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Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.
Algebraic topology. --- K-theory. --- Algebraic topology --- Homology theory --- Topology --- Topology. --- K-Theory. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- K-theory
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This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.
Mathematical optimization. --- Integral Transforms. --- Calculus of Variations and Optimal Control; Optimization. --- Integral Transforms, Operational Calculus. --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Multivariate analysis --- MATLAB. --- Integral calculus & equations. --- Computer programs. --- Calculus of variations. --- Integral transforms. --- Operational calculus. --- Operational calculus --- Differential equations --- Electric circuits --- Isoperimetrical problems --- Variations, Calculus of
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The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September 1993, on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'. They are intended to give a snapshot of the status of work on the Novikov Conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry and analysis. Volume 1 contains: • A detailed historical survey and bibliography of the Novikov Conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; • An annotated problem list; • The texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and • Research/survey papers on the Novikov Conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg.
Index theorems --- Novikov conjecture --- Conjecture, Novikov --- Novikov's conjecture --- Manifolds (Mathematics) --- Differential operators --- Global analysis (Mathematics) --- Index theory (Mathematics) --- Rigidity (Geometry) --- Congresses. --- Novikov conjecture - Congresses. --- Index theorems - Congresses.
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The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September, 1993, on the subject of `Novikov Conjectures, Index Theorems and Rigidity'. They are intended to give a snapshot of the status of work on the Novikov Conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, analysis.
Novikov conjecture --- Index theorems --- Rigidity (Geometry) --- Geometric rigidity --- Rigidity theorem --- Discrete geometry --- Differential operators --- Global analysis (Mathematics) --- Index theory (Mathematics) --- Manifolds (Mathematics) --- Conjecture, Novikov --- Novikov's conjecture
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Bringing together scholars from the fields of musicology and international history, this book investigates the significance of music to foreign relations, and how it affected the interaction of nations since the late 19th century. For more than a century, both state and non-state actors have sought to employ sound and harmony to influence allies and enemies, resolve conflicts, and export their own culture around the world. This book asks how we can understand music as an instrument of power and influence, and how the cultural encounters fostered by music changes our ideas about international
Music and diplomacy. --- Music and state. --- Music--Political aspects--History--20th century. --- Music --- Music and diplomacy --- Music and state --- Music, Dance, Drama & Film --- Music Philosophy --- State and music --- Cultural policy --- Diplomacy and music --- Diplomacy --- Art music --- Art music, Western --- Classical music --- Musical compositions --- Musical works --- Serious music --- Western art music --- Western music (Western countries) --- History --- Political aspects --- Social aspects --- Musique --- Musique et diplomatie --- Aspect politique --- Histoire --- Politique gouvernementale --- 1900 - 1999
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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Chirurgie (Topologie) --- Heelkunde (Topologie) --- Surgery (Topology) --- Differential topology --- Homotopy equivalences --- Manifolds (Mathematics) --- Topology --- Algebraic topology (object). --- Algebraic topology. --- Ambient isotopy. --- Assembly map. --- Atiyah–Hirzebruch spectral sequence. --- Atiyah–Singer index theorem. --- Automorphism. --- Banach algebra. --- Borsuk–Ulam theorem. --- C*-algebra. --- CW complex. --- Calculation. --- Category of manifolds. --- Characterization (mathematics). --- Chern class. --- Cobordism. --- Codimension. --- Cohomology. --- Compactification (mathematics). --- Conjecture. --- Contact geometry. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dirac operator. --- Disk (mathematics). --- Donaldson theory. --- Duality (mathematics). --- Embedding. --- Epimorphism. --- Excision theorem. --- Exponential map (Riemannian geometry). --- Fiber bundle. --- Fibration. --- Fundamental group. --- Group action. --- Group homomorphism. --- H-cobordism. --- Handle decomposition. --- Handlebody. --- Homeomorphism group. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy extension property. --- Homotopy fiber. --- Homotopy group. --- Homotopy. --- Hypersurface. --- Intersection form (4-manifold). --- Intersection homology. --- Isomorphism class. --- K3 surface. --- L-theory. --- Limit (category theory). --- Manifold. --- Mapping cone (homological algebra). --- Mapping cylinder. --- Mostow rigidity theorem. --- Orthonormal basis. --- Parallelizable manifold. --- Poincaré conjecture. --- Product metric. --- Projection (linear algebra). --- Pushout (category theory). --- Quaternionic projective space. --- Quotient space (topology). --- Resolution of singularities. --- Ricci curvature. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Ring homomorphism. --- Scalar curvature. --- Semisimple algebra. --- Sheaf (mathematics). --- Sign (mathematics). --- Special case. --- Sub"ient. --- Subgroup. --- Submanifold. --- Support (mathematics). --- Surgery exact sequence. --- Surgery obstruction. --- Surgery theory. --- Symplectic geometry. --- Symplectic vector space. --- Theorem. --- Topological conjugacy. --- Topological manifold. --- Topology. --- Transversality (mathematics). --- Transversality theorem. --- Vector bundle. --- Waldhausen category. --- Whitehead torsion. --- Whitney embedding theorem. --- Yamabe invariant.
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This benchmark study of the political party–interest group relationship—crucial in shaping the characteristics of democratic political systems—provides an in-depth analysis of the connection between special interests and political parties across thirteen democracies: Argentina, Britain, the Czech Republic, France, Germany, Israel, Italy, Japan, Mexico, Poland, Spain, Sweden, and the United States.
Political parties. --- Pressure groups. --- Democracy. --- Comparative government. --- Advocacy groups --- Interest groups --- Political interest groups --- Special interest groups (Pressure groups) --- Functional representation --- Political science --- Representative government and representation --- Lobbying --- Policy networks --- Political action committees --- Social control --- Parties, Political --- Party systems, Political --- Political party systems --- Divided government --- Intra-party disagreements (Political parties) --- Political conventions --- Comparative political systems --- Comparative politics --- Government, Comparative --- Political systems, Comparative --- Self-government --- Equality --- Republics
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