Дисертації з теми "Family symmetry"

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Includes bibliographical references (p. 77-79).<br>In this thesis we investigate building models of family symmetry that give the Higgs fields family structure. We construct several models, starting with 2 generation models then moving onto 3 generation models. These models are described sequentially in chapters 2 through 6. All of these models are supersymmetric and they did not previously exists in the literature. In these models, quark (and lepton) masses and mixings are determined the vacuum expectation values of the family sector. These vacuum expectation values (VEV) can have a hierarchal structure because they correspond to flat directions of a superpotential. At low energies these models contain just one light pair of Higgs fields. Experimentally, the most interesting feature of these models are couplings between the low energy Higgs and moduli of the family sector. These couplings should be observable at the Large Hadron Collider.<br>by Brian Lawrence Patt.<br>Ph.D.

In this thesis work we analyze a wide class of 1+1 dimensional integrable scattering theories with Uq(sl(2)) quantum group symmetry, whose asymptotic states are multiplets of particles with iso-spin k/2. Their two-body S-matrices have been recently found in terms of the R matrix of the quantum group. Since they satisfy Yang-Baxter equation, unitarity and crossing symmetry, they represent a consistent integrable factorized scattering theory. The question of finding the corresponding underlying QFT can be addressed once the Thermodynamic Bethe Ansatz (TBA) is obtained. In this work we get the TBA equations and we compare them to previous known results of S. R. Aladim e M. J. Martins for the particular case when q→1.

The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family which is examined.

During the twentieth century, particle physics developed into a cornerstone of modern physics, culminating in the Standard Model. Even though this theory has proved to be of extraordinary power, it is still incomplete in several respects. It is our aim in this bachelor thesis to discuss some possible theories beyond the Standard Model, the main focus being on Grand Unified Theories, while also taking a look at attempts of further unication via discrete family symmetry. At the heart of all these theories lies the concept of local gauge invariance, which is introduced as a fundamental principle, followed by an overview of the Standard Model itself. No theory has so far managed to unify all elementary particles and their interactions, but some interesting features are highlighted. We also give a hint at some possible paths to go in the future in the quest for a unication in particle physics.<br>Under 1900-talet utvecklades partikelfysiken till en av de fundamentala teorierna inom fysiken, och kom att sammanfattas i den s.k. Standardmodellen. Även om denna modell rönt exceptionella framgånger vad gäller beskrivningen av elementarpartiklar och deras växelverkan, är den fortfarande ofullständig på flera sätt. Syftet med denna kandidatuppsats är att diskutera möjliga teorier bortom Standardmodellen såsom Storförenande Teorier och diskreta familjesymmetrier vars avsikt är att koppla samman de tre familjerna av fermioner i Standardmodellen. Men först introduceras idén om lokal gaugeinvarians, vilken ligger till grund for dessa teorier, varpå en översikt av Standardmodellen följer. Ingen teori har ännu lyckats ge en helt tillfredsställande bild av elementarpartiklar och deras interaktion, men en del intressanta egenskaper hos föreslagna teorier belyses i denna uppsats. Slutligen ges en del spekulativa förslag på väger att gå i framtida försök till föreningar inom partikelfysiken.

We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.

The purpose of this study was to describe and analyze IntimatePartner Violence (IPV). How does contemporary science illustrate men as victimsand women as perpetrators in these relationships? Ten articles were presentedand analyzed in a systematic literature study. The results show that men beingabused by their female intimate partner, do exist and that they in many ways doconform to abused women. There are many underlying causes to the violence inclose relationships. There are also many shapes and degrees in violence and inIntimate Partner Violence (IPV). Furthermore, Intimate Partner Violence (IPV) exhibitssymmetry in socio-demographic characteristics, such as gender and ethnicity. Thefindings also points out that Common Couple Violence (CCV) are a much morecommon form of violence than Intimate Terrorism (IT) and that both forms areused by men and women. Finally, violence is ambiguous, includes many aspectsand is not easy to explain among cultural values, norms and social contexts.Still, violence is a universal human issue which demands social interventions.

