No description available.

We study finite groups $G$ having a nontrivial subgroup $H$ and $D \subset G \setminus H$ such that (i) the multiset $\{ xy^{-1}:x,y \in D\}$ has every element that is not in $H$ occur the same number of times (such a $D$ is called a {\it relative difference set}); (ii) $G=D\cup D^{(-1)} \cup H$; (iii) $D \cap D^{(-1)} =\emptyset$. We show that $|H|=2$, that $H$ has to be normal, and that $G$ is a group with a single involution. We also show that $G$ cannot be abelian. We give examples of such groups, including certain dicyclic groups, by using results of Schmidt and Ito. We describe an infinite family of dicyclic groups with these relative difference sets, and classify which groups of order up to $72$ contain them. We also define a relative difference set in dicyclic groups having additional symmetries, and completely classify when these exist in generalized quaternion groups. We make connections to Schur rings and prove additional results.

Yes / A quasi-orthogonal space time block coding (QO-STBC) scheme that exploits Hadamard matrix properties is studied and evaluated. At first, an analytical solution is derived as an extension of some earlier proposed QO-STBC scheme based on Hadamard matrices, called diagonalized Hadamard space-time block coding (DHSBTC). It explores the ability of Hadamard matrices that can translate into amplitude gains for a multi-antenna system, such as the QO-STBC system, to eliminate some off-diagonal (interference) terms that limit the system performance towards full diversity. This property is used in diagonalizing the decoding matrix of the QOSTBC system without such interfering elements. Results obtained quite agree with the analytical solution and also reflect the full diversity advantage of the proposed QO-STBC system design scheme. Secondly, the study is extended over an interference-free QO-STBC multi-antenna scheme, which does not include the interfering terms in the decoding matrix. Then, following the Hadamard matrix property advantages, the gain obtained (for example, in 4x1 QO-STBC scheme) in this study showed 4-times louder amplitude (gain) than the interference-free QOSTBC and much louder than earlier DHSTBC for which the new approach is compared with.

The problem of determining an objective means for assessing local characteristics of television subpictures in a Hadamard transform multicoder scheme is stated and discussed. Detailed investigations of transform domain coefficient statistical characteristics for different test images have been conducted. Both monochrome and colour signals were used, as well as different transform sizes and shapes. " Directing Indexes " are proposed which, depending on the inter-relationships among transform coefficients and groups of coefficients, direct each subpicture to the appropriate coder. Three indexes in the case of monochrome signals are proposed, each with its own computational procedures and application requirements. Necessary modifications and changes for application of some indexes on colour signals are also discussed. The proposed technique of indexing eliminates the necessity of equal distribution of subpictures among 'activity classes', a major disadvantage encountered in present activity index. Coders to be used with each directing index are devised and tested, subject to an arbitrary bit rate of 2 bits per pixel, with satisfactory performance compared with some published results for other techniques.

In this thesis, we address several problems related to the bosonic classical and algebraic quantum field theories in curved spacetime. In particular, the main question is: how do the theories change under finite global variations of the spacetime metric tensor? To answer this question a new deformation tool, the paracausal deformation, is developed and studied on its own as a new approach to investigate the structure of the space of globally hyperbolic metric tensors associated with a smooth manifold $\M$. Then the classical M{\o}ller maps are constructed to compare solutions of the hyperbolic PDEs defining the classical field theories and the quantum M{\o}ller $*$-isomorphisms follow to compare the CCR quantum algebras associated to the propagation of the quantum fields on the different background geometries. These maps possess the important property of preserving Hadamard states, providing a new way to implement the deformation argument used to prove the existence of such states in general globally hyperbolic spacetime. Moreover, the algebraic quantization of the Proca field, i.e the massive spin 1 field, on a general globally hyperbolic spacetime is for the first time studied in detail: by employing techniques coming from microlocal analysis and spectral theory a Hadamard state is constructed on ultrastatic spacetimes and then the M{\o}ller operator is used to prove the existence of such states in general globally hyperbolic spacetimes. A discussion about the definition of Hadamard states for the massive vector fields closes the work. The thesis is based on two works on algebraic quantization of bosonic field theories and Hadamard states: \cite{Norm}, \cite{Proca}. The papers are co-authored by my supervisor Prof. Valter Moretti (UniTN) and cosupervisor Simone Murro (UniGe). The first \cite{DefArg1} has not been included since, at the time it was written, the paracausal deformation, the construction of M{\o}ller operators, the right approach to intertwine the causal propagators and all the other tools developed in the subsequent works were still at a rough stage.

No description available.

No description available.

No description available.

No description available.

In recent years, chemical instrumentation has become much more sophisticated. Most analytical equipment now incorporates a microprocessor or is interfaced to a microcomputer. As a result, chemists can collect an immense amount of data on a single sample in a short period of time. While there may be an advantage to gathering such a great deal of information, problems can arise from too much information. Today, analysts commonly are faced with the dual problems of storing and analyzing the resulting flood of information. The goal of this research has been to address the problems of data storage and data analysis. Specifically, data compression techniques and spectral search and match algorithms have been developed. The data compression techniques developed utilize the Hadamard Transform and the modified zero-crossing clipping algorithm. The spectral search technique utilizes the unique format of the compressed and clipped data to greatly accelerate spectrum identification. To demonstrate the feasibility of this technique, three-dimensional fluorescence spectra of polynuclear aromatic compounds have been used. The results indicate data compression techniques and the application of these techniques to a library search system for three-dimensional fluorescence spectroscopy were both successful. / Ph. D.