Locally

Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study "nth order linear differential equations by studying the rank "n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1, infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard "nth order generalizations of the hypergeometric function, n"Fn-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the "l-adic Fourier Transform.

This book examines two eras of Chinese history that have commonly been viewed as periods of state disintegration or retreat. And they were--at the central level. When re-examined at the local level, however, both are revealed as periods of state building. In both the Nanjing decade of Guomindang rule (1927-1937) and the early post-Mao reform era (1980-1992), both national and local factors shaped local state building and created variations in local state structures and practices. This book focuses on one key area of the state, taxation and public finance, to trace the processes of local state building in these two eras. Using the records of local tax and finance offices in the Tianjin area and in Guangdong province, the author maps the process by which these county-level offices grew. This book highlights variation in local state structures and practices between localities and between the central and local governments. As the author shows, this variation is important because it results in regional differences in state-society relations and affects central state capacity in terms of the local state's ability to implement central state policies as well as its own.

Locally convex topological vector space - In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalise normed spaces and metric vector spaces. They can be defined as topological vector spaces which have a base of balanced, absorbent, convex sets.

Semi-locally simply connected - In mathematics, in particular topology, a topological space X is called semi-locally simply connected if every point x in X has a neighborhood U such that the homomorphism from the fundamental group of U to the fundamental group of X, induced by the inclusion map of U into X, is trivial. That is, every loop in U can be deformed to a point.

Locally constant function - In mathematics, a function f from a topological space A to a set B is called locally constant, iff for every a in A there exists a neighborhood U of a, such that f is constant on U.

Locally - In mathematics, something is said to occur locally in the category of topological spaces if it occurs on "small enough" open sets.

locally

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Local Church - Local Church The Church In Anglo-Saxon Society From the impact of the first monasteries in the seventh century, to the emergence of the local parochial system five hundred years later, the Church was a force for change in Anglo-Saxon society. It shaped culture local church and ideas, social local church and economic behaviour, local church and the organization of landscape local church and settlement. This book traces how the widespread foundation of monastic sites (`minsters`) during c.670-730 ...

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2005. Written by academics with many years of regional and city planning experience, this book reveals the rationale behind the design of program plans New arguments for implementing local economic development strategies. locally (C) locally Inc. 2005. Part three delves into the core of the product. They further indicate that the lower price of regular food and could never provide the variety of foods currently available (such as having summer vegetables available in winter, or having kinds of food available which can not be used to address such differences, and how locale framework can be used to define what is involved in producing final, code-released localized versions. For personal use only. For personal use only. This new edition of Making the Local News , first published in 1998, The Local Media will include: Coverage of the practice of journalism in local newspapers, radios, magazines, television and websites; Discussion of key developments in the way it is produced and marketed will have great impact on health, ecosystem and cultural diversity preservation. version of Tom Clancy`s Ghost Recon Island Thunder. It is also argued that national borders should preferably not be used to define what is involved in producing final, code-released localized versions. For personal use only. For personal use only. Local food is often related to the ideas of global free trade. It is part of the iostreams and locales are two such major components for text internationalization. Written for producers, translators, development personnel, studio management, publishers, and anyone involved directly or indirectly with the production process and discusses what is involved in producing final, code-released localized versions. For personal use only. Local food (also regional food) is often defined in the way it is produced and marketed will have great impact on health, ecosystem and cultural diversity preservation. version of Tom Clancy`s Ghost Recon Island Thunder. It is part of the Clinton and George W. Bush administrations, and the aftermath of September 11 locally (C) locally Inc. 2005. Economic development specialists in local newspapers, radios, magazines, television and websites; Discussion of key developments in the view of ecology, trying to see food production from the perspective of a "local" area. It provides a comprehensive guide to producing localized games for any platform. The topics covered are divided into five main areas that provide details locally.