Completely normal matrices

Normal matrices in which all submatrices are normal are said to be completely normal. We characterize this class of matrices, determine the possible inertias of a particular completely normal matrix, and show that real matrices in this class are closed under (general) Schur complementation. We provide explicit formulas for the Moore–Penrose inverse of a completely normal matrix of size at least four. A result on irreducible principally normal matrices is derived as well.     

High-nuclearity iridium carbonyl clusters containing phenylgermyl ligands: synthesis, structures, and reactivity

The reaction of Ir4(CO)12 with Ph3GeH at 97 degrees C has yielded the new tetrairidium cluster complexes Ir4(CO)7(GePh3)(mu-GePh2)2[mu3-eta3-GePh(C6H4)](mu-H)2 (10) and Ir4(CO)8(GePh3)2(mu-GePh2)4 (11). The structure of 10 consists of a tetrahedral Ir4 cluster with seven terminal CO groups, two bridging GePh2) ligands, an ortho-metallated bridging mu3-eta3-GePh(C6H4) group, a terminal GePh3 ligand, and two bridging hydrido ligands. Compound 11 consists of a planar butterfly arrangement of four iridium atoms with four bridging GePh2 and two terminal GePh3 ligands. The same reaction at 125 degrees C yielded the two new triiridium clusters Ir3(CO)5(GePh3)(mu-GePh2)3(mu3-GePh)(mu-H) (12) and Ir3(CO)6(GePh3)3(mu-GePh2)3 (13). Compound 12 contains a triangular Ir3 cluster with three bridging GePh2), one triply bridging GePh, and one terminal GePh3 ligand. The compound also contains a hydrido ligand that bridges one of the Ir-Ge bonds. Compound 13 contains a triangular Ir3 cluster with three bridging GePh2 and three terminal GePh3 ligands. At 151 degrees C, an additional complex, Ir4H4(CO)4(mu-GePh2)4(mu4-GePh)2 (14), was isolated. Compound 14 consists of an Ir4 square with four bridging GePh2, two quadruply bridging GePh groups, and four terminal hydrido ligands. Compound 12 reacts with CO at 125 degrees C to give the compound Ir3(CO)6(mu-GePh2)3(mu3-GePh) (15). Compound 15 is formed via the loss of the hydrido ligand and the terminal GePh3 ligand and the addition of one carbonyl ligand to 12. All compounds were fully characterized by IR, NMR, single-crystal X-ray diffraction analysis, and elemental analysis.     

Synthesis and characterization of a chlorofunctionalized unsaturated carbosilane oligomer

Acyclic diene metathesis (ADMET) polymerization offers a viable route for the synthesis of chlorofunctionalized unsaturated carbosilane oligomers. The Si Cl bond in unsaturated carbosilane monomers remains inert during metathesis and the use of a highly reactive molybdenum-based, Lewis acid-free alkylidene catalyst affords unsaturated chlorofunctionalized carbosilane oligomers with known vinyl end groups. The first synthesis of an unsaturated carbosilane oligomer functionalized with a Si Cl bond was performed. A chlorofunctionalized silacyclopentene product was also observed, due to a backbiting reaction. This new class of functionalized oligomers has a low glass transition temperature and sites of unsaturation which may be used for further reaction. ADMET chemistry now provides access to a variety of chlorofunctionalized unsaturated carbosilanes which can be used to tailor make hydrolytically stable carbosilane oligomers and polymers via nucleophilic grafting reactions.     

Copolymerization of acrylic acid to nylon-6 by trapped radicals—I. Vapour phase grafting

Film of nylon-6 has been γ-irradiated in vacuo to various doses D. Grafting has been effected by subsequent exposure in vacuo to vapour at 50° of composition 9.1 wt% acrylic acid and 90.9 wt% water. Determinations have been made of total vapour uptake as well as the individual swellings due to monomer and water. For D ? ca. 2 Mrad, the initial rate of grafting R_g increased with D in accord with R_g ∝ D^β with β = 0.45 ± 0.05, thus suggesting bimolecular chain termination. However, for D ? ca. 2 Mrad, there is no further increase in R_g. This is attributed in part to the fact that the radical yield is proportional to dose only for D ? ca. 2.5 Mrad. Diffusion controlled grafting has been predicted elsewhere to be characterized by β = 0.67. Grafting proceeds from the surface and the initial stages are concluded to be essentially free from diffusion control, since (a) β ≠ 0.67, (b) the rate of uptake of monomer vapour >R_g and (c) a large change in film thickness yields only a very small change in R_g.     

Ξ Resonances in Ξ− Be interactions II. Properties of Ξ(1820) and Ξ(1960) in the\Lambda \bar K^0 and\Sigma ^0 \bar K^0 channels

In an experiment at the CERN-SPS charged hyperon beam, we have investigated the inclusive \(\Lambda \bar K^0 \) and \(\Sigma ^0 \bar K^0 \) final states formed in Ξ^? Be interactions. In the \(\Lambda \bar K^0 \) channel, we observe a signal at 1826 MeV/c² which can be identified with the known Ξ(1820) resonance. We determine its mass and width to be:M=1826±4 MeV/c², Г=12±14 MeV/c². A moment analysis is consistent with a spin of 3/2 and indicates a negative parity for this spin assignment. Also in the \(\Lambda \bar K^0 \) channel, we observe a 3.6σ signal with the following parameters:M=1963±5 MeV/c², Г=25±15 MeV/c². This state, which we call Ξ(1960), is not observed in the \(\Sigma ^0 \bar K^0 \) channel, leading to an upper limit on the ratio of partial widths \(\Sigma \bar K/\Lambda \bar K\) of 2.3 (90% confidence level). A moment analysis of the \(\Lambda \bar K^0 \) final state indicates a spin of 5/2 or greater in the natural spin-parity series 5/2⁺, 7/2^?, etc.