Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Implementazione di un modulatore sigma-delta digitale per la sintesi di segnali pwm ad alta fedelta.

La modulazione a durata d'impulso (PWM) è utilizzata soprattutto perchè permette di ottenere alta efficenza energetica. In ambito accademico è stato proposto un modulatore PWM che sfrutta la tecnica di noise shaping, Sigma Delta, per avere elevata fedeltà. Il lavoro di questa tesi è stato l'implementazione su FPGA del modulatore Sigma DeltaDigitale utilizzato: quarto ordine, con quantizzatore a 4 bit e SNR in banda di 60 dB. Il dimensionamento è stato fatto determinando l'effetto che la lunghezza delle parole dei segnali ha sul rumore prodotto dal sistema. Questo studio è stato svolto con analisi euristiche ed algoritmi di ricerca implementati in ambiente MATLAB. Lo studio fatto è di carattere generale ed estendibile a generiche architetture Sigma Delta.

A universal delta model

This thesis presents a universal model of documents and deltas. This model formalize what it means to find differences between documents and to shows a single shared formalization that can be used by any algorithm to describe the differences found between any kind of comparable documents. The main scientific contribution of this thesis is a universal delta model that can be used to represent the changes found by an algorithm. The main part of this model are the formal definition of changes (the pieces of information that records that something has changed), operations (the definitions of the kind of change that happened) and deltas (coherent summaries of what has changed between two documents). The fundamental mechanism tha makes the universal delta model a very expressive tool is the use of encapsulation relations between changes. In the universal delta model, changes are not always simple records of what has changed, they can also be combined into more complex changes that reflects the detection of more meaningful modifications. In addition to the main entities (i.e., changes, operations and deltas), the model describes and defines also documents and the concept of equivalence between documents. As a corollary to the model, there is also an extensible catalog of possible operations that algorithms can detect, used to create a common library of operations, and an UML serialization of the model, useful as a reference when implementing APIs that deal with deltas. The universal delta model presented in this thesis acts as the formal groundwork upon which algorithm can be based and libraries can be implemented. It removes the need to recreate a new delta model and terminology whenever a new algorithm is devised. It also alleviates the problems that toolmakers have when adapting their software to new diff algorithms.

Die Messung der Gluonpolarisation durch die Produktion von Hadronpaaren mit großen Transversalimpulsen in tiefinelastischer Myonstreuung am Nukleon

Am COMPASS-Experiment am CERN-SPS wird die Spinsstruktur des Nukleons mit Hilfe der Streuung von polarisierten Myonen an polarisierten Nukleonen untersucht. Der in der inklusiven tiefinelastischen Streuung gemessene Beitrag der Quarks zum Nukleonspin reicht nicht aus, um den Spin des Nukleons zu erklären. Daher soll geklärt werden, wie die Gluonpolarisation und die Bahndrehimpulse von Quarks und Gluonen zum Gesamtspin des Nukleons beitragen. Da sich die Gluonpolarisation aus der $Q^{2}$-Abhängigkeit der Asymmetrien in der inklusiven Streuung nur abschätzen lässt, wird eine direkte Messung der Gluonpolarisation benötigt. Die COMPASS-Kollaboration bestimmt daher die Wirkungsquerschnittsasymmetrien für Photon-Gluon-Fusionprozesse, indem sie zum einen die offene Charmproduktion und zum anderen die Produktion von Hadronpaaren mit großen Transversalimpulsen verwendet. In dieser Arbeit wird die Messung der Gluonpolarisation mit den COMPASS-Daten der Jahre 2003 und 2004 vorgestellt. Für die Analyse werden die Ereignisse mit großem Impulsübertrag ($Q^{2}>1$ $GeV^{2}/c^{2}$) und mit Hadronpaaren mit großem Transversalimpuls ($p_{perp}>0.7$ $GeV/c$) verwendet. Die Photon-Nukleon-Asymmetrie wurde aus dem gewichteten Doppelverhältnis der selektierten Ereignisse bestimmt. Der Schnitt auf $p_{perp}>0.7$rn$GeV/c$ unterdrückt die Prozesse führender Ordnung und QCD-Compton Prozesse, so dass die Asymmetrie direkt mit der Gluonpolarisation über die Analysierstärke verknüpft ist. Der gemessene Wert ist sehr klein und verträglich mit einer verschwindenden Gluonpolarisation. Zur Vermeidung von falschen Asymmetrien aufgrund der Änderung der Detektorakzeptanz wurden Doppelverhältnisse untersucht, bei denen sich der Wirkungsquerschnitt aufhebt und nur die Detektorasymmetrien übrig bleiben. Es konnte gezeigt werden, dass das COMPASS-Spektrometer keine signifikante Zeitabhängigkeit aufweist. Für die Berechnung der Analysierstärke wurden Monte Carlo Ereignisse mit Hilfe des LEPTO-Generators und des COMGeant Software Paketes erzeugt. Dabei ist eine gute Beschreibung der Daten durch das Monte Carlo sehr wichtig. Dafür wurden zur Verbesserung der Beschreibung JETSET Parameter optimiert. Es ergab sich ein Wert von rn$frac{Delta G}{G}=0.054pm0.145_{(stat)}pm0.131_{(sys)}pm0.04_{(MC)}$ bei einem mittleren Impulsbruchteil von $langle x_{gluon}rangle=0.1$ und $langle Q^{2}rangle=1.9$ $GeV^{2}/c^{2}$. Dieses Ergebnis deutet auf eine sehr kleine Gluonpolarisation hin und steht im Einklang mit den Ergebnissen anderer Methoden, wie offene Charmproduktion und mit den Ergebnissen, die am doppelt polarisierten RHIC Collider am BNL erzielt wurden.

