A unique three-dimensional coordination cluster based on a silver carbene complex

In an attempt to perform a simple anion-exchange reaction on a pincer-carbene-ligated nickel complex using AgNO(3), we instead obtained an unexpected three-dimensional (3D) Ag(7) cluster containing a [Ag(6)] core in a twisted-bowtie geometry. The reverse-transmetalation reaction by which the carbene is transferred from nickel to silver is virtually unprecedented. The CNC pincer-carbene ligands exhibit unusual bridging modes of ligand bonding for all three donor atoms. Another unique feature is that the final structure exhibits a 3D structure brought about by the connection of two-dimensional layers of the [Ag(6)] core via a seventh Ag ion.     

A note on the Hilbert scheme of twisted cubics

We show the component of the Hilbert scheme of twisted cubic curves is the blowup of the variety of determinantal nets along the subvariety of nets with a fixed plane.     

Boundaries of Coxeter Matroids

The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQ_iofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3).     

Hilbert-Carleman and regularized determinants for linear operators

A general theory of regularized and Hilbert-Carleman determinants in normed algebras of operators acting in Banach spaces is proposed. In this approach regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators. We characterize the algebras for which such extensions exist, describe the main properties of the extended determinants, obtain Cramer's rule and the formulas for the resolvent which are expressed via the extended tracestr(A ^k ) of iterations and regularized determinants.This paper is a continuation of the paper [GGKr].     

Electron spin resonance spectrum of the diphenylcyclobutene anion radical

The anion radical of 1,2-diphenylcyclobutene was studied by electron spin resonance. The hyperfine splittings were found to be 0·47 and 0·74 G for the meta-positions, 2·23 and 2·69 G for the ortho-positions and 4·21 G for the para-positions of the phenyl rings. The methylene proton splittings were 4·27 G, which would imply that the value of Q is 27 G, much lower than that of other cyclobutene anions. It was also estimated that the angle between the axis of the p-orbitals of the ethylene group and that of the phenyl group is about 30°, in agreement with that found for the tetraphenylethylene anion.     

On the space-filling enneahedra

A space-filling polyhedron is one whose replications can be packed to fill three-space completely. The space-filling polyhedra of four to eight faces have been previously reported. The search is here extended to the convex space-fillers of nine faces. The number of types is found to be at least 40.     

Can projectiles traversing solids bind electrons at all velocities?

PAC measurements on the 4.43 MeV ¹²C(2⁺) state on recoil in magnetized iron at velocities υ_ion = 0.058c, 0.071c yield integral nuclear precession angles of Φ = ?0.18 (30), +0.17 (39) mrad respectively. Evidently, the high electron-spin-polarization transfer to the innermost carbon orbits implied by a previous measurement (υ_ion = 0.03c, Φ = +0.85 (14) mrad) is suppressed at higher ion velocities.