This thesis considers two isoperimetric inequalities for the eigenvalues of the Laplacian on a family of spherically symmetric Riemannian manifolds. The Payne-Pólya-Weinberger Conjecture (PPW) states that for a bounded domain Ω in Euclidean space Rn, the ratio λ1(Ω)/λ0(Ω) of the first two eigenvalues of the Dirichlet Laplacian is bounded by the corresponding eigenvalue ratio for the Dirichlet Laplacian on the ball BΩof equal volume. The Szegö-Weinberger inequality states that for a bounded domain Ω in Euclidean space Rn, the first nonzero eigenvalue of the Neumann Laplacian μ1(Ω) is maximized on the ball BΩ of the same volume. In the first three chapters we will look at the known work for the manifolds Rn and Hn. Then we will take a family a spherically symmetric manifolds given by Rn with a spherically symmetric metric determined by a radially symmetric function f. We will then give a PPW-type upper bound for the eigenvalue gap, λ1(Ω) − λ0(Ω), and the ratio λ1(Ω)/λ0(Ω) on a family of symmetric bounded domains in this space. Finally, we prove the Szegö-Weinberger inequality for this same class of domains.

A family of C2-symmetric catalysts was designed and synthesized with the intent to polymerize propylene. The catalyst was designed to be C2-symmetric for the specific goal that the catalyst would have two identical sites for the propagation of the polymer and therefore eliminate some of the stereoerrors that occur in the propagation of the polymer chain. This catalyst would also operate under simple enantiomorphic site control and therefore the insertion of the monomer would be governed by the ligand surrounding the active site. The ligands were synthesized with increasing degrees of steric bulk with the intention to determine if a catalyst system could generate elastomeric polypropylene. Enantiomorphic site control polypropylene utilizes statistical methods to determine the Si and Re content of a given polymer chain as a function of the variable E. Polypropylene samples generated by the catalyst family were analyzed using high temperature pentad analysis of the methyl region to calculate the E value. The goal was to observe E to be equal to 0.78 provided that the number molecular weight of the polymer was 100,000. The catalyst systems generated polymers with values higher and lower than the desired 0.78, indicating too high or too low enantioselectivity of the catalyst systems respectively at Tp = 0°C.

