Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 31-32).

Working at the prime p = 3, we construct a stably finite spectrum, Z, with a v_2^1 self map f. Further, both Ext_A(H*(Z),Z_3) and Ext_A(H*(Z),H*(Z)) have a vanishing line of slope 1/16 in (t-s,s) coordinates, and the map f is represented by an element a of Ext where multiplication by a is parallel to the vanishing line. To accomplish this construction, we prove a result about the connection between particular self maps of spectra and their effect on the Margolis homology of related modules over the Steenrod Algebra.

We investigate quotient-fine nearness frames, showing that they are reflective in the category of strong nearness frames, and that, in those with spatial completion, any near subset is contained in a near grill. We construct two categories, each of which is shown to be equivalent to that of quotient-fine nearness frames. We also consider some subcategories of the category of nearness frames, which are co-hereditary and closed under coproducts. We give due attention to relations between these subcategories. We introduce totally strong nearness frames, whose category we show to be closed under completions. We investigate N-homomorphisms and remote points in the context of totally bounded uniform frames, showing the role played by these uniform N-homomorphisms in the transfer of remote points, and their relationship with C -quotient maps. A further study on grills enables us to establish, among other things, that grills are precisely unions of prime filters. We conclude the thesis by showing that the lattice of all nearnesses on a regular frame is a pseudo-frame, by which we mean a poset pretty much like a frame except for the possible absence of the bottom element. / Mathematical Sciences / Ph.D. (Mathematics)

Abstract This thesis describes part of the work that has been done in the Chemical Process Engineering Laboratory of the University of Oulu to systematize conceptual process design. The aim has been to develop a design methodology, i.e. how process design is done, based on a carefully elaborated concept analysis. The starting point has been that all the knowledge related to process design, i.e. not only the procedural knowledge related to the design activity itself, but also the declarative knowledge related to the design target (process) and the environment (project) in which the design is done, should be systematized. The process design methodology can be represented within a single formalism by treating the activity, target and resources as structural parts of the project object. In that case, each design decision becomes properly constrained by the goal and the resources available, and is also stored together with the domain knowledge on which the decision was based. This holistic approach was adopted when the phenomenon driven process design methodology was built to systematize chemical process development while simultaneously supporting creativity. This thesis concentrates on knowledge generation activity as part of the phenomenon driven process design methodology. A brief description of the generic chemical process object model is presented, after which the focus is on the design activity and the strategy of design. The phenomenon driven process design of an MTBE production process is described as an illustration of the methodology. It is shown how combinations of reaction and separation, such as reactive distillation, evolve naturally during a design project. For the evaluation of attainable state distributions, which is an important design task implied by the methodology, a robust method was developed to solve the modified MESH equations of reactive distillation. The method was also applied when developing a rigorous calculation method for the determination of minimum energy demand of multicomponent distillation.

No description available.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1981 / Bibliography: leaves 102-103. / by Javier Bracho. / Ph. D. / Ph.D. Massachusetts Institute of Technology, Department of Mathematics

Operads are objects that model operations with several inputs and one output. We define such structures in the context of graphs, namely oriented trees. Then we generalize operads to properads and modular operads by taking general graphs with, or without, orientation. Further we construct the cobar complex of operads and properads and illustrate the construction on the examples of the associative operad Ass and the Frobenius properad Frob. Algebras over the cobar complex of operads correspond to certain homotopy algebras, for our example of Ass it is A1. We find its Maurer-Cartan equation and convert it from coderivations to derivations. Similarly we find the Maurer-Cartan equation for cobar complex of Frobenius properad. Powered by TCPDF (www.tcpdf.org)

No description available.

Nonlinear partial differential equations are difficult to solve, with many of the approximate solutions in the literature being numerical in nature. In this work, we apply the Homotopy Analysis Method to give approximate analytical solutions to nonlinear ordinary and partial differential equations. The main goal is to apply different linear operators, which can be chosen, to solve nonlinear problems. In the first three chapters, we study ordinary differential equations (ODEs) with one or two linear operators. As we progress, we apply the method to partial differential equations (PDEs) and use several linear operators. The results are all purely analytical, meaning these are approximate solutions that we can evaluate at points and take their derivatives. Another main focus is error analysis, where we test how good our approximations are. The method will always produce approximations, but we use residual errors on the domain of the problem to find a measure of error. In the last two chapters, we apply similarity transforms to PDEs to transform them into ODEs. We then use the Homotopy Analysis Method on one, but are able to find exact solutions to both equations.