Recursos de colección

DSpace at MIT (104.280 recursos)

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Mathematics - Master's degree

Mostrando recursos 1 - 20 de 43

  1. Arithmetic properties and decomposability of Jacobians

    Park, Soohyun, S.M. Massachusetts Institute of Technology
    We first give an overview of methods used to study the decomposability of Jacobians of curves over the complex numbers. This involves studying the action of a finite group on an abelian variety in general. Next, we use methods for point counting properties of curves over finite fields to study the decomposability of Jacobians over number fields and finite fields. For example, we show that the genus of curves over number fields whose Jacobians are isomorphic to a product of elliptic curves satisfying certain reduction conditions is bounded and give restrictions on curves over number fields whose Jacobians are isomorphic...

  2. List coloring in general graphs

    Sengupta, Rik
    In this thesis we explore some of the relatively new approaches to the problem of list-coloring graphs. This is a problem that has its roots in classical graph theory, but has developed an entire theory of its own, that uses tools from structural graph theory, probabilistic approaches, as well as heuristic and algorithmic approaches. This thesis details two approaches one can take to understand list-coloring and prove results for several classes of graphs; one of them is to use the idea of graph kernels, and the other is to look at list-edge-coloring. In this thesis we present the state-of-the-art research...

  3. List coloring in general graphs

    Sengupta, Rik
    In this thesis we explore some of the relatively new approaches to the problem of list-coloring graphs. This is a problem that has its roots in classical graph theory, but has developed an entire theory of its own, that uses tools from structural graph theory, probabilistic approaches, as well as heuristic and algorithmic approaches. This thesis details two approaches one can take to understand list-coloring and prove results for several classes of graphs; one of them is to use the idea of graph kernels, and the other is to look at list-edge-coloring. In this thesis we present the state-of-the-art research...

  4. Statistical models and mental health: an analysis of records from a mental health center

    Kaplan, Edward Harris
    by Edward Harris Kaplan.

  5. Rewriting rules applied to the formation of strategy in games,

    Lewis, Clayton
    by Clayton Hall Lewis.

  6. On a posteriori finite element bound procedures for nonsymmetric Eigenvalue problems

    Chow, Chak-On, 1968-
    by Chak-On Chow.

  7. Equivalent statements to exotic p.1. structures on the 4-sphere.

    Gerra, Ralph Alexander
    Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973.

  8. Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula

    Tabony, Sawyer
    In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series...

  9. Rings of regular functions on spherical nilpotent orbits for complex classical groups

    Suk, Tonghoon
    Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a G-module. In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits.

  10. Differential posets and dual graded graphs

    Qing, Yulan, S.M. Massachusetts Institute of Technology
    In this thesis I study r-differential posets and dual graded graphs. Differential posets are partially ordered sets whose elements form the basis of a vector space that satisfies DU-UD=rI, where U and D are certain order-raising and order-lowering operators. New results are presented related to the growth and classification of differential posets. In particular, we prove that the rank sequence of an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In...

  11. Self maps of quaternionic projective spaces

    Granja, Gustavo, 1971-
    by Gustavo Granja.

  12. Homotopy colimits

    Rehmeyer, Julie
    by Julie Rehmeyer.

  13. Applications of 3-manifold Floer Homology

    Elson, Ilya
    In this thesis we give an exposition of some of the topological preliminaries necessary to understand 3-manifold Floer Homology constructed by Peter Kronheimer and Tomasz Mrowka in [16], along with some properties of this theory, calculations for specific manifolds, and applications to 3-manifold topology.

  14. A model of efficiency and trading opportunities in financial markets

    Huang, Jennifer, 1973-
    by Chunyan Jennifer Huang.

  15. Graph polynomials and statistical physics

    Kim, Jae Ill, S.M. Massachusetts Institute of Technology
    We present several graph polynomials, of which the most important one is the Tutte polynomial. These various polynomials have important applications in combinatorics and statistical physics. We generalize the Tutte polynomial and establish its correlations to the other graph polynomials. Finally, our result about the decomposition of planar graphs and its application to the ice-type model is presented.

  16. Symmetry properties of semilinear elliptic equations with isolated singularities

    Drugan, Gregory (Gregory Michael)
    In this thesis we use the method of moving planes to establish symmetry properties for positive solutions of semilinear elliptic equations. We give a detailed proof of the result due to Caffarelli, Gidas, and Spruck that a solution in the punctured ball, B\{0}, behaves asymptotically like its spherical average at the origin. We also show that a solution with an isolated singularity in the upper half space Rn+ must be cylindrically symmetric about some axis orthogonal to the boundary aRn+.

  17. Cluster analysis

    Holt, Anatol W
    by Anatol W. Holt.

  18. A Legendre spectral element method for the rotational Navier-Stokes equations

    Harkin, Anthony
    by Anthony Harkin.

  19. Coloring with defects

    Jesurum, Caroline Esther, 1969-
    by C.E. Jesurum.

  20. A survey of primary decomposition using Gröbner bases

    Wilson, Michelle Marie Lucy
    by Michelle Wilson.

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