Search results for "Perimeter"

showing 10 items of 46 documents

Notions of Dirichlet problem for functions of least gradient in metric measure spaces

2019

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain. Peer reviewed

Pure mathematicsGeneral MathematicsPoincaré inequalitycodimension 1 Hausdorff measure01 natural sciencesMeasure (mathematics)symbols.namesakeMathematics - Analysis of PDEsMathematics - Metric GeometryFOS: Mathematicsinner trace0101 mathematicsleast gradientMathematicsDirichlet problemDirichlet problemp-harmonicDirect method010102 general mathematicsA domainMetric Geometry (math.MG)perimeterfunction of bounded variationmetric measure spacePoincaré inequalityBounded functionMetric (mathematics)symbolsAnalysis of PDEs (math.AP)
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A quantitative isoperimetric inequality for fractional perimeters

2011

Abstract Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.

Pure mathematicsMathematics::Functional Analysis010102 general mathematicsFractional Sobolev spaces01 natural sciencesFunctional Analysis (math.FA)PerimeterSobolev spaceMathematics - Functional AnalysisQuantitative isoperimetric inequalityMathematics::Group TheoryMathematics - Analysis of PDEs0103 physical sciencesFractional perimeterFOS: MathematicsOrder (group theory)Mathematics::Metric Geometry010307 mathematical physicsMathematics::Differential Geometry0101 mathematicsIsoperimetric inequalityAnalysisMathematicsAnalysis of PDEs (math.AP)
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Indecomposable sets of finite perimeter in doubling metric measure spaces

2020

We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure.

Pure mathematicsSocial connectednessvariaatiolaskentaSpace (mathematics)01 natural sciencesMeasure (mathematics)differentiaaligeometriaPerimeterMathematics - Analysis of PDEsMathematics - Metric Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsExtreme pointRepresentation (mathematics)MathematicsApplied Mathematics010102 general mathematicsdifferential equationsMetric Geometry (math.MG)metriset avaruudetFunctional Analysis (math.FA)Mathematics - Functional AnalysisMetric (mathematics)mittateoria010307 mathematical physicsvariation26B30 53C23Indecomposable moduleAnalysisAnalysis of PDEs (math.AP)Calculus of Variations and Partial Differential Equations
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Flow resistance of overland flow on a smooth bed under simulated rainfall

2020

In this paper a recently theoretically deduced flow resistance equation, based on a power-velocity profile, was tested using laboratory measurements by Yoon and Wenzel for an overland flow on a smooth bed under rainfall. These measurements of the Darcy-Weisbach friction factor, corresponding to a wide range of the flow Reynolds number (191–5700), were carried out for an overland flow under a simulated rainfall characterized by different intensity values ranging from 13 to 381 mm h−1. At first, the available measured values of flow velocity, water depth, cross sectional area, wetted perimeter and bed slope were used to calibrate the relationship between the velocity profile parameter Γ, the …

RainfallDimensional analysi010504 meteorology & atmospheric sciencesFlow (psychology)01 natural sciencessymbols.namesakeWetted perimeterOverland flowVelocity profileFroude numberRange (statistics)Settore AGR/08 - Idraulica Agraria E Sistemazioni Idraulico-Forestali0105 earth and related environmental sciencesEarth-Surface ProcessesTurbulenceReynolds number04 agricultural and veterinary sciencesMechanicsSelf-similarityFlow velocityFlow resistance040103 agronomy & agriculturesymbols0401 agriculture forestry and fisheriesGeologyIntensity (heat transfer)
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Comparison results for Monge - Ampère type equations with lower order terms

2003

In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.

RearrangementsMathematics::Complex VariablesIndependent equationApplied MathematicsMathematical analysisMathematics::Analysis of PDEsComparison resultsSymmetrizationLower orderType (model theory)Monge-Ampère equationsPerimeterSettore MAT/05 - Analisi MatematicaSimultaneous equationsFully nonlinear elliptic equationsSymmetrizationAmpereAnalysisMathematics
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The Strange Case of the Protective Perimeter: Liberties and Claims to Non-Interference

