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Convection In The Melt, John Bryant Drake
Convection In The Melt, John Bryant Drake
Doctoral Dissertations
A physical problem involving the melting/freezing of a phase-change material (PCM) is the applied setting of this research. The development of models that couple the partial differential equations for energy transport and fluid motion with phases of differing densities is a primary goal of the research. In Chapter 2, a general framework is developed for the formulation of conservation laws that admit interfaces. A notion of weak solution is developed and its relation with classical and other weak formulations is discussed. Conditions that hold across various kinds of interfaces are also developed. The formulation is examined for the conservation of …
Lcm-Stability Of Power Series Extensions Characterizes Dedekind Domains, John T. Condo
Lcm-Stability Of Power Series Extensions Characterizes Dedekind Domains, John T. Condo
Doctoral Dissertations
In this dissertation, we prove the following main result in Chapter 3. A (communicative integral) domain R is a Dedekind domain if and only if R[[X]] ⊂ T[[X]] is LCM-stable of each domain T containing R as a subring. Analogous results on flatness are given in Chapter 4. Complete statements of results cited from the literature appear in Chapter 2, while Chapter 1 places the above stated main result in historical context, as extending work of F. Richman and H. Uda.