Det One


Book Description

From the Foreword: "The story of the Marine Corps U.S. Special Operations Command Detachment, which became known as Det One, is an extraordinary tale. On its face, the story would not rate a minute's glance. One small group of Marines, about a hundred in number, formed, trained, and went to war. This all happened as the nation was 18 months into the Global War on Terrorism and as the Marine Corps was deploying I Marine Expeditionary Force in Operation Iraqi Freedom. Yet the story behind the basic facts is not only far more intricate and fascinating, with dramatic episodes and intrepid characters from the Pentagon to Camp Pendleton, it portended great significance for the Marine Corps. What makes the Det One story extraordinary is the shift in Marine Corps policy that brought it about, the maturation of the special operations capabilities of forward-deployed Marine expeditionary units that made it possible, and the patriotism, valor, fidelity, and abilities of the Marines and Navy Corpsmen who manned it. Although Det One has passed now into the history books, its legacy survives in the formation of Marine Corps Special Operations Command and in the lessons learned and experiences of its members, who now continue to serve in dozens of units. Lieutenant Colonel John P. Piedmont Marine Field Historian in Iraq in April 2004, saw the historical significance of Det One and decided to pursue its history as a project. Under the director of the History and Museums Division at the time, Colonel John W. Ripley, he was given permission to proceed with his collections with a view toward turning them into a monograph. What follows here is the culmination of his efforts, the product of two years' work, more than 60 interviews done in Iraq, Washington, D.C., Virginia, and California, and the collection of hundreds of documents."--Dr. Charles P. Neimeyer.




Grammaticalization


Book Description

This volume contains a selection of papers on grammaticalization from a broad perspective. Some of the papers focus on basic concepts in grammaticalization research such as the concept of 'grammar' as the endpoint of grammaticalization processes, erosion, (uni)directionality, the relation between grammaticalization and constructions, subjectification, and the relation between grammaticalization and analogy. Other papers shed a critical light on grammaticalization as an explanatory parameter in language change. New case studies of micro-processes of grammaticalization complete the selection. The empirical evidence for (and against) grammaticalization comes from diverse domains: subject control, clitics, reciprocal markers, pronouns and agreement markers, gender markers, auxiliaries, aspectual categories, intensifying adjectives and determiners, and pragmatic markers. The languages covered include English and its varieties, German, Dutch, Italian, Spanish, French, Slavonic languages, and Turkish. The book will be valuable to scholars working on grammaticalization and language change as well as to those interested in individual languages.




The Air Reservist


Book Description




Random Matrices, Frobenius Eigenvalues, and Monodromy


Book Description

The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.




Linear Algebra:


Book Description

Linear Algebra is designed for postgraduate and undergraduate students of Mathematics. This book explains the basics comprehensively and with clarity. The flowing narrative of the book provides a refreshing approach to the subject. Drawing on decad







Calculus of Variations


Book Description

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.




IV: Analysis of Operators


Book Description

BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical PhysicsThis revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.




Hypoelliptic Laplacian and Orbital Integrals


Book Description

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.