Search results for "Radon"
showing 10 items of 116 documents
Childhood cancer and residential radon exposure - results of a population-based case-control study in Lower Saxony (Germany)
1999
A population-based case-control study on risk factors for childhood malignancies was used to investigate a previously reported association between elevated indoor radon concentrations and childhood cancer, with special regard to leukaemia. The patients were all children suffering from leukaemia and common solid tumours (nephroblastoma, neuroblastoma, rhabdomyosarcoma, central nervous system (CNS) tumours) diagnosed between July 1988 and June 1993 in Lower Saxony (Germany) and aged less than 15 years. Two population-based control groups were matched by age and gender to the leukaemia patients. Long-term (1 year) radon measurements were performed in those homes where the children had been liv…
Do nuclei go pear-shaped? Coulomb excitation of 220Rn and 224Ra at REX-ISOLDE (CERN)
2014
Artículo escrito por muchos autores, sólo se referencian el primero, los autores que firman como Universidad Autónoma de Madrid y el grupo de colaboración en el caso de que aparezca en el artículo
Loomis-Whitney inequalities in Heisenberg groups
2021
This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical Heisenberg projections to the hyperplanes $\{x_j=0\}$, respectively, and $|\cdot|$ refers to a natural Haar measure on either $\mathbb{H}^n$, or one of the hyperplanes. The Loomis-Whitney inequality in the first Heisenberg group $\mathbb{H}^1$ is a direct consequence of known $L^p$ improving properties of the standard Radon transform in $\mathbb{R}^2$. In this note, we show how the Loomis-Whitney inequalities in higher dimensional Heisenberg groups can be deduced…
On Radon Transforms on Tori
2014
We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere. We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients. These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.
On Radon transforms on compact Lie groups
2016
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.
The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
2021
We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation basis induced by a von Neumann lifting. As a consequence, we obtain a lifting theorem for the space of sections of a measurable Banach bundle and a disintegration theorem for vector measures whose target is a Banach space with the Radon-Nikod\'{y}m property.
Equivalence Relations on Stonian Spaces
1996
Abstract Quotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved.
METRIC DIFFERENTIABILITY OF LIPSCHITZ MAPS
2013
AbstractAn extension of Rademacher’s theorem is proved for Lipschitz mappings between Banach spaces without the Radon–Nikodým property.
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
Hyperfine structure and isotope shift investigations in $^{202-222}$Rn for the study of nuclear structure beyond Z = 82
1986
The hyperfine structure (hfs) and isotope shift (IS) in the isotopic chain of the radioactive element radon have been studied for the first time. The measurements were carried out by collinear fast-beam laser spectroscopy at the mass separator facility ISOLDE at CERN. The IS between 16 isotopes in the mass range 202≦A≦222 and the hfs of 7 odd-A isotopes were determined in the transitions 7s [3/2]2-7p [5/2]3 (745 nm) of Rn I. The nuclear spins and moments, as well as the observed inversion of the odd-even staggering for218–222Rn, can be associated with the effects of octupole instability around N=134.