La surface de Bolza est la surface hyperbolique orientable compacte la plus symétrique de genre 2. Pour tout genre supérieur à 2, il existe une surface orientable compacte construite de manière similaire à la surface de Bolza et ayant le même type de symétries. Nous appelons ces surfaces des surfaces hyperboliques symétriques. Cette thèse porte sur le calcul des triangulations de Delaunay (TD) de surfaces hyperboliques symétriques. Les TD de surfaces compactes peuvent être considérées comme des TD périodiques de leur revêtement universel (dans notre cas, le plan hyperbolique). Une TD est pour nous un complexe simplicial. Cependant, les ensembles de points ne définissent pas tous une décomposition simpliciale d'une surface hyperbolique symétrique. Dans la littérature, un algorithme a été proposé pour traiter ce problème avec l'utilisation de points factices : initialement une TD de la surface est construite avec un ensemble de points connu, puis des points d'entrée sont insérés avec le célèbre algorithme incrémental de Bowyer, et enfin les points factices sont supprimés, si la triangulation reste toujours un complexe simplicial. Pour la surface de Bolza, les points factices sont spécifiés. L'algorithme existant calcule une DT de la surface de Bolza comme une DT périodique du plan hyperbolique, ce qui nécessite de travailler dans un sous-ensemble approprié du plan hyperbolique. Nous étudions les propriétés des TD de la surface de Bolza définies par des ensembles de points contenants l'ensemble proposé de points factices, et nous décrivons en détail une implémentation de l'algorithme incrémentiel pour cette surface. Nous commençons par définir un représentant canonique unique qui est contenu dans un sous-ensemble borné du plan hyperbolique pour chaque face d'une TD de la surface. Nous donnons une structure de données pour représenter une TD de la surface de Bolza via les représentants canoniques de ses faces. Nous détaillons les étapes de la construction d'une telle triangulation et les opérations supplémentaires qui permettent de localiser les points et de retirer des sommets. Nous présentons également les résultats sur le degré algébrique des prédicats nécessaires pour toutes les opérations. Nous fournissons une implémentation entièrement dynamique pour la surface de Bolza, en offrant l'insertion de nouveaux points, la suppression des sommets existants, la localisation des points, et la construction d'objets duaux. Notre implémentation est basée sur la bibliothèque CGAL (Computational Geometry Algorithms Library), et est actuellement en cours de révision pour être intégrée dans la bibliothèque. L'intégration de notre code dans CGAL nécessite que tous les objets que nous introduisons soient compatibles avec le cadre existant et conformes aux standards adoptés par la bibliothèque. Nous donnons une description détaillée des classes utilisées pour représenter et traiter les triangulations hyperboliques périodiques et les objets associés. Des analyses comparatives et des tests sont effectués pour évaluer notre implémentation, et une application simple est donnée sous la forme d'une démonstration CGAL. Nous discutons une extension de notre implémentation à des surfaces hyperboliques symétriques de genre supérieur à 2. Nous proposons trois méthodes pour engendrer des ensembles de points factices pour chaque surface et présentons les avantages et les inconvénients de chaque méthode. Nous définissons un représentant canonique contenu dans un sous-ensemble borné du plan hyperbolique pour chaque face d'une TD de la surface. Nous décrivons une structure de données pour représenter une telle triangulation via les représentants canoniques de ses faces, et donnons des algorithmes pour l'initialisation de la triangulation. Enfin, nous discutons une implémentation préliminaire dans laquelle nous examinons les difficultés d'avoir des prédicats exacts efficaces pour la construction de TD de surfaces hyperboliques symétriques<br>The Bolza surface is the most symmetric compact orientable hyperbolic surface of genus 2. For any genus higher than 2, there exists one compact orientable surface constructed in a similar way as the Bolza surface having the same kind of symmetry. We refer to this family of surfaces as symmetric hyperbolic surfaces. This thesis deals with the computation of Delaunay triangulations of symmetric hyperbolic surfaces. Delaunay triangulations of compact surfaces can be seen as periodic Delaunay triangulations of their universal cover (in our case, the hyperbolic plane). A Delaunay triangulation is for us a simplicial complex. However, not all sets of points define a simplicial decomposition of a symmetric hyperbolic surface. In the literature, an algorithm has been proposed to deal with this issue by using so-called dummy points: initially a triangulation of the surface is constructed with a set of dummy points that defines a Delaunay triangulation of the surface, then input points are inserted with the well-known incremental algorithm by Bowyer, and finally the dummy points are removed, if the triangulation remains a simplicial complex after their removal. For the Bolza surface, the set of dummy points to initialize the triangulation is given. The existing algorithm computes a triangulation of the Bolza surface as a periodic triangulation of the hyperbolic plane and requires to identify a suitable subset of the hyperbolic plane in which to work. We study the properties of Delaunay triangulations of the Bolza surface defined by sets of points containing the proposed set of dummy points, and we describe in detail an implementation of the incremental algorithm for it. We begin by identifying a subset of the hyperbolic plane that contains at least one representative for each face of a Delaunay triangulation of the surface, which enables us to define a unique canonical representative in the hyperbolic plane for each face on the surface. We give a data structure to represent a Delaunay triangulation of the Bolza surface via the canonical representatives of its faces in the hyperbolic plane. We detail the construction of such a triangulation and additional operations that enable the location of points and the removal of vertices. We also report results on the algebraic degree of predicates needed for all operations. We provide a fully dynamic implementation for the Bolza surface, supporting insertion of new points, removal of existing vertices, point location, and construction of dual objects. Our implementation is based on CGAL, the Computational Geometry Algorithms Library, and is currently under revision for integration in the library. To incorporate our code into CGAL, all the objects that we introduce must be compatible with the existing framework and comply with the standards adopted by the library. We give a detailed description of the classes used to represent and handle periodic hyperbolic triangulations and related objects. Benchmarks and tests are performed to evaluate our implementation, and a simple application is given in the form of a CGAL demo. We discuss an extension of our implementation to symmetric hyperbolic surfaces of genus higher than 2. We propose three methods to generate sets of dummy points for each surface and present the advantages and shortcomings of each method. We identify a suitable subset of the hyperbolic plane that contains at least one representative for each face of a Delaunay triangulation of the surface, and we define a canonical representative in the hyperbolic plane for each face on the surface. We describe a data structure to represent such a triangulation via the canonical representatives of its faces, and give algorithms for the initialization of the triangulation with dummy points. Finally, we discuss a preliminary implementation in which we examine the difficulties of having efficient exact predicates for the construction of Delaunay triangulations of symmetric hyperbolic surfaces

Microarray technology allows the simultaneous measurement of thousands of gene expressions simultaneously. As a result of this, many statistical methods emerged for identifying differentially expressed genes. Kerr et al. (2001) proposed analysis of variance (ANOVA) procedure for the analysis of gene expression data. Their estimators are based on the assumption of normality, however the parameter estimates and residuals from this analysis are notably heavier-tailed than normal as they commented. Since non-normality complicates the data analysis and results in inefficient estimators, it is very important to develop statistical procedures which are efficient and robust. For this reason, in this work, we use Modified Maximum Likelihood (MML) and Adaptive Maximum Likelihood estimation method (Tiku and Suresh, 1992) and show that MML and AMML estimators are more efficient and robust. In our study we compared MML and AMML method with widely used statistical analysis methods via simulations and real microarray data sets.

