Green-emissive transparent BaSi2O5:Eu film phosphor on quartz glass created by a sputtering thermal diffusion process

Eu²⁺-doped BaSi₂O₅ film phosphors on quartz substrates are fabricated by radio-frequency magnetron sputtering thermal diffusion. The BaSi₂O₅: Eu²⁺ phosphor crystals have some preferred orientations that are lattice-spacing matched with the crystallized β- SiO₂ crystals, and they show pore and grain boundary-free morphology with a rod-like shape fused into the crystallized β- SiO₂ crystals. The BaSi₂O₅: Eu²⁺ film phosphor has a high transparency, with a transmittance of about 30% in visible light. The BaSi₂O₅: Eu²⁺ film phosphor shows 510 nm green emission from the f–d transition of the Eu²⁺ ions, and in particular the best sample shows a green photoluminescence brightness of about 5% of a BaSi₂O₅: Eu²⁺ powder phosphor screen. These excellences in optical properties can be explained by less optical scattering at pores or grain boundaries, and less reflection at the continuously index-changed interface.     

Reactions of bis(hexamethylbenzene)iron(0) with carbon monoxide and with unsaturated hydrocarbons

Thermal decomposition of bis(hexamethylbenzene)iron(0) in the presence of carbon monoxide yields a novel carbonyl iron complex, [C₆(CH₃)₆]Fe(CO)₂. The cyclohexadiene complex [C₆(CH₃)₆]Fe(C₆H₈) is obtained from reaction of bis(hexamethylbenzene)iron(0) with either 1,3-cyclohexadiene or benzene, and the yield is much greater in the presence of hydrogen gas. Interaction of bis-(hexamethylbenzene)iron(0) with 2-butyne induces a catalytic cyclotrimerization to give more hexamethylbenzene. Kinetic and isotope distribution studies indicate that the primary step in these reactions is not a direct loss of one ring ligand, but rather an insertion of the iron center into one of the ligand methyl CH bonds, leading to a benzyl hydride complex species. Mechanisms for the subsequent reactions of this iron hydride species are proposed.     

纳米晶FeCuNbMSiB（M＝Nb，V，Mo）合金的微结构及其电阻率与压力的关系

 X射线衍射和透射电镜的结果表明：非晶FeCuNbMSiB（M＝Nb，V，Mo）合金在540 ℃退火20 min，表面析出的纳米晶是α-FeSi固溶体，粒度为10~20 nm。此外，在0.000 1~2.4 GPa范围内测量了它们的常压室温电阻率以及电阻率随静水压的变化，得到了电阻率与压力的线性关系式。最后探讨了热处理方式和温度对非晶Fe_73.1Cu_1.2Nb_3.2Si_12.5B₁₀合金退火形成纳米晶的影响。     

Large Discrepancy In Homogenous Quasi-Arithmetic Progressions

We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and gives a better bound on the discrepancy.     

The tetrahedron algebra and its finite-dimensional irreducible modules

Recently Terwilliger and the present author found a presentation for the three-point sl₂ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ? by generators and relations and displayed an isomorphism from ? to the three-point sl₂ loop algebra. In this paper we classify the finite-dimensional irreducible ?-modules.     

Sub-Bergman Hilbert spaces in the unit disk, II

For a finite Blaschke product B let T_B denote the analytic multiplication operator (also called a Toeplitz operator) on the Bergman space of the unit disk. We show that the defect operators and both map the Bergman space to the Hardy space and the Hardy space to the Dirichlet space.     

More on Kleinewillinghöfer Types of Flat Laguerre Planes

Polster and Steinke [Result. Math., 46 (2004), 103–122] determined the possible Kleinewillingh?fer types of flat Laguerre planes. These types reflect transitivity properties of groups of certain central automorphisms. We exclude three more types from the list given there with respect to Laguerre homotheties. This yields a complete determination of all possible single types with respect to Laguerre homotheties that can occur in flat Laguerre planes. Building on results by M?urer and Hartmann to characterize ovoidal or miquelian Laguerre planes we further characterize certain flat Laguerre planes in terms of their Kleinewillingh?fer types. Received: January 16, 2007. Revised: July 26, 2007.     

Infinitesimal 2-braidings and differential crossed modules

We categorify the notion of an infinitesimal braiding in a linear strict symmetric monoidal category, leading to the notion of a (strict) infinitesimal 2-braiding in a linear symmetric strict monoidal 2-category. We describe the associated categorification of the 4-term relations, leading to six categorified relations. We prove that any infinitesimal 2-braiding gives rise to a flat and fake flat 2-connection in the configuration space of n particles in the complex plane, hence to a categorification of the Knizhnik–Zamolodchikov connection. We discuss infinitesimal 2-braidings in a certain monoidal 2-category naturally assigned to every differential crossed module, leading to the notion of a symmetric quasi-invariant tensor in a differential crossed module. Finally, we prove that symmetric quasi-invariant tensors exist in the differential crossed module associated to Wagemann's version of the String Lie-2-algebra. As a corollary, we obtain a more conceptual proof of the flatness of a previously constructed categorified Knizhnik–Zamolodchikov connection with values in the String Lie-2-algebra.