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The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Translation Surfaces by Jayadev S. Athreya,Howard Masur Pdf
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.
The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.
Functionalization of Semiconductor Surfaces by Franklin Tao,Steven Bernasek Pdf
This book presents both fundamental knowledge and latest achievements of this rapidly growing field in the last decade. It presents a complete and concise picture of the the state-of-the-art in the field, encompassing the most active international research groups in the world. Led by contributions from leading global research groups, the book discusses the functionalization of semiconductor surface. Dry organic reactions in vacuum and wet organic chemistry in solution are two major categories of strategies for functionalization that will be described. The growth of multilayer-molecular architectures on the formed organic monolayers will be documented. The immobilization of biomolecules such as DNA on organic layers chemically attached to semiconductor surfaces will be introduced. The patterning of complex structures of organic layers and metallic nanoclusters toward sensing techniques will be presented as well.
Lectures on Surfaces by A. B. Katok,Vaughn Climenhaga Pdf
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approach the subject from a completely geometric point of view although heavily relying on algebraic methods. Some of the techniques presented in this book can be applied to the study of algebraic surfaces of other types. We hope that it will make this book of particular interest to a wider range of research mathematicians and graduate students. Acknowledgements. The undertaking of this project was made possible by the support of several institutions. Our mutual cooperation began at the University of Warwick and the Max Planck Institute of Mathematics in 1982/83. Most of the work in this volume was done during the visit of the first author at the University of Michigan in 1984-1986. The second author was supported during all these years by grants from the National Science Foundation.
Life at Rock Surfaces by Burkhard Büdel,Thomas Friedl Pdf
Rock surfaces provide a challenging habitat for a broad diversity of micro- or small-sized organisms. They interact with each other forming complex communities as well with their substrate causing biodeterioration of rock. Extreme fluctuation in light, temperature and hydration are the main factors that determine the rock surface habitats. The habitat includes epilithic organisms which thrive on the surface without penetrating the rock, endolithic organisms which live just beneath the surface using a thin layer of the rock surface for protection against adverse conditions of the environment (e.g. light protection, storage of water) and chasmo-endolithic organisms which use fractures of the rock surface for a more habitable environment. The book will provide an overview of the various organismal groups, from prokaryotes to vascular plants and arthropods, as well as survey organism-mediated interactions with the rock surface. The latter include biogenic weathering (biogeochemistry, state-of-the art imaging methods), photosynthesis and nitrogen fixation at and inside the rock surface.
Volume 1 of the landmark series Flora of New South Wales was first published in 1990, and describes the naturally occurring and naturalized ferns, cycads, conifers and some of the flowering plants of that state. Since 1990, parts of Volume 1 have been made substantially out of date by wide-ranging revisions to taxonomy and the discovery or identification of new plant species - such as the 'living fossil' Wollemi pine, featured on the cover of this revised edition. This revised edition of Volume 1 incorporates a 64 page insert that lists all the updates to the information contained within the book, including taxonomic changes, new species descriptions, new data about species and changes to keys. These changes are cross-referenced from the original species or key entry in the volume to the relevant section of the insert, so where necessary readers can quickly check to see what changes have occurred. Additionally, the reference list, glossary and index have all been revised.
Implant dentistry has come a long way since Dr. Branemark introduced the osseointegration concept with endosseous implants. The use of dental implants has increased exponentially in the last three decades. As implant treatment became more predictable, the benefits of therapy became evident. The demand for dental implants has fueled a rapid expansion of the market. Presently, general dentists and a variety of specialists offer implants as a solution to partial and complete edentulism. Implant dentistry continues to evolve and expand with the development of new surgical and prosthodontic techniques. The aim of Implant Dentistry - A Rapidly Evolving Practice, is to provide a comtemporary clinic resource for dentists who want to replace missing teeth with dental implants. It is a text that relates one chapter to every other chapter and integrates common threads among science, clinical experience and future concepts. This book consists of 23 chapters divided into five sections. We believe that, Implant Dentistry: A Rapidly Evolving Practice, will be a valuable source for dental students, post-graduate residents, general dentists and specialists who want to know more about dental implants.
The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.
Solid Surfaces, Interfaces and Thin Films by Hans Lüth Pdf
Solid Surfaces, Interfaces and Thin Films examines both experimental and theoretical aspects of surface, interface and thin film physics. Coverage of magnetic thin films has been expanded, and now includes giant magnetoresistance and the spin-transfer torque mechanism.
The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
X-Ray Photoelectron Spectroscopy of Solid Surfaces by V.I. Nefedov Pdf
This volume outlines the physical and methodical concepts of X-ray photoelectron spectroscopy (XPS) specifically for surface studies using both inner and valence electron levels. It discusses the theory and practice of XPS qualitative and quantitative analysis of solid state surfaces and provides lists of extended experimental and theoretical data necessary for the determination of concentration and thin film thicknesses. In addition it covers the many problems concerning in-depth profiling, ion sputtering rate and damages of the structure of altered layers, as well as applications of angular dependence of the intensities and photoelectron diffraction for surface studies. Also provided are the applications of XPS for the investigations of catalysts, adsorption, electronic surface states, oxydation of semi-conductors and alloys, minerals, including lunar regolith and natural gold, glasses, radiation damage, surface diffusion, polymers, etc.