The thesis has been written on the basis of main architectural concepts and their application in real life within a historical context investigation. Main architectural concepts are represented in a harmony of architectural composition that deals with relations among form, structure and space in the unique art work. Genius loci play very important role in the architectural creation - it represents a special and extra-ordinary urban locality and its architectural value in the historical, geographical and cultural context. The origin of Ostravice village within the historical frame concept of Moravia domain is the topic of this thesis. Other historical documents gave information about Bruneswerde as the Brno Castle. That means Brno Castle had to be founded not in Brno (as it has been consid-ered for many years) but it was located in Beskydy at Ostravice. The sacred city – Civitas Dei had been located in Bruneswerde region in early ages as the centre of European culture, education and spiritual life. Civitas Dei – divine Jerusalem in the transcription of St. Augustine's book De civitate Dei – is not only glorification of God and religious fantasy. It is also one of significant clues for recognition of historical architecture. The depiction of unknown settlement from the book of unde-fined origin is a superb testimony about extinct architectural works. They are legible from cadastral maps. Brno Castle - residence of nobility and power served shelter to St. Vojtěch, St. Prokop, St. Václav and St. Ludmila as it is obvious for the mentioned picture. Three major temples, three com-position axes symbolized by three towers on coins are in analogical relation to Brno triangle of four saints - the Saint family of Brno temples. Powerful ambitions of Brno City principals and clergy are inscribed into the urban structure in the way of composition relations which are legible to them who devoted themselves to the mystery of harmony. The absence of historical continuity affects personal attitudes and also identity of the whole community. The architecture truly reflects the past state of polis and it is eloquent even after its death. The architectural composition relations influence the natural environment for long time, longer than the architectural work existence. The geometric order of Renaissance Brno existence has not been in attention of architects so far. The features were discovered in characteristic paintings by Albrecht Durer. They are evidently secret works of the genius. A meaningful collaborator and follower in the extensive project was also his friend Jan Čert from Brno and lately from Vienna. His noble genealogy played a significant role in history of Silesia and Moravia for centuries. It is tendency to consider him as Austrian or even German architect. It is because of the fact that the genealogy tree of his noble family had roots in Moravia. It is supposed that Durer with Jan Čert´s support created the extraordinarily monumental architectural and urban works in Brno. A remarkable consensus in the urban composition of two squares and transition of traditional urban structure of Ostravice Civitas Dei into the modern Brno is also confirmed due to the identification of noble creators and owners, who were at the foundation, transformation and extinction of elements of the Moravian urban structure.

The study of the muon decay process μ+ → e+νeν ̄μ is a powerful constraint on the behaviour of the weak interaction, without contamination of the other, stronger, fundamental interactions. The spectrum measured from the momentum and angles of the decay positrons is parametrized using a set of four decay parameters. The purpose of the TWIST experiment is to measure these decay parameters to an unprecedented precision; an order of magnitude improvement in the uncertainties over measurements completed before the TWIST experiment. Measurements of the muon decay parameters constrain the values of a series of 19 weak coupling constants. In the standard model, V-A weak interaction, 18 of these constants are 0, while the remaining constant describes interactions between left handed particles, gV_LL= 1.The decay parameter ρ quantifies the behaviour of the spectrum with respect to momentum. According to the standard model the value of this parameter is 3/4. TWIST measured a value of ρ = 0.74991±0.00009(stat)±0.00028(sys). The measurement is limited by its systematic uncertainty, so a large focus of the experiment was on the determination and control of these uncertainties. The systematic uncertainties are derived from uncertainties in the detector construction and uncertainties in the biases generated by differences between the data and a matching Monte Carlo. Muon decay also limits the possibility of family symmetry breaking interactions. TWIST can be used to search for the possibility of muons decaying into a positron and a single unidentified neutral particle μ+ → e+X0 that does not otherwise interact with normal matter. The large momentum and angle acceptance of the TWIST spectrometer allows for searches of two body decays for masses of the X0 boson mX0 ∈ [0,80] MeV/c, with a variety of behaviours with respect to the angle of the positron track. Upper limits on massive and mass-less X0 decays are set with a 90% confidence level separately at parts per million for massive decays and parts in 10000 for mass-less decays.