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Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

In this work a low voltage and highly linear current-mode current to delay (CTD) converter is presented. The proposed current to delay converter has the improved linearity of about 23.5% when compared with a conventional–delay inverter over the input dynamic current range of 50µA. When used as front-end block in current-mode delay-mode analog to digital converter an 11-bit resolution is obtained. The design is implemented in TSMC 90 nm CMOS technology. Monte Carlo analysis and process corner analysis is performed on the proposed circuit to analyze the amount of mismatch that will degrade the performance of the circuit in a system level. A Process, Voltage, and Temperature (PVT) variation insensitive circuit is used to bias the designed CTD converter to obtain 57% reduction of variation when compared with the simple current mode biasing technique.

A comparative study is done on the Mini Drift Chamber (MDC) and the Scintillating Electromagnetic Calorimeter (SEC), two main components of the WASA detector. The purpose of the study is to determine the most effective way to calculate the mass of the η−meson by determining the invariant mass of the final products in the η → e+e− decay. When calculating the invariant mass of the lepton pair the distribution from the MDC had a standard deviation of σMDC = (4.212 ± 0.080) · 10−2 GeV/c2 and from the SEC σSEC = (3.563±0.011)·10−2 GeV/c2. To get a precise measurement, events with a lepton scattering at a polar angle below 30◦ have to be rejected, and to achieve highest precision, it is favorable to use the SEC for momenta above 0.28 GeV/c and the MDC below, respectively. In this study, a combined method is developed which results in an invariant mass resolution of σMix = (3.341±0.012)·10−2 GeV/c2. Thus, the combined method gives a small improvement compared to using the SEC alone, but a considerable improvement compared to using only the MDC.

In this thesis we discuss amenability properties of the Banach algebra-valued continuous functions on a compact Hausdorff space X. Let A be a Banach algebra. The space of A-valued continuous functions on X, denoted by C(X,A), form a new Banach algebra. We show that C(X,A) has a bounded approximate diagonal (i.e. it is amenable) if and only if A has a bounded approximate diagonal. We also show that if A has a compactly central approximate diagonal then C(X,A) has a compact approximate diagonal. We note that, unlike C(X), in general C(X,A) is not a C*-algebra, and is no longer commutative if A is not so. Our method is inspired by a work of M. Abtahi and Y. Zhang. In addition to the above investigation, we directly construct a bounded approximate diagonal for C0(X), the Banach algebra of the closure of compactly supported continuous functions on a locally compact Hausdorff space X.

This thesis contributes towards the maximal-in-time well-posedness theory of three nonlinear dispersive partial differential equations (PDEs). We are interested in questions that extend beyond the usual well-posedness theory: what is the ultimate fate of solutions? How does Hamiltonian structure influence PDE dynamics? How does randomness, within the PDE or the initial data, interact with well-posedness of the Cauchy problem? The first topic of this thesis is the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of surface water waves. We prove a mass concentration property for H^1-solutions, analogous to the one known for the L^2-critical nonlinear Schrodinger equation. We also prove a mass concentration result for L^2-solutions. The second topic of this thesis is the invariance of the Gibbs measure for the (gauge transformed) periodic quartic KdV equation. The Gibbs measure is a probability measure supported on H^s for s<1/2, and local solutions to the quartic KdV cannot be obtained below H^{1/2} by using the standard fixed point method. We exhibit nonlinear smoothing when the initial data are randomized, and establish almost sure local well-posedness for the (gauge transformed) quartic KdV below H^{1/2}. Then, using the invariance of the Gibbs measure for the finite-dimensional system of ODEs given by projection onto the first N>0 modes of the trigonometric basis, we extend the local solutions of the (gauge transformed) quartic KdV to global solutions, and prove the invariance of the Gibbs measure under the flow. Inverting the gauge, we establish almost sure global well-posedness of the (ungauged) periodic quartic KdV below H^{1/2}. The third topic of this thesis is well-posedness of the stochastic KdV-Burgers equation. This equation is studied as a toy model for the stochastic Burgers equation, which appears in the description of a randomly growing interface. We are interested in rigorously proving the invariance of white noise for the stochastic KdV-Burgers equation. This thesis provides a result in this direction: after smoothing the additive noise (by a fractional derivative), we establish (almost sure) local well-posedness of the stochastic KdV-Burgers equation with white noise as initial data. We also prove a global well-posedness result under an additional smoothing of the noise.

