Hypernumbers and Extrafunctions

Author: Mark Burgin
Publisher: Springer Science & Business Media
ISBN: 9781441998750
Release Date: 2012-05-16
Genre: Mathematics

“Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.


Author: Ashish Tewari
Publisher: Springer
ISBN: 9781493923687
Release Date: 2015-03-24
Genre: Mathematics

This monograph presents the state of the art in aeroservoelastic (ASE) modeling and analysis and develops a systematic theoretical and computational framework for use by researchers and practicing engineers. It is the first book to focus on the mathematical modeling of structural dynamics, unsteady aerodynamics, and control systems to evolve a generic procedure to be applied for ASE synthesis. Existing robust, nonlinear, and adaptive control methodology is applied and extended to some interesting ASE problems, such as transonic flutter and buffet, post-stall buffet and maneuvers, and flapping flexible wing. The author derives a general aeroservoelastic plant via the finite-element structural dynamic model, unsteady aerodynamic models for various regimes in the frequency domain, and the associated state-space model by rational function approximations. For more advanced models, the full-potential, Euler, and Navier-Stokes methods for treating transonic and separated flows are also briefly addressed. Essential ASE controller design and analysis techniques are introduced to the reader, and an introduction to robust control-law design methods of LQG/LTR and H2/H∞ synthesis is followed by a brief coverage of nonlinear control techniques of describing functions and Lyapunov functions. Practical and realistic aeroservoelastic application examples derived from actual experiments are included throughout. Aeroservoelasiticity fills an important gap in the aerospace engineering literature and will be a valuable guide for graduate students and advanced researchers in aerospace engineering, as well as professional engineers, technicians, and test pilots in the aircraft industry and laboratories.

Understanding Analysis

Author: Stephen Abbott
Publisher: Springer
ISBN: 9781493927128
Release Date: 2015-05-19
Genre: Mathematics

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

Organic Materials in Civil Engineering

Author: Yves Mouton
Publisher: John Wiley & Sons
ISBN: 9781118613795
Release Date: 2013-03-01
Genre: Technology & Engineering

This book provides an inventory of organic materials and products, the major components of all civil engineering projects, in terms of their scientific and technical background, including the regulations that cover their use and their predicted useful life. Such materials include: bitumen on the roads; geotextiles for retaining walls; membranes for bridges; tunnel and reservoir waterproofing; paint binders to protect metallic and concrete structures or to create road markings; injection resins; gluing products; concrete admixtures; and composite materials. The presentation is based on a physicochemical approach, which is essential if these products are to be considered as part of sustainable development: as such, those studying or working in these fields will find this an invaluable source of information.

Adaptive Aeroservoelastic Control

Author: Ashish Tewari
Publisher: John Wiley & Sons
ISBN: 9781118457634
Release Date: 2016-02-08

This is the first book on adaptive aeroservoelasticity and it presents the nonlinear and recursive techniques for adaptively controlling the uncertain aeroelastic dynamics Covers both linear and nonlinear control methods in a comprehensive manner Mathematical presentation of adaptive control concepts is rigorous Several novel applications of adaptive control presented here are not to be found in other literature on the topic Many realistic design examples are covered, ranging from adaptive flutter suppression of wings to the adaptive control of transonic limit-cycle oscillations

Developments and Trends in Infinite Dimensional Lie Theory

Author: Karl-Hermann Neeb
Publisher: Springer Science & Business Media
ISBN: 0817647414
Release Date: 2010-10-17
Genre: Mathematics

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Brain Imaging in Behavioral Neuroscience

Author: Cameron S. Carter
Publisher: Springer Science & Business Media
ISBN: 9783642287114
Release Date: 2011-11-04
Genre: Medical

This volume highlights the remarkable new developments in brain imaging, including those that apply magnetic resonance imaging (MRI) and Positron Emission Tomography (PET), that allow us to non invasively study the living human brain in health and in disease. These technological advances have allowed us to obtain new and powerful insights into the structure and function of the healthy brain as it develops across the life cycle, as well as the molecular make up of brain systems and circuits as they develop and change with age. New brain imaging technologies have also given us new insights into the causes of many common brain disorders, including ADHD, schizophrenia, depression and Alzheimer’s disease, which collectively affect a large segment of the population. These new insights have major implications for understanding and treating these brain disorders, and are providing clinicians with the first ever set of biomarkers that can be used to guide diagnosis and monitor treatment effects. The advances in brain imaging over the last 20 years, summarized in this volume, represent a major advance in modern biomedical sciences.

Hypergeometric Summation

Author: Wolfram Koepf
Publisher: Springer
ISBN: 9781447164647
Release Date: 2014-06-10
Genre: Computers

Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system MapleTM. The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.

