Tabelle di Young e statistiche sulle permutazioni

La presente tesi è suddivisa in due parti: nella prima parte illustriamo le definizioni e i relativi risultati della teoria delle tabelle di Young, introdotte per la prima volta nel 1900 da Alfred Young; mentre, nella seconda parte, diamo la nozione di numeri Euleriani e di Polinomi Euleriani. Nel primo capitolo abbiamo introdotto i concetti di diagramma di Young e di tabelle di Young standard. Inoltre, abbiamo fornito la formula degli uncini per contare le tabelle di Young della stessa forma. Il primo capitolo è focalizzato sul teorema di Robinson-Schensted, che stabilisce una corrispondenza biunivoca tra le permutazioni di Sn e le coppie di tabelle di Young standard della stessa forma. Ne deriva un'importante conseguenza che consiste nel poter trovare in modo efficiente la massima sottosequenza crescente di una permutazione. Una volta definite le operazioni di evacuazione e "le jeu de taquin" relative alle tabelle di Young, illustriamo una serie di risultati riferibili alla corrispondenza biunivoca R-S che variano in base alla permutazione che prendiamo in considerazione. In particolare, enunciamo il teorema di simmetria di M.P.Schüztenberger, che dimostriamo attraverso la costruzione geometrica di Viennot. Nel secondo capitolo, dopo aver dato la definizione di discesa di una permutazione, descriviamo altre conseguenze della corrispondenza biunivoca R-S: vediamo così che esiste una relazione tra le discese di una permutazione e la coppia di tabelle di Young associata. Abbiamo trattato approfonditamente i numeri Euleriani, indicati con A(n,k) = ]{σ ∈ Sn;d(σ) = k}, dove d(σ) indica il numero di discese di una permutazione. Descriviamo le loro proprietà e simmetrie e vediamo che sono i coefficienti di particolari polinomi, detti Polinomi Euleriani. Infine, attraverso la nozione di eccedenza di una permutazione e la descrizione della mappa di Foata arriviamo a dimostrare un importante risultato: A(n,k) conta anche il numero di permutazioni di Sn con k eccedenze.

Successioni di polinomi di tipo binomiale e operatori delta

In questa tesi riportiamo le definizioni ed i risultati principali relativi alla corrispondenza tra le successioni di polinomi di tipo binomiale (particolari basi dello spazio dei polinomi a coefficienti reali) e gli operatori delta, cioè operatori lineari sullo spazio dei polinomi che commutano con gli operatori di traslazione e il cui nucleo è costituito dai polinomi costanti. Nel capitolo 1 richiamiamo i concetti fondamentali sull'algebra delle serie formali e definiamo l'algebra degli operatori lineari invarianti per traslazione, dimostrando in particolare l'isomorfismo tra queste algebre. Nel capitolo 2, dopo aver dimostrato l'unicità della successione di base relativa ad un operatore delta, ricaviamo come esempio le successioni di base di tre operatori delta, che useremo durante tutto il capitolo: l'operatore derivata, l'operatore di differenza in avanti e l'operatore di differenza all'indietro. Arriviamo quindi a dimostrare un importante risultato, il Primo Teorema di Sviluppo, in cui facciamo vedere come le potenze di un operatore delta siano una base per l'algebra degli operatori invarianti per traslazione. Introducendo poi le successioni di Sheffer, possiamo dimostrare anche il Secondo Teorema di Sviluppo in cui esplicitiamo l'azione di un operatore invariante per traslazione su un polinomio, tramite un operatore delta fissato e una sua successione di Sheffer. Nell'ultima parte della tesi presentiamo i formalismi e alcune semplici operazioni del calcolo umbrale, che useremo per determinare le cosiddette costanti di connessione, ovvero le costanti che definiscono lo sviluppo di una successione binomiale in funzione di un'altra successione binomiale usata come base dello spazio dei polinomi.

Renormalization group flows between non-unitary conformal models

Recentemente sono stati valutati come fisicamente consistenti diversi modelli non-hermitiani sia in meccanica quantistica che in teoria dei campi. La classe dei modelli pseudo-hermitiani, infatti, si adatta ad essere usata per la descrizione di sistemi fisici dal momento che, attraverso un opportuno operatore metrico, risulta possibile ristabilire una struttura hermitiana ed unitaria. I sistemi PT-simmetrici, poi, sono una categoria particolarmente studiata in letteratura. Gli esempi riportati sembrano suggerire che anche le cosiddette teorie conformi non-unitarie appartengano alla categoria dei modelli PT-simmetrici, e possano pertanto adattarsi alla descrizione di fenomeni fisici. In particolare, si tenta qui la costruzione di determinate lagrangiane Ginzburg-Landau per alcuni modelli minimali non-unitari, sulla base delle identificazioni esistenti per quanto riguarda i modelli minimali unitari. Infine, si suggerisce di estendere il dominio del noto teorema c alla classe delle teorie di campo PT-simmetriche, e si propongono alcune linee per una possibile dimostrazione dell'ipotizzato teorema c_{eff}.

Simulations of charged droplet collisions in shear flow

Acknowledgments This research has been enabled by the use of computing resources provided by WestGrid, the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca), and Compute/Calcul Canada. O.S. thanks NSERC for an Alexander Graham Bell Canada Graduate Scholarship.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

First-principles calculation of P-type alloy scattering in Si1-xGex

The p-type carrier scattering rate due to alloy disorder in Si1-xGex alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys..

