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The Method of Intrinsic Scaling : A Systematic Approach to Regularity for Degenerate and Singular PDEs
This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs. In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. This approach brings to light what is really essential in the method, leaving aside technical refinements needed to deal with more general equations, and is entirely self-contained. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions. The aim is to convince the reader of the strength of the method as a systematic approach to regularity for this important class of equations.
The Method of Approximate Inverse : Theory and Applications
Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions.
The Metaphysics of Science : An Account of Modern Science in Terms of Principles, Laws and Theories
The roots of this work lie in my earlier book, Scientific Progress, which first appeared in 1981. One of its topics, the distinction - tween scientific laws and theories, is there treated with reference to the same distinction as drawn by N. R. Campbell in his Physics: The Elements. Shortly after completing Scientific Progress, I read Rom Harré’s The Principles of Scientific Thinking, in which the concept of theory is even more clearly delineated than in Campbell, being directly connected to the notion of a model – as it was in my book. In subsequent considerations regarding science, Harré’s work thus - came my main source of inspiration with regard to theories, while Campbell’s remained my main source with respect to empirical laws. Around the same time I also read William Whewell’s Philosophy of the Inductive Sciences.
The McGraw-Hill Education handbook of English grammar and usage ; 3rd ed.
Written by two expert grammarians, the book provides bottom-line definitions, tips, and simple rules that summarize the essentials you need to know. You’ll find clear examples of usage and as well guidance on communication via text, email, and social media.
The Maximum Principle
Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
The Mathematics of the Bose Gas and its Condensation
This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem.It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area .The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.
The Mathematics of Minkowski Space-Time : With an Introduction to Commutative Hypercomplex Numbers
Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in the book. In particular, an exhaustive solution of the "twin paradox" is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, an appendix on general properties of commutative hypercomplex systems with four unities is presented.
The Mathematics of Arbitrage
This long-awaited book aims at a rigorous mathematical treatment of the theory of pricing and hedging of derivative securities by the principle of 'no arbitrage'. The first part presents a relatively elementary introduction, restricting itself to the case of finite probability spaces. The second part consists of an updated edition of seven original research papers by the authors, which analyse the topic in the general framework of semi-martingale theory.
The Mathematics Education of Prospective Secondary Teachers Around the World
This volume shares and discusses significant new trends and developments in research and practices related to various aspects of preparing prospective secondary mathematics teachers from 2005–2015. It provides both an overview of the current state-of-the-art and outstanding recent research reports from an international perspective. The authors completed a thorough review of the literature by examining major journals in the field of mathematics education, and other journals related to teacher education and technology.
The Mathematical Theory of Finite Element Methods
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara'e-Friedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout.
The Mathematica GuideBook for Symbolics
"The Mathematica GuideBook for Symbolics"deals with Mathematica's symbolic mathematical capabilities. Structural and mathematical operations on single and systems of polynomials are fundamental to many symbolic calculations and they are covered in considerable detail. The solution of equations and differential equations, as well as the classical calculus operations (differentiation, integration, summation, series expansion, limits) are exhaustively treated.
The Mathematica GuideBook for Numerics
Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility.The available types of arithmetic (machine, high-precision, and interval) are introduced, discussed, and put to use. Fundamental numerical operations, such as compiling programs, fast Fourier transforms, minimization, numerical solution of equations, ordinary/partial differential equations are analyzed in detail and are applied to a large number of examples in the main text and solutions to the exercises.
The Math Problems Notebook
The problems cover many topics, including number theory, algebra, combinatorics, geometry and analysis, of varying levels of difficulty. The presentation of each topic begins with simple exercises and follows with more difficult problems, challenging enough even for the experienced problem solver. The easier problems focus on basic methods and tools, while the more advanced problems develop problem-solving techniques, intuition and promote further research.
The Market for Corporate Control in Japan : M&As, Hostile Takeovers and Regulatory Framework
This book analyzes the modern trend in the Japanese M and A market. It reveals from different perspectives the process of convergence to a new monitoring model of the corporation: "the market for corporate control". The book contains a systematic survey of all relevant economic and legal information in this field.
The Map of My Life
In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.
The Many Scales in the Universe : JENAM 2004 Astrophysics Reviews
The book gathers the invited talks to the XIII JENAM conference, organized this time by the European Astronomical Society (EAS) and the Spanish Astronomical Society (SEA), and hosted by the Instituto de Astrofísica de Andalucía (CSIC). All branches of astrophysics are encompassed from the largest scales and cosmology to the solar system and the Sun, through the galaxies and the stars, including a section on astronomical instrumentation. Very relevant experts from all over the world speak in a single book about the most recent, exciting results from their fields in a way which is useful for both researchers in these fields and colleagues working in other disciplines. The book is accompanied by a CD-ROM including the remaining contributions of the meeting in PDF format, hence opening a wide panorama of what is going on in astrophysics nowadays.
The Malliavin Calculus and Related Topics
In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s,p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe’s work. Chapter 2, includes a general estimate for the density of a one-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe’s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented.
The Machines of Leonardo Da Vinci and Franz Reuleaux : Kinematics of Machines from the Renaissance to the 20th Century
This book is about the evolution of these machines and the inv- tors and engineers who created them from the early Renaissance to the early 20th century. I have chosen two personalities who are icons of these two machine ages, Leonardo da Vinci [1452–1519] and Franz Reuleaux [1829– 1905], recognizing both the cadre of machine designers who in?uenced them as well as those who were in?uenced by the accomplishments of these two engineers. A major thesis of this book is that the evolution of machine design methodology, from the intuitive methods of the workshop to the math-based, engineering science analysis and synthesis of modern industrial design, was of equal achievement as the creation of the marvelous machines themselves. In the past two decades there has been increasing interest in rational me- ods of design from topology and optimization theories to genetic algorithms. In the teaching of design at the novitiate level, the importance of design - cles and iteration is emphasized. Yet often the historical background for e- lution of machine design is minimal or missing.
The Lucky Few : Between the Greatest Generation and the Baby Boom
Born during the Great Depression and World War Two (1929 – 1945) - between the Greatest Generation and the Baby Boom - an entire generation has slipped between the cracks of history. Yet behind the scenes, these Lucky Few became the first American generation smaller than the one before them, and the luckiest generation of Americans ever. Lucky Few women married earlier than any other generation of the century and helped give birth to the Baby Boom, yet also gained in education compared to earlier generations. More than any other generation, Lucky Few men advanced into professional and white-collar jobs while Lucky Few women concentrated in the clerical "pink-collar ghetto." Even in retirement and old age the Lucky Few remain in the right place at the right time. Here is their story, and the story of how they have affected other recent generations of Americans before and since.
The Logistic Map and the Route to Chaos : From the Beginnings to Modern Applications
Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