2011

In this paper I aim at pointing out some difficulties raised by the so-called thesis of the protective perimeter of liberties (ToPP), that is: the thesis according to which: neither a privilege necessarily involves a claim to non-interference, nor a claim to non-interference necessarily presupposes a privilege. As to the first aspect of the thesis, I argue that it relies on a misleading concept of ‘interference with a liberty’, which surfaces in the examples to which the thesis is made applicable. As to the second aspect of the thesis, I argue that the idea of someone having a claim to be unimpeded in wronging another person is a misleading description of the situation taken into considerat…

Rights. Protective perimeter of liberties. Claims to non-interference.Settore IUS/20 - Filosofia Del DirittoPublic interest theoryNon interferencePrivilege (computing)PhilosophyGeneral dutyLawSociologyPolitical philosophyPhilosophy of lawSettore IUS/17 - Diritto PenaleLawLaw and economicsLaw and Philosophy
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6 Self-organising Maps To Analyse Effects Of Low Intensity Concentric Combined With Blood Flow Restriction

2014

Introduction Self-Organising Maps (SOM) are a type of Artificial Neural Network (ANN) model used to visualise multidimensional data [Kohonen-00]. SOM provides a correspondence between the original N-dimensional space and a twodimensional space [Haykin-08]. In the case presented in this work, this means that two subjects with similar values of the different variables should appear near in the two-dimensional space [Kohonen-00], [Haykin-08]. Method In order to test this method, 15 athletes were selected. Subjects’ measurements were performed in three different periods: before the exercise test, immediately after performing the exercise and twenty-four hours later. The control measures were th…

Self-organizing mapAchilles tendonPhysical Therapy Sports Therapy and RehabilitationGeometryGeneral MedicineConcentricTendonIntensity (physics)Cross section (geometry)Perimetermedicine.anatomical_structureOcclusionmedicineOrthopedics and Sports MedicineMathematicsBritish Journal of Sports Medicine
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Nonlocal Minimal Surfaces and Nonlocal Curvature

2019

Recall that if a set E has minimal local perimeter in a bounded set Ω, then it has zero mean curvature at each point of ∂E ∩ Ω (see [51]), and the equation that says that the curvature is equal to zero is the Euler–Lagrange equation associated to the minimization of the perimeter of a set.

Set (abstract data type)PerimeterMinimal surfaceBounded set (topological vector space)Mathematical analysisZero (complex analysis)Point (geometry)MinificationCurvatureMathematics
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Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

2017

We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.

Statistics and ProbabilityGaussianGaussian isoperimetric inequality01 natural sciencesPerimeterSet (abstract data type)symbols.namesakeMathematics - Analysis of PDEsDimension (vector space)quantitative isoperimetric inequalityFOS: MathematicsMathematics::Metric Geometry0101 mathematicsSymmetric differenceGaussian isoperimetric inequalityQuantitative estimatesMathematics010102 general mathematicsMathematical analysisProbability (math.PR)49Q20Gaussian measure010101 applied mathematicssymbolsHigh Energy Physics::Experiment60E15Statistics Probability and UncertaintyMathematics - ProbabilityAnalysis of PDEs (math.AP)
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Estudio transversal de medición de la composición corporal en pacientes con cáncer mediante antropometría y técnicas de imagen médica

2019

Introducción: Analizar la composición corporal tanto mediante técnicas antropométricas y parámetros bioquímicos clásicos, como mediante técnicas modernas utilizando tomografía computarizada (TC), en pacientes oncológicos antes de iniciar el tratamiento con radioterapia.Metodología: Se analizaron de forma retrospectiva 22 pacientes con diversos tumores del aparato digestivo, que fueron sometidos al TC de planificación antes de iniciar el tratamiento con radioterapia, y que disponían de un corte axial en la tercera vértebra lumbar. Para analizar la composición corporal, se determinaron tanto parámetros antropométricos y bioquímicos clásicos, como la determinación de la masa muscular mediante …

TomografíaDesnutriciónRC620-627WaistDesnutrición.Perimeter03 medical and health sciences0302 clinical medicineRadioterapiaHounsfield scaleMedicineTX341-641Composición CorporalNutritional diseases. Deficiency diseasesNutrition and DieteticsNutrition. Foods and food supplybusiness.industryAnthropometryCircumferenceClinical Practice030220 oncology & carcinogenesis030211 gastroenterology & hepatologyRadiotherapy treatmentNuclear medicinebusinessFood ScienceArithmetic mean
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