Stabilizing an uncertain production system

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp _ki . Requests arrive for parts, one at a time. With probability _i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

Adducts of Rh2[MTPA]4 with some phosphine chalcogenides: nature of binding and ligand exchange

Adducts of four phosphine chalcogenides with the chiral dirhodium complex ([Rh-Rh]) were investigated by variable-temperature 1H and 31P NMR spectroscopy in order to compare their properties as axial ligands. Whereas the selenide (1) and the sulfide (2) are strong ligands with electrostatic attraction and, in addition, a significant orbital (HOMO-LUMO) interaction, the phosphine oxide compounds (P=O) bind primarily via electrostatic attraction and are relatively weak donors. Moreover, the overall bond strength in these adducts depends on steric congestion around the P=O group.