Relativity (Physics). ; Anisotropy -- Mathematical models. ; Einstein field equations. ; Newtonian fluids. ; Astrophysics.
We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound spheres. We consider the full general-relativistic and Newtonian treatment of this problem and obtain exact solutions for various forms...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Ζ[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the...
Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of...
Information retrieval -- Mathematical models. ; Electronic information resource searching. ; Computer algorithms. ; Decision making -- Data processing. ; Mathematical optimization.
This thesis presents a unified method for simultaneous solution of three problems in Information Retrieval--metasearch (the fusion of ranked lists returned by retrieval systems to elicit improved performance), efficient system evaluation (the...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...