This study measured the Lorentz-Lorenz function for ethane as determined by [formula omitted] for densities from 1 to 200 amagats, where ℒ is the Lorentz-Lorenz function, ρ is the density, and n is the index of refraction for a wavelength of 6328 Å. ℒ was found to be constant to within ½ % with an average value of .3794± .0003 cc/gm for values of ℒ corresponding to ∣ρ−ρc∣ ≤ .2. The index of refraction of ethane was measured by using a light-weight cell which had two sapphire windows set at an angle to each other and through which a plane wave of monochromatic light was passed. A micrometer-driven mirror was used to direct the light into a collimating telescope and the angle of deflection was then related to n. ρ was measured by weighing the cell and its contents on a precision balance. Ethane could be released from the cell to vary ρ. The coexistence curve was measured and three parameters used to fit the curve. This enabled extrapolation for the critical temperature which was found to be 32.079 ± .001 °C . Extrapolation of the rectilinear diameter gave a critical density of .2062 ± .0003 gm/cc. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The anisothermal and isothermal phase transformations in the Ag-20.1 to 27 at% Al alloys were examined. The cooling rates employed during continuous cooling had a distinct effect on the phase transformations. In the 24, 25, 26 and 27 at% Al alloys the low temperature transformations required cooling rates of 0.3-0.6°C per minute in order to obtain the phases predicted from the phase diagram. The 20.1 and 23 at% Al alloys exhibited much less μ-phase at room temperature after cooling at 0.3°C per minute than anticipated from the phase diagram. The μ-phase developed within the (ξ + μ) field in the 24 and 25 at% alloys resembles Widmannsfatten plates. The WidmannstStten structure was also present in the 25 at% alloy at room temperature. During the transformation ξ →(ξ → μ) in the two phase field the parent ξ matrix develops a polygonized substructure. This substructure is interpreted in terms of dislocation rearrangements in the accommodation region adjacent to the μ-phase plates. It .was found that the quenched β-phase exhibits precipitation hardening during low temperature ageing. At 200°C the μ-phase grows in the β-matrix as spherical particles. The radius of these particles is a linear function of time. Thus the β → μ transformation was classified as an interface controlled process. The kinetic data obtained during the isothermal transformation of the quenched ξ-phase into the μ-phase at 160 and 200°C indicatesthat the overall growth rate of this reaction is also interface controlled. However, the growth characteristics and the surface distortion accompanying the ξ → μ transformation indicate that more than one atomic process operates during the ξ → μ reaction. The X-ray and electron microscopy analyses suggest that there is not a random distribution of the Ag and Al atoms in the μ-phase. It .appears that the μ-phase contains layers rich in Ag or Al atoms. The regular stacking of: these layers may give rise to a long range superlattice as suggested by the X-ray diffraction patterns. The designation of the μ-phase as an isomorphic β-Mn structure seems incorrect. Electron transmission microscopy of the.isothermally produced μ + ξ structures in the 24 at% alloy established that there is a crystallographic relationship between the parent and the product. The structure relationship between the Widmannstatten μ-phase and the ξ-matrix in the 25 at% alloy was also obtained using X-ray Laue techniques. ξ-phase single crystals transformed into μ-phase polycrystals. The orientation of the μ-crystallites was not completely random. Although, a high degree of randomness was indicated when using X-ray D.S. techniques on fine rods. "Fragmentation" of the ξ-phase single crystal into a polycrystal takes place during room temperature deformation of the quenched ξ-phase. Relatively small amounts of deformation introduces numerous twin lamellae into the ξ-phase. Although the ductility of the deformed ξ-phase decreased rapidly with increasing deformation, no presence of a strain induced transformation product was detected using X-ray methods. The ξ → μ isothermal transformation bears a strong resemblance to the ξ → ξ transformation in the Ag-Zn alloy. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

Given a topological space (X,Ʊ), let H(X,Ʊ), be the class of all homeomorphisms of (XƱ ) onto itself. This paper is devoted to study the following problem posed by Everett and Ulam [1], [11] in 1948. When and how a new topology Ʋ can be constructed on X such that H(X,Ʊ) = H(X,Ʋ), i.e., these two topological spaces have exactly the same class of homeomorphisms. Some of the results obtained are original, and other results agree essentially with the work done previously by Yu-Lee Lee [5], [6], [7], [8], [9]. / Science, Faculty of / Mathematics, Department of / Graduate

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A dissertation submitted to the Faculty of Science, School of Mathematics University of the Witwatersrand Johannesburg South Africa / Linear second order ordinary di erential boundary value problems feature prominently in many scienti c eld, such as physics and engineering. Solving these problems is often riddled with complications though a myriad of techniques have been devised to alleviate these di culties. One such method is by transforming a problem into a more readily solvable form or a problem which behaves in a manner which is well understood. The Darboux-Crum transformation is a particularly interesting transformation characterised by some surprising properties, and an increase in the number of works produced in the last few years related to this transformation has prompted this investigation. The classical orthogonal polynomials, namely those of Jacobi, Legendre, Hermite and Laguerre, have been nominated as test candidates and this work will investigate how these orthogonal families are a ected when transformed via Darboux-Crum transformations.

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