Treewidth: theory and applications to computer science

This report is an introduction to the concept of treewidth, a property of graphs that has important implications in algorithms. Some basic concepts of graph theory are presented in the first chapter for those readers that are not familiar with the notation. In Chapter 2, the definition of treewidth and some different ways of characterizing it are explained. The last two chapters focus on the algorithmic implications of treewidth, which are very relevant in Computer Science. An algorithm to compute the treewidth of a graph is presented and its result can be later applied to many other problems in graph theory, like those introduced in the last chapter.

Nonpolar m-plane thin film GaN and InGaN/GaN light-emitting diodes on LiAlO2(100) substrates

The nonpolar m-plane (1 (1) over bar 00) thin film GaN and InGaN/GaN light-emitting diodes (LEDs) grown by metal-organic chemical vapor deposition on LiAlO2 (100) substrates are reported. The LEDs emit green light with output power of 80 mu W under a direct current of 20 mA for a 400x400 mu m(2) device. The current versus voltage (I-V) characteristic of the diode shows soft rectifying properties caused by defects and impurities in the p-n junction. The electroluminescence peak wavelength dependence on injection current, for currents in excess of 20 mA, saturates at 515-516 nm. This proves the absence of polarization fields in the active region present in c-plane structures. The light output intensity versus current (L-I) characteristic of the diode exhibits a superlinear relation at low injection current caused by nonradiative centers providing a shunt path and a linear light emission zone at high current level when these centers are saturated. (c) 2007 American Institute of Physics.

Theory and simulation of the optical response of novel nanomaterials from visible to terahertz

133 p.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.