This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.
This is the biggest, most comprehensive, and most prestigious compilation of articles on control systems imaginable. Every aspect of control is expertly covered, from the mathematical foundations to applications in robot and manipulator control. Never before has such a massive amount of authoritative, detailed, accurate, and well-organized information been available in a single volume. Absolutely everyone working in any aspect of systems and controls must have this book!
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.This text uses X-ray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI. Audience The book is appropriate for one- or two-semester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis. Contents Preface to the Second Edition; Preface; How to Use This Book; Notational Conventions; Chapter 1: Measurements and Modeling; Chapter 2: Linear Models and Linear Equations; Chapter 3: A Basic Model for Tomography; Chapter 4: Introduction to the Fourier Transform; Chapter 5: Convolution; Chapter 6: The Radon Transform; Chapter 7: Introduction to Fourier Series; Chapter 8: Sampling; Chapter 9: Filters; Chapter 10: Implementing Shift Invariant Filters; Chapter 11: Reconstruction in X-Ray Tomography; Chapter 12: Imaging Artifacts in X-Ray Tomography; Chapter 13: Algebraic Reconstruction Techniques; Chapter 14: Magnetic Resonance Imaging; Chapter 15: Probability and Random Variables; Chapter 16: Applications of Probability; Chapter 17: Random Processes; Appendix A: Background Material; Appendix B: Basic Analysis; Index.
Sifting through the variety of control systems applications can be a chore. Diverse and numerous technologies inspire applications ranging from float valves to microprocessors. Relevant to any system you might use, the highly adaptable Control System Fundamentals fills your need for a comprehensive treatment of the basic principles of control system engineering. This overview furnishes the underpinnings of modern control systems. Beginning with a review of the required mathematics, major subsections cover digital control and modeling. An international panel of experts discusses the specification of control systems, techniques for dealing with the most common and important control system nonlinearities, and digital implementation of control systems, with complete references. This framework yields a primary resource that is also capable of directing you to more detailed articles and books. This self-contained reference explores the universal aspects of control that you need for any application. Reliable, up-to-date, and versatile, Control System Fundamentals answers your basic control systems questions and acts as an ideal starting point for approaching any control problem.
The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
When it comes to electronics, demand grows as technology shrinks. From consumer and industrial markets to military and aerospace applications, the call is for more functionality in smaller and smaller devices. Culled from the second edition of the best-selling Electronics Handbook, Microelectronics, Second Edition presents a summary of the current state of microelectronics and its innovative directions. This book focuses on the materials, devices, and applications of microelectronics technology. It details the IC design process and VLSI circuits, including gate arrays, programmable logic devices and arrays, parasitic capacitance, and transmission line delays. Coverage ranges from thermal properties and semiconductor materials to MOSFETs, digital logic families, memory devices, microprocessors, digital-to-analog and analog-to-digital converters, digital filters, and multichip module technology. Expert contributors discuss applications in machine vision, ad hoc networks, printing technologies, and data and optical storage systems. The book also includes defining terms, references, and suggestions for further reading. This edition features two new sections on fundamental properties and semiconductor devices. With updated material and references in every chapter, Microelectronics, Second Edition is an essential reference for work with microelectronics, electronics, circuits, systems, semiconductors, logic design, and microprocessors.
From industrial and teaching experience the authors provide a blend of theory and practice of digital signal processing (DSP) for advanced undergraduate and post-graduate engineers reading electronics. This fast-moving, developing area is driven by the information technology revolution. It is a source book in research and development for embedded system design engineers, designers in real-time computing, and applied mathematicians who apph DSP techniques in telecommunications, aerospace (control systems), satellite communications, instrumentation, and medical technology (ultrasound and magnetic resonance imaging).The book is particularly useful at the hardware end of DSP, with its emphasis on practical I)SP devices and the integration of basic processes with appropriate software. It is unique to find in one volume the implementation of the equations as algorithms, not only in \IATLAB but right up to a working DSP-based scheme. Other relevant architectural features include number representations, multiply-accumulate, special addressing modes, zero overhead iteration schemes. and single and multiple nlicroprocessors which will allow the readers to compare and understand both current processors and future DSP developments.Fundamental signal processing procedures are introduced and developed: also convolution. correlation, the Discrete Fourier Transform and its fast computation algorithms. Then follo finite impulse response (FIR) filters, infinite impulse response (IlR) filters, multirate filters, adaptive filters, and topics from communication and control. I)esign examples are given in all of these cases, taken through an algorithm testing stage using MATLAB. The design of the latter. using C language models, is explained together with the experimental results of real time integer implementations.Academic prerequisites are first and second year university mathematics, an introductor knowledge of circuit theor 'and microprocessors. and C Language. - Provides an unusual blend of theory and practice of digital signal processing (DSP) - Discusses fundamental signal processing procedures, convolution, correlation, the Discrete Fourier Transform and its fast computation algorithms - Includes number representations, multiply-accumulate, special addressing modes, zero overhead iteration schemes, and single and multiple instructions
This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.