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Book 3 in the Princeton Mathematical Series. Originally published in 1950.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Geometry, Differential. --- Calculus of tensors. --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Differential geometry --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis

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This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed ste

Geometry, Differential. --- Calculus of tensors. --- Continuum mechanics. --- Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Differential geometry

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C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

Physics. --- Quantum Field Theories, String Theory. --- Mathematical Physics. --- Algebra. --- Physique --- Algèbre --- Calculus of tensors. --- Quantum field theory. --- Von Neumann algebras. --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Relativistic quantum field theory --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Mathematical physics. --- String theory. --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- C*-algebras --- Hilbert space --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Mathematics --- Mathematical analysis --- Physical mathematics --- Models, String --- String theory --- Nuclear reactions

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Comprehensive review of diseases of poverty and public health strategies to combat them

Public Health --- Communicable Disease Control. --- World Health. --- Poverty. --- Communicable Diseases --- Absolute Poverty --- Extreme Poverty --- Indigents --- Low Income Population --- Indigency --- Low-Income Population --- Indigent --- Low Income Populations --- Low-Income Populations --- Population, Low Income --- Population, Low-Income --- Populations, Low Income --- Populations, Low-Income --- Poverty, Absolute --- Poverty, Extreme --- Working Poor --- International Health --- Worldwide Health --- International Health Problems --- World Health --- Health Problem, International --- Health Problems, International --- Health, Global --- Health, International --- Health, World --- Health, Worldwide --- Healths, International --- International Health Problem --- International Healths --- Problem, International Health --- Problems, International Health --- World Health Organization --- Parasite Control --- Flatten the Curve of Epidemic --- Flattening the Curve, Communicable Disease Control --- Control, Communicable Disease --- Control, Parasite --- Infectious Disease Medicine --- Disease Eradication --- methods. --- epidemiology. --- prevention & control --- Global Health. --- Federal Poverty Threshold --- Poverty Threshold, Federal --- Poverty Thresholds, Federal --- Thresholds, Federal Poverty --- Federal Poverty Level --- Federal Poverty Levels --- Level, Federal Poverty --- Poverty Level, Federal

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Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms.This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.

Buildings (Group theory) --- Combinatorial geometry. --- Geometric combinatorics --- Geometrical combinatorics --- Combinatorial analysis --- Discrete geometry --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Linear algebraic groups --- Bruhat-Tits building. --- Clifford invariant. --- Coxeter diagram. --- Coxeter group. --- Coxeter system. --- Euclidean plane. --- Fundamental Theorem of Descent. --- Moufang building. --- Moufang condition. --- Moufang polygon. --- Moufang quadrangle. --- Moufang set. --- Moufang structure. --- Pfister form. --- Structure Theorem. --- Tits index. --- abelian group. --- absolute Coxeter diagram. --- absolute Coxeter system. --- absolute rank. --- affine building. --- algebraic group. --- anisotropic pseudo-quadratic space. --- anisotropic quadratic space. --- anti-isomorphism. --- apartment. --- arctic region. --- automorphism. --- bilinear form. --- biquaternion division algebra. --- building. --- canonical isomorphism. --- chamber. --- compatible representation. --- descent group. --- descent. --- discrete valuation. --- exceptional Moufang quadrangle. --- exceptional quadrangle. --- finite dimension. --- fixed point building. --- fixed point theory. --- gem. --- generalized quadrangle. --- hyperbolic plane. --- hyperbolic quadratic module. --- hyperbolic quadratic space. --- involutory set. --- isomorphism. --- isotropic quadratic space. --- length function. --- non-abelian group. --- parallel residues. --- polar space. --- projection map. --- proper indifferent set. --- proper involutory set. --- pseudo-quadratic space. --- pseudo-split building. --- quadratic form. --- quadratic module. --- quadratic space. --- quaternion division algebra. --- ramified quadrangle. --- ramified quaternion division algebra. --- ramified separable quadratic extension. --- relative Coxeter diagram. --- relative Coxeter group. --- relative Coxeter system. --- relative rank. --- residual quadratic spaces. --- residue. --- root group sequence. --- root. --- round quadratic space. --- scalar multiplication. --- semi-ramified quadrangle. --- separable quadratic extension. --- simplicial complex. --- special vertex. --- spherical building. --- split quadratic space. --- standard involution. --- subbuilding of split type. --- subbuilding. --- tamely ramified division algebra. --- thick building. --- thin T-building. --- trace map. --- trace. --- unramified quadrangle. --- unramified quadratic space. --- unramified quaternion division algebra. --- unramified separable quadratic extension. --- vector space. --- vertex. --- weak isomorphism. --- wild quadratic space.