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.     

Group Scheduling with Controllable Setup and Processing Times: Minimizing Total Weighted Completion Time

The following single machine scheduling problem is studied. A partition of a set of n jobs into g groups on the basis of group technology is given. The machine processes jobs of the same group contiguously, with a sequence independent setup time preceding the processing of each group. The setup times and the job processing times are controllable through the allocation of a continuously divisible or discrete resource to them. Each job uses the same amount of the resource. Each setup also uses the same amount of resource, which may be different from that for the jobs. Polynomial-time algorithms are constructed for variants of the problem of finding an optimal job sequence and resource values so as to minimize the total weighted job completion time, subject to given restrictions on resource consumption. The algorithms are based on a polynomial enumeration of the candidates for an optimal job sequence and solving the problem with a fixed job sequence by linear programming. This research was supported in part by The Hong Kong Polytechnic University under grant number G-T246 and the Research Grants Council of Hong Kong under grant number PolyU 5191/01E. In addition, the research of M.Y. Kovalyov was supported by INTAS under grant number 00-217.     

Proper Holomorphic Maps from Domains in C2 with Transverse Circle Action

The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.     

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.