Author: Augusto C. Ponce
Publisher: European Mathematical Society
Release Date: 2016
Genre: Differential equations, Elliptic
Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis whose connections are usually not emphasized in introductory graduate courses. Yet one cannot dissociate the notions of mass or electric charge, naturally described in terms of measures, from the physical potential they generate. Having such a principle in mind, this book illustrates the beautiful interplay between tools from PDEs and GMT in a simple and elegant way by investigating properties such as existence and regularity of solutions of linear and nonlinear elliptic PDEs. Inspired by a variety of sources, from the pioneer balayage scheme of Poincare to more recent results related to the Thomas-Fermi and Chern-Simons models, the problems covered in this book follow an original presentation, intended to emphasize the main ideas in the proofs. Classical techniques such as regularity theory, maximum principles and the method of sub- and supersolutions are adapted to the setting where merely integrability or density assumptions on the data are available. The distinguished role played by capacities and precise representatives is also explained. Other special features are: the remarkable equivalence between Sobolev capacities and Hausdorff contents in terms of trace inequalities; the strong approximation of measures in terms of capacities or densities, normally absent from GMT books; and the rescue of the strong maximum principle for the Schrodinger operator involving singular potentials. This book invites the reader on a trip through modern techniques in the frontier of elliptic PDEs and GMT and is addressed to graduate students and researchers with a deep interest in analysis. Most of the chapters can be read independently, and only a basic knowledge of measure theory, functional analysis, and Sobolev spaces is required.
-A new edition of this definitive book, marking the 60th anniversary of the Speedmaster -Includes new features and additional historical information "The OMEGA Speedmaster Professional - the Moonwatch - has done things that no other timepiece has done and it has been worn in places that only a few human beings have been." - Captain Eugene Cernan, last man on the moon "It is an indescribable reference work and a true must-have for every Speedmaster collector." - Forbes There are very few timepieces in the world that deserve a definitive and comprehensive book. The OMEGA Speedmaster Professional Moonwatch is one of them. Initially designed for automobile racing teams and engineers, the Omega Speedmaster embarked on a very different trajectory when NASA chose it to accompany astronauts heading for the Moon in 1965. Its involvement in the space adventure has propelled the Moonwatch to the top of the list of celebrated timepieces. After years of research and observation, the authors present a complete panorama of the Moonwatch in a systematic work that is both technical and attractive, making it the unparalleled reference book for this legendary watch. This new edition, marking the 60th anniversary of the Speedmaster, has been enriched with numerous new features and additional historical information. Contents: Foreword by Raynald Aeschlimann, President and CEO of OMEGA; Foreword by Captain Eugene Cernan, Commander of Apollo 17; Why a Speedmaster Moonwatch guide?; Part 1 - Speedmaster History; 1, Major Dates; 2, Speedmaster and NASA 25; Part 2 - Main Components and Accessories; 1, An Original Approach; 2, The Caliber; 3, The Caseband; 4, The Dial; 5, The Bezel; 6, The Hands; 7, The Caseback; 8, The Crown; 9, The Pushers; 10, The Glass; 11, The Bracelet; 12, The Presentation Box; 13, The Documents; Part 3 - The Models; 1, Introduction; 2, Standard Production; 3, Special and Limited Series; 4, Personalized Models and Special Projects; 5, The Alaska Project; Part 4 - 60 Years of Innovation; Part 5 - How to Start Collecting Speedmasters; 1, Budget; 2, Choosing a Model; 3, Sales Channels; Part 6 - Appendices; 1, Model Codes; 2, Tables & Bibliography; 3, Contributions; 4, Identification Aid
Author: Alexander Balanov
Publisher: Springer Science & Business Media
Release Date: 2008-11-23
This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.
This contributed volume celebrates the work of Tayfun E. Tezduyar on the occasion of his 60th birthday. The articles it contains were born out of the Advances in Computational Fluid-Structure Interaction and Flow Simulation (AFSI 2014) conference, also dedicated to Prof. Tezduyar and held at Waseda University in Tokyo, Japan on March 19-21, 2014. The contributing authors represent a group of international experts in the field who discuss recent trends and new directions in computational fluid dynamics (CFD) and fluid-structure interaction (FSI). Organized into seven distinct parts arranged by thematic topics, the papers included cover basic methods and applications of CFD, flows with moving boundaries and interfaces, phase-field modeling, computer science and high-performance computing (HPC) aspects of flow simulation, mathematical methods, biomedical applications, and FSI. Researchers, practitioners, and advanced graduate students working on CFD, FSI, and related topics will find this collection to be a definitive and valuable resource.
