Combining All Pairs Shortest Paths and All Pairs Bottleneck Paths Problems

We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs and real edge capacities in $\tilde{O}(\sqrt{t}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}n^{2.843})$ time, where $n$ is the number of vertices, $t$ is the number of distinct edge capacities (flow amounts) and $O(n^{\omega}) < O(n^{2.373})$ is the time taken to multiply two $n$-by-$n$ matrices over a ring. Secondly we extend the problem to graphs with positive integer edge costs and present an algorithm with $\tilde{O}(\sqrt{t}c^{(\omega+5)/4}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}c^{1.843}n^{2.843})$ worst case time complexity, where $c$ is the upper bound on edge costs

Global well-posedness for KdV in Sobolev Spaces of negative index

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in H^s({\mathbb{R}), -3/10<s.Comment: 5 pages. Electronic Journal of Differential equations (submitted

Search for Neutrinoless Double Beta Decay with NEMO 3 and SuperNEMO

Since 2003 the NEMO~3 experiment has been searching for neutrinoless double beta decay using about 10 kg of enriched isotopes. A limit of T_(1/2)(0nu) > 5.8 10**23 years at 90 % CL has been obtained for 100-Mo from the first two years of data. Several measurements of two-neutrino double beta decays have also been performed. A first NEMO 3 measurement of the half-life of 130-Te is presented, giving a value of T_(1/2)(2nu) = (7.6 +- 1.5 (stat) +- 0.8 (syst)) 10**20 years. In parallel, there is an active R&D programme for the SuperNEMO experiment which is expected to commence data taking in 2012-2013 with 100-200 kg of enriched isotopes.Comment: 6 pages, 3 figures, Proceedings of the 2007 Europhysics Conference on High Energy Physics, in Manchester, England, 19-25 July 200

The read-out system of spatial distribution of thermoluminescence in meteorites

The thermoluminescence (TL) technique used for dating the terrestrial age of meteorites is based on the TL fading of interior samples. The depth dependence of the TL for Antarctic meteorites with fusion crust is measured. Usually, meteorites are powdered and their TL measured under a photomultiplier. In this case, a TL spatial distribution of a cross section of antarctic meteorites is measured using a read out system of spatial distribution of TL, since a meteorite is made up of inhomogeneous material. Antarctic meteorites MET-78028(L6) and ALH-77278(L13) are used