Control of Electric Machine Drive Systems

Author: Seung-Ki Sul
Publisher: John Wiley & Sons
ISBN: 9781118099568
Release Date: 2011-04-20
Genre: Technology & Engineering

A unique approach to sensorless control and regulator design of electric drives Based on the author's vast industry experience and collaborative works with other industries, Control of Electric Machine Drive Systems is packed with tested, implemented, and verified ideas that engineers can apply to everyday problems in the field. Originally published in Korean as a textbook, this highly practical updated version features the latest information on the control of electric machines and apparatus, as well as a new chapter on sensorless control of AC machines, a topic not covered in any other publication. The book begins by explaining the features of the electric drive system and trends of development in related technologies, as well as the basic structure and operation principles of the electric machine. It also addresses steady state characteristics and control of the machines and the transformation of physical variables of AC machines using reference frame theory in order to provide a proper foundation for the material. The heart of the book reviews several control algorithms of electric machines and power converters, explaining active damping and how to regulate current, speed, and position in a feedback manner. Seung-Ki Sul introduces tricks to enhance the control performance of the electric machines, and the algorithm to detect the phase angle of an AC source and to control DC link voltages of power converters. Topics also covered are: Vector control Control algorithms for position/speed sensorless drive of AC machines Methods for identifying the parameters of electric machines and power converters The matrix algebra to model a three-phase AC machine in d-q-n axes Every chapter features exercise problems drawn from actual industry experience. The book also includes more than 300 figures and offers access to an FTP site, which provides MATLAB programs for selected problems. The book's practicality and realworld relatability make it an invaluable resource for professionals and engineers involved in the research and development of electric machine drive business, industrial drive designers, and senior undergraduate and graduate students. To obtain instructor materials please send an email to [email protected] To visit this book's FTP site to download MATLAB codes, please click on this link: ftp://ftp.wiley.com/public/sci_tech_med/electric_machine/ MATLAB codes are also downloadable from Wiley Booksupport Site at http://booksupport.wiley.com

Formal Algorithmic Elimination for PDEs

Author: Daniel Robertz
Publisher: Springer
ISBN: 9783319114453
Release Date: 2014-10-13
Genre: Mathematics

Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.

Functional Neuroimaging in Exercise and Sport Sciences

Author: Henning Boecker
Publisher: Springer Science & Business Media
ISBN: 9781461432937
Release Date: 2012-06-19
Genre: Medical

Regular physical exercise is associated with substantial health benefits. Recent evidence not only holds for cardiovascular effects promoting "physical health", but also for the central nervous system believed to promote "brain health”. Moderate physical exercise has been found to improve learning, memory, and attentional processing, with recent research indicating that neuroprotective mechanisms and associated plasticity in brain structure and function also benefit. Physical exercise is also known to induce a range of acute or sustained psychophysiological effects, among these mood elevation, stress reduction, anxiolysis, and hypoalgesia. Today, modern functional neuroimaging techniques afford direct measurement of the acute and chronic relation of physical exercise on the human brain, as well as the correlation of the derived physiological in vivo signals with behavioral outcomes recorded during and after exercise. A wide range of imaging techniques have been applied to human exercise research, ranging from electroencephalography (EEG), magnetoencephalography (MEG), near infrared spectroscopy (NIRS), magnetic resonance imaging (MRI) to positron emission tomography (PET). All of these imaging methods provide distinct information, and they differ considerably in terms of spatial and temporal resolution, availability, cost, and associated risks. However, from a “multimodal imaging” perspective, neuroimaging provides an unprecedented potential to unravel the neurobiology of human exercise, covering a wide spectrum ranging from structural plasticity in gray and white matter, network dynamics, global and regional perfusion, evoked neuronal responses to the quantification of neurotransmitter release. The aim of this book is to provide the current state of the human neuroimaging literature in the emerging field of the neurobiological exercise sciences and to outline future applications and directions of research.

Mathematical Methods for Elastic Plates

Author: Christian Constanda
Publisher: Springer
ISBN: 9781447164340
Release Date: 2014-06-24
Genre: Mathematics

Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one. The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions. The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system, which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. The presentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students with a basic knowledge of advanced calculus.

Algebraic Approximation A Guide to Past and Current Solutions

Author: Jorge Bustamante
Publisher: Springer Science & Business Media
ISBN: 9783034801942
Release Date: 2011-11-15
Genre: Mathematics

This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.

Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Author: Gunnar Fløystad
Publisher: Springer Science & Business Media
ISBN: 3642194923
Release Date: 2011-05-16
Genre: Mathematics

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.

Convergence Estimates in Approximation Theory

Author: Vijay Gupta
Publisher: Springer Science & Business Media
ISBN: 9783319027654
Release Date: 2014-01-08
Genre: Mathematics

The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.