Search results for "Convex set"

showing 10 items of 35 documents

A laplace type problem for three lattices with non-convex cell

2016

In this paper we consider three lattices with cells represented in Fig. 1, 3 and 5 and we determine the probability that a random segment of constant length intersects a side of lattice. c ⃝2016 All rights reserved.

0209 industrial biotechnologyAlgebra and Number TheoryLaplace transformHigh Energy Physics::Lattice020208 electrical & electronic engineeringMathematical analysisRegular polygon02 engineering and technologyGeometric probabilityRandom setsGeometric probability stochastic geometry random sets random convex sets and integral geometry020901 industrial engineering & automationRandom convex sets and integral geometrySettore MAT/05 - Analisi MatematicaLattice (order)0202 electrical engineering electronic engineering information engineeringStochastic geometrySettore MAT/03 - GeometriaAnalysisMathematics
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Convex bodies and convexity on Grassmann cones

1962

CombinatoricsConvex analysisMixed volumeGeneral MathematicsConvex polytopeProper convex functionConvex setGeometrySubderivativeChoquet theoryConvexityMathematicsArchiv der Mathematik
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On Certain Metrizable Locally Convex Spaces

1986

Publisher Summary This chapter discusses on certain metrizable locally convex spaces. The linear spaces used are defined over the field IK of real or complex numbers. The word "space" will mean "Hausdorff locally convex space". This chapter presents a proposition which states if U be a neighborhood of the origin in a space E. If A is a barrel in E which is not a neighborhood of the origin and F is a closed subspace of finite codimension in E’ [σ(E’,E)], then U° ∩ F does not contain A° ∩ F. Suppose that U° ∩ F contain A° ∩ F. Then A° ∩ F is equicontinuous hence W is also equicontinuous. Since W° is contained in A, it follows that A is a neighborhood of the origin, a contradiction.

CombinatoricsLocally convex topological vector spaceMetrization theoremConvex setHausdorff spaceMathematics::General TopologyField (mathematics)CodimensionSpace (mathematics)EquicontinuityMathematics
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Uniform properties of collections of convex bodies

1991

CombinatoricsMixed volumeGeneral MathematicsConvex setRegular polygonConvex bodyMathematicsMathematische Annalen
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Normed vector spaces consisting of classes of convex sets

1965

CombinatoricsStrictly convex spaceConvex analysisGeneral MathematicsLocally convex topological vector spaceUniformly convex spaceAbsolutely convex setReflexive spaceTopologyMathematicsDual pairNormed vector spaceMathematische Zeitschrift
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A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter

2021

The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.

Control and Optimizationconvex setsBoundary (topology)variaatiolaskenta01 natural sciencesSet (abstract data type)Perimeter0103 physical sciencesquantitative isoperimetric inequalityConvex setBall (mathematics)0101 mathematicsEigenvalues and eigenvectorsMathematicsosittaisdifferentiaaliyhtälötominaisarvot010102 general mathematicsMathematical analysisRegular polygonMathematics::Spectral Theorymatemaattinen optimointiQuantitative isoperimetric inequalityComputational MathematicsHausdorff distanceControl and Systems EngineeringRobin eigenvalue010307 mathematical physicsLaplace operator
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On the number of singularities, zero curvature points and vertices of a simple convex space curve

1995

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

Convex analysisCombinatoricsFundamental theorem of curvesConvex polytopeConvex curveMathematical analysisConvex setTotal curvatureFour-vertex theoremGeometry and TopologyCurvatureMathematicsJournal of Geometry
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A four vertex theorem for strictly convex space curves

1993

Convex analysisDiscrete mathematicsConvex hullConvex setSpace curfFour-vertex theoremVertex theoremKrein–Milman theoremConvex spaceStrictly convex spaceVertex (curve)Danskin's theoremGeometry and TopologyMathematics
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Fixed point theory for almost convex functions

1998

Traditionally, metric fixed point theory has sought classes of spaces in which a given type of mapping (nonexpansive, assymptotically or generalized nonexpansive, uniformly Lipschitz, etc.) from a nonempty weakly compact convex set into itself always has a fixed point. In some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used. With this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings.

Convex analysisLeast fixed pointPure mathematicsApplied MathematicsMathematical analysisConvex setSubderivativeAbsolutely convex setFixed pointKakutani fixed-point theoremFixed-point propertyAnalysisMathematics
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Non absolutely convergent integrals of functions taking values in a locally convex space

2006

Properties of McShane and Kurzweil-Henstock integrable functions taking values in a locally convex space are considered and the relations with other integrals are studied. A convergence theorem for the Kurzweil-Henstock integral is given

Convex analysisMcShane integralGeneral MathematicsMathematical analysisConvex setProper convex functionSubderivativeKurzweil-Henstock integralChoquet theory28B05McShaneintegral Pettis integralSettore MAT/05 - Analisi MatematicaLocally convex topological vector spacelocally convex spacesPettis integralConvex combinationAbsolutely convex setMathematics46G10
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