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Galois Connections and Applications
Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint sit...
Catalogue of the Birds in the British Museum: Game birds (Pterocletes, Gallinæ, Opisthocomi, Hemipodii) by W.R. Ogilvie-Grant. 1893
This enormous undertaking, which, according to one of the prefaces, professes to be a complete list of every bird known at the time of publication, kept growing even as it was being written. The Museum added eagerly to their already vast collections during the decades of publication, acquiring by gift the great collections of A.O. Hume on Asian birds, and those of Sclater and Salvin and Godwin on Neotropical birds, so that the size of the collection nearly tripled between 1874 and 1888. Sharpe originally intended to do all the work himself, but others were called in when this became clearly impossible. The plates are all of birds not previously illustrated. In the decades following its publication this catalogue was universally acclaimed as the most important work on systematic ornithology that has ever been published. (Zimmer, p. 96). And even after one hundred years it remains an essential reference for the serious ornithologist, as it underpins a great deal of modern bird classification. With 387 plates, most hand-coloured lithographs, some chromolithographs, by William Hart, J.G. Keulemans, Joseph and Peter Smit.
Philologia Oreintals
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Neogene Mammals
Neogene Mammals: New Mexico Museum of Natural History and Science Bulletin 44
Formal Concept Analysis
Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. It thereby allows us to mathematically represent, analyze, and construct conceptual structures. The formal concept analysis approach has been proven successful in a wide range of application fields. This book constitutes a comprehensive and systematic presentation of the state of the art of formal concept analysis and its applications. The first part of the book is devoted to foundational and methodological topics. The contributions in the second part demonstrate how formal concept analysis is successfully used outside of mathematics, in linguistics, text retrieval, association rule mining, data analysis, and economics. The third part presents applications in software engineering.
Algebras and Orders
In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in ...
