Grassmann manifold of aJH-algebra

We study the set of rankp idempotents in a topologically simple Hilbert Jordan algebra (JH-algebra for short). To produce the differential geometric structure on, we establish Jordan algebraic results concerning the structure of some two-generator subalgebras. We identify geodesics, the Riemannian distance and the sectional curvature of by using the Jordan algebraic structure.     

Density results for uniform families

A familyF of subsets is calledk-dense if there exists ak-element setA such that all 2 ^k of its subsets can be obtained in the formAF for someFF. Best possible bounds are obtained for the maximum number of sets in notk-densek-partite families. This is a consequence of a new rank formula for inclusion matrices.     

Observation of magnetic order of Cu-moment aroundx=0.12 in La2−x Ba x CuO4 and La2−x sr x CuO4 by μ+SR

Zero field positive muon spin rotation method ( ⁺SR) is applied on La_2–x Sr _x CuO₄ around forx=0.12 at which the high-T _c superconductivity (SC) is suppressed. The magnetically ordered state of Cu-moments, which is not a spin glass state but an antiferromagnetic like state, appears below 15 K for 0.105x0.120. The magnetic phase boundary is very similar to the one of the La_2–x Ba _x CuO₄ in which the structural transition from the low temperature orthorhombic (LTO) phase to the low temperature tetragonal (LTT) phase is observed aroundx=0.12. The present study suggests that there is no big difference of the electronic state of the CuO₂ plane between the La-Ba system and the La-Sr system and that the magnetic ordering of Cu-moments plays an important role for the suppression of the high-T _c SC aroundx=0.12 in both of the systems, although the LTO-LTT structural transition has not been observed yet in the La-Sr system.     

Nitrosation of Phenolic Substrates under Mildly Basic Conditions: Selective Preparation of p-Quinone Monooximes and Their Antiviral Activities

Nitrosation of 3-methoxyphenol and 1-naphthol were examined under both acidic (NaNO(2)-EtCO(2)H-H(2)O) and basic (i-AmNO(2)-K(2)CO(3)-DMF) conditions. Acidic nitrosations afforded ortho-directed products, whereas para-directed nitrosations were observed under basic conditions to yield p-quinone monooximes. The basic para-directed nitrosation was further examined using 15 phenols, two naphthols, and four phenolic heterocyclics. A one-pot operation of the basic nitrosation followed by methylation with dimethyl sulfate gave the corresponding methyl ethers in high yield. Two p-quinone monooximes derived from 3-methoxyphenol and 8-hydroxyquinoline showed a moderate activity against HSV-1, and the latter oxime was also effective against HSV-2. On the other hand, p-quinone monooximes derived from methyl salicylate, 1-naphthol, 7-hydroxy-2-methylbenzo[b]furan, and 8-hydroxycoumarin showed the comparable activity to that of DDI against HIV-1.     

Key aspects of crystalline Mo-V-O-based catalysts active in the selective oxidation of propane

Mo-V-O-based complex metal oxide catalysts were synthesized hydrothermally for the first time, characterized structurally and tested in the selective oxidation of propane to acrylic acid, and the results obtained were compared on the basis of catalyst crystal structures in order to clarify key aspects of alkane selective oxidation over multifunctional metal oxide catalysts. The catalysts tested were black solids of rod-shaped crystals, which had a layer structure in the direction of fiber axis and various high dimensional arrangements of metal octahedra in the cross-section plane. A strong dependency on the octahedra arrangements and a facet dependency were observed, and the roles of metal elements in the course of selective oxidation of propane were clarified by comparing the catalytic performance of various Mo-V-O-based catalysts. We discuss the multi-functional character derived from high dimensional structures of the catalysts and mechanism of the selective oxidation of propane.