Thesis (Ph. D.)--York University, 1998. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 73-77). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004 & res_dat=xri:pqdiss & rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation & rft_dat=xri:pqdiss:NQ39271.

Thesis (Ph.D.)--University of Wyoming, 2007. / Title from PDF title page (viewed on June 17, 2009). Includes bibliographical references (p. 91-97).

We prove several theorems in the intersection of harmonic analysis, combinatorics, probability and number theory. In the second section we use combinatorial methods to construct various sets with pathological combinatorial properties. In particular, we answer a question of P. Erdos and V. Sos regarding unions of Sidon sets. In the third section we use incidence bounds and bilinear methods to prove several new endpoint restriction estimates for the Paraboloid over finite fields. In the fourth and fifth sections we study a variational maximal operators associated to orthonormal systems. Here we use probabilistic techniques to construct well-behaved rearrangements and base changes. In the sixth section we apply our variational estimates to a problem in sieve theory. In the seventh section, motivated by applications to sieve theory, we disprove a maximal inequality related to multiplicative characters. / text

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This thesis suggests an approach to compute the short-time behaviour of the hypoelliptic heat kernel corresponding to sub-Riemannian structures on unimodular Lie groups of type I, without previously holding a closed form expression for this heat kernel. Our work relies on the use of classical non-commutative harmonic analysis tools, namely the Generalized Fourier Transform and its inverse, combined with the Trotter product formula from the theory of perturbation of semigroups. We illustrate our main results by computing, to our knowledge, a first expression in short-time for the hypoelliptic heat kernel on the Engel and the Cartan groups, for which there exist no closed form expression. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2011-10-08 01:32:32.896

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The opera bouffe Les mamelles de Tiresias (1944) by Francis Poulenc (1899-1963) stands at the crossroad between the composer's formative and mature works. The opera exhibits a number of harmonic features characteristics of Poulenc's eclectic, idiosyncratic style. This thesis attempts to address the lack of attention given this work in particular and Poulenc's output in general. / The thesis consists of two volumes. Volume I contains the introduction, three chapters and the conclusion. Volume 2 contains musical examples, analytical graphs and reproductions of Act 1, Scenes 1 and 2, and Act 2, Scenes 7 and 8 from the piano-vocal score of Les mamelles de Tiresias. / The first chapter of Volume 1 reviews two Ph.D. dissertations that examine Poulenc's harmonic language; and summarizes the more recent analyses by Vivan Wood, Pamela Poulin and Keith Daniels. Figures (the musical examples) for Chapter 1 are given in Volume 2. / Chapter 2 of Volume 1 examines the large-scale harmonic organization in pivotal scenes that are representative of the musical language in the opera. / Chapter 3 of Volume I extends Warren Werner's and Richard Bobbitt's approach to show how local events and large-scale harmonic motions can be viewed as leitmotives that symbolize key events in the drama. Figures (the musical examples) and Graphs (the analytical graphs) for Chapter 3 are given in Volume 2. / The conclusion reviews there observations of the study and makes some general remarks about Poulenc's harmonic language. (Abstract shortened by UMI.)

An accurate, intuitive and tractable transform as been identified and developed from which the spatial harmonics of reticle patterns defined in polar coordinates can be obtained. A description of reticles and generic methods for describing them mathematically are presented along with some background on general harmonic analysis. Focus then turns to candidate transforms for analysis of reticle patterns and the most promising are investigated in more detail. A fast linear algorithm is devised to overcome some problems with implementation of a fast transform and this is followed by analysis of the transform basis functions to assist with interpretation of the transform in azimuth and radius. A sampling guideline is presented so that aliasing can be avoided and, finally, the transforms of some representative reticle patterns are shown along with some insight into their interpretation. / Thesis (MSc(AppliedPhysics))--University of South Australia, 2005.

A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L (???g), along with a quadruple (s, E, j, E#), where s is a ???# - invariant, open neighbourhood of 0 in L G/L H, E is a test-function subspace of C??? (Exp s), j ?? C??? (s), and E# is a test-function subspace of C??? (s) which contains { j.f Exp: f ?? E }. Of interest is the question: Is the function ???: ?? ??? ????, where ??: f ??? j.f Exp, a local associative algebra homomorphism from F# with multiplication defined via convolution with respect to a function e: s x s ??? C, to F, with the usual convolution for its multiplication (where F is the space of all ??? - invariant distributions of E and F# is the space of all ???# - invariant distributions of E#)? For this system of objects, we can show that, to some extent, the choice of the function j is not critical, for it can be ???absorbed??? into the function e. Also, when K is compact, we can show that ??? ker ?? = { f ?? E : ???k f (???g) dg = 0}. These results turn out to be very useful for calculations on s2 ??? G/H, where G = SO(3) and H??? SO(3) with H ??? SO(2) with ??? : h ??? Lh, as we can use these results to show that there is no quadruple (s, E, j, E#) for SO(3)/H with j analytic in some neighbourhood of 0 such that ??? is a local homomorphism from F# to F. Moreover, we can show that there is more than one solution for the case where s, E and E# are as chosen by Rouviere, if e is does not have to satisfy e(??,??) = e(??,??).