Synthesis of uniform anatase TiO2 nanoparticles by gel-sol method. 1. Solution chemistry of Ti(OH)(4-n)+(n) complexes

The mole fractions of hydroxo complexes of titanium(IV) ion in an aqueous solution with 0.10 mol dm(-3) NaClO4 at 25 degrees C have been determined as a function of pH by a newly developed analytical procedure based on UV spectrophotometry, using a metastable homogeneous solution of 1.25 x 10(-4) mol dm(-30 in total concentration of Ti(IV). Also, the total concentration of the hydroxo complexes in equilibrium with Ti(OH)4 solid, or the solubility of Ti(OH)4 solid in an inhomogeneous system, has been obtained by ICP measurement for the solution phase. A combination of these data yielded the absolute concentration of each complex species in equilibrium with Ti(OH)4 solid. Finally, Ti(OH)+3 complex has been assigned to the precursor for the formation of anatase TiO2 nanoparticles transformed from Ