Search results for "convex sets"

showing 5 items of 5 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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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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A Laplace type problem for a lattice with cell composed by two trapezius and a triangle

2014

In the previous papers, [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10] the authors study some Laplace problem for different lattices. In this paper we determine the probability that a random segment of constant length intersects a side of lattice with cell represented in fig.1

Pure mathematicsLaplace transformSettore MAT/05 - Analisi MatematicaApplied MathematicsLattice (order)GeometryGeometric Probability stochastic geometry random sets random convex sets and integral geometryMathematicsApplied Mathematical Sciences
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Analysis of the railway network operations safety, with of different obstacles along the route, by the study of Buffon-Laplace type problems: the cas…

2016

In this paper we use an approach based on a Buffon-Laplace type problem for an irregular hexagonal lattice and obstacles to study some problems about analysis of the railway network operations safety in the presence of different obstacles on the route.

Random setsRandom convex sets and integral geometryLaplace transformSettore MAT/05 - Analisi MatematicaComputer scienceHexagonal crystal systemApplied MathematicsStochastic geometrySettore MAT/03 - GeometriaType (model theory)TopologyGeometric ProbabilityNetwork operations centerApplied Mathematical Sciences
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ON SOME GENERALIZATION OF SMOOTHING PROBLEMS

2015

The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.

interpolating splinesBox splineGeneralizationsmoothing splinesRegular polygonHilbert spaceCharacterization (mathematics)CombinatoricsSmoothing splinesymbols.namesakeModeling and Simulationmixed splinesQA1-939symbolsApplied mathematicssplines in convex setsMathematicsAnalysisSmoothingComputingMethodologies_COMPUTERGRAPHICSMathematicsMathematical Modelling and Analysis
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