Programa de Doctorat en Matemàtica Aplicada: Recent submissions
Now showing items 101-120 of 193
A contribution to the theory of convolutional codes from systems theory piont of view
Information is such a valuable good of our time. Given that the transmission of information has always been subject to precision problems, knowing the obstacles existing between the transmitter and the receiver, eventual ...
Propagació d'informació en grafs i digrafs que modelen xarxes d'interconnexió simètriques
L'objectiu d'aquesta tesi és aprofondir en l'estudi d'una certa família de dígrafs, els dígrafs de prefix-cicle, donant nous detalls sobre la seva estructura, noves maneres d'enfocar el seu estudi, i dissenyant bons esquemes ...
Study of invariant manifolds in two different problems : the Hopf-zero singularity and neural synchrony
The main object of study of this thesis are invariant manifolds in the field of dynamical systems. We deal with two different and independent topics, namely, the study of exponentially small splitting of invariant manifolds ...
Engineering patterns of wrinkles and bubbles in supported graphene through modeling and simulation
Graphene deposited on a substrate often exhibits out-of-plane deformations with different features and origins. Networks of localized wrinkles have been observed in graphene synthesized through CVD, as a result of compressive ...
Subespacios hiperinvariantes y característicos : una aproximación geométrica
The aim of this thesis is to study the hyperinvariant and characteristic subspaces of a matrix, or equivalently, of an endomorphism of a finite dimensional vector space. We restrict ourselves to the case of matrices A with ...
Machine learning in multiscale modeling and simulations of molecular systems
Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. ...
Application of dynamical system methods to galactic dynamics : from warps to double bars
Most galaxies have a warped shape when they are seen from an edge-on point of view. In this work we apply dynamical system methods to find an explanation of this phenomenon that agrees with its abundance among galaxies, ...
Diffusion through non-transverse heteroclinic chains : a long-time instability for the NLS
En l'article [CKSTT] els autors proven una inestabilitat global per a l'equació de Schrödinger cúbica desenfocant en el tor 2-dimensional. Per aconseguir-ho, detecten un sistema finit d'equacions diferencials ordinàries, ...
A cotangent bundle Hamiltonian tube theorem and its applications in reduction theory
The Marle-Guillemin-Sternberg (MGS) model is an extremely important tool for the theory of Hamiltonian actions on symplectic manifolds. It has been extensively used to prove many local results both in symplectic geometry ...
Estimación bayesiana de cópulas extremales en procesos de Poisson
The estimation of occurrence probabilities of extremal quantities is essential in the study of hazards associated with natural phenomena. The extremal quantities of interest usually correspond to phenomena characterized ...
Matroids : h-vectors, zonotopes, and Lawrence polytopes
The main objects of study in this thesis are matroids. In particular we are interested in three particular classes matroids: regular matroids, arithmetic matroids, and internally perfect matroids. Of these families, regular ...
Evolutionary dynamics of populations with genotype-phenotype map
In this thesis we develop a multi-scale model of the evolutionary dynamics of a population of cells, which accounts for the mapping between genotype and phenotype as determined by a model of the gene regulatory network. ...
Rational points on Shimura curves and Galois representations
This thesis explores one of the essential arithmetical and diophantine properties of Shimura curves and their Atkin-Lehner quotients: the existence of rational points on these families of curves over both number fields and ...
Decomposition techniques for computational limit analysis
Limit analysis is relevant in many practical engineering areas such as the design of mechanical structure or the analysis of soil mechanics. The theory of limit analysis assumes a rigid, perfectly-plastic material to model ...
Geometrical structures of higher-order dynamical systems and field theories
Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics ...
Arithmetic properties of non-hyperelliptic genus 3 curves
This thesis explores the explicit computation of twists of curves. We develope an algorithm for computing the twists of a given curve assuming that its automorphism group is known. And in the particular case in which the ...
Beyond the classical Stefan problem
In this thesis we develop and analyse mathematical models describing phase change phenomena linked with novel technological applications. The models are based on modifications to standard phase change theory. The mathematical ...
Elliptic and parabolic PDEs : regularity for nonlocal diffusion equations and two isoperimetric problems
The thesis is divided into two parts. The first part is mainly concerned with regularity issues for integro-differential (or nonlocal) elliptic and parabolic equations. In the same way that densities of particles with ...
Integro-differential equations : regularity theory and Pohozaev identities
The main topic of the thesis is the study of Elliptic PDEs. It is divided into three parts: (I) integro-differential equations, (II) stable solutions to reaction-diffusion problems, and (III) weighted isoperimetric and ...
Global instability in the elliptic restricted three body problem
The goal of this thesis is to show global instability or Arnold's diffusion in the elliptic restricted three body problem (ERTBP) by proving the existence of pseudo-trajectories diffusing along the phase space for certain ...
