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Now showing items 31-40 of 311

#### An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics: a staggered dissipation-control differencing algorithm.

(2006-08-01)

A new unsplit staggered mesh algorithm (USM) that solves multidimensional magnetohydrodynamics (MHD) on a staggered mesh is introduced and studied. Proper treatments of multidimensional flow problems are required for MHD ...

#### ERGODIC PROPERTIES OF GIBBS MEASURES FOR EXPANDING MAPS

(2013)

Gibbs measure which are also called Sinai-Ruelle-Bowen Measure describe asymptotic behavior and statistical properties of typical trajectories in many physical systems. In this work we review several methods of studying ...

#### UNDERSTANDING AND TEACHING RATIONAL NUMBERS: A CRITICAL CASE STUDY OF MIDDLE SCHOOL PROFESSIONAL DEVELOPMENT

(2009)

A lot of money is spent each year on teacher professional development, but researchers and policymakers are still trying to determine what that investment yields in terms of improvements in teacher knowledge and practice. ...

#### Long time stability of rotational Euler dynamics

(2007-05-16)

We study the stabilizing effect of rotational forcing in the nonlinear setting of two-dimensional shallow-water and Euler equations. We prove that when rotational force dominates the pressure, it prolongs the life-span ...

#### An inexact interior-point algorithm for conic convex optimization problems

(2006-10-02)

In this dissertation we study an algorithm for convex optimization
problems in conic form. (Without loss of generality, any convex
problem can be written in conic form.)
Our algorithm belongs to the class of interior-point methods
(IPMs), which have been associated with many recent theoretical and
algorithmic advances in mathematical optimization.
In an IPM one solves a family of slowly-varying
optimization problems that converge in some sense to the original
optimization problem. Each problem in the family depends on a so-called

**barrier function**that is associated with the problem data. Typically IPMs require evaluation of the gradient and Hessian of a suitable (``self-concordant'') barrier function. In some cases such evaluation is expensive; in other cases formulas in closed form for a suitable barrier function and its derivatives are unknown. We show that even if the gradient and Hessian of a suitable barrier function are computed**inexactly**, the resulting IPM can possess the desirable properties of polynomial iteration complexity and global convergence to the optimal solution set. In practice the best IPMs are primal-dual methods, in which a convex problem is solved together with its dual, which is another convex problem. One downside of existing primal-dual methods is their need for evaluation of a suitable barrier function, or its derivatives, for the**dual**problem. Such evaluation can be even more difficult than that required for the barrier function associated with the original problem. Our primal-dual IPM does not suffer from this drawback---it does not require exact evaluation, or even estimates, of a suitable barrier function for the dual problem. Given any convex optimization problem, Nesterov and Nemirovski showed that there exists a suitable barrier function, which they called the**universal barrier function**. Since this function and its derivatives may not be available in closed form, we explain how a Monte Carlo method can be used to estimate the derivatives. We make probabilistic statements regarding the errors in these estimates, and give an upper bound on the minimum Monte Carlo sample size required to ensure that with high probability, our primal-dual IPM possesses polynomial iteration complexity and global convergence....#### Understanding a Chaotic Saddle with Focus on a 9-Variable Model of Planar Couette Flow

(2005-07-27)

We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. We find trajectories on the ...

#### MULTIVARIATE ERROR COVARIANCE ESTIMATES BY MONTE-CARLO SIMULATION FOR OCEANOGRAPHIC ASSIMILATION STUDIES

(2005-08-04)

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. Simple covariances are usually prescribed, rarely are cross-covariances between
different model ...

#### Generalized Multiresolution Analysis: Construction and Measure Theoretic Characterization

(2005-08-03)

In this dissertation, we first study the theory of frame multiresolution analysis (FMRA) and extend some of the most significant results to d - dimensional Euclidean spaces. A main feature of this theory is the fact that ...

#### Generalized Volatility Model And Calculating VaR Using A New Semiparametric Model

(2005-12-05)

The first part of the dissertation concerns financial volatility models. Financial volatility has some stylized facts, such as excess kurtosis, volatility clustering and leverage effects. A good volatility model should be ...

#### Turaev Torsion of 3-Manifolds with Boundary

(2006-04-24)

We study the Turaev torsion of 3-manifolds with boundary; specifically how certain ``leading order'' terms of the torsion are related to cohomology operations. Chapter 1 consists mainly of definitions and known results, providing some proofs of known results when the author hopes to present a new perspective.
Chapter 2 deals with generalizations of some results of Turaev. Turaev's results relate leading order terms of the Turaev torsion of closed, oriented, connected 3-manifolds
to certain ``determinants'' derived from cohomology operations such as the alternate trilinear form on the first
cohomology group given by cup product. These determinants unfortunately do not generalize directly to
compact, connected, oriented 3-manifolds with nonempty boundary, because one must incorporate the cohomology of the manifold relative to
its boundary. We define the new determinants that will be needed,
and show that with these determinants enjoy a similar relationship to the one
given by Turaev between torsion and the known determinants. These definitions and results are given for integral cohomology, cohomology with mod-

**r**coefficients for certain integers**r**, and for integral Massey products. Chapter 3 shows how to use the results of Chapter 2 to derive Turaev's results for integral cohomology, by studying how the determinant defined in Chapter 2 changes when gluing solid tori along boundary components, and also how this determinant is related to Turaev's determinant when one glues enough solid tori along the boundary to obtain a closed 3-manifold. One can then use known gluing formulae for torsion to derive Turaev's results relating torsion and cohomology of closed 3-manifolds to the results in Chapter 2....