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.
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.
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)
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.
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.
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…
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…
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.
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.
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. …