A193Ir Mössbauer study of Pt−Ir catalysts prepared by impregnantion of silica with H2MCl6

The state of iridium on Pt?Ir catalysts prepared by impregnation of amorphous silica with H₂IrCl₆ and H₂PtCl₆ was studied by¹⁹³Ir Mössbauer spectroscopy after different steps of preparation. The Ir is adsorbed in its trivalent state, presumably as [IrCl₆]^3?. Calcination in air at 450°C converts this to IrO₂. The metallic clusters formed by subsequent reduction in H₂ at 200°C show a strong tendency towards segregation of Ir and Pt and re-oxidize partially when exposed to air at ambient temperature. In both respects the behaviour is similar to that of samples prepared by co-exchange from [Ir(NH₃)₅Cl]Cl₂ and Pt(NH₃)₄Cl₂. H₂O.     

Phase transitions and positive definite couplings

The method of infrared bounds is extended to a large class of nearest neighbour interactions in classical spin systems. Temperature controlled bounds on fluctuations follow whenever the coupling function is a positive definite kernel. Existence of phase transitions is demonstrated for the RP ^Nmodel for d3.     

On combinatorial and projective geometry

Cross ratios constitute an important tool in classical projective geometry. Using the theory of Tutte groups as discussed in [6] it will be shown in this note that the concept of cross ratios extends naturally to combinatorial geometries or matroids. From a thorough study of these cross ratios which, among other observations, includes a new matroid theoretic version and proof of the Pappos theorem, it will be deduced that for any projective space M= _n (K) of dimension n2 of M over some skewfield K the inner Tutte group is isomorphic to the commutator factor group K ^*/[K ^*, K ^*] of K ^*K{0}. This shows not only that in case M= _n (K) our matroidal cross ratios are nothing but the classical ones. It can also be used to correlate orientations of the matroid M= _n (K) with the orderings of K. And it implies that Dieudonné's (non-commutative) determinants which, by Dieudonné's definition, take their values in K ^*/[K ^*, K ^*] as well, can be viewed as a special case of a determinant construction which works for just every combinatorial geometry.Research supported by the DFG (Deutsche Forschungsgemeinschaft).     

Groupwise density and related cardinals

We prove several theorems about the cardinal associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by sets are below all non-feeble filters. If then and . (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from by Laflamme are shown to be equivalent to .