National Institute of Standards and Technology における超伝導研究及び生活

Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are methods specifically tailored to systems with special properties such as special forms of symmetry and those depending on one or more parameters. Copyright © 2006 John Wiley & Sons, Ltd.

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Recent computational developments in krylov subspace methods for linear systems

Communication systems: An introduction to signals and noise in electrical communication

Oxygen saturation in the arterial blood (SaO2) provides information on the adequacy of respiratory function. SaO2 can be assessed noninvasively by pulse oximetry, which is based on photoplethysmographic pulses in two wavelengths, generally in the red and infrared regions. The calibration of the measured photoplethysmographic signals is performed empirically for each type of commercial pulse-oximeter sensor, utilizing in vitro measurement of SaO2 in extracted arterial blood by means of co-oximetry. Due to the discrepancy between the measurement of SaO2 by pulse oximetry and the invasive technique, the former is denoted as SpO2. Manufacturers of pulse oximeters generally claim an accuracy of 2%, evaluated by the standard deviation (SD) of the differences between SpO2 and SaO2, measured simultaneously in healthy subjects. However, an SD of 2% reflects an expected error of 4% (two SDs) or more in 5% of the examinations, which is in accordance with an error of 3%-4%, reported in clinical studies. This level of accuracy is sufficient for the detection of a significant decline in respiratory function in patients, and pulse oximetry has been accepted as a reliable technique for that purpose. The accuracy of SpO2 measurement is insufficient in several situations, such as critically ill patients receiving supplemental oxygen, and can be hazardous if it leads to elevated values of oxygen partial pressure in blood. In particular, preterm newborns are vulnerable to retinopathy of prematurity induced by high oxygen concentration in the blood. The low accuracy of SpO2 measurement in critically ill patients and newborns can be attributed to the empirical calibration process, which is performed on healthy volunteers. Other limitations of pulse oximetry include the presence of dyshemoglobins, which has been addressed by multiwavelength pulse oximetry, as well as low perfusion and motion artifacts that are partially rectified by sophisticated algorithms and also by reflection pulse oximetry.

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Pulse oximetry: fundamentals and technology update

THIS is a thoroughly good book which deserves to run through many editions. It is not (as its title might suggest) a book on mathematical logic or philosophy: it deals not with the nature of mathematics but with its content. Its purpose is to show, not by general disquisitions but by concrete examples, drawn from almost every branch of pure mathematics, how mathematicians think and what they do. What is Mathematics? An Elementary Approach to Ideas and Methods. By Richard Courant and Herbert Robbins. Pp. xix + 521. (London, New York and Toronto: Oxford University Press, 1941.) 25s. net.

What is Mathematics

We present a preliminary study of a new phenom- ena associated with the Euler-Poisson equations — the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic,ON1O critical thresh- old. We investigate a class of Euler-Poisson equations, ranging from one-dimensional problems with or without various forcing mech- anisms to multi-dimensional isotropic models with geometrical symmetry. These models are shown to admit a critical thresh- old which is reminiscent of the conditional breakdown of waves on the beach; only waves above certain initial critical threshold experience finite-time breakdown, but otherwise they propagate smoothly. At the same time, the asymptotic long time behavior of the solutions remains the same, independent of crossing these initial thresholds. A case in point is the simple one-dimensional problem where the unforced inviscid Burgers' solution always forms a shock dis- continuity, except for the non-generic case of increasing initial profile,u 0 0. In contrast, we show that the corresponding one- dimensional Euler-Poisson equation with zero background has global smooth solutions as long as its initialN0;u 0O-configuration satisfiesu 0 p 2k0 - see (2.11) below, allowing a finite, crit- ical negative velocity gradient. As is typical for such nonlinear convection problems, one is led to a Ricatti equation which is balanced here by a forcing acting as a 'nonlinear resonance', and which in turn is responsible for this critical threshold phenom- ena.

Critical thresholds in euler-poisson equations

Formation of singularities in the Euler and Euler-Poisson equations

"Digital Signal Processing" is a mathematically rigorous but accessible treatment of digital signal processing that intertwines basic theoretical techniques with hands-on laboratory instruction. Divided into three parts, the book covers various aspects of the digital signal processing (DSP) 'problem'. It begins with the analysis of discrete-time signals and explains sampling and the use of the discrete and fast Fourier transforms. The second part of the book - covering digital to analog and analog to digital conversion - provides a practical interlude in the mathematical content before Part III lays out a careful development of the Z-transform and the design and analysis of digital filters. MATLAB[registered] and Simulink[registered] are employed extensively to allow the reader to experience the beautiful mathematics underlying this important discipline, and to demonstrate the subject's engineering relevance. The practical microprocessor-oriented parts of Digital Signal Processing are introduced with special reference to the ADuC841, a lab manual for which can be downloaded from online. These labs can be easily transposed for other microprocessors. Problems are provided at the end of each chapter and an electronic solutions manual is available for tutors. Academic tutors of courses in DSP will find this book to be an invaluable aid in explaining the fundamental mathematics of digital signal processing and drawing out its significance for engineers. Electrical and computer engineers working in signals- and communications-related fields can use the book as a reference or for self-tuition and for deepening their understanding of the techniques they use. Graduate applied mathematics, electrical, electronic and computer engineering students interested in DSP will learn the underlying mathematics of a vital engineering discipline and how to apply it in practical laboratory situations.

Digital Signal Processing: An Experimental Approach

We consider comparator-based nonlinear feedback systems, and use Tsypkin's method to develop a strategy with which to find systems with low-pass linear part for which the describing function technique erroneously predicts limit cycles. We produce an infinite set of examples of systems with very low-pass linear parts for which the describing function technique predicts spurious limit cycles, and also provide a more practical example in which limit cycles are erroneously predicted.

Limitations of the describing function for limit cycle prediction

* Mathematical Preliminaries * Transfer Functions * Feedback -- An Introduction * The Routh-Hurwitz Criterion * The Principle of the Argument and Its Consequences * The Root Locus Diagram * Compensation * Some Nonlinear Control Theory * An Introduction to Modern Control * Control of Hybrid Systems * Answers to Selected Exercises

Shlomo Engelberg

Papers

Critical thresholds in euler-poisson equations

Formation of singularities in the Euler and Euler-Poisson equations

Digital Signal Processing: An Experimental Approach

Limitations of the describing function for limit cycle prediction

A mathematical introduction to control theory