Inaug.-diss.--Kiel. / Lebenslauf.

Thesis (Ph.D.)-University of Chicago, 1915. / Vita. Published also as Cambridge tracts in mathematics and mathematical physics, no. 13, Cambridge, University press, 1911. Bibliography : p. [96]-100.

Thesis (Ph.D.)--Brown University, 2005. / Vita. Thesis advisor: Joseph Silverman. Includes bibliographical references (leaves 43-45). Also available online.

In this work the chromium solubility in MC, and M in Cr3C2 and Cr7C3 carbides in the Ti-Cr-C and Ta-Cr-C system have been examined experimentally. Special attention is given to the cubic MC phase due to its frequent use in industrial cemented carbides. A sample series was made where half of the samples were arc-melted and all samples were heat-treated at different temperatures. By arc-melting some of the samples it was possible to compare the arc-melted and non arc-melted samples to confirm equilibrium. Three phases were expected in each sample. The microstructure was examined by LOM and SEM. The phases were identified by XRD and the amount of Cr in each phase was measured by WDS in FEG-SEM or by microprobe analysis. A higher temperature for the heat-treatment allows more Cr to dissolve in the cubic carbide. Arc-melted samples allow more Cr to dissolve than the same system which has not been arc-melted. The Cr solubility in the cubic carbide in non arc-melted samples at 1400 degree Celcius is 8,1±0,4 at% in (Ti, Cr)C and 7,6±0,3 at% in (Ta, Cr)C. According to the samples the phase diagrams based on thermodynamic calculations are different to experimental data. Therefore, more experimental data should be made to update existing ternary diagrams.

No description available.

Let Nm(f(x)) denote the number of solutions of the congruence equation f(x)≡0 (modm), where m≥2 is any composite integer and f(x) is a cubic polynomial. In this thesis, we use different theorems and corollaries to find a number of solutions of the congruence equations without solving then we also construct the general expression of corresponding congruence equations to demonstrate the solutions of the equations. In this thesis, we use Mathematica software as a tool.

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Breslau, 1912. / Vita. Includes bibliographical references.

published_or_final_version / Mathematics / Master / Master of Philosophy

This research presents an approach to accurately simulate flow experiments through a fractured core using experimental, stochastic, and simulation techniques. Very often, a fracture is assumed as a set of smooth parallel plates separated by a constant width. However, the flow characteristics of an actual fracture surface are quite different, affected by tortuosity and the impact of surface roughness. Though several researchers have discussed the effect of friction on flow reduction, their efforts lack corroboration from experimental data and have not converged to form a unified methodology for studying flow on a rough fracture surface. In this study, an integrated methodology involving experimental, stochastic, and numerical simulations that incorporate the fracture roughness and the friction factor is shown to describe flow through single fractures more efficiently. Laboratory experiments were performed to support the study in quantifying the flow contributions from the matrix and the fracture. The results were used to modify the cubic law through reservoir simulations. Observations suggest that the fracture apertures need to be distributed to accurately model the experimental results. The methodology successfully modeled fractured core experiments, which were earlier not possible using the parallel plate approach. A gravity drainage experiment using an X-ray CT scan of a fractured core has also validated the methodology.

Thesis (Ph.D.)--Johns Hopkins University. / Plate printed on both sides. Vita.