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This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.

Structural analysis (Engineering) --- Engineering mathematics. --- Rigidity (Geometry)

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The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.

Hypersurfaces. --- Threefolds (Algebraic geometry) --- Surfaces, Algebraic. --- Rigidity (Geometry)

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This paper considers two sets of theories attempting to explain wage rigidities and unemployment: implicit contract theory and the efficiency wage theory. The basic thesis of the paper is that the former set of theories do not provide a convincing explanation of the kind of wage rigidity which is associated with cyclical unemployment,while the latter theories do. Several of the more recent versions of implicit contract theory are considered: implicit contracts with asymmetric information may give rise to over employment rather than underemployment, and the forms of contracts to be expected, were asymmetric information considerations paramount, are not observed.Other versions of the asymmetric information implicit contract model, explicitly long term in nature, may give rise to full employment. One version of implicit contract theory which does give rise to lay-offs arises when search is costly and cannot be monitored. But even this extension does not explain certain important features of observed patterns of unemployment. In contrast, the efficiency wage models not only provide an explanation of the existence of unemployment equilibrium in competitive economies, but they also provide part of the explanation of the observed patterns of unemployment. They also explain why different firms may pay similar workers different wages, why wages may be sticky, why firms maynot loose much if they fail to adjust their wages, and why, when they adjust their wages optimally, they adjust them slowly.The policy implications of the efficiency wage model are markedly different from those of models in which wages are absolutely rigid aswell as from those in which unemployment arises from asymmetric information.

Wages --- Rigidity (Geometry) --- Contracts Mathematical models. --- Equilibrium (Economics) --- Unemployment. --- Econometric models. --- Mathematical models.

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Torsion --- Torsion (mécanique) --- Rigidity (Geometry) --- Rigidité (géométrie) --- Pression hydrostatique --- Hydrostatic pressure

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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.