Search results for "Radon measure"

THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS

2004

In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …

Mobility determination of lead isotopes in glass for retrospective radon measurements rad

2008

In retrospective radon measurements, the 22-y half life of 210Pb is used as an advantage. 210Pb is often considered to be relatively immobile in glass after alpha recoil implanted by 222Rn progenies. The diffusion of 210Pb could, however, lead to uncertain wrong retrospective radon exposure estimations if 210Pb is mobile and can escape from glass, or lost as a result of cleaning-induced surface modification. This diffusion was studied by a radiotracer technique, where 209Pb was used as a tracer in a glass matrix for which the elemental composition is known. Using the ion guide isotope separator on-line technique, the 209Pb atoms were implanted into the glass with an energy of 39 keV. The di…

Gaussian plane and spherical means in separable Hilbert spaces

1982