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President of Yale University from 1978 to 1986, A. Bartlett Giamatti was one of the voices who, in his own words, "repositioned the academy in a changed world". In these essays he defines the essence of liberal education and sets forth his commitment to an education that "will constantly test rather than impose the values it cherishes".
This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.
Which public and whose space? The understanding of public space as an arena where individuals can claim full use and access hides a reality of constant negotiation, conflict and surveillance. This collection uses case studies concerning the management, use, and transgression of public space to invite reflection on the way in which everyday social interaction is framed and shaped by the physical environment and vice versa. International experts from fields including geography, criminology, sociology and urban studies come together to debate the concepts of order and conflict in public space. This book is divided into two parts: spaces of control, and spaces of transgression. Section I focuses on formal and informal surveillance and the politics of control, using case studies to compare strategies in spaces including Olympic cities, luxury skyscrapers, residential neighbourhoods and shopping malls. Section II focuses on transgressive or deviant behaviour in public spaces, with case studies examining behaviour in nightlife districts, governance of homelessness, boy-racer culture and abortion protests. The epilogue concludes the book with an exploration of possible future avenues for research on public space, and a critical appraisal of the concept of public space itself. This interdisciplinary collection will be of interest to students, researchers and professionals in the areas of criminology, sociology, surveillance studies, human and social geography, and urban studies and planning.
The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field – the Cartesian vector field – given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.
ARCHITECTURE THE GOLD STANDARD IN INTRODUCTORY ARCHITECTURE TEXTS, FULLY UPDATED TO REFLECT THE LATEST DEVELOPMENTS IN THE FIELD For more than forty years, the beautifully illustrated Architecture: Form, Space, and Order has served as the classic introduction to the basic vocabulary of architectural design. In this fifth edition, more recent additions to the architectural panoply illustrate how contemporary digital and building technologies have influenced the development of architectural forms and spaces and how architectural siting and design have responded to the call for more environmentally responsible buildings. It is designed to encourage critical thought and to promote a more evocative understanding of architecture. The fifth edition is updated with many new urban design and building precedents from a diverse range of cultural and geographic areas New content focuses on the latest technology and trends in structure, construction, materials, and sustainability Includes more than 800 illustrations, many hand-drawn, which demonstrate the foundations and concepts every architect must master Architecture: Form, Space, and Order distills complex concepts of design into a clear focus and brings difficult abstractions to life. It explains form and space in relation to light, view, openings, and enclosures and explores the organization of space, and the elements and relationships of circulation, as well as proportion and scale. In addition, the text’s detailed illustrations demonstrate the concepts presented and reveal the relationships between fundamental elements of architecture through the ages and across cultures.
This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.