First-principles calculation of alloy scattering in GexSi1-x

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si1-xGex alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

Numerical Investigation on the Heat Transfer Enhancement Using Micro/Nano Phase-Change Particulate Flow

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re=600-900 and phase change material particle concentrations ¡Ü0.25 , as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (0.5-0.7) slurry flow. By using the two newly-defined parameters, named effectiveness factor and performance index, respectively, it is found that there exists an optimal relation between the channel design parameters, particle volume fraction, Reynolds number, and the wall heat flux. The influence of the particle volume fraction, particle size, and the particle viscosity, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed.

Breves notas sobre un posible sentido común crítico ante los desafíos actuales

Basado en elementos de la filosofía clásica, el common sense británico y la Escuela de Frankfurt, el autor postula un sentido común guiado críticamente, que serviría para evaluar las tendencias históricas y los modelos de modernización en el Tercer Mundo. Evitando extremos, este teorema rechazaría tanto las pretensiones de verdad de muchos enfoques racionalistas como el relativismo epistemológico y ético. La existencia de leyes y etapas obligatorias de la historia es uno de esos extremos; otro es la opción teórica que afirma que los modelos culturales son incomparables e inconmensurables entre sí. La existencia de un solo paradigma normativo-positivo de desarrollo es insostenible, pero igualmente la posición que decreta la diversidad e incomparabilidad totales de los regímenes civilizatorios. Es conveniente adoptar una línea intermedia entre universalismo y particularismo y alcanzar una síntesis fructífera de ambos.

Illness and Fall in Albert Camus

This article focuses on the theme of illness in Albert Camus. Special emphasis is placed on his last published novel, La Chute. The issue of disease is usually focused in relation to death and finitude both in literature and philosophy. This article focuses on the relation between the existential experience of illness and the decay of the plenitude of life. The case of Albert Camus is especially significant for his chronical illness and because disease has a prominent place in his literary works. Here La Chute is chosen because it offers a great richness of interpretative levels unparalleled in other camusian works. Two different reading levels are proposed. The distinction and the analysis of these two levels will allow for more nuanced view of the relationship of the author to his work and of the controversy about the social role of the intellectual. The conclusion of this article differs both from the critics who only consider the novel in relation to the polemic with Jean-Paul Sartre, and those who interpret it as a disguised confession.

"Raíñas de pedra": a Humanizing Review of Inés de Castro’s Life and Death

The tragic love between Pedro I from Portugal and Inés de Castro became, in its earlier stages, a recurrent theme of the Portuguese, Spanish and European cultural scene. The dead queen came to represent the universal myth of the innocent woman sacrificed due to the Reason of State and she became the personification of the victory of love beyond death. However, despite its strong connection with Galicia, this figure was excluded from Galician literature for many years. This article’s purpose is to review and analyse the main work that introduced the figure of Inés de Castro to the Galician literary scene, Raíñas de Pedra, by Cándido Pazó, emphasising its originality and innovation in relation to the rest of the corpus.

„Welch werthvolle und kunstreich geschmiedete kleine Sache.“

Richard Schaukal (1874-1942) wurde als Dichter ignoriert, als Übersetzer geschätzt und als Literaturkritiker geachtet. Es ist erstaunlich, dass dieses Tätigkeitsfeld unvollständig aufgearbeitet ist, zumal bedeutende Exponenten der Zeit wie Thomas Mann, Hermann Hesse oder Rainer Maria Rilke Schaukal um Besprechungen ihrer Werke baten. Er verfasste für zahlreiche Publikationsorgane meist unbequeme Essays, die sich − mehr noch als seine dichterischen Arbeiten − in den Diskurs der kulturkonservativen kritischen Moderne einschrieben. Mit Blick auf seine frühe Phase als Literaturkritiker werden Richard Schaukals ästhetische Positionen, Einflüsse und Funktionen untersucht. Abschließend wird sein Aufsatz über Ferdinand von Saar (1899) einer exemplarischen Analyse unterzogen.

Imperative, subjunctive, and the desiderative-appellative space in Spanish

After defining the “enunciative scheme” (sentence type) as a communicative unit, the imperative is characterized as a morphologized modality of appellative kind used when the following conditions occur: appellative meaning, 2nd person, future tense and absence of negation. In Spanish, any variation of any of these requirements determines that the subjunctive is used. We reject the idea that the imperative is a variant of subjunctive specialized in appellative function and that both modes share a desiderative morpheme. Working in this way means attributing to a morphological category of the verb a property that actually corresponds to the enunciative schemes (sentence types). We propose to integrate the imperative and subjunctive in the framework of what we call the “desiderative-appellative space”. This “space” brings together various grammatical or grammaticalized means based on the imperative and the subjunctive. Semantically, it is organized around a component of desirability (action appears as desirable) that, by varying several factors, configures a route that goes from a center (the imperative) to a periphery (the expression of desire).

El surgimiento de HTML5; un nuevo paradigma en los estándares Web

Gracias al crecimiento, expansión y popularización de la World Wide Web, su desarrollo tecnológico tiene una creciente importancia en la sociedad. La simbiosis que protagonizan estos dos entornos ha propiciado una mayor influencia social en las innovaciones de la plataforma y un enfoque mucho más práctico. Nuestro objetivo en este artículo es describir, caracterizar y analizar el surgimiento y difusión del nuevo estándar de hipertexto que rige la Web; HTML5. Al mismo tiempo exploramos este proceso a la luz de varias teorías que aúnan tecnología y sociedad. Dedicamos especial atención a los usuarios de la World Wide Web y al uso genérico que realizan de los Medios Sociales o "Social Media". Sugerimos que el desarrollo de los estándares web está influenciado por el uso cotidiano de este nuevo tipo de tecnologías y aplicaciones. 

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.