Download or read book Regularity of Free Boundaries in Obstacle Type Problems written by Arshak Petrosyan and published by American Mathematical Soc.. This book was released on 2012 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.

Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Download or read book Obstacle Problems in Mathematical Physics written by J.-F. Rodrigues and published by Elsevier. This book was released on 1987-03-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics. The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

Download or read book Elliptic Differential Equations and Obstacle Problems written by Giovanni Maria Troianiello and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the few years since their appearance in the mid-sixties, variational inequalities have developed to such an extent and so thoroughly that they may now be considered an "institutional" development of the theory of differential equations (with appreciable feedback as will be shown). This book was written in the light of these considerations both in regard to the choice of topics and to their treatment. In short, roughly speaking my intention was to write a book on second-order elliptic operators, with the first half of the book, as might be expected, dedicated to function spaces and to linear theory whereas the second, nonlinear half would deal with variational inequalities and non variational obstacle problems, rather than, for example, with quasilinear or fully nonlinear equations (with a few exceptions to which I shall return later). This approach has led me to omit any mention of "physical" motivations in the wide sense of the term, in spite of their historical and continuing importance in the development of variational inequalities. I here addressed myself to a potential reader more or less aware of the significant role of variational inequalities in numerous fields of applied mathematics who could use an analytic presentation of the fundamental theory, which would be as general and self-contained as possible.

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

Download or read book The Obstacle Is the Way written by Ryan Holiday and published by Penguin. This book was released on 2014-05-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: #1 Wall Street Journal Bestseller The Obstacle is the Way has become a cult classic, beloved by men and women around the world who apply its wisdom to become more successful at whatever they do. Its many fans include a former governor and movie star (Arnold Schwarzenegger), a hip hop icon (LL Cool J), an Irish tennis pro (James McGee), an NBC sportscaster (Michele Tafoya), and the coaches and players of winning teams like the New England Patriots, Seattle Seahawks, Chicago Cubs, and University of Texas men’s basketball team. The book draws its inspiration from stoicism, the ancient Greek philosophy of enduring pain or adversity with perseverance and resilience. Stoics focus on the things they can control, let go of everything else, and turn every new obstacle into an opportunity to get better, stronger, tougher. As Marcus Aurelius put it nearly 2000 years ago: “The impediment to action advances action. What stands in the way becomes the way.” Ryan Holiday shows us how some of the most successful people in history—from John D. Rockefeller to Amelia Earhart to Ulysses S. Grant to Steve Jobs—have applied stoicism to overcome difficult or even impossible situations. Their embrace of these principles ultimately mattered more than their natural intelligence, talents, or luck. If you’re feeling frustrated, demoralized, or stuck in a rut, this book can help you turn your problems into your biggest advantages. And along the way it will inspire you with dozens of true stories of the greats from every age and era.

Download or read book Linear and Nonlinear Functional Analysis with Applications written by Philippe G. Ciarlet and published by SIAM. This book was released on 2013-10-10 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

Download or read book Least Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Download or read book Hybrid High Order Methods written by Matteo Cicuttin and published by Springer Nature. This book was released on 2021-11-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.

Download or read book Good Strategy Bad Strategy written by Richard Rumelt and published by Currency. This book was released on 2011-07-19 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good Strategy/Bad Strategy clarifies the muddled thinking underlying too many strategies and provides a clear way to create and implement a powerful action-oriented strategy for the real world. Developing and implementing a strategy is the central task of a leader. A good strategy is a specific and coherent response to—and approach for—overcoming the obstacles to progress. A good strategy works by harnessing and applying power where it will have the greatest effect. Yet, Rumelt shows that there has been a growing and unfortunate tendency to equate Mom-and-apple-pie values, fluffy packages of buzzwords, motivational slogans, and financial goals with “strategy.” In Good Strategy/Bad Strategy, he debunks these elements of “bad strategy” and awakens an understanding of the power of a “good strategy.” He introduces nine sources of power—ranging from using leverage to effectively focusing on growth—that are eye-opening yet pragmatic tools that can easily be put to work on Monday morning, and uses fascinating examples from business, nonprofit, and military affairs to bring its original and pragmatic ideas to life. The detailed examples range from Apple to General Motors, from the two Iraq wars to Afghanistan, from a small local market to Wal-Mart, from Nvidia to Silicon Graphics, from the Getty Trust to the Los Angeles Unified School District, from Cisco Systems to Paccar, and from Global Crossing to the 2007–08 financial crisis. Reflecting an astonishing grasp and integration of economics, finance, technology, history, and the brilliance and foibles of the human character, Good Strategy/Bad Strategy stems from Rumelt’s decades of digging beyond the superficial to address hard questions with honesty and integrity.

Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Download or read book The Finite Element Method for Elliptic Problems written by P.G. Ciarlet and published by Elsevier. This book was released on 1978-01-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments should provide many suggestions for conducting seminars.

Download or read book How to Solve a Problem written by Ashima Shiraishi and published by Make Me a World. This book was released on 2020-04-07 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Ashima Shiraishi, one of the world's youngest and most skilled climbers, comes a true story of strength and perseverance--in rock climbing and in life. To a rock climber, a boulder is called a "problem," and you solve it by climbing to the top. There are twists and turns, falls and scrapes, and obstacles that seem insurmountable until you learn to see the possibilities within them. And then there is the moment of triumph, when there's nothing above you but sky and nothing below but a goal achieved. Ashima Shiraishi draws on her experience as a world-class climber in this story that challenges readers to tackle the problems in their own lives and rise to greater heights than they would have ever thought possible.

Download or read book Down and Dirty written by Matt Davis and published by Fair Winds Press (MA). This book was released on 2014-07 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVThis book from Matt B. Davis offers a down-and-dirty overview of the most popular races before tackling the most important concerns for any racer: preparation and training. /div

Download or read book Obstacle Race Training Bible written by James Villepigue and published by Penguin. This book was released on 2012-12-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first how-to guide to help readers prepare for and conquer a new and growing form of distance racing popping up all over the country, written by bestselling fitness author James Villepigue. Obstacle Race Training Bible provides readers with one-stop access to everything you need to know to prepare for and successfully complete a Tough Mudder, Spartan Race, Warrior Dash, or any of the other international or regional obstacle races that are taking the world by storm. All of these races combine running various distances and terrain with hard-core obstacles that are both physically and mentally challenging: climbing through pitch-black flooded tubes and over walls, carrying logs uphill, traversing monkey bars, crawling through mud and under barbed wire, leaping over burning hay bales, swimming in ice cold water, navigating through live wires, and more. This combination of running and obstacles is what gives participants a very different kind of challenge than they get with a 5K, marathon, or triathlon. It's a combination that also requires a very different approach to training and preparation, and that's what this book provides. Coverage includes: Profiles of all the major races: running distance, obstacles involved, completion percentage, fitness level required, etc. Obstacle overviews, including photos of what they look like, the mental and physical challenges involved, and the most effective strategies for completing them Obstacle-specific exercises that condition participants for the strength, stamina, flexibility, and mental toughness needed to complete the obstacle 8-week training programs designed for complete novices, elite athletes, and everyone in between Important information on what to wear, nutrition during training, and race day strategies

Download or read book An Introduction to Variational Inequalities and Their Applications written by David Kinderlehrer and published by SIAM. This book was released on 2000-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.

Download or read book The Alignment Problem Machine Learning and Human Values written by Brian Christian and published by W. W. Norton & Company. This book was released on 2020-10-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: A jaw-dropping exploration of everything that goes wrong when we build AI systems and the movement to fix them. Today’s “machine-learning” systems, trained by data, are so effective that we’ve invited them to see and hear for us—and to make decisions on our behalf. But alarm bells are ringing. Recent years have seen an eruption of concern as the field of machine learning advances. When the systems we attempt to teach will not, in the end, do what we want or what we expect, ethical and potentially existential risks emerge. Researchers call this the alignment problem. Systems cull résumés until, years later, we discover that they have inherent gender biases. Algorithms decide bail and parole—and appear to assess Black and White defendants differently. We can no longer assume that our mortgage application, or even our medical tests, will be seen by human eyes. And as autonomous vehicles share our streets, we are increasingly putting our lives in their hands. The mathematical and computational models driving these changes range in complexity from something that can fit on a spreadsheet to a complex system that might credibly be called “artificial intelligence.” They are steadily replacing both human judgment and explicitly programmed software. In best-selling author Brian Christian’s riveting account, we meet the alignment problem’s “first-responders,” and learn their ambitious plan to solve it before our hands are completely off the wheel. In a masterful blend of history and on-the ground reporting, Christian traces the explosive growth in the field of machine learning and surveys its current, sprawling frontier. Readers encounter a discipline finding its legs amid exhilarating and sometimes terrifying progress. Whether they—and we—succeed or fail in solving the alignment problem will be a defining human story. The Alignment Problem offers an unflinching reckoning with humanity’s biases and blind spots, our own unstated assumptions and often contradictory goals. A dazzlingly interdisciplinary work, it takes a hard look not only at our technology but at our culture—and finds a story by turns harrowing and hopeful.