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.
This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers. In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of continuous and discrete spectrum, multiple scales in space and time, and the ill-posedness of these problems. This volume collects a series of lectures which introduce into the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.
Strictly off limits to the public, Plum Island is home to virginal beaches, cliffs, forests, ponds -- and the deadliest germs that have ever roamed the planet. Lab 257 blows the lid off the stunning true nature and checkered history of Plum Island. It shows that the seemingly bucolic island in the shadow of New York City is a ticking biological time bomb that none of us can safely ignore. Based on declassified government documents, in-depth interviews, and access to Plum Island itself, this is an eye-opening, suspenseful account of a federal government germ laboratory gone terribly wrong. For the first time, Lab 257 takes you deep inside this secret world and presents startling revelations on virus outbreaks, biological meltdowns, infected workers, the periodic flushing of contaminated raw sewage into area waters, and the insidious connections between Plum Island, Lyme disease, and the deadly West Nile virus. The book also probes what's in store for Plum Island's new owner, the Department of Homeland Security, in this age of bioterrorism. Lab 257 is a call to action for those concerned with protecting present and future generations from preventable biological catastrophes.
This is the final book in the Plum Flower Trilogy by Afaa Michael Weaver, published by the University of Pittsburgh Press. The two previous books, The Plum Flower Dance: Poems 1985 to 2005 and The Government of Nature, reveal similar themes that address the author's personal experience with childhood abuse through the context of Daoist renderings of nature as a metaphor for the human body, with an eye to recovery and forgiveness in a very eclectic spiritual life. City of Eternal Spring chronicles Weaver's travels abroad in Taiwan and China, as well as showing the limits of cultural influence.
PLUM RAINS ON HAPPY HOUSE" IS A TOUR DE FORCE OF CULTURE-CLASHING, SIDE-SPLITTING HUMOR! In Japan, the little inn called Happy House welcomes its guests ... unless it's rainy season. When the "plum rains" arrive, trying times of volatility and decadence begin for everyone. The American in Room 1, however, is dead-set on turning the derelict Happy House into a burgeoning English school. The house has other plans, and Room 1's attempts are thwarted by a freakish creature that lives under the floorboards called "the Crat." Happy House hosts a collection of the most unhinged characters you'll ever find under one roof! You'll never look at Japan the same way again! SCROLL UP AND GRAB A COPY NOW!
Have you ever wanted to visit China on your own? Follow along with Michael Faris as he takes the plunge into a wonderful discovery of the world's last original civilization known as the Middle Kingdom - China. Plum Blossom, Gentle Dragon is the second volume in the series Forever Laowai.
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