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.     

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.     

Binaural summation and lateralization of transients: a combined analysis

Subjects judged the loudness and the lateral position of dichotic transient signals, which were presented at equal and unequal levels, synchronously and asynchronously, to the two ears. Binaural loudness summation of clicks does not obey a law of linear addition: It is partial at low level and superadditive at high level. Supersummation is greater for interaurally delayed clicks than for coincidental ones. The relation between click loudness and sound pressure (over moderate SLs) can be described as a power function with a greater exponent for the binaural function. Lateral positions spread over a greater range for interaural level differences than for interaural time differences. The time-intensity trading ratio was greater than is typically reported for tones. When sound lateralization was induced by interaural time difference, but not by intensity difference, a virtually perfect negative correlation between loudness and extent of off-center displacement existed.