Analisi del sistema di gestione della produzione in Mase Generators S.p.A.

Analisi del sistema di gestione dell'azienda Mase Generators S.p.A. In particolare dopo aver introdotto l'importanza di un accurato flusso delle informazioni, si sono raccolti alcuni dati relativi alla produzione dell'impresa studiata per poter fare alcune considerazioni su valore di magazzino, livello di servizio ed ore di produzione caricate sulla commessa, al fine di individuare i punti di forza e le criticità del metodo adottato. Non esiste infatti un sistema di gestione che sappia rispondere a tutte le necesseità, ma una volta determinate le strategie esse devono essere ottimizzate e coerenti con gli obiettivi dell'azienda.

High mobility rates during the period of the "Celtic migrations"? - 87 Sr, 86 Sr and delta 18 O evidence from Early La Tène Europe

Although the period of the historic “Celtic migrations” is archaeologically extensively studied, the long-lasting question whether mass migration or increased individual mobility caused the expansion of the La Tène culture throughout continental Europe persist. Strontium (Sr) and in part oxygen (O) isotope analysis of human remains from the early La Tène cemeteries of Nebringen (Germany), Münsingen-Rain (Switzerland), Monte Bibele (Italy) and the Czech cemeteries of Radovesice I, Radovesice II and Kutná Hora was, therefore, carried out to investigate the importance of residential changes during this time period. These isotope analyses showed that most analysed individuals either came from the area they were buried in or from the surrounding area of the cemetery. An exception was formed by the Czech cemeteries, where almost a quarter of the studied individuals appeared non-local. Together with Nebringen, these cemeteries also had the most varied Sr isotope ratios, which suggest highly mobile communities in which individuals regularly changed their residency. The isotopic ratios of the cemeteries of Münsingen-Rain and Monte Bibele appeared far less varied. In part, these differences might be explained by the community structures of these cemeteries. Morphological kinship analysis in Münsingen-Rain demonstrated biological relatedness among most of the analysed individuals. These related individuals also shared similar isotope signatures, which suggest an origin from the surrounding Aar Valley. In the vicinity of the cemetery of Monte Bibele, an associated settlement site was discovered. The deceased presumably not only shared this settlement, but also cultivated the same land plots. Dispersed settlement structures were suggested for Nebringen, Radovesice and Kutná Hora, as these agriculturally favourable landscapes were densely populated during prehistoric times. Connected to these community structures are the prevailing geological conditions in these areas. Both Münsingen-Rain and Monte Bibele are located in a region where homogeneous geological conditions prevail, whereas the landscapes of Nebringen, Radovesice and Kutná Hora are characterised by complex heterogeneous geological conditions. As the majority of individuals in Nebringen and the Czech cemeteries correspond to the expected isotope values for the studied areas, regularly changing land plots might have contributed to the observed variation. Although mass migration as depicted by the historical sources was not observed individual mobility of a small part of these studied communities certainly played a role. Males appeared, thereby, to have slightly more often a non-local birthplace or moved during childhood. Male mobility was, however, not always associated with burial as a warrior. Females, on the other hand, originated more often from the region. Patrilocal residential patterns, with the exception of the Czech cemeteries, were nevertheless not observed. Objects and ideas also seem to have been exchanged freely, as there are no indications that individuals with particular grave goods came from specific areas. It rather appears that the individuals buried with them were either local or had different places of origin. This can be explained by the fact that the exact origin of grave goods is difficult to establish and the occurrence of similar 87Sr/86Sr values in different areas. This study provided important new insights on the period of the “Celtic migrations” and the way of life of these prehistoric people.

Efficient algorithms for NLO QCD event generators

In this thesis we present techniques that can be used to speed up the calculation of perturbative matrix elements for observables with many legs ($n = 3, 4, 5, 6, 7, ldots$). We investigate several ways to achieve this, including the use of Monte Carlo methods, the leading-color approximation, numerically less precise but faster operations, and SSE-vectorization. An important idea is the use of enquote{random polarizations} for which we derive subtraction terms for the real corrections in next-to-leading order calculations. We present the effectiveness of all these methods in the context of electron-positron scattering to $n$ jets, $n$ ranging from two to seven.

Studio morfo-batimetrico dei canali distributori del delta del Po di Pila

In questa tesi sono state analizzate, a partire da dati batimetrici ad alta risoluzione ottenuti tramite tecnologia multibeam, le morfologie caratteristiche dei tre canali tributari del Delta del Po di Pila: Busa di Dritta, Busa di Tramontana, Busa di Scirocco. Lo studio è stato effettuato col software Global Mapper, che ha permesso la mappatura e l’analisi morfometrica dei principali elementi morfologici osservati, ovvero aree depresse, zone con presenza di forme di fondo, zone a fondo piano e depositi da instabilità gravitativa sulle sponde dei canali. La loro distribuzione nei vari tratti dei canali è stata messa in relazione alle caratteristiche morfologiche e idrauliche del tratto fluviale e ai processi erosivi e deposizionali che interessano i tre canali ad intensità variabile, nell’ambito dell’evoluzione molto recente di questa porzione del delta. I risultati di questo studio indicano come l’utilizzo in ambito fluviale delle più recenti tecniche di acquisizione dei dati batimetrici multibeam possa costituire la base per un dettagliato studio delle morfologie fluviali e delle dinamiche ad esse associate.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.