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. / This paper deals with methods of Chebyshev approximation. In particular polynomial approximation of continuous functions on a finite interval are discussed. Chapter I deals with the existence and uniqueness of Chebyshev or C-polynomials. In addition, some properties of the extremal points of the error function are derived, where the error fUnction E(x) = f(x) - p(x), p(x) being the C-polynomial. Chapter II discusses a method for finding the C-polynomial of degree n--the exchange method. After choosing a set of n+2 distinct abscissas, or a reference set, the so-called levelled reference polynomial is computed by the method of divided differences or by using the approximation errors of this polynomial. A point xj of maximal error is obtained and introduced into a new reference. A new levelled reference polynomial is then computed. This process continues until a reference is gotten, whose reference deviation equals the maximal approximating error of the levelled reference polynomial. The reference deviation is the common absolute value of the levelled reference polynomial at each of the reference points. The levelled reference polynomial for this reference is then shown to be the desired C-polynomial. Chapter III deals with phase methods for constructing the a-polynomial. It is shown that under suitable restrictions, if a Pn, A and €(phi) can be found such that the basic relation f(cos phi) = Pn(cos phi) + A cos[(n+1)phi + E(phi)] is satisfied on the approximation interval, then Pn is the a-polynomial. Two methods for finding the amplitude A and the phase function €(phi) are discussed. The complex method assumes f to be analytic on a domain and uses Cauchy's integral formula to obtain new values of €(phi), starting with a set of initial values. These values in turn generate new values of Pn and A. The values of Pn as well as values of A and €(phi) at certain points are gotten through convergence of this iterative scheme. Then an interpolation formula is used to obtain Pn from its values at these points. The second method attempts to find A, €(phi) and Pn so as to satisfy the basic relation only on a discrete set of points. First, assuming €(phi) so small that cos €(phi) may be replaced by 1, an expression is obtained for Pn(cos phi). In the general case, a system of phase equations is given, from which €(phi), A and hence Pn may be obtained. Although these results are valid only on a discrete set of points in the approximation interval, the polynomial derived in this way represents a good approximation to f(x). / 2031-01-01

Fu Annie Yuen Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 97-108). / Abstracts in English and Chinese. / ABSTRACT (ENGLISH) --- p.iii / ABSTRACT (CHINESE) --- p.iv / ACKNOWLEDGMENTS --- p.v / TABLE OF CONTENTS --- p.vi / LIST OF FIGURES --- p.ix / LIST OF TABLES --- p.xi / Chapter CHAPTER ONE: --- BACKGROUND INFORMATION --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Deoxyribonucleic Acid --- p.1 / Chapter 1.2.1 --- Nomenclature and Symbols --- p.1 / Chapter 1.2.2 --- Torsion Angles --- p.4 / Chapter 1.2.3 --- Conformation --- p.5 / Chapter 1.3 --- DNA Studies --- p.8 / Chapter 1.3.1 --- Base --- p.8 / Chapter 1.3.2 --- Base-Pair --- p.10 / Chapter 1.3.3 --- Summary --- p.11 / Chapter 1.4 --- Cisplatin Studies --- p.11 / Chapter 1.4.1 --- Reaction --- p.12 / Chapter 1.4.2 --- Cisplatin-DNA Products --- p.14 / Chapter 1.4.3 --- Summary --- p.15 / Chapter 1.5 --- Scope of This Thesis --- p.15 / Chapter CHAPTER TWO: --- COMPUTATION AND METHODOLOY --- p.17 / Chapter 2.1 --- Introduction --- p.17 / Chapter 2.2 --- Hartree-Fock Approximation --- p.17 / Chapter 2.3 --- Geometry Optimization --- p.18 / Chapter 2.4 --- Molecular Orbital (MO) Calculation --- p.20 / Chapter 2.5 --- Verification of Methodology --- p.20 / Chapter 2.5.1 --- Backbone Torsion Angles --- p.20 / Chapter 2.5.2 --- N7-N7 Distance --- p.26 / Chapter 2.5.3 --- Location of HOMO --- p.30 / Chapter 2.6 --- Summary --- p.31 / Chapter CHAPTER THREE: --- UNDERSTANDING OF THE CISPLATIN-DNA CROSSLINKS --- p.33 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.2 --- MO Analysis --- p.33 / Chapter 3.3 --- Potential Binding Sites of DNA --- p.34 / Chapter 3.3.1 --- "1,2-d(GpG) Intrastrand Crosslink" --- p.40 / Chapter 3.3.2 --- "l,2-d(ApG) Intrastrand Crosslink" --- p.40 / Chapter 3.3.3 --- "l,3-d(GpXpG) Intrastrand Crosslink" --- p.41 / Chapter 3.3.4 --- d(GpC)d(GpC) Interstrand Crosslink --- p.41 / Chapter 3.3.5 --- d(GpXpC)d(GpXpC) Interstrand Crosslink --- p.41 / Chapter 3.3.6 --- Summary --- p.42 / Chapter 3.4 --- Empirical Selection Rule --- p.44 / Chapter 3.4.1 --- Convention --- p.44 / Chapter 3.4.2 --- Selection of Potential HOMO Location (or Active Site) --- p.45 / Chapter 3.4.3 --- Selection of Potential HOMO-Nearby Active Site --- p.47 / Chapter 3.4.4 --- Applications --- p.48 / Chapter 3.5 --- Cisplatin --- p.51 / Chapter 3.6 --- Cisplatin-DNA Crosslinks --- p.52 / Chapter 3.6.1 --- "l,2-d(GpG) and l,2-d(ApG) Intrastrand Crosslinks" --- p.52 / Chapter 3.6.2 --- "l,2-d(ApG) versus l,2-d(GpA) Intrastrand Crosslinks" --- p.53 / Chapter 3.6.3 --- "l,3-d(GpXpG) Intrastrand and d(GpXpC)d(GpXpC) Interstrand Crosslinks" --- p.54 / Chapter 3.6.4 --- Platination at Terminal Positions --- p.55 / Chapter 3.7 --- Structural Parameters --- p.59 / Chapter 3.7.1 --- Optimized Geometries --- p.59 / Chapter 3.7.2 --- DNA Sequences from PDB --- p.67 / Chapter 3.7.3 --- Backbone Torsion Angles --- p.70 / Chapter 3.8 --- Summary --- p.70 / Chapter CHAPTER FOUR: --- CONCLUDING REMARKS --- p.72 / APPENDIX I BACKBONE TORSION ANGLES AND SUGAR RING CONFORMATION OF THE OPTIMIZED GEOMETRIES --- p.74 / APPENDIX II BACKBONE TORSION ANGLES OF THE EXPERIMENTAL SEQUENCES FROM NUCLEIC ACID DATABASE (NDB) --- p.82 / REFERENCES --- p.97

