Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1959. / Vita. / Includes bibliographical references (leaf 20). / by Donald George Brennan. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 85-88). / We present a combined theoretical and experimental investigation of two systems in which flexible bodies are induced to oscillate by steady flows. The first system we study consists of multiple thin sheets of paper in a steady flow, clamped at the downstream end, which we call the "clapping book". Pages sequentially lift off, accumulating in a stack of paper held up by the wind. When the elasticity and weight of the pages overcome the aerodynamic force, the book claps shut; this process then repeats. We investigate this system experimentally and theoretically, using the theory of beams in high Reynolds number flow, and test our predictions of the clapping period. The second system we consider is inspired by free-reed musical instruments, which produce sound by the oscillation of reeds, thin strips of metal tuned to specific pitches. Each reed is mounted above a slot on the upstream side of a support plate, a geometry that allows a steady flow to induce finite-amplitude oscillations. We study this system experimentally and propose models, also based on the theory of elastic beams in high Reynolds number flow. The relative merits of these models is assessed by comparing their predictions with experiments. / by Peter Buchak. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 121-123). / Recently, unexpected connections have been discovered between characters of representations and lattice models in statistical mechanics. The bridge was first formed from Kuperberg's solution to the alternating sign matrix (ASM) conjecture. Kuperberg's proof of this conjecture, which enumerates ASMs, utilized a Yang-Baxter equation for a square ice model from statistical mechanics. In earlier work, Tokuyama and okada gave representation theoretic quantities as generating functions on certain symmetry classes of ASMs or generalizations of them. Brubaker, Bump, and Priedberg used a Yang-Baxter equation to reprove Tokuyama's result and this work seeks to do the same for a generalization of Okada's results in type B. We begin by defining the particular lattice model we study. We then imbue the lattice model with Boltzmann weights suggested by a bijection with a set of symmetric ASMs. These weights define a partition function, whose properties are studied by combinatorial and symmetric function methods over the next few chapters. This course of study culminates in the use of the Yang-Baxter equation for our ice model to prove that the partition function factors into a deformation of the Weyl denominator and a generalized character of a highest weight representation, both in type B. We conjecture that the resulting function is connected to metaplectic spherical Whittaker functions. In the last two chapters, we deal with two rather different approaches to computing Whittaker coefficients of metaplectic forms - one using a factorization of the unipotent radical to perform an integration and the other via Hecke operators on the metaplectic group. / by Sawyer James Tabony. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996. / Includes bibliographical references (p. 46-47). / by Ana M.L.G. Canas da Silva. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1984. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaf 102. / by Alan William Magnuson. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997. / Includes bibliographical references (p. 119-121). / by Catherine Huafei Yan. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. / Includes bibliographical references (p. 83-84). / We define the overconvergent de Rham-Witt complex ... for a smooth affine variety over a perfect field in characteristic p. We show that, after tensoring with Q, its cohomology agrees with Monsky-Washnitzer cohomology. If dim C < p, we have an isomorphism integrally. One advantage of our construction is that it does not involve a choice of lift to characteristic zero. To prove that the cohomology groups are the same, we first define a comparison map ... (See Section 4.1 for the notation.) We cover our smooth affine C with affines B each of which is finite, tale over a localization of a polynomial algebra. For these particular affines, we decompose ... into an integral part and a fractional part and then show that the integral part is isomorphic to the Monsky-Washnitzer complex and that the fractional part is acyclic. We deduce our result from a homotopy argument and the fact that our complex is a Zariski sheaf with sheaf cohomology equal to zero in positive degrees. (For the latter, we lift the proof from [4] and include it as an appendix.) We end with two chapters featuring independent results. In the first, we reinterpret several rings from p-adic Hodge theory in such a way that they admit analogues which use big Witt vectors instead of p-typical Witt vectors. In this generalization we check that several familiar properties continue to be valid. In the second, we offer a proof that the Frobenius map on W(...) is not surjective for p > 2. / by Christopher Davis. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. / Includes bibliographical references (p. 225-241). / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / In the metric uncapacitated facility location problem (UFLP), we are given a set of clients, a set of facilities, an opening cost for each facility, and a connection cost between each client and each facility satisfying the metric inequality. The objective is to open a subset of facilities and connect each client to an open facility so that the total cost of opening facilities and connecting clients to facilities is minimized. As the UFLP is NP-hard, much effort has been devoted to designing approximation algorithms for it. As our main result, we introduce a method called dual fitting and use it in conjunction with factor-revealing programs to obtain improved approximation algorithms for the UFLP. Our best algorithm achieves an approximation factor of 1.52 (currently the best known factor) and runs in quasilinear time. We demonstrate the versatility of our techniques by using them to analyze the approximation factors of a cycle cover algorithm and a Steiner packing algorithm, as well as the competitive factor of an online buffer management algorithm. We also use our algorithms and other techniques to improve the approximation factors of several variants of the UFLP. In particular, we introduce the notion of bifactor approximate reductions and use it to derive a 2-approximation for the soft-capacitated FLP. Finally, we consider the UFLP in a game-theoretic setting and prove tight bounds on schemes for dividing up the cost of a solution among players. Our result combined with the scheme proposed by Pal and Tardos shows that 1/3 is the best possible approximation factor of any cross-monotonic cost-sharing scheme for the UFLP. Our proof uses a novel technique that we apply to several other optimization problems. / by Mohammad Mahdian. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. / Includes bibliographical references (p. 107-109). / We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant counts of real pseudoholomorphic curves. Furthermore, we calculate the new invariant for the real quintic threefold in genus 0 and degree 1 to be 30. The techniques we introduce lay the groundwork for verifying predictions of mirror symmetry for the real quintic. / by Jake P. Solomon. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1986. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 80-81. / by Kwok Wing Chow. / Ph.D.