Search results for "Theorem"
showing 10 items of 1250 documents
A score model for the continuous grading of early allograft dysfunction severity
2014
Early allograft dysfunction (EAD) dramatically influences graft and patient outcomes. A lack of consensus on an EAD definition hinders comparisons of liver transplant outcomes and management of recipients among and within centers. We sought to develop a model for the quantitative assessment of early allograft function [Model for Early Allograft Function Scoring (MEAF)] after transplantation. A retrospective study including 1026 consecutive liver transplants was performed for MEAF score development. Multivariate data analysis was used to select a small number of postoperative variables that adequately describe EAD. Then, the distribution of these variables was mathematically modeled to assig…
Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena
2022
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.
Orthogonal switching of AMS axes during type-2 fold interference : Insights from integrated X-ray computed tomography, AMS and 3D petrography
2017
We applied X-ray computed microtomography (μ-CT) in combination with anisotropy of magnetic susceptibility (AMS) analysis to study metamorphic rock fabrics in an oriented drill core sample of pyrite-pyrrhotite-quartz-mica schist. The sample is extracted from the Paleoproterozoic Martimo metasedimentary belt of northern Finland. The μ-CT resolves the spatial distribution, shape and orientation of 25,920 pyrrhotite and 153 pyrite grains localized in mm-thick metapelitic laminae. Together with microstructural analysis, the μ-CT allows us to interpret the prolate symmetry of the AMS ellipsoid and its relationship to the deformation history. AMS of the sample is controlled by pyrrhotite porphyro…
Conditional predictive inference for online surveillance of spatial disease incidence
2011
This paper deals with the development of statistical methodology for timely detection of incident disease clusters in space and time. The increasing availability of data on both the time and the location of events enables the construction of multivariate surveillance techniques, which may enhance the ability to detect localized clusters of disease relative to the surveillance of the overall count of disease cases across the entire study region. We introduce the surveillance conditional predictive ordinate as a general Bayesian model-based surveillance technique that allows us to detect small areas of increased disease incidence when spatial data are available. To address the problem of mult…
On multivalued weakly Picard operators in partial Hausdorff metric spaces
2015
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
SOME EXAMPLES RELATED TO A CLASS OF FUNCTIONALS WITHOUT GLOBAL MINIMA
2012
Abstract: In this paper, we provide six examples which show the sharpness of the assumptions of a recent deep result of Ricceri about a class of functionals without global minima.
Recovering a variable exponent
2021
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using the properties of a moment problem after reducing the inverse problem to determining a function from its $L^p$-norms.
The Bishop-Phelps-Bollobás property for bilinear forms and polynomials
2014
For a $\sigma$-finite measure $\mu$ and a Banach space $Y$ we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on $L_1(\mu)\times Y$, that is, a (continuous) bilinear form on $L_1(\mu)\times Y$ almost attaining its norm at $(f_0,y_0)$ can be approximated by bilinear forms attaining their norms at unit vectors close to $(f_0,y_0)$. In case that $Y$ is an Asplund space we characterize the Banach spaces $Y$ satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.
The variance of the ℓnp-norm of the Gaussian vector, and Dvoretzky's theorem
2018
Let n be a large integer, and let G be the standard Gaussian vector in Rn. Paouris, Valettas and Zinn (2015) showed that for all p∈[1,clogn], the variance of the ℓnp-norm of G is equivalent, up to a constant multiple, to 2ppn2/p−1, and for p∈[Clogn,∞], to (logn)−1. Here, C,c>0 are universal constants. That result left open the question of estimating the variance for p logarithmic in n. In this paper, the question is resolved by providing a complete characterization of Var∥G∥p for all p. It is shown that there exist two transition points (windows) in which the behavior of Var∥G∥p changes significantly. Some implications of the results are discussed in the context of random Dvoretzky's theore…
Uniqueness of positive solutions to some Nonlinear Neumann Problems
2017
Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem ⎧ ⎨ ⎩ div (ya∇u(x, y)) = 0, x ∈ Rn,y > 0, lim y→0+yauy(x, y) = −f(u(x, 0)), x ∈ Rn, under general nonlinearity assumptions on the function f : R → R for any constant a ∈ (−1, 1). peerReviewed