Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
This comprehensive contributed volume presents an account of current research and applications of chemical processes occurring at the interfaces of water with naturally occurring solids. Interactions of solutes with the solid surfaces are looked at from a mechanistic and dynamic point of view rather than a descriptive one. Processes discussed and concepts presented are applicable to all natural waters (oceans and fresh waters as well as soil and sediment water systems) and to the surfaces of natural solids such as minerals, soils, sediments, biota, and humus. Chapters progress from theoretical models and laboratory studies to applications in natural water, soil, and geochemical systems, emphasizing those processes that regulate the distribution and concentration of elements and compounds. Topics covered include adsorption mechanisms in aquatic surface chemistry, the electric double layer at the solid-solution interface, aspects of molecular structure in surface complexes: spectroscopic investigations, interpretation of metal complexation by heterogeneous complexants, the role of colloids in the partitioning of solutes in natural waters, and from molecules to planetary environments and understanding global change.
This book takes a multidisciplinary approach to the paradigm of biosurfaces and biomaterials through experts working in the arena of interfacing materials with bio-engineering. Starting with the concepts of biomaterials, the book builds upon the real-life applications elucidating the contrasting requirements of materials in their interfaces with biological environment. A birdseye overview of critical requirements is provided, followed by a description of the fundamental mechanisms of protein adsorption, platelet and cell-adhesion. Case studies on mechanical properties, and laser engineering of surfaces that fulfill the critical requirements in constructing successful implants are included. The concept of non-wetting, required especially for anti-biofouling surfaces, via super-hydrophobicity will be discussed. Ethics, legal issues, and a perspective on the future of the biomaterials field conclude the book.
This definitive eBook on silver bullion investing written by Doug West is for investors who want to enter the world of silver investing armed with all the information they need in order to succeed. The book discusses the buying power of silver. It is written in a way that easily convinces anyone who is still on the fence with regard to investing in silver bullion to make the decision by presenting facts and figures.>>> The definitive resource on silver investingThe point that is stressed in this eBook is that silver is a commodity that enjoys an increasing demand while having a limited supply. Because the world's remaining silver deposits lying deep in the earth silver is becoming more expensive to process and remove. Nevertheless, silver is still a very useful commodity and definitely worth a serious investor's attention.
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5  and proceeded to prove the h-cobordism theorem . This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes . Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
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