Search results for "Polyhedron"

showing 10 items of 38 documents

Characterizing extreme points of polyhedra an extension of a result by Wolfgang Bühler

1982

This paper reconsiders the characterization given by Buhler admitting convex polyhedra of probability distributions on a finite or countable set which are given by systems of linear inequalities more complex than those considered before.

Discrete mathematicsGeneral MathematicsRegular polygonInteger points in convex polyhedraManagement Science and Operations ResearchCombinatoricsPolyhedronLinear inequalityConvex polytopeCountable setExtreme pointSoftwareSpherical polyhedronMathematicsZeitschrift für Operations Research
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Shrinking and boundedly complete Schauder frames in Fréchet spaces

2014

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsShrinkingReflexivitySchauder basisFunction space(LB)-spacesApplied MathematicsMathematics::Analysis of PDEsConvex setMathematics::General TopologyFréchet spacesSchauder basisAtomic decompositionSchauder fixed point theoremSchauder frameLocally convex spacesLocally convex topological vector spaceBoundedly completeDual polyhedronAtomic decompositionMATEMATICA APLICADAAnalysisMathematics
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Stochastic factorizations, sandwiched simplices and the topology of the space of explanations

2003

We study the space of stochastic factorizations of a stochastic matrix V, motivated by the statistical problem of hidden random variables. We show that this space is homeomorphic to the space of simplices sandwiched between two nested convex polyhedra, and use this geometrical model to gain some insight into its structure and topology. We prove theorems describing its homotopy type, and, in the case where the rank of V is 2, we give a complete description, including bounds on the number of connected components, and examples in which these bounds are attained. We attempt to make the notions of topology accessible and relevant to statisticians.

Discrete mathematicsRank (linear algebra)General MathematicsHomotopyGeneral EngineeringStochastic matrixGeneral Physics and AstronomyType (model theory)Space (mathematics)TopologyPolyhedronTopology (chemistry)MathematicsMorse theoryProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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Dynamic shakedown of structures under repeated seismic loads

1995

Elastic, perfectly plastic structures are considered under the action of repeated short-duration exitations of seismic type acting in an unknown time sequence, but belonging to a given polyhedral excitation domain. The basic excitations (vertices of the polyhedron) are chosen as discrete-spectrum waves each with frequencies coincident with the first natural frequencies of the structure, and amplitudes related to the ground features and earthquake intensity (according to the Kanai and Tajimi filter model) in such a way that every admissible excitation-obtained as a linear convex combination of the basic ones-has a maximum power not exceeding a given value. In the framework of unrestricted dy…

EngineeringComputer simulationbusiness.industryMechanical EngineeringComputationMathematical analysisSeismic loadingStructural engineeringDynamic ShakedownShakedownMultiplier (Fourier analysis)PolyhedronMechanics of MaterialsLimit loadConvex combinationbusinessSettore ICAR/08 - Scienza Delle Costruzioni
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The General Routing Problem polyhedron: Facets from the RPP and GTSP polyhedra

1998

[EN] In this paper we study the polyhedron associated with the General Routing Problem (GRP). This problem, first introduced by Orloff in 1974, is a generalization of both the Rural Postman Problem (RPP) and the Graphical Traveling Salesman Problem (GTSP) and, thus, is NP -hard. We describe a formulation of the problem such that from every non-trivial facet-inducing inequality for the RPP and GTSP polyhedra, we obtain facet-inducing inequalities for the GRP polyhedron, We describe a new family of facet-inducing inequalities for the GRP, the honeycomb constraints, which seem to be very useful for solving GRP and RPP instances. Finally, new classes of facets obtained by composition of facet-i…

Facet (geometry)Information Systems and ManagementGeneral Computer ScienceGeneralizationHoneycomb (geometry)Facets of polyhedraGraph theoryManagement Science and Operations ResearchTravelling salesman problemIndustrial and Manufacturing EngineeringRural Postman ProblemGeneral Routing ProblemCombinatoricsPolyhedronModeling and SimulationGraphical Traveling Salesman ProblemCombinatorial optimizationMathematics::Metric GeometryRouting (electronic design automation)MATEMATICA APLICADAMathematicsRouting
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On the proper homotopy invariance of the Tucker property

2006

A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.

Fundamental groupHomotopy lifting propertyApplied MathematicsGeneral MathematicsHomotopyMathematics::Optimization and ControlhomotopyproperComputer Science::Numerical AnalysisRegular homotopyCombinatoricsn-connectedPolyhedronEquivalence relationtucker propertySimplicial mapMathematics
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An unusual magnetic response in a π-stacked 66-dia net structure of [4 + 2] copper(II) cubane

2015

A phenoxo bridged antiferromagnetic copper(II) cubane features a π-stacked 66-dia net framework and creates long range ferromagnetic ordering, as evidenced from a coercivity maximum (∼2000 Oe) at 20 K with very unusual saturation magnetization.

General Chemical Engineeringchemistry.chemical_elementGeneral ChemistryMagnetic responseCoercivityCoppercopper(II) cubaneCrystallographychemistry.chemical_compoundmagnetic responsechemistryFerromagnetismCubaneNet (polyhedron)Antiferromagnetismta116RSC Advances
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Properties of some conformal field theories with M-theory duals

2007

24 pages.-- ISI Article Identifier: 000245078200049.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-th/0611219

High Energy Physics - TheoryPhysicsM-theoryNuclear and High Energy PhysicsClass (set theory)Field (physics)TruncationSupergravityGauged supergravityFOS: Physical sciencesConformal mapM-TheoryHigh Energy Physics::TheoryAdS-CFT correspondenceHigh Energy Physics - Theory (hep-th)Dual polyhedronMathematical physicsJournal of High Energy Physics
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Boolean-controlled systems via receding horizon and linear programing

2009

We consider dynamic systems controlled by boolean signals or decisions. We show that in a number of cases, the receding horizon formulation of the control problem can be solved via linear programing by relaxing the binary constraints on the control. The idea behind our approach is conceptually easy: a feasible control can be forced by imposing that the boolean signal is set to one at least one time over the horizon. We translate this idea into constraints on the controls and analyze the polyhedron of all feasible controls. We specialize the approach to the stabilizability of switched and impulsively controlled systems.

Inventory controlMathematical optimizationControl and OptimizationLinear programmingApplied MathematicsHorizonSIGNAL (programming language)Binary numberSet (abstract data type)PolyhedronControl and Systems EngineeringControl theoryHybrid systemSignal ProcessingImpulse control inventory control hybrid systemsMathematics
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Combining EXAFS and XRay Powder Diffraction to Solve Structures Containing Heavy Atoms

2005

Determination of structures using x-ray powder diffraction is complicated if the reflection intensities are mainly influenced by the scattering from heavy atoms and the atomic coordinates of light atoms remain uncertain. A method like EXAFS, which is sensitive to short range order, gives reliable atomic distances in the surroundings of heavy atoms with a precision of ±0.02 A. The probability for obtaining the complete structure from x-ray powder diffraction increases if one includes parameters derived from EXAFS measurements as restraints during the procedure of structure solving. We demonstrate the potential of combining EXAFS and x-ray powder diffraction by solving the structure UO2[H2AsO…

Materials scienceExtended X-ray absorption fine structureScatteringCondensed Matter PhysicsMolecular physicsAtomic and Molecular Physics and OpticsCondensed Matter::Materials SciencePolyhedronReflection (mathematics)Condensed Matter::SuperconductivityDirect methodsAtomStructure factorMathematical PhysicsPowder diffractionPhysica Scripta
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