Browsing Mathematics  Ph.D. / Sc.D. by Title
Now showing items 297316 of 746

I. A pressure Poisson method for the incompressible NavierStokes equations : II. Long time behavior of the KleinGordon equations
(Massachusetts Institute of Technology, 2011)In this thesis, we address two problems involving partial differential equations. In the first problem, we reformulate the incompressible NavierStokes equations into an equivalent pressure Poisson system. The new system ... 
Ideals in triangulated categories : phantoms, ghosts and skeleta
(Massachusetts Institute of Technology, 1997) 
Immersions of symmetric spaces,
(Massachusetts Institute of Technology, 1970) 
Improving a bounding result for weaklyscattered theories
(Massachusetts Institute of Technology, 2006)In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weaklyscattered theory. Using this predecessor function, we improve a recent bounding result by Sacks ... 
The indecomposable integral representations of finite cyclic groups
(Massachusetts Institute of Technology, 1962) 
Index theorems and magnetic monopoles on asymptotically conic manifolds
(Massachusetts Institute of Technology, 2010)In this thesis, I investigate the index of Callias type operators on asymptotically conic manifolds (also known as asymptotically locally Euclidean manifolds or scattering manifolds) and give an application to the moduli ... 
Inducedcharge electrokinetics at large voltages
(Massachusetts Institute of Technology, 2008)The classical transport theory cannot explain the experimental behavior of electrochemical systems in the extreme operating conditions required by modern microfluidics devices. Some experimental puzzles include strange ... 
An infinite loop space structure for Ktheory of bimonoidal categories
(Massachusetts Institute of Technology, 2010)In recent work of BaasDundasRichterRognes, the authors introduce the notion of the K theory of a bimonoidal category R, and show that it is equivalent to the algebraic Ktheory space of the ring spectrum KR. In this ... 
Initial data to vacuum Einstein equations with asymptotic expansion
(Massachusetts Institute of Technology, 1998) 
The instability of timedependent jets
(Massachusetts Institute of Technology, 2002)The central focus of my thesis is to study the instability jets of various complexity by analyzing the linear and nonlinear dynamics. We applied this methodology to four different situations in order to learn the following. ... 
Instanton correction, wall crossing and mirror symmetry of Hitchin's moduli spaces
(Massachusetts Institute of Technology, 2011)We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instantoncorrected form according to ... 
Integral geometry, Hamiltonian dynamics, and Markov Chain Monte Carlo
(Massachusetts Institute of Technology, 2016)This thesis presents applications of differential geometry and graph theory to the design and analysis of Markov chain Monte Carlo (MCMC) algorithms. MCMC algorithms are used to generate samples from an arbitrary probability ... 
Integration in finite terms with elementary functions and dilogarithms
(Massachusetts Institute of Technology, 1994) 
Interactions between combinatorics, lie theory and algebraic geometry via the Bruhat orders
(Massachusetts Institute of Technology, 1981) 
Intercalation dynamics in lithiumion batteries
(Massachusetts Institute of Technology, 2009)A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeablebattery electrode materials. It is based on the CahnHilliard equation coupled to ... 
The intersection homology with twisted coefficients of toric varieties
(Massachusetts Institute of Technology, 1991) 
Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
(Massachusetts Institute of Technology, 2006)We define a new family of open GromovWitten 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 ... 
Invariant theoretical applications of supersymmetric algebra
(Massachusetts Institute of Technology, 1995) 
Invariants linked to models of curves over discrete valuation rings
(Massachusetts Institute of Technology, 2016)This thesis consists of two parts. In part one of this thesis, we study the relationship between the Artin conductor and the minimal discriminant of a hyperelliptic curve defined over the fraction field K of a discrete ... 
Invariants of Legendrian links
(Massachusetts Institute of Technology, 2001)We introduce new, readily computable invariants of Legendrian knots and links in standard contact threespace, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is ...