341,120 research outputs found

    The Theory of Quasiconformal Mappings in Higher Dimensions, I

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    We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and limited) by the theme of the author's interests. Thus we will discuss the basic theory as it developed in the 1960s in the early work of F.W. Gehring and Yu G. Reshetnyak and subsequently explore the connections with geometric function theory, nonlinear partial differential equations, differential and geometric topology and dynamics as they ensued over the following decades. We give few proofs as we try to outline the major results of the area and current research themes. We do not strive to present these results in maximal generality, as to achieve this considerable technical knowledge would be necessary of the reader. We have tried to give a feel of where the area is, what are the central ideas and problems and where are the major current interactions with researchers in other areas. We have also added a bit of history here and there. We have not been able to cover the many recent advances generalising the theory to mappings of finite distortion and to degenerate elliptic Beltrami systems which connects the theory closely with the calculus of variations and nonlinear elasticity, nonlinear Hodge theory and related areas, although the reader may see shadows of this aspect in parts

    Gravity as a Gauge Theory of Translations

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    The Poincar\'e group can be interpreted as the group of isometries of a minkowskian space. This point of view suggests to consider the group of isometries of a given space as the suitable group to construct a gauge theory of gravity. We extend these ideas to the case of maximally symmetric spaces to reach a realistic theory including the presence of a cosmological constant. Introducing the concept of "minimal tetrads" we deduce Einstein gravity in the vacuum as a gauge theory of translations.Comment: 14 pages. LaTeX 2

    The familes Lonchopteridae, Opetiidae and Pipunculidae of Malta (Diptera, Aschiza)

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    An account is given of the three Aschiza families of Diptera: one species of Lonchopteridae, one species of Opetiidae and four species of Pipunculidae that occur in Malta and which are all new records for this countrypeer-reviewe

    Diptera Carnoidea of the Maltese Islands

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    An account is given of the families in the Carnoidea (Diptera: Schizophora) that have not been recorded previously from Malta. These are Braulidae, one species, Canacidae, one species, Carnidae, two species and Milichiidae, seven species.peer-reviewe
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