Small deviations, JIT sequencing and symmetric case of Fraenkel's conjecture

We prove Fraenkel's conjecture for the special case of symmetric words, and show that this proof implies the conjecture of Brauner and Crama [Facts and questions about the maximum deviation just-in-time scheduling problem, Discrete Appl. Math. 134 (2004) 25-50] concerning instances of the just-in-time sequencing problem with maximum deviation .     

Identical part production in cyclic robotic cells: Concepts, overview and open questions

Robotic cells consist of a flow-shop with a robot for material handling. A single part is to be produced cyclically and the objective is to minimize production rate. This document introduces basic concepts and tools for dealing with cyclic production. In particular, it concentrates on k-cycles which are production cycles where exactly k parts enter and leave the cell. One defines the cycle function which is the smallest value of k so that the set of all k-cycles up to size contains an optimal cycle for all instances. Known results and conjectures on these functions are given for the classical case where parts can remain on the machine waiting for the robot and for the no-wait case where parts have to be removed from the machine as soon as their processing is finished.     

Temperature dependence of standard model CP violation

We analyze the temperature dependence of CP violation effects in the standard model by determining the effective action of its bosonic fields, obtained after integrating out the fermions from the theory and performing a covariant gradient expansion. We find nonvanishing CP violating terms starting at the sixth order of the expansion, albeit only in the C-odd-P-even sector, with coefficients that depend on quark masses, Cabibbo-Kobayashi-Maskawa matrix elements, temperature and the magnitude of the Higgs field. The CP violating effects are observed to decrease rapidly with temperature, which has important implications for the generation of a matter-antimatter asymmetry in the early Universe. Our results suggest that the cold electroweak baryogenesis scenario may be viable within the standard model, provided the electroweak transition temperature is at most of order 1 GeV.