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interest because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan's theory of quantization of Lie bi-algebras. Classical knots inject into virtual knots}, and flat virtual knots is the quotient of virtual knots which equates the real positive and negative crossings, and in this sense is complementary to classical knot theory within virtual knot theory. We classify flat virtual tangles with no closed components and give bases for its ``infinitesimal'' algebras. The classification of the former can be used as an invariant on virtual tangles with no closed components and virtual braids. In a subsequent paper, we will show that the infinitesimal algebras are the target spaces of any universal finite-type invariants on the respective variants of the flat virtual tangles.

An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric n-tuple V. The structure of a free semigroup algebra contains a great deal of information about V. Thus it is natural to study this algebra in order to study V. A free semigroup algebra is said to be analytic if it is isomorphic to the noncommutative analytic Toeplitz algebra, which is a higher-dimensional generalization of the classical algebra of bounded analytic functions on the complex unit disk. This notion of analyticity is of central importance in the general theory of free semigroup algebras. A vector x in H is said to be wandering for an isometric n-tuple V if the set of words in the entries of V map x to an orthonormal set. As in the classical case, the analytic structure of the noncommutative analytic Toeplitz algebra is determined by the existence of wandering vectors for the generators of the algebra. In the first part of this thesis, we prove the following dichotomy: either an isometric n-tuple V has a wandering vector, or the free semigroup algebra it generates is a von Neumann algebra. This implies the existence of wandering vectors for every analytic free semigroup algebra. As a consequence, it follows that every free semigroup algebra is reflexive, in the sense that it is completely determined by its invariant subspace lattice. In the second part of this thesis we prove a decomposition for an isometric tuple of operators which generalizes the classical Lebesgue-von Neumann-Wold decomposition of an isometry into the direct sum of a unilateral shift, an absolutely continuous unitary and a singular unitary. The key result is an operator-algebraic characterization of an absolutely continuous isometric tuple in terms of analyticity. We show that, as in the classical case, this decomposition determines the weakly closed algebra and the von Neumann algebra generated by the tuple.

Virus recognition by visual examination of electron microscope (EM) images is time consuming and requires highly trained and experienced medical specialists. For these reasons, it is not suitable for screening large numbers of specimens. The objective of this research was to develop a reliable and robust pattern recognition system that could be trained to detect and classify different types of viruses from two-dimensional images obtained from an EM. This research evaluated the use of radial spectra of higher order spectral invariants to capture variations in textures and differences in symmetries of different types of viruses in EM images. The technique exploits invariant properties of the higher order spectral features, statistical techniques of feature averaging, and soft decision fusion in a unique manner applicable to the problem when a large number of particles were available for recognition, but were not easily registered on an individual basis due to the low signal to noise ratio. Experimental evaluations were carried out using EM images of viruses, and a high statistical reliability with low misclassification rates was obtained, showing that higher order spectral features are effective in classifying viruses from digitized electron micrographs. With the use of digital imaging in electron microscopes, this method can be fully automated.

This thesis investigates the use of local search methods in solving constraint problems. Such problems are very hard in general and local search offers a useful and successful alternative to existing techniques. The focus of the thesis is to analyze the techniques of invariants used in local search. The use of invariants have recently become the cornerstone of local search technology as they provide a declarative way to specify incremental algorithms. We have produced a series of program libraries in C++ known as the One-Way-Solver. The One-Way-Solver includes the implementation of incremental data structures and is a useful tool for the implementation of local search. The One-Way-Solver is applied to two challenging constraint problems, the Boolean Satisfiability Testing (SAT) and university course timetabling problems.