Search results for "Map of lattices"

showing 5 items of 5 documents

From Lattice Valued Theories to Lattice Valued Analysis

2015

We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.

Condensed Matter::Quantum GasesAlgebraDiscrete mathematicsReciprocal latticeInterconnectionLattice (order)Residuated latticeExtension principleCongruence lattice problemMap of latticesFuzzy logicMathematics
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Disjointness of Lattice Elements

1992

We examine the relations between various disjointness properties in lattices with least elements, and in special lattices like section semicomplemented lattices and section complemented lattices.

Pure mathematicsHigh Energy Physics::LatticeGeneral MathematicsLattice (order)Map of latticesMathematicsMathematische Nachrichten
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Posets That Locally Resemble Distributive Lattices

2000

Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.

Modular latticeDiscrete mathematicsDistributive latticeCongruence lattice problemMap of latticesTheoretical Computer ScienceComplemented latticeCombinatoricsGraded posetComputational Theory and MathematicsSemimodular latticeDiscrete Mathematics and CombinatoricsBirkhoff's representation theoremMathematicsJournal of Combinatorial Theory, Series A
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A new lattice action for studying topological charge

1996

We propose a new lattice action for non-abelian gauge theories, which will reduce short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. If the latter is fine enough, the action of all configurations with non-zero topological charge will satisfy the continuum bound. As a simpler example we consider the $O(3)$ $\sigma$-model in two dimensions, where a numerical analysis of discretized continuum instantons indicates that a finer lattice with half the lattice spacing of the original is enough to satisfy the continuum bound.

InstantonNuclear and High Energy PhysicsHigh Energy Physics::LatticeLattice field theoryFOS: Physical sciencesTheoretical physicsLattice constantHigh Energy Physics - LatticeHamiltonian lattice gauge theoryLattice (order)Lattice gauge theoryCovariant transformationGauge theoryScalingTopological quantum numberMathematicsPhysicsQuantum gauge theoryNumerical analysisHigh Energy Physics - Lattice (hep-lat)FísicaLattice QCDMap of latticesAtomic and Molecular Physics and OpticsReciprocal latticeQuantum electrodynamicsLattice model (physics)Nuclear Physics B - Proceedings Supplements
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Projective Geometry on Modular Lattices

1995

Publisher Summary This chapter focuses on projective geometry on modular lattices. Incidence and Order are basic concepts for a foundation of modern synthetic geometry. These concepts describe the relative location or containment of geometric objects and have led to different lines of geometry, an incidence-geometric and a lattice-theoretic one. Modularity is one of the fundamental properties of classical projective geometry. It makes projections into join-preserving mappings and yields perspectivities to be (interval) isomorphisms. It is therefore natural that order-theoretic generalizations of projective geometry are based on modular lattices and even more, the theory of modular lattices …

Discrete mathematicsPure mathematicsCollineationHigh Energy Physics::LatticeDuality (projective geometry)Ordered geometryProjective spaceErlangen programProjective differential geometryMap of latticesMathematicsProjective geometry
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