Thesis--University of Toronto, 1956. / Photocopy (positive) of microfilm from University of Toronto Library. Microfilm made by Standard Microfilming Co., Toronto. Vita. Bibliography: leaf 88.

Thesis--University of Toronto, 1956. / Photocopy (positive) of microfilm from University of Toronto Library. Microfilm made by Standard Microfilming Co., Toronto. Vita. Bibliography: leaf 88.

Thesis (M.S.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 69-75.

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.

No description available.

In this thesis we explore the geometric representation theory of shifted quantum affine algebras 𝒜^𝜇, using the critical K-theory of certain moduli spaces of infinite flags of quiver representations resembling the moduli of quasimaps to Nakajima quiver varieties. These critical K-theories become 𝒜^𝜇-modules via the so-called critical R-matrix 𝑅, which generalizes the geometric R-matrix of Maulik, Okounkov, and Smirnov. In the asymptotic limit corresponding to taking infinite instead of finite flags, singularities appear in 𝑅 and are responsible for the shift in 𝒜^𝜇. The result is a geometric construction of interesting infinite-dimensional modules in the category 𝒪 of 𝒜^𝜇, including e.g. the pre-fundamental modules previously introduced and studied algebraically by Hernandez and Jimbo. Following Nekrasov, we provide a very natural geometric definition of qq-characters for our asymptotic modules compatible with the pre-existing definition of q-characters. When 𝒜^𝜇 is the shifted quantum toroidal gl₁ algebra, we construct asymptotic modules DT_𝜇 and PT_𝜇 whose combinatorics match those of (1-legged) vertices in Donaldson--Thomas and Pandharipande--Thomas theories. Such vertices control enumerative invariants of curves in toric 3-folds, and finding relations between (equivariant, K-theoretic) DT and PT vertices with descendent insertions is a typical example of a wall-crossing problem. We prove a certain duality between our DT_𝜇 and PT_𝜇 modules which, upon taking q-/qq-characters, provides one such wall-crossing relation.

Thesis. 1979. Ph.D.--Massachusetts Institute of Technology. Dept. of Mechanical Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Ph.D.

Ion traps can easily be miniaturized to become portable mass spectrometers. Trapped ions can be ejected by adjusting voltage settings of the radiofrequency (RF) signal applied to the electrodes. Several ion trap designs include the quadrupole ion trap (QIT), cylindrical ion trap (CIT), linear ion trap (LIT), rectilinear ion trap (RIT), toroidal ion trap, and cylindrical toroidal ion trap. Although toroidal ion traps are being used more widely in miniaturized mass spectrometers, there is a lack of fundamental understanding of how the toroidal electric field affects ion motion, and therefore, the ion trap's performance as a mass analyzer. Simulation programs can be used to discover how traps with toroidal geometry can be optimized. Potential mapping, field calculations, and simulations of ion motion were used to compare three types of toroidal ion traps: a symmetric and an asymmetric trap made using hyperbolic electrodes, and a simplified trap made using cylindrical electrodes. Toroidal harmonics, which represent solutions to the Laplace equation in a toroidal coordinate system, may be useful to understand toroidal ion traps. Ion trapping and ion motion simulations were performed in a time-varying electric potential representing the symmetric, second-order toroidal harmonic of the second kind—the solution most analogous to the conventional, Cartesian quadrupole. This potential distribution, which we call the toroidal quadrupole, demonstrated non-ideal features in the stability diagram of the toroidal quadrupole which were similar to that for conventional ion traps with higher-order field contributions. To eliminate or reduce these non-ideal features, other solutions to the Laplace equation can be added to the toroidal quadrupole, namely the toroidal dipole, toroidal hexapole, toroidal octopole, and toroidal decapole. The addition of a toroidal hexapole component to the toroidal quadrupole provides improvement in ion trapping, and is expected to play an important role in optimizing the performance of all types of toroidal ion trap mass spectrometers.The cylindrical toroidal ion trap has been miniaturized for a portable mass spectrometer. The first miniaturized version (r0 and z0 reduced by 1/3) used the same central electrode and alignment sleeve as the original design, but it had too high of capacitance for the desired RF frequency. The second miniaturized version (R, r0, and z0 reduced by 1/3) was designed with much less capacitance, but several issues including electrode alignment and sample pressure control caused the mass spectra to have poor resolution. The third miniaturized design used a different alignment method, and its efficiency still needs to be improved.