In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
With cutting-edge materials and minute electronic devices being produced by the latest nanoscale fabrication technology, it is essential for scientists and engineers to rely on first-principles (ab initio) calculation methods to fully understand the electronic configurations and transport properties of nanostructures. It is now imperative to introduce practical and tractable calculation methods that accurately describe the physics in nanostructures suspended between electrodes.This timely volume addresses novel methods for calculating electronic transport properties using real-space formalisms free from geometrical restrictions. The book comprises two parts: The first details the basic formalism of the real-space finite-difference method and its applications. This provides the theoretical foundation for the second part of the book, which presents the methods for calculating the properties of electronic transport through nanostructures sandwiched by semi-infinite electrodes./a
Japanese semiconductor firms are well known for obtaining dynamics in a short period of time and achieving even global leadership. A significant portion of their success are attributable to cooperative interfirm relations and the development of intermediate organizational structure based on long-term relationship between firms. The purpose of this book is to explain how interfirm relations contributed to their dynamics during the golden age of the semiconductor industry. Meanwhile this book clarifies the real source of dynamics in interfirm relations and how the firms have interacted. The author concludes that the competitive-cum-cooperative (CCC) interfirm interaction are observed. Quantitative and qualitative findings show that firms enjoy not only flexible cooperation based synergy effects, but also dynamics market-like effects by creating competition among partners through CCC interaction.
Water covers more than 70% of the earth's surface and is an essential and major component of all living matter. However, artificially hydrated materials, including hydrophilic materials, are far fewer than one might expect. Currently, these materials are in a state of development for applications in fields such as biomedicine, environmental enginee
The area of physics involving muons and neutrinos has become exciting in particle physics. Using their high intensity sources, physicists undertake, in various ways, extensive searches for new physics beyond the Standard Model, such as tests of supersymmetric grand unification (SUSY-GUT) and precision measurements of the muon and neutrino properties, which will in future extend to ambitious studies such as determination of the three-generation neutrino mixing matrix elements and CP violation in the lepton sector. The physics of this field is advancing, with potential improvements of the sources. Many R&D projects, such as those concerning high intensity, low energy muon sources or a neutrino factory, are being carried out or planned at various places. Some of those topics are included in this book. Contents: Muon Applied Science: Status at the End of the 20th Century (K Nagamine); Lepton Flavor Violation and Supersymmetric Models with Right-Handed Neutrino (D Nomura); Neutrino Oscillation Scenarios and GUT Model Predictions (C Albright); The MECO Experiment (J Sculli); CP Violation and Atmospheric Neutrinos (I Stancu et al.); Neutrino Oscillations with Four Generations (O Yasuda); Ambiguities of Theoretical Parameters and CP/T Violation in Neutrino Factories (M Koike et al.); Testing Neutrino Properties at Long Baseline Experiments and Neutrino Factories (S Pakvasa); Next Generation Water Cherenkov Detector at Kamioka (K Nakamura); and other papers. Readership: High energy physicists.
Praise for LEARNING PRACTICAL FINTECH FROM SUCCESSFUL COMPANIES "Throughout my career I've seen the world of finance transformed by technology, from the earliest days of online lending to the current innovations happening with blockchain and cryptocurrency. I believe we're at a critical point in history where a new Internet of Value is starting to emerge, and I'm excited to see so many talented entrepreneurs tackling problems in global finance today." CHRIS LARSEN, Cofounder and Executive Chairman of Ripple "Blockchain technology is changing the way the world does business. This book offers an inside look at how institutions from all corners of financial services and other areas of commerce are collaborating with software firms like R3 to re- engineer the infrastructure that enables money, goods, and information to flow around the globe." DAVID RUTTER, Founder, Chief Executive Officer of R3 "When we think about FinTech, we often think about New York, Silicon Valley, and London, but this book tackles the awakening dragon that is Asian FinTech. Do yourself a huge favor and read this book. Asia is where the real FinTech evolution is happening." BRETT KING, Author of Augmented and BANK 4.0, Host of the Breaking Banks Radio Show, Founder of Moven
Part of a series on the modern Japanese economy which explores all the major areas of Japanese economic life, this book examines the managerial hierarchies of large-scale Japanese industrial companies since their emergence.
The authors have perfected a thick-tissue preparation method for observing hair at various stages of growth, and their findings challenge the currently held three-stage common hair cycle. They have put forward a new hypothesis, the four-stage essential hair cycle, that incorporates their discovery that stem cells are located in the isthmal portion of the sebaceous gland. The essential hair cycle is then used to review the factors contributing to the process of androgenetic alopecia, or premature balding, as it is commonly called. This is followed by an explanation of some general measures for the prevention of androgenetic alopecia and a description of the treatments available.
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
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