A phase space for gravitational radiation

We give a new definition, based on considerations of well-posedness for a certain asymptotic initial value problem, of the phase space for the radiative degrees of freedom of the gravitational field in exact General Relativity. This space fibres over the space of final states, with the fibres being the purely radiative degrees of freedom. The symplectic form is rigorously identified.The infrared sectors are shown to be the level surfaces of a moment map of an action of the quotient group Supertranslations/Translations. A similar result holds for Electromagnetism in Minkowski space.     

Robust Capacity Assignment in Telecommunications

In telecommunications, the demand is a key data that drives network planning. The demand exhibits considerable variability, due to customers movement and introduction of new services and products in the present competitive markets. To deal with this uncertainty, we consider capacity assignment problem in telecommunications in the framework of robust optimization proposed in Ben-Tal and Nemcrovski (Math Oper Res 23(4):769–805, 1998, MPS-SIAM series on optimization, 2001) and Kouvelis and Yu. We propose a decomposition scheme based on cutting plane methods. Some preliminary computational experiments indicate that the Elzinga–Moore cutting plane method (Elzinga and Moore in Math Program 8:134–145, 1975) can be a valuable choice. Since in some situations different possible uncertainty sets may exist, we propose a generalization of these models to cope at a time with a finite number of plausible uncertainty sets. A weight is associated with each uncertainty set to determine its relative importance or worth against another.     

Sum List Coloring Graphs

Let G=(V,E) be a graph with n vertices and e edges. The sum choice number of G is the smallest integer p such that there exist list sizes (f(v):v ∈ V) whose sum is p for which G has a proper coloring no matter which color lists of size f(v) are assigned to the vertices v. The sum choice number is bounded above by n+e. If the sum choice number of G equals n+e, then G is sum choice greedy. Complete graphs K_n are sum choice greedy as are trees. Based on a simple, but powerful, lemma we show that a graph each of whose blocks is sum choice greedy is also sum choice greedy. We also determine the sum choice number of K_2,n, and we show that every tree on n vertices can be obtained from K_n by consecutively deleting single edges where all intermediate graphs are sc-greedy.     

The robust shortest path problem in series-parallel multidigraphs with interval data

In this paper the robust shortest path problem in edge series-parallel multidigraphs with interval costs is examined. The maximal regret criterion is applied to calculate the optimal solution. It is shown that this problem is NP-hard. A pseudopolynomial algorithm for the studied problem is constructed.     

On the generation of non-continuous semigroups

A generalization of a part of a theorem of W. Arendt about integrated semigroups is given, and a generation theorem for non-continuous semigroups is presented.     

SSNTD and radiochemical studies on the transmutation of nuclei using relativistic ions

Extended targets were irradiated for transmutation studies with relativistic heavy ions. For this, a metal core was surrounded by a paraffin moderator. The metal is either copper or lead and it was irradiated with deuterium, alpha, or carbon beams of 1.5 or 3.7 GeV/u at the SYNCHROPHASOTRON, LHE, JINR, Dubna, Russia. During this irradiation copious amounts of secondary neutrons are produced and studied with SSNTD detectors and radiochemical sensors, for example ¹³⁹La (n, γ) ¹⁴⁰La→β⁻. The yield of reaction products allows an estimation of secondary neutron fluxes. The yields of all kinds of reactions produced with deuterium and alpha beams obey to some extent the law of “limiting fragmentation”, i.e. they show little influence on the energy and the kind of incoming particles. However, one observes with 44 GeV ¹²C ions always enhanced nuclear cross-sections induced by secondary particles. This behavior could not be confirmed with theoretical estimations based on the Dubna Cascade Model in its Cascade Evaporation Model version (DCM-CEM). Finally, some results for transmutation studies on ¹²⁷I and Cu will be presented.