In this dissertation we study an algorithm for convex optimization problems in conic form. (Without loss of generality, any We address three problems arising in the theory of infinite-dimensional dynamical systems. First, we study the extent to which the Hausdorff dimension and the dimension spectrum of a fractal measure supported…
Contents
1 Introduction
2 Projections of Fractal Sets and Measures
2.1 Introduction
2.2 Preliminaries
2.2.1 Prevalence
2.2.2 The Dimension Spectrum
2.2.3 The Thickness Exponent
2.3 Main Results
2.4 Nonpreservation of Hausdorff Dimension
3 The Viscous Lake Equations
3.1 Introduction
3.2 The Shallow Water Model
3.3 The Attractor
3.3.1 Absorbing Set in H
3.3.2 Absorbing Set in V
3.4 Upper Bound on the Attractor Dimension
3.4.1 Uniform Lyapunov Exponents
3.4.2 The Estimate
3.5 The Weighted Lieb-Thirring Inequality
4 Learning About Reality From Observation
4.1 Introduction
4.1.1 The case of linear f and φ
4.1.2 What does “typical” mean?
4.1.3 Overview of this paper
4.1.4 The Transference Method
4.2 Prevalence
4.2.1 Cardinality Preservation
4.2.2 Preservation of Unboundedness
4.3 Enveloping Manifolds
4.4 Platonic Embedology
4.5 Observing A Continuous Dynamical System….
………..
Author: Ott, William Raymond
Source: University of Maryland