properties of countable graphs. Of interest to us will be some of the members of L. Much of our focus will be on hom-properties. We analyze their behaviour and consider their link to solving the long standing Hedetniemi Conjecture. We then discuss universal graphs and construct a universal graph for hom-properties. We then use these universal graphs to prove a theorem by Szekeres and Wilf. Lastly we off er a new proof of a theorem by Du ffus, Sands and Woodrow. / Dissertation (MSc)--University of Pretoria, 2013. / Mathematics and Applied Mathematics / Unrestricted

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Call number: LD2668 .T4 1984 T33 / Master of Science

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This paper is a contribution to the study of countable Borel equivalence relations on standard Borel spaces. We concentrate here on the study of the nature of translation equivalence. We study these known hyperfinite spaces in order to gain insight into the approach necessary to classify certain variables as either being hyperfinite or not. In Chapter 1, we will give the basic definitions and examples of spaces used in this work. The general construction of marker sets is developed in this work. These marker sets are used to develop several invariant tilings of the equivalence classes of specific variables . Some properties that are equivalent to hyperfiniteness in the certain space are also developed. Lastly, we will give the new result that there is a continuous injective embedding from certain defined variables.