Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Determination of the Lipophilicity of Xanthines by Reversed-Phase Liquid Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

31P and 1h NMR as probes of domain alignment in a rigid crystalline surfactant mesophase

A viscous reverse hexagonal surfactant mesophase containing bis(2-ethylhexyl) sodium sulfosuccinate (AOT) and alpha-phosphatidylcholine (lecithin), with comparable volume fractions of isooctane and water, was characterized by Fourier transform (31)P and (1)H NMR spectroscopy. Shear alignment was reflected through both (31)P NMR and (1)H NMR spectra. A complicated (31)P spectrum was observed as a result of superposition of chemical shifts according to the distribution of crystalline domains prior to shear. The initially disordered samples with polydomain structures become macroscopically aligned after Couette shear. (31)P NMR chemical shift anisotropy characteristics are used to elucidate orientation of the hexagonal phase. Interestingly, (1)H NMR spectra exhibit spectral changes upon shear alignment closely corresponding with that of (31)P NMR spectra. These observations complement the findings of mesophase alignment obtained using SANS and imply that (31)P and (1)H NMR spectroscopy can be used as probes to define microstructure and monitor orientation changes in this binary surfactant system. This is especially beneficial if these mesophases are used as templates for materials synthesis.     

On relatively short and long sides of convex pentagons

By the relative distance of pointsa andb of a convex bodyC we mean the ratio of the Euclidean distance ofa andb to the half of the Euclidean distance ofa, b C such thatab is a longest chord ofC parallel to the segmentab. We say that a sideab of a convexn-gon is relatively short (respectively: relatively long) if the relative distance ofa andb is at most (respectively: at least) the relative distance of two consecutive vertices of the regularn-gon. We show that every convexn-gon, wheren 5, has a relatively short side and a relatively long side, and that it is affine-regular if and only if all its sides are of equal relative lengths.Research supported in part by Komitet Bada Naukowych (Committee of Scientific Research), grant number 2 2005 92 03.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.     

Systematic analysis of the PSI experiment to directly measure the sticking probabilityω s in dt fusion

Starting in 1989 an experiment was run at PSI to directly measure the final sticking probability in muon catalyzed dt fusion. This experiment was based on an active-target ionization chamber (IC) built at Gatchina, Russia, and an array of plastic neutron counters. In three runs approximately 5×10⁶ isolated alpha signals were recorded with around one half of these occurring in the inner chamber region where we have more complete understanding of the systematic errors. Particularly from a long run in 1992 we were able to obtain a very clean sticking peak of some 5000 events. However, to reach an accurate value of sticking, all systematic effects and several major backgrounds had to be understood in detail. To this end a Monte Carlo code was written to simulate the full electrostatic environment of the IC and to recreate completely each signal type including the actual tritium decay noise from the live experiment. A slightly model dependent value of approx. 0.56±0.04% is obtained for final sticking.     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.