Universitat Politècnica de Catalunya
Les línies d’investigació del Departament de Matemàtica Aplicada I es centren principalment en la teoria de sistemes de control, la cohomologia de varietats algebraiques, les equacions en derivades parcials, els sistemes dinàmics (especialment, mecànica celeste) i història de la ciència i de la tècnica.
Col·lecció tancada des d'octubre de 2015.
Si sou doctor o doctora per la Universitat Politècnica de Catalunya i voleu publicar la vostra tesi a TDX, contacteu amb tdx@upc.edu. Per a més informació consulteu les preguntes més freqüents
In the nineteenth century, at the Atacama Desert, a phenomenon of competition occurred between different industrial water desalination techniques, one of which had excellent results and a long life using solar energy. It ...
Consider the billiard map defined inside an analytic closed strictly convex curve Q. Given q>2 and 0<p<q relatively prime integers, there exist at least two (p,q)-periodic trajectories inside Q. The main goal of this thesis ...
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 ...
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 ...
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 ...
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 ...
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, ...
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, ...
This thesis is focused on the study of dynamics and control of a multi-tethered satellite formation, where a multi-tethered formation is made up with several satellites (agents) connected by means of cables (tethers). The ...
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. ...
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 ...
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 ...
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 ...
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 ...
This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of ...
In the first part, we formally study the phenomenon of the so-called big bang bifurcations, both for one and two-dimensional piecewise-smooth maps with a single switching boundary. These are a special type of organizing ...
In this dissertation we have investigated the credit risk measurement of a credit portfolio by means of the wavelets theory. Banks became subject to regulatory capital requirements under Basel Accords and also to the ...
L’àlgebra de Rees R(I) d’un ideal I d’un anell Noetherià local R juga un paper molt important en àlgebra commutativa i geometria algebraica, perquè Proj(R(I)) és l’explosió (blowup) de l’esquema afí Spec(R) al llarg del ...
This thesis shows an approach to geometric quantisation of integrable systems. It extends some results by Guillemin, Kostant, Rawnsley, Sniatycki and Sternberg in geometric quantisation, considering regular fibrations as ...
In this thesis we study the geography of irregular complex projective (or compact Kähler) varieties, paying special attention to the existence of fibrations. The thesis is divided into two parts. In the first one we ...
