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The lebesgue density theorem in abstract measure spacesYevick, Miriam Amalie Lipschutz January 1947 (has links)
Thesis (Ph.D.) Massachusetts Institute of Technology. Dept. of Mathematics, 1947. / Vita. / Bibliography: 32-[33]. / by Miriam Amalie Lipschutz Yevick. / Ph.D.
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The maximal rank conjectureLarson, Eric Kerner January 2018 (has links)
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 57-58). / Let C be a general curve of genus g, embedded in Pr via a general linear series of degree d. In this thesis, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C Pr. / by Eric Kerner Larson. / Ph. D.
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The eta invariant for manifolds with boundary and holomorphic maps into the the restricted GrassmannianLei, Yue, 1969- January 2001 (has links)
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. / Includes bibliographical references (p. 71-74). / by Yue Lei. / Ph.D.
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Immersions of symmetric spaces,Kelly, Edmund Francis Aloysius January 1970 (has links)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1970. / Vita. / Bibliography: leaves 61-63. / by Edmund Francis Kelly. / Ph.D.
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Fast and scalable solvers for the Helmholtz equationZepeda-Núñ̃ez, Leonardo Andrés January 2015 (has links)
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 143-154). / In this thesis we develop a new family of fast and scalable algorithms to solve the 2D high-frequency Helmholtz equation in heterogeneous medium. The algorithms rely on a layered domain decomposition and a coupling between subdomains using the Green's representation formula, which reduces the problem to a boundary integral system at the interfaces between subdomains. Simultaneously, we introduce a polarization of the waves in up- and down-going components using incomplete Green's integrals, which induces another equivalent boundary integral formulation that is easy to precondition. The computation is divided in two stages: an offline stage, a computationally expensive but embarrassingly parallel precomputation performed only once; and an online stage, a highly parallel computation with low complexity performed for each right-hand side. The computational efficiency of the algorithms is achieved by shifting most of the computational burden to an offline precomputation, and by reducing the sequential bottleneck in the online stage using an efficient preconditioner, based on the polarized decomposition, coupled with compressed linear algebra. The resulting algorithms have online runtime O(N/P), where N is the number of unknowns, and P is the number of nodes in a distributed memory environment; provided that P = O (N [alpha]). Typically [alpha] = 1/5 or 1/8. / by Leonardo Andrés Zepeda-Núñ̃ez. / Ph. D.
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Cut structures and randomized algorithms in edge-connectivity problemsBenczúr, András A January 1997 (has links)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997. / Includes bibliographical references (leaves 195-202 / by András A. Benczúr. / Ph.D.
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Adiabatic limit and SzegÅ projectionsTataru, Grigore Raul, 1976- January 2003 (has links)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. / Includes bibliographical references (p. 57-58). / by Grigore Raul Tataru. / Ph.D.
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The geometry and topology of quotient varietiesHu, Yi January 1991 (has links)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991. / Includes bibliographical references (p. 98-99). / by Yi Hu. / Ph.D.
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On spherical probability distributionsArnold, Kenneth J., 1914- January 1941 (has links)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1941. / Vita. / by Kenneth James Arnold. / Ph.D.
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A precision calculus of paired Lagrangian distributionsJoshi, Mark S. (Mark Suresh) January 1994 (has links)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (p. 112-113). / by Mark S. Joshi. / Ph.D.
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