Synthesis and spectral properties of mixed binuclear complexes derived from the ion pentacyano(4,4′-bipyridine)ferrate(II)

New complex analogous to Prussian Blue were synthesized both in solid phase and in aqueous solution by mixing the sodium salt of pentacyano(4,4-bipyridine)-ferrate(II) with Cu(II) and Fe(III) salts. Infrared and visible spectral data of these compounds indicate formation of a polymeric structure involving a cyanide bridge that connects the two metallic centers. Preference of cyanide over 4,4-bipyridine bridging can be explained on the basis of its greater basicity when coordinated to a pentacyanoferrate(II) moiety.Members of the Carrera del Investigador Científico, Conicet, Argentina.     

The history of differential forms from Clairaut to Poincaré

The history of differential forms is examined from its origins in the work of Clairaut on the theory of differential equations through the end of the 19th century. In particular, we explore the developments leading to the concept of the exterior derivative, the Poincaré lemma and its converse, and the notion of the period of an exact differential. We also note that whereas the original motivation for the idea of the integral of an n-form lay in the theory of complex variables, much of its development was done by physicists.     

Nonnegative integral generalized inverses

Necessary and sufficient conditions are given for a nonnegative integral matrix to have nonnegative integral generalized inverses of various types, and the possible ranks of these inverses are determined. More generally, conditions are also given for matrices to have generalized inverses over certain subsets of the nonnegative reals forming monoids under addition and multiplication. Many of our results are adapted from results of Berman and Plemmons [3–6] on real matrices.     

Preferred frames and oscillating universes

A metric theory of gravitation is presented. It is based on the existence of a preferred ‘cosmic’ time. It agrees with all present experimental facts regarding gravitation and leads to singularity-free oscillating universes.     

Quasi-phase-matching in chiral materials

The second-order nonlinear optical coefficients associated with chirality differ in sign for the two mirror-image forms (enantiomers) of a chiral material. Structures comprised of alternating stacks of the enantiomers can therefore be used for quasi-phase-matched frequency conversion, as we demonstrate here by second-harmonic generation from Langmuir-Blodgett films of a helicenebisquinone. Such structures could lead to new types of frequency converters in which both the second-order nonlinear response and quasi-phase-matching arise from the chirality of a material rather than its polar order.     

Grand unification signal from ultrahigh energy cosmic rays?

The spectrum of ultrahigh energy (above approximately 10(9) GeV) cosmic rays is consistent with the decay of grand unification scale particles. The predicted mass is m(X) = 10(b) GeV, where b = 14.6(+1.6)(-1.7).