Some binuclear complexes of iron and cobalt with isocyanide ligands

Whereas Co₂(CO)₈ and RNC (R= Me, Et, and Cy) react to give mixtures of [(RNC)₅Co] [Co(CO)₄] and the covalent, carbonyl-bridged [(RNC)_mCo₂(CO)_8?m] derivatives (m = 1–3), [(π-dienyl)Fe(CO)₂]₂ give only [(π-dienyl)₂Fe₂(CO)_4?n(CNR)_n] complexes (dienyl = C₅H₅, MeC₅H₄ and C₉H₇; n = 1–2) that exist in solution as mixtures of cis- and trans-CO- and RNC-bridged tautomers with the μ-RNC species decreasing in importance as the bulk of R increases.     

The GHS inequality and the Riemann hypothesis

LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4 _– exp(ixt–V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.Communicated by Richard Varga.     

Percolation in half-spaces: equality of critical densities and continuity of the percolation probability

Renormalization arguments are developed and applied to independent nearest-neighbor percolation on various subsets of ^d ,d2, yielding:

s] and [sh] as a function of linguapalatal contact place and sibilant groove width

Sibilant groove place and width were initially examined during [s] [s] in isolation and in CV and VC syllables. The [s] was found to be produced through a 6- to 8-mm-wide groove near the front of the alveolar ridge by one talker and near the back of the ridge by the other. [s] was produced through a 10- to 12-mm groove behind the posterior border of the alveolar ridge by both. In the second experiment three subjects used visual articulatory feedback to vary sibilant groove width and place systematically. One subject was able to do this with comparatively few retrials; one had difficulty with certain targeted grooves; one had difficulty with many targeted grooves. The noises generated were replayed to 14 listeners who labeled them as "s," "probably s," "probably sh," or "sh." They usually heard the sound as [s] when the grooves were narrow and near the front of the alveolar process, [s] when the groove was wider and behind the alveolar process. Noise through grooves that matched natural speech places and widths usually produced higher listener recognition scores. Exceptions were found when the subjects had unusual difficulty in achieving stipulated groove widths and places.     

Instabilities of certain empty Robertson-Walker space-times

Results are established concerning perturbations of each empty Robertson-Walker space-time (M, g) with a nonvanishing cosmological constant. The perturbed space-times have the general form ( ) with an extension ofM, and lying in an open neighborhood of g in a type ofW ^m topology. These results indicate that large classes of such perturbations give rise to space-times which suffer from one of two types of incompleteness.     

Critical point dominance in one dimension

The renormalized, dimensionless 4-point coupling constant of scalar one dimensional field theories is maximized uniquely by the critical point theories (obtainable as the scaling limit of ⁴ models). The renormalized coupling constant of certain scalar one dimensional lattice field theories is maximized uniquely (for fixed correlation length) by the corresponding spin-1/2 model.Alfred P. Sloan Research Fellow, on leave from Indiana University. Research supported in part by NSF Grant MCS 77-20683 and by the U.S.-Israel Binational Science Foundation     

Reactions of trimethylgallium with silicon hydrides,germane and diborane

Methylation of SiH₄, MeSiH₃, Si₂H₆, GeH₄ and B₂H₆, but not of PH₃ or AsH₃, was observed during reaction (230–324°C) with GaMe₃. The products from the SiH₄ and Si₂H₆ reactions were MeSiH₃, Me₂SiH₂ and Me₃SiH. The GeH₄-derived products were similar, with Me₄Ge also being formed. The only methylated products from B₂H₆ was BMe₃. The silane reactions were surface-catalyzed (presumably by surface hydroxyl groups), while those of GeH₄ and B₂H₆ may have occurred via gas-phase free radical processes.     

The GHS and other correlation inequalities for a class of even ferromagnets

We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin –1/2 Ising models, ⁴ field theories, and other continuous spin models. The proofs are based on the properties of a classG ^– of probability measures which contains all measures of the form const exp(–V(x))dx, whereV is even and continuously differentiable anddV/dx is convex on [0, ). A new proof of the GKS inequalities using similar ideas is also given.Supported in part by National Science Foundation Grant MPS 71-02838 A 04.Supported by National Science Foundation Grant MPS 74-24696.Supported in part by National Science Foundation Grant MPS 74-04870.