Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

Sets of reflections defining twisted Bruhat orders

Twisted Bruhat orders are certain partial orders on a Coxeter system (W,S) associated to initial sections of reflection orders, which are certain subsets of the set of reflections T of a Coxeter system. We determine which subsets of T give rise to a partial order on W in the same way.     

Complexes of 2,2′,2″-Nirtilotriphenol. Part IV. Cage Compounds with Phosphorus(III) and Phosphorus(V)

The ligand 2,2′,2″-nitrilotriphenol reacts with P(III) and P(V) compounds to form corresponding phosphorus complexes. Syntheses and NMR data of 2,2′,2″-nitrilotriphenyl phosphite ( II ), 2,2′,2″-nitrilotriphenyl phosphate ( III ) and of a hydrolysis product of II , 2,2′-[N-(2-hydroxyphenyl)imino]diphenly phosphonate ( IV ), are reported, as well as crystal structures of II and IV . Phosphite II shows a bicycloundecane framework; no N?Pinteraction is present. The phosphonate IV shows two coordinated and one dangling phenol group; the N-atom does not interact with the P-atom. Strong acids protonate II as well as III to form cations: in these, NMR evidence indicates coordination of the N-atom to the P-atom.     

Optical properties of a high-efficiency glass ceramic X-ray storage phosphor

The turbidity, photoluminescence, and photo-stimulated luminescence (PSL) of fluorozirconate glass containing barium chloride nano- and micro-crystals have been measured for samples prepared by isochronal (70 min) annealing over a temperature range of 220–283°C, and correlated with the microstructure as determined by X-ray diffraction measurements. Crystallization of hexagonal phase barium chloride commences at around 220°C, but until 275°C the material retains excellent transparency although it displays negligible PSL. Between 275°C and 277°C, the hexagonal phase converts to the orthorhombic phase, the transparency abruptly decreases, and the PSL rises to a value of around 13% of that found for the commercial storage phosphor BaFBr:Eu. For a slightly higher temperature of 280°C, new phases appear which correspond to the onset of bulk crystallization, and at 283°C the relative PSL rises to 33%, while the transparency falls further. The trade-off between optical transparency and PSL over this narrow temperature window for X-ray imaging plate applications is briefly discussed.     

New developments in X-ray storage phosphors

We found a significant PSL effect in Eu²⁺-doped fluorozirconate glasses (ZBLAN) which were additionally doped with Br⁻ or Cl⁻ ions. The PSL is attributed to the characteristic emission of Eu²⁺ present in nano-crystallites of BaBr₂ or BaCl₂, which form in the glass upon annealing. The metastable hexagonal form of BaX₂ (X=Br,Cl) is always formed first before it is converted into the stable orthorhombic form. The particle size increases upon annealing and so does the PSL efficiency of the glass ceramic. However, there is a saturation of the PSL efficiency, which is for Br⁻ doping about 9% and for Cl⁻-doping about 80% of the Eu-doped BaFBr standard. The particle size was determined by transmission electron microscopy (TEM). The TEM results show a clear tendency for bigger particles for longer annealing at the expense of its number. The particle size for the most efficient phosphor is about 100 nm.     

A note on a paper by Massa and Pagani

Massa and Pagani [1] have given a neat refutal to the conjecture [2] that the Riemann tensor is derivable from a tensor potential. Their method consists of assuming such a relationship does exist and examining the resulting integrability conditions; they show that the existence of such a potential will impose nontrivial restrictions on the Riemann tensor and so conclude that, in general, such a potential cannot exist. Although Massa and Pagani posed the problem and interpreted the conclusion in ordinary tensor notation the actual derivation of the crucial constraint equation was carried out in the language of tensor-valued differential forms, and is quite involved. In this note it is shown that the crucial equation can be obtained quite naturally and easily in ordinary tensor notation.