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In recent years there have been exciting developments in techniques for producing multilayered structures of different materials, often with thicknesses as small as only a few atomic layers. These artificial structures, known as superlattices, can either be grown with the layers stacked in an alternating fashion (the periodic case) or according to some other well-defined mathematical rule (the quasiperiodic case). This book describes research on the excitations (or wave-like behavior) of these materials, with emphasis on how the material properties are coupled to photons (the quanta of the l

Periodic functions. --- Lattice theory. --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Functions, Periodic

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The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as

Algebraic logic. --- Lattice theory. --- Algebraic logic --- Lattice theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Logic, Symbolic and mathematical

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Ordered algebraic structures --- Lattice theory. --- Automorphisms. --- Théorie des treillis --- Automorphismes --- 51 <082.1> --- Mathematics--Series --- Théorie des treillis --- Automorphisms --- Lattice theory --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Symmetry (Mathematics)

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Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups. Topics covered include: [bulleted list] residuated mappings Galois connections modular, distributive, and complemented lattices Boolean algebras pseudocomplemented lattices Stone algebras Heyting algebras ordered groups lattice-ordered groups representable groups Archimedean ordered structures ordered semigroups naturally ordered regular and inverse Dubreil-Jacotin semigroups [end od bulleted list] Featuring material that has been hitherto available only in research articles, and an account of the range of applications of the theory, there are also many illustrative examples and numerous exercises throughout, making it ideal for use as a course text, or as a basic introduction to the field for researchers in mathematics, logic and computer science. T. S. Blyth is Professor Emeritus at St. Andrews University, UK.

Ordered algebraic structures. --- Lattice theory. --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Algebra. --- Order, Lattices, Ordered Algebraic Structures. --- Mathematics --- Mathematical analysis

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Geography --- Lattice theory. --- Géographie --- Théorie des treillis --- Mathematics. --- Mathématiques --- Lattice theory --- Mathematics --- -Lattice theory --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Cosmography --- Earth sciences --- World history --- Géographie --- Théorie des treillis --- Mathématiques --- Methodology --- Geography - Mathematics