Browsing Mathematics  Ph.D. / Sc.D. by Title
Now showing items 539558 of 746

Radiation field for Einstein vacuum equations
(Massachusetts Institute of Technology, 2010)The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions ... 
Random partitions and the quantum BenjaminOno hierarchy
(Massachusetts Institute of Technology, 2016)Stanley's Cauchy identity for Jack symmetric functions defines a Jack measure, a model random partitions for every analytic real function v(w) on the unit circle and parameters E2 < 0 < E1. Jacks are eigenfunctions of the ... 
Random tilings : gap probabilities, local and global asymptotics
(Massachusetts Institute of Technology, 2017)In the thesis we explore and develop two different approaches to the study of random tiling models. First, we consider tilings of a hexagon by rombi, viewed as 3D random stepped surfaces with a measure proportional to ... 
Randomness versus nondeterminism in distributed computing
(Massachusetts Institute of Technology, 1995) 
Rational families of vector bundles on curves
(Massachusetts Institute of Technology, 2002)We find and describe the irreducible components of the space of rational curves on moduli spaces M of rank 2 stable vector bundles with odd determinant on curves C of genus g [greater than or equal to] 2. We prove that the ... 
Rational matrix differential operators and integrable systems of PDEs
(Massachusetts Institute of Technology, 2017)A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite ... 
Real, complex and quaternionic toric spaces
(Massachusetts Institute of Technology, 1993) 
A reciprocity theorem for ergodic actions,
(Massachusetts Institute of Technology, 1971) 
Recognition of topological invariants by iterative arrays.
(Massachusetts Institute of Technology, 1969) 
Recursion on inadmissible ordinals
(Massachusetts Institute of Technology, 1976) 
Reducibilities in recursive function theory.
(Massachusetts Institute of Technology, 1966) 
Regularity and boundary variations for the Neumann problem
(Massachusetts Institute of Technology, 1997) 
Regularity and removal lemmas and their applications
(Massachusetts Institute of Technology, 2017)In this thesis, we analyze the regularity method pioneered by Szemerédi, and also discuss one of its prevalent applications, the removal lemma. First, we prove a new lower bound on the number of parts required in a version ... 
Regularity aspects of the theory of infinite dimensional representations of Lie groups.
(Massachusetts Institute of Technology, 1970) 
Regularity of Neumann solutions to an elliptic free boundary problem
(Massachusetts Institute of Technology, 2003)We examine the regularity properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... ... 
Relations in the homotopy of simplicial abelian Hopf algebras
(Massachusetts Institute of Technology, 1994) 
Relative Hilbert scheme methods in pseudoholomorphic geometry
(Massachusetts Institute of Technology, 2004)This thesis takes up a program initiated by S. Donaldson and I. Smith aimed at using symplectic Lefschetz fibration techniques to obtain information about pseudoholomorphic curves in symplectic 4manifolds. Donaldson and ... 
Relativization of the theory of computational complexity.
(Massachusetts Institute of Technology, 1972) 
Reliable validation : new perspectives on adaptive data analysis and crossvalidation
(Massachusetts Institute of Technology, 2018)Validation refers to the challenge of assessing how well a learning algorithm performs after it has been trained on a given data set. It forms an important step in machine learning, as such assessments are then used to ... 
Representation of quantum algebras arising from noncompact quantum groups : quantum orbit method and supertensor products
(Massachusetts Institute of Technology, 1996)