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Rigidity (Geometry)

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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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This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.

Rigidity (Geometry) --- Abelian groups. --- Commutative groups --- Group theory --- Geometric rigidity --- Rigidity theorem --- Discrete 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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This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Carathéodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all mot

Nonholonomic dynamical systems. --- Geometry, Differential. --- Rigidity (Geometry) --- Caratheodory measure. --- Measure, Caratheodory --- Algebra, Boolean --- Measure theory --- Geometric rigidity --- Rigidity theorem --- Discrete geometry --- Differential geometry --- Dynamical systems, Nonholonomic --- Non-holonomic systems --- Nonholonomic systems --- Differentiable dynamical systems --- Rigidity (Geometry).