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--York University, 2004. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 160-165). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99262

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This study deals specifically with classical cubic splines. Based on a lemma of John Rice, best approximation in the uniform norm by cubic splines is explored. The purpose of this study is to characterize the best approximation to a given continuous function f(x) by a cubic spline with fixed knots by counting alternating extreme points of its error function E(t). / Graduation date: 1991

The problem of robotic mapping, also known as simultaneous localization and mapping (SLAM), by a mobile agent for large distributed environments is addressed in this dissertation. This has sometimes been referred to as the holy grail in the robotics community, and is the stepping stone towards making a robot completely autonomous. A hybrid solution to the SLAM problem is proposed based on "first localize then map" principle. It is provably consistent and has great potential for real time application. It provides significant improvements over state-of-the-art Bayesian approaches by reducing the computational complexity of the SLAM problem without sacrificing consistency. The localization is achieved using a feature based extended Kalman filter (EKF) which utilizes a sparse set of reliable features. The common issues of data association, loop closure and computational cost of EKF based methods are kept tractable owing to the sparsity of the feature set. A novel frequentist mapping technique is proposed for estimating the dense part of the environment using the sensor observations. Given the pose estimate of the robot, this technique can consistently map the surrounding environment. The technique has linear time complexity in map components and for the case of bounded sensor noise, it is shown that the frequentist mapping technique has constant time complexity which makes it capable of estimating large distributed environments in real time. The frequentist mapping technique is a stochastic approximation algorithm and is shown to converge to the true map probabilities almost surely. The Hybrid SLAM software is developed in the C-language and is capable of handling real experimental data as well as simulations. The Hybrid SLAM technique is shown to perform well in simulations, experiments with an iRobot Create, and on standard datasets from the Robotics Data Set Repository, known as Radish. It is demonstrated that the Hybrid SLAM technique can successfully map large complex data sets in an order of magnitude less time than the time taken by the robot to acquire the data. It has low system requirements and has the potential to run on-board a robot to estimate large distributed environments in real time.

The first topic of this thesis proposes an 8-bit, 20 MSample/s pipeline analog-to-digital converter (ADC). The sharing amplifiers technique is employed to reduce the overall number of the amplifiers wherein dynamic comparators are adopted to reduce the power consumption. The proposed design is implemented by 0.35 £gm CMOS technology. The simulation results show that maximum power consumption is 45 mW given a 3.3 V power supply, and the SFDR is 45 dB with a sinusoidal input at 5 MHz. The second topic is to describe a 5-bit, 2.4 MSample/s, low power analog-to-digital converter for ZigBee receiver using 868/915 MHz band. The converter uses the successive approximation architecture. By using 0.18 £gm CMOS technology, the simulation results show the worst-case power consumption is merely 449.6 £gW. The converter achieves the maximum differential nonlinearity of 0.3 LSB, the maximum integral nonlinearity of 0.5 LSB.

Bin packing is a very important and popular research area in the computer science field. Past work showed many good and real-world packing algorithms. How- ever, due to the complexity of the problem in multiple-dimensional bin packing, also called hyperbox packing, we need more practical packing algorithms for its real-world applications. In this dissertation, we extend 1D packing algorithms to hyperbox packing prob- lems via a general framework that takes two inputs of a 1D packing algorithm and an instance of hyperbox packing problem and outputs a hyperbox packing algorithm. The extension framework significantly enriches the family of hyperbox-packing algorithms, generates many framework-based algorithms, and simultaneously calls for the analysis for those algorithms. We also analyze the performance of a couple of framework-based algorithms from two perspectives of worst-case performance and average-case performance. In worst- case analysis, we use the worst-case performance ratio as our metric and analyze the relationship of the ratio of framework-based algorithms and that of the corresponding 1D algorithms. We also compare their worst-case performance against two baselines: strip optimal algorithms and optimal algorithms. In average-case analysis, we use expected waste as a metric, analyze the waste of optimal hyperbox packing algorithms, and estimate the asymptotic forms of the waste for framework-based algorithms.

Habilitation à diriger des recherches : Informatique : Rennes 1 : 1996. / Bibliogr. p.29-31.