Search results for " Variation"

showing 10 items of 1712 documents

Nonlinear diffusion in transparent media: the resolvent equation

2017

Abstract We consider the partial differential equation u - f = div ⁡ ( u m ⁢ ∇ ⁡ u | ∇ ⁡ u | ) u-f=\operatornamewithlimits{div}\biggl{(}u^{m}\frac{\nabla u}{|\nabla u|}% \biggr{)} with f nonnegative and bounded and m ∈ ℝ {m\in\mathbb{R}} . We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ℋ N - 1 {{\mathcal{H}}^{N-1}} -Hausdorff measure. Results and proofs extend to more general nonlinearities.

Dirichlet problemPure mathematicsTotal variation; transparent media; linear growth Lagrangian; comparison principle; Dirichlet problems; Neumann problems35J25 35J60 35B51 35B99Applied Mathematics010102 general mathematicsMathematics::Analysis of PDEsBoundary (topology)01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsBounded functionBounded variationFOS: MathematicsNeumann boundary conditionUniquenessNabla symbol0101 mathematicsAnalysisAnalysis of PDEs (math.AP)ResolventMathematics
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A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation

2009

In this paper we introduce the notion of $\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the one for real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\mathbb{R}$ possesses a $\Phi$-variation preserving extension to the whole real line.

Discrete mathematicsInjective metric spaceextensionstructural theoremTotally bounded space54C35$\Phi$-bounded variation54E35Intrinsic metricmetric space valued mapings variation $Phi$-variation extension structural theorem.metric space valued mappingsUniform normSettore MAT/05 - Analisi MatematicaBounded functionBounded variationGeometry and Topologyvariation26A45Metric differentialReal lineAnalysisMathematics
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Quadratic variation of martingales in Riesz spaces

2014

We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)

Discrete mathematicsPure mathematicsRiesz potentialRiesz representation theoremApplied MathematicsmartingaleRiesz spaceRiesz spacevector latticeQuadratic variationquadratic variationM. Riesz extension theoremSettore MAT/05 - Analisi MatematicaAustin’s theorem Martingale Measure-free stochastic processes Quadratic variation Riesz space Vector latticemeasure-free stochastic processesAustinʼs theoremMartingale (probability theory)AnalysisMathematics
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Geometric Properties of Planar BV -Extension Domains

2009

We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.

Discrete mathematicsQuasiconformal mappingMathematics::Analysis of PDEsGeometric propertySobolev spaceQuasiconvex functionExtension domains; Sobolev spaces; Functions with bounded variationPlanarSobolev spacesFunctions with bounded variationBounded functionSimply connected spaceInvariant (mathematics)Extension domainsMathematics
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A new Cartan-type property and strict quasicoverings when p = 1 in metric spaces

2018

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of $1$-finely open \emph{strict subsets} and \emph{strict quasicoverings} of $1$-finely open sets. As an application, we study fine Newton-Sobolev spaces in the case $p=1$, that is, Newton-Sobolev spaces defined on $1$-finely open sets.

Discrete mathematicsfine Newton–Sobolev spaceProperty (philosophy)General Mathematicsta111010102 general mathematicsOpen setfine topologystrict quasicoveringType (model theory)function of bounded variationmetriset avaruudet01 natural sciencesMeasure (mathematics)Complete metric spaceCartan propertyfunktioteoria010101 applied mathematicsMetric spacemetric measure spacepotentiaaliteoria0101 mathematicsFine topologyMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
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The effect of wavelet and discrete cosine transform compression of digital radiographs on the detection of subtle proximal caries. ROC analysis.

2007

The study compared diagnostic performances of 2 different image compression methods: JPEG (discrete cosine transform; Joint Photographic Experts Group compression standard) versus JPEG2000 (discrete wavelet transform), both at a compression ratio of 12:1, from the original uncompressed TIFF radiograph with respect to the detection of non-cavitated carious lesions. Therefore, 100 approximal surfaces of 50 tooth pairs were evaluated on the radiographs by 10 experienced observers using a 5-point confidence scale. Observations were carried out on a standardized viewing monitor under subdued light conditions. The proportion of diseased surfaces was balanced to approximately 50% to avoid bias. Tr…

