Proefschrift--Utrecht. / "Conspectus" (in Latin) : p. [75]-76. "Stellingen" (2 leaves) inserted. "References" at end of each chapter.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 107-112). Also available in electronic version. Access restricted to campus users.

Thesis (M.S.)--University of Wisconsin--Madison, 1966. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 68.

Proefschrift--Utrecht. / "Conspectus" (in Latin) : p. [75]-76. "Stellingen" (2 leaves) inserted. "References" at end of each chapter.

If r > 1 is an integer then U(r) denotes the vector space of r-fold symmetric tensors and Pr[U] is the set of rank 1 tensors in U(r). Let U be a finite-dimensional vector space over an algebraically closed field of characteristic not a prime p if r = p[formula omitted] for some positive integer k. We first determine the maximal subspaces of rank 1 symmetric tensors. Suppose h is a linear mapping of U(r) such that h(Pr[U]) ⊆ Pr[U] and ker h ⋂ Pr[U] = 0. We have shown that every such h is induced by a non-singular linear mapping of U, provided dim U > r+1 . This work partially answers a question raised by Marcus and Newman (Ann. of Math., 75, (1962) p.62.). / Science, Faculty of / Mathematics, Department of / Graduate

We begin by constructing a vector space over a field F , which we call a (G,σ) space of the set W = V₁xV₂... xVn , a cartesian product, where Vi is a finite-dimensional vector space over an arbitrary field F , G is a subgroup of the full symmetric group Sn and σ is a linear character of G . This space generalizes the spaces called the symmetry class of tensors defined by Marcus and Newman [1]. We can obtain the classical spaces, namely the Tensor space, the Grassman space and the symmetric space, by particularizing the group G and the linear character σ in our (G,σ) space. If (v₁,v₂,..., vn ) ∈ W , we shall denote the "decomposable" element in our space by v₁Δv₂…Δvn and call it the (G,σ) product or the Pure product if there is no confusion regarding G and σ, of the vectors v₁,v₂,..., vn . This corresponds to the tensor product, the skew symmetric product and the symmetric product in the classical spaces. The purpose of this thesis is to determine a necessary and sufficient condition for the vanishing of the (G,σ) product of the vectors v₁,v₂,..., vn in the general case. The results for the classical spaces are well-known and are deduced from our main theorem. We use the "universal mapping property" of the (G,σ) space to prove the necessity of our condition. These conditions are stated in terms of determinant-like functions of the matrices associated with the set of vectors v₁,v₂,...,vn. / Science, Faculty of / Mathematics, Department of / Graduate

The electric quadrupole splitting of the 11B nuclear magnetic resonance signal have been studied in a single crystal of datolite (H Ca B SiO5) placed in a magnetic field of 6350 Gauss and the methods developed by Volkoff and coworkers have been used to analyse the data. The space group of datolite, P 2 1/C, permits two different orientations of the otherwise identical quadrupole coupling tensors existing at the four boron sites in the unit cell. The observed five line 11B (I = 3/2) spectrum is consistent with the crystal symmetry. The quadrupole coupling constant, eqQ/h, and asymmetry parameter, η, at the unique boron site have been determined as well as the orientation of the principal axes of the electric field gradient tensor. The value of 172±1 Kc/sec found for eqQ/h in datolite is consistent with the overall range of values observed for BO4 tetrahedra in other crystals. / Thesis / Master of Science (MSc)

No description available.

Dans cette thèse nous explorons différentes facettes des modèles de tenseurs aléatoires. Les modèles de tenseurs aléatoires ont été introduits en physique dans le cadre de l'étude de la gravité quantique. En effet les modèles de matrices aléatoires, qui sont un cas particuliers de modèles de tenseurs, en sont une des origines. Ces modèles de matrices sont connus pour leur riche combinatoire et l'incroyable diversité de leurs propriétés qui les font toucher tous les domaines de l'analyse, la géométrie et des probabilités. De plus leur étude par les physiciens ont prouvé leur efficacité en ce qui concerne l'étude de la gravité quantique à deux dimensions. Les modèles de tenseurs aléatoires incarnent une généralisation possible des modèles de matrices. Comme leurs cousins, les modèles de matrices, ils posent questions dans les domaines de la combinatoire (comment traiter les cartes combinatoires d dimensionnelles ?), de la géométrie (comment contrôler la géométrie des triangulations générées ?) et de la physique (quel type d'espace-temps produisent-ils ? Quels sont leurs différentes phases ?). Cette thèse espère établir des pistes ainsi que des techniques d'études de ces modèles. Dans une première partie nous donnons une vue d'ensemble des modèles de matrices. Puis, nous discutons la combinatoire des triangulations en dimensions supérieures ou égales à trois en nous concentrant sur le cas tridimensionnelle (lequel est plus simple à visualiser). Nous définissons ces modèles et étudions certaines de leurs propriétés à l'aide de techniques combinatoires permettant de traiter les cartes d dimensionnelles. Enfin nous nous concentrons sur la généralisation de techniques issues des modèles de matrices dans le cas d'une famille particulières de modèles de tenseurs aléatoires. Ceci culmine avec le dernier chapitre de la thèse donnant des résultats partiels concernant la généralisation de la récurrence topologique de Eynard et Orantin à cette famille de modèles de tenseurs. / In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short introduction to few aspects of random matrix models and recalling a physical motivation called Group Field Theory, we start exploring the world of random tensor models and its relation to geometry, quantum gravity and combinatorics. We first define these models in a natural way and discuss their geometry and combinatorics. After these first explorations we start generalizing random matrix methods to random tensors in order to describes the mathematical and physical properties of random tensor models, at least in some specific cases.

A consensus model is a statistical approach that uses a family of signals or in our case, a family of images to generate a predictive model. In this thesis, we consider a family of images that are represented as tensors. In particular, our images are (2,0)-tensors. The consensus model is produced by utilizing the quantum Fourier transform of a family of images as tensors to transform images to images. We write a quantum Fourier transform in the numerical computation library for Python, known as Theano to produce the consensus spectrum. From the consensus spectrum, we produce the consensus model via the inverse quantum Fourier transform. Our method seeks to improve upon the phase reconstruction problem when transforming images to images under a 2-dimensional consensus model by considering images as (2,0)-tensors.