Book Description
This digital document is an article from Canadian Chemical News, published by Thomson Gale on February 1, 2006. The length of the article is 655 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: In memoriam.(Henry Taube, J. E. Guillet)(Obituary)
Publication: Canadian Chemical News (Magazine/Journal)
Date: February 1, 2006
Publisher: Thomson Gale
Volume: 58Issue: 2Page: 4(1)

Article Type: Obituary

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Book Description
This book focuses on the differential equations and related subjects that are commonly used today by working life scientists. It emphasizes both the mathematics and how the mathematics is employed in order to introduce some potentially useful tools and modes of thought to future experimental biologists. Chapter topics include phase plane analysis, vectors, linear and non-linear systems, matrix notation, advection, diffusion equations, separation of variables, traveling waves, and periodic solutions.For individuals interested in biology and the life sciences, and aware of how they will play a major role in our society in the coming century.y. ... Read more

Book Description
In this book, the author's goal is to provide an introduction tosome of the analytic underpinnings for the geometry of anti-selfduality in 4-dimensions. Anti-self duality is rather special to4-dimensions and the imposition of this condition on curvaturesof connections on vector bundles and on curvatures of Riemannianmetrics has resulted in some spectacular mathematics.

The book reviews some basic geometry, but it is assumed that thereader has a general background in differential geometry (aswould be obtained by reading a standard text on the subject).Some of the fundamental references include Atiyah, Hitchin andSinger, Freed and Uhlenbeck, Donaldson and Kronheimer, andKronheimer and Mrowka. The last chapter contains open problemsand conjectures. ... Read more

Customer Reviews (1)

Out of date, but still could be useful
The results in this book have been superseded by the results of Nathan Seiberg and Edward Witten that appeared a short time after this book was published. The Seiberg-Witten theory caused great excitement among the mathematical community who do research in differential geometry and differential topology, particularly in the area of the differential toplogy of 4-dimensional manifolds. Proclaiming the "end of the Donaldson theory", mathematicians moved on to study the properties of the Seiberg-Witten equation, which is still nonlinear enough to be interesting.

Thus the discussions in this book are somewhat dated, but still could be of interest from a mathematical history standpoint or with the goal perhaps of motivating the Seiberg-Witten theory, although the self-dual Yang-Mills equations, a cornerstone of the Donaldson theory, are not discussed in the book. Instead the author studies the anti-self dual equations. These arise uniquely in four dimensions due to the fact thatthe Lie algebra so(4) of the special orthogonal group SO(4) is not simple, but instead decomposes as the direct sum of two copies of the Lie algebra so(3) of SO(3). This enables one to decompose the tangent bundle of the manifold into a direct sum of two oriented 3-plane bundles. The curvature of the Levi-Civita connection then splits with respect to this decomposition, the decomposition having entries involving the scalar curvature, the traceless Ricci tensor, and the self-dual and anti-self dual Weyl curvature tensors. The question of the existence of metrics on the manifold for which the anti-self dual part vanishes is the subject of the book, with particular attention paid to complex vector bundles over the manifold. The anti-self dual equations are consequently a set of algebraic equations for the curvature, which are equivalent, over an open set in the manifold, to a first-order differential equation involving a 1-form over this open set and taking values in the Lie algebra of complex 2-space.The main strategy the author employs for studying these equations is to showthat they linearize to Fredholm equations. Thus a kind of generalization of the Fredholm property holds here in the context of (infinite-dimensional) vector bundles. A section of an infinite-dimensional vector bundle which linearizes to a Fredholm operator acts essentially like a section of a finite dimensional bundle over a finite dimensional manifold.

The book could also be used to motivate a study of the connection between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. That there is such a connection was recently conjectured and some promising work in proving this conjecture has appeared lately. There has also been recent interest in examining the anti-self dual equations on noncommutative four-dimensional Euclidean space, because of its connection with string theory. ... Read more

Book Description
The book contains a complete proof of the remarkable result relating the Seiberg-Witten and Gromov invariants of symplectic four manifolds.The first chapter proves that pseudo-holomorphic curves can be sonstruction from solutions to the Seiberg-Witten equations.The second chapter describes how the Gromov invariant for compact symplectic 4-manifolds assigns an integer to each dimension 2-cohomology class (or roughly speaking, counts with suitable weights, compact, pseudo-holomorphic submanifolds whose fundamental class is Poincare dual to the cohomology class in question.The third chapter continues the proof of the equivalence of Gromov invariants and the Seiberg-Witten invariants.In this chapter, a construction which associates solutions of the one-parameter family of Weiber-Witten equations to certain symplectic submanifolds in X (Pseudo-holomorphic ones.)The final chapter shows that counting for the two invariants yeilds the same answer. ... Read more

Product Description
Stories of Jewish youth who were victims of the Holocaust. ... Read more