Author: Harold Rabinowitz
Release Date: 2009-06-12
Much like the Chicago Manual of Style, The Manual of Scientific Style addresses all stylistic matters in the relevant disciplines of physical and biological science, medicine, health, and technology. It presents consistent guidelines for text, data, and graphics, providing a comprehensive and authoritative style manual that can be used by the professional scientist, science editor, general editor, science writer, and researcher. Scientific disciplines treated independently, with notes where variances occur in the same linguistic areas Organization and directives designed to assist readers in finding the precise usage rule or convention A focus on American usage in rules and formulations with noted differences between American and British usage Differences in the various levels of scientific discourse addressed in a variety of settings in which science writing appears Instruction and guidance on the means of improving clarity, precision, and effectiveness of science writing, from its most technical to its most popular
Author: Klaus D. Sattler
Publisher: CRC Press
Release Date: 2010-09-17
Many bottom-up and top-down techniques for nanomaterial and nanostructure generation have enabled the development of applications in nanoelectronics and nanophotonics. Handbook of Nanophysics: Nanoelectronics and Nanophotonics explores important recent applications of nanophysics in the areas of electronics and photonics. Each peer-reviewed chapter contains a broad-based introduction and enhances understanding of the state-of-the-art scientific content through fundamental equations and illustrations, some in color. This volume discusses how different nanomaterials, such as quantum dots and nanotubes, are used in quantum computing, capacitors, and transistors. Leading international experts review the potential of the novel patterning techniques in molecular electronics as well as nanolithography approaches for producing semiconductor circuits. They also describe optical properties of nanostructures, nanowires, nanorods, and clusters, including cathodoluminescence, photoluminescence, and polarization-sensitivity. In addition, the book covers nanophotonic devices and nanolasers. Nanophysics brings together multiple disciplines to determine the structural, electronic, optical, and thermal behavior of nanomaterials; electrical and thermal conductivity; the forces between nanoscale objects; and the transition between classical and quantum behavior. Facilitating communication across many disciplines, this landmark publication encourages scientists with disparate interests to collaborate on interdisciplinary projects and incorporate the theory and methodology of other areas into their work.
Author: Carles Casacuberta
Publisher: Springer Science & Business Media
Release Date: 2001-12-01
The Third European Congress of Mathematics (3ecm) took place from July 10th to July 14th, 2000 in Barcelona. It was organised by the Societat Catalana de Matematiques (Catalan Mathematical Society), under the auspices of the Euro pean Mathematical Society (EMS). As foreseen by the EMS and the International Mathematical Union, this Congress was a major event in World Mathematical Year 2000. In addition to reviewing outstanding research achievements, important aspects of the life of European mathematics were discussed. Mathematics is undergoing a period of rapid changes. Effective computation and applications in science and technology go ever more hand in hand with con ceptual developments. It was one of the aims of 3ecm to reflect this mutual enrich ment, while steering present and future trends of mathematical sciences. In fact, the motto of the Congress, Shaping the 21st Century, was meant to capture these views. Nearly 1400 people from 87 countries gathered together in the Palau de Con gressos of Barcelona in order to take part in the activities of the 3ecm scientific programme: Nine plenary lectures, thirty invited lectures in parallel sessions, lec tures given by EMS prize winners, ten mini-symposia on special topics, seven round tables, poster sessions, presentations of mathematical software and video exhibitions. Twenty events were satellites of 3ecm in various countries.
Author: Joel H. Shapiro
Publisher: American Mathematical Soc.
Release Date: 2018-06-14
Genre: Convolutions (Mathematics)
This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques—all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.
Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.
Author: John Robert Burger
Publisher: Springer Science & Business Media
Release Date: 2013-05-31
This book models an idealized neuron as being driven by basic electrical elements, the goal being to systematically characterize the logical properties of neural pulses. In order to constitute a system, neurons as pulsating devices may be represented using novel circuit elements as delineated in this book. A plausible brain system is implied by the delineated elements and logically follows from known and likely properties of a neuron. New to electrical science are novel pulse-related circuit elements involving recursive neurons. A recursive neuron, when properly excited, produces a self-sustaining pulse train that when sampled, provides a true output with a specified probability, and a false output with complementary probability. Because of its similarity to the qubits of quantum mechanics, the recursive pulsating neuron is termed a simulated qubit. Recursive neurons easily function as controlled toggle devices and so are capable of massively parallel calculations, this being a new dimension in brain functioning as described in this book. Simulated qubits and their possibilities are compared to the qubits of quantum physics. Included in the book are suggested neural circuits for associative memory search via a randomized process of cue selection, and neural circuits for priority calculations. These serve to select returns from long term memory, which in turn determines one's next conscious thought or action based on past memorized experiences. The book reports on proposals involving electron tunneling between synapses, and quantum computations within neurons. Although not a textbook, there are easy exercises at the ends of chapters, and in the appendix there are twelve simulation experiments concerning neurons.
Author: Ming-Yang Kao
Publisher: Springer Science & Business Media
Release Date: 2008-08-06
One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.
This edited book aims at presenting current research activities in the field of robust variable-structure systems. The scope equally comprises highlighting novel methodological aspects as well as presenting the use of variable-structure techniques in industrial applications including their efficient implementation on hardware for real-time control. The target audience primarily comprises research experts in the field of control theory and nonlinear dynamics but the book may also be beneficial for graduate students.