Discrete H∞ Optimization


Book Description

Discrete H¿ Optimization is concerned with the study of H¿ optimization for digital signal processing and discrete-time control systems. The first three chapters present the basic theory and standard methods in digital filtering and systems from the frequency-domain approach, followed by a discussion of the general theory of approximation in Hardy spaces. AAK theory is introduced, first for finite-rank operators and then more generally, before being extended to the multi-input/multi-output setting. This mathematically rigorous book is self-contained and suitable for self-study. The advanced mathematical results derived here are applicable to digital control systems and digital filtering.




Discrete Mathematics and Its Applications


Book Description

The companion Web site -- To the student -- The foundations : logic, sets, and functions -- The fundamentals : algorithms, the integers, and matrices -- Mathematical reasoning -- Counting -- Advanced counting techniques -- Relations -- Graphs -- Trees -- Boolean algebra -- Modeling computation










Non-Classical Logics and their Applications to Fuzzy Subsets


Book Description

Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics. The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic.




Invariant Measures for Stochastic Nonlinear Schrödinger Equations


Book Description

This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.




Probability with Applications in Engineering, Science, and Technology


Book Description

This updated and revised first-course textbook in applied probability provides a contemporary and lively post-calculus introduction to the subject of probability. The exposition reflects a desirable balance between fundamental theory and many applications involving a broad range of real problem scenarios. It is intended to appeal to a wide audience, including mathematics and statistics majors, prospective engineers and scientists, and those business and social science majors interested in the quantitative aspects of their disciplines. The textbook contains enough material for a year-long course, though many instructors will use it for a single term (one semester or one quarter). As such, three course syllabi with expanded course outlines are now available for download on the book’s page on the Springer website. A one-term course would cover material in the core chapters (1-4), supplemented by selections from one or more of the remaining chapters on statistical inference (Ch. 5), Markov chains (Ch. 6), stochastic processes (Ch. 7), and signal processing (Ch. 8—available exclusively online and specifically designed for electrical and computer engineers, making the book suitable for a one-term class on random signals and noise). For a year-long course, core chapters (1-4) are accessible to those who have taken a year of univariate differential and integral calculus; matrix algebra, multivariate calculus, and engineering mathematics are needed for the latter, more advanced chapters. At the heart of the textbook’s pedagogy are 1,100 applied exercises, ranging from straightforward to reasonably challenging, roughly 700 exercises in the first four “core” chapters alone—a self-contained textbook of problems introducing basic theoretical knowledge necessary for solving problems and illustrating how to solve the problems at hand – in R and MATLAB, including code so that students can create simulations. New to this edition • Updated and re-worked Recommended Coverage for instructors, detailing which courses should use the textbook and how to utilize different sections for various objectives and time constraints • Extended and revised instructions and solutions to problem sets • Overhaul of Section 7.7 on continuous-time Markov chains • Supplementary materials include three sample syllabi and updated solutions manuals for both instructors and students




Class Field Theory and L Functions


Book Description

The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras. While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020). The main features of the book are: A detailed study of Pontrjagin’s dualtiy theorem. A thorough presentation of the cohomology of profinite groups. A introduction to simple algebras. An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language. The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse. The study of holomorphy domains and their relevance for class field theory. Simple classical proofs of the functional equation for L functions both for number fields and function fields. A self-contained presentation of the theorems of representation theory needed for Artin L functions. Application of Artin L functions for arithmetical results.




Selected Topics in Structronics and Mechatronic Systems


Book Description

In the past twenty years, the scientific community has witnessed a technological revolution in products and processes, from consumer goods to factory automation systems. This revolution is based on the integration, right from the design phase, of the best that current technology can offer in electronics, control systems, computers, structures and mechanics. The terms that have emerged, for the synergetic approach to design, and integration of sensors, actuators, computers, structures and mechanics, are OC structronicsOCO and OC mechatronicsOCO. Structronics can be viewed as an integration of mechatronic systems into structures, which emphasizes a synergistic integration beginning at fertilization. Similar to mechatronics (established in the 1980s), structronics is recognized as one of the essential technologies in the 21st century. This comprehensive reference book gives an overview of the current state of structronics and mechatronics in both structural/mechanical and material systems. Consisting of nine self-contained chapters, it presents recent developments and covers emerging topics in the field. The key features include: . OCo treatment of the nonholonomic variables in robotics. OCo attenuation of fluid flow pulsation in hydraulic systems. OCo presentation of mathematical modeling and experiments on complex nonlinear dynamics of washing machines. OCo a survey of research findings in hydraulic gap control of rolling mills. OCo detailed description of mathematical modeling and nonlinear control of a temper controlling mill. OCo applications of high frequency dynamics in engineering structures. OCo development of novel computational methods to include plasticity and damage in flexible multibody systems. OCo new trends in optimal design of engineering structures. OCo a review of ionic polymer metal composites (IPMCs) as sensors, actuators and artificial muscles. Selected Topics in Structronics and Mechatronic Systems will be of interest to engineers, materials scientists, physicists and applied mathematicians. Contents: On the Use of Nonholonomic Variables in Robotics (H Bremer); Compensators for the Attenuation of Fluid Flow Pulsations in Hydraulic Systems (J Mikota); Some Aspects of Washing Complex Nonlinear Dynamics (M BolteAcentsar); Analysis and Nonlinear Control of Hydraulic Systems in Rolling Mills (R M Novak); Mathematical Modeling and Nonlinear Control of a Temper Rolling Mill (S Fuchshumer et al.); Combining Continuous and Discrete Energy Approaches to High Frequency Dynamics of Structures (A K Belyaev); Computational Methods for Elasto-Plastic Multibody Systems (J Gerstmayr); New Trends in Optimal Structural Control (K G Arvanitis et al.); Ionic PolymerOCoConductor Composites (IPCC) as Biomimietic Sensors, Actuators and Artificial Muscles (M Shahinpoor & A Guran). Readership: Engineers, materials scientists, physicists and applied mathematicians."




Scale Space and Variational Methods in Computer Vision


Book Description

This book constitutes the refereed proceedings of the 6th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2017, held in Kolding, Denmark, in June 2017. The 55 revised full papers presented were carefully reviewed and selected from 77 submissions. The papers are organized in the following topical sections: Scale Space and PDE Methods; Restoration and Reconstruction; Tomographic Reconstruction; Segmentation; Convex and Non-Convex Modeling and Optimization in Imaging; Optical Flow, Motion Estimation and Registration; 3D Vision.