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by Yuen Chung Man. / Bibliography: leaves 47-48 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

by Ng Yin Fun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 50-51). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.4 / Chapter 1.1 --- Hilbert C*-modules --- p.4 / Chapter 2 --- Self-dual Hilbert C*-modules --- p.14 / Chapter 2.1 --- Self-duality --- p.14 / Chapter 2.2 --- Self-duality and some related concepts --- p.22 / Chapter 2.3 --- A criterion of self-duality of HA --- p.23 / Chapter 3 --- Hilbert W*-modules --- p.25 / Chapter 3.1 --- Extension of the inner product to --- p.25 / Chapter 3.2 --- Extension of operators to --- p.33 / Chapter 3.3 --- Self-dual Hilbert W*-modules --- p.36 / Chapter 3.4 --- Some equivalent conditions for a Hilbert W*-module to be self-dual --- p.43 / Bibliography --- p.50

Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The purpose of this paper is to present a modified version of Riesz's proof of the spectral theorem for bounded linear operators. The modifications employed are those suggested by S. K. Berberian (5, page 1049). The basic properties of Hilbert space are presented in Chapter I. Chapter II is a discussion of linear operators which includes consideration of functionals, self-adjoint operators, and the spectrum of an operator. The spectral decomposition of a bounded self-adjoint operator is presented in Chapter III. The material in the paper is based primarily on the references in the bibliography. Most of the nontrival proofs have been carried out in detail. / 2031-01-01

Bibliography: leaves 127-128.

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Many people have abnormal heartbeats from time to time. A Holter monitor is a device used to record the electrical impulses of the heart when people do ordinary activities. Holter monitoring systems that can record heart rate and rhythm when you feel chest pain or symptoms of an irregular heartbeat (called an arrhythmia) and automatically perform electrocardiogram (ECG) signal analysis are desirable.<p>The use of the Hilbert transform (HT) in the area of electrocardiogram analysis is investigated. A property of the Hilbert transform, i.e., to form the analytic signal, was used in this thesis. Subsequently pattern recognition can be used to analyse the ECG data and lossless compression techniques can be used to reduce the ECG data for storage.<p>The thesis discusses one part of the Holter Monitoring System, Input processing.<p>Four different approaches, including the Time-Domain approach, the Frequency-Domain approach, the Boche approach and the Remez filter approach for calculating the Hilbert transform of an ECG wave are discussed in this thesis. By comparing them from the running time and the ease of software and hardware implementations, an efficient approach (the Remez approach) for use in calculating the Hilbert transform to build a Holter Monitoring System is proposed. <p>Using the Parks-McClellan algorithm, the Remez approach was present, and a digital filter was developed to filter the data sequence. <p>Accurate determination of the QRS complex, in particular, accurate detection of the wave peak, is important in ECG analysis and is another task in this thesis. A program was developed to detect the wave peak in an ECG wave.<p>The whole algorithm is implemented using Alteras Nios SOPC (system on a program chip) Builder system development tool. The performance of the algorithm was tested using the standard ECG waveform records from the MIT-BIH Arrhythmia database. The results will be used in pattern recognition to judge whether the ECG wave is normal or abnormal.

L'objet de ce travail est d'exposer la démonstration de l'indécidabilité du dixième problème de Hilbert fournie par Matiiassevitch dans son livre Le dixième problème de Hilbert. Son indécidabilité paru en 1995. Le problème consiste à fournir une méthode permettant de déterminer l'existence d'une solution en nombres entiers relatifs d'une équation polynomiale à coefficients entiers quelconque, dite équation diophantienne. Après un exposé des notions préliminaires, on réduit le problème aux entiers naturels. On s'attache ensuite à clarifier les mécanismes fournis par Matiiassevitch (1995) qui permettent de déterminer le caractère "diophantien" de l'exponentiation dans les entiers naturels. Ceci constitue la difficulté centrale de la démonstration. Sa résolution fut le fait de Matiiassevitch (1970). Ce fait établi, on s'attache à commenter et expliciter la nouvelle preuve fournie par Matiiassevitch (1995) qui utilise des méthodes de codage s'appuyant sur l'exponentiation. On voit comment leur utilisation judicieuse permet de coder les machines de Turing à l'aide d'équations diophantiennes. Ceci mène à l'équivalence entre les ensembles semi-décidables et les ensembles codés par les équations diophantiennes. Enfin, on étudie la preuve de l'indécidabilité par l'utilisation d'une méthode diagonale portant sur les équations diophantiennes. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Décidabilité, Dixième problème de Hilbert, Équations diophantiennes, Machine de Turing, Matiiassevitch.

Many people have abnormal heartbeats from time to time. A Holter monitor is a device used to record the electrical impulses of the heart when people do ordinary activities. Holter monitoring systems that can record heart rate and rhythm when you feel chest pain or symptoms of an irregular heartbeat (called an arrhythmia) and automatically perform electrocardiogram (ECG) signal analysis are desirable.<p>The use of the Hilbert transform (HT) in the area of electrocardiogram analysis is investigated. A property of the Hilbert transform, i.e., to form the analytic signal, was used in this thesis. Subsequently pattern recognition can be used to analyse the ECG data and lossless compression techniques can be used to reduce the ECG data for storage.<p>The thesis discusses one part of the Holter Monitoring System, Input processing.<p>Four different approaches, including the Time-Domain approach, the Frequency-Domain approach, the Boche approach and the Remez filter approach for calculating the Hilbert transform of an ECG wave are discussed in this thesis. By comparing them from the running time and the ease of software and hardware implementations, an efficient approach (the Remez approach) for use in calculating the Hilbert transform to build a Holter Monitoring System is proposed. <p>Using the Parks-McClellan algorithm, the Remez approach was present, and a digital filter was developed to filter the data sequence. <p>Accurate determination of the QRS complex, in particular, accurate detection of the wave peak, is important in ECG analysis and is another task in this thesis. A program was developed to detect the wave peak in an ECG wave.<p>The whole algorithm is implemented using Alteras Nios SOPC (system on a program chip) Builder system development tool. The performance of the algorithm was tested using the standard ECG waveform records from the MIT-BIH Arrhythmia database. The results will be used in pattern recognition to judge whether the ECG wave is normal or abnormal.