Discrete wavelet transformDental CariesSensitivity and SpecificityDiagnosis DifferentialWaveletComputer Science::MultimediaDiscrete cosine transformHumansDental EnamelGeneral DentistryLossless JPEGTransform codingMathematicsObserver VariationMicroscopybusiness.industryPattern recognitioncomputer.file_formatMicrotomyRadiography Dental DigitalData CompressionJPEGROC CurveJPEG 2000DentinArtificial intelligencebusinesscomputerAlgorithmsImage compressionCaries research
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Approximation of Elliptic Hemivariational Inequalities

1999

From the previous chapter we know that there exist many important problems in mechanics in which constitutive laws are expressed by means of nonmonotone, possibly multivalued relations (nonmonotone multivalued stress-strain or reaction-displacement relations,e.g). The resulting mathematical model leads to an inclusion type problem involving multivalued nonmonotone mappings or to a substationary type problem for a nonsmooth, nonconvex superpotential expressed in terms of calculus of variation. It is the aim of this chapter to give a detailed study of a discretization of such a type of problems including the convergence analysis. Here we follow closely Miettinen and Haslinger, 1995, Miettinen…

DiscretizationMathematical analysisConvergence (routing)Variational inequalitySuperpotentialApplied mathematicsCalculus of variationsType (model theory)Bilinear formFinite element methodMathematics
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On the integration of Riemann-measurable vector-valued functions

2016

We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.

Dominated convergence theoremRiemann-measurable functionPure mathematicsMeasurable functionGeneral Mathematics02 engineering and technologyLebesgue measurable gaugeLebesgue integration01 natural sciencessymbols.namesakeConvergence (routing)0202 electrical engineering electronic engineering information engineeringCalculusMathematics (all)0101 mathematicsMathematicsBirkhoff McShane Henstock and Pettis integralMathematics::Complex Variables010102 general mathematicsRiemann integralRiemann hypothesisBounded variationBounded variationAlmost uniform convergencesymbols020201 artificial intelligence & image processingVector-valued function$$ACG_*$$ACG∗and $$ACG_delta ^*$$ACGδ∗functionMonatshefte für Mathematik
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Simultaneous bilateral occurrence of a M. extensor digiti medii and a M. extensor digitorum brevis.

1993

Summary For the first time, the simultaneous and bilateral occurrence of two variants of the extensors of the fingers, M. extensor digiti medii and M. extensor digitorum brevis, is reported. The extensor of the middle finger arises from the distal fourth of the radius and runs to the base of the proximal phalanx. The short extensor of the fingers arises from the metacarpal region and inserts into the dorsal aponeurosis. Both muscles are innervated by the R. profundus n. radialis.

DorsumExtensor digitorum brevisProximal phalanxMetacarpal regionMusclesGenetic VariationGeneral MedicineAnatomyBiologyMiddle fingermusculoskeletal systembody regionsFingersmedicine.anatomical_structuremedicineM. extensor digitorum brevisHumansAponeurosisFemaleAnatomyDevelopmental BiologyAgedAnnals of anatomy = Anatomischer Anzeiger : official organ of the Anatomische Gesellschaft
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Association between Opioid Receptor mu 1 (OPRM1) Gene Polymorphisms and Tobacco and Alcohol Consumption in a Spanish Population.

2015

Evidence gained from animals and humans suggests that the encephalic opioid system might be involved in the development of drug addiction through its role in reward. Our aim is to assess the influence of genetic variations in the opioid receptor mu 1 on alcohol and tobacco consumption in a Spanish population. 763 unrelated individuals (465 women, 298 men) aged 18-85 years were recruited between October 2011 and April 2012. Participants were requested to answer a 35-item questionnaire on tobacco and alcohol consumption, as well as to complete the AUDIT and Fagerström tests. Individuals were genotyped for three polymorphisms in the opioid receptor mu 1 (OPRM1) gene, using a TaqMan® protocol. …

DrugAdultMaleAdolescentAlcohol DrinkingGenotypeSubstance-Related Disordersmedia_common.quotation_subjectReceptors Opioid muAlcoholDrug abusechemistry.chemical_compoundTobacco UseYoung AdultSex FactorsGene FrequencyPolymorphism (computer science)Surveys and QuestionnairesTobaccoGenetic variationmedicineHumansAssociation (psychology)media_commonAgedGeneticsAged 80 and overlcsh:R5-920Genetic polymorphismPolymorphism Geneticbusiness.industryAddictionMiddle Agedmedicine.diseaseSubstance abusePhenotypechemistryHaplotypesSample size determinationSpainCase-Control StudiesFemaleGene-Environment InteractionAlcohollcsh:Medicine (General)businessDemographyResearch ArticleBosnian journal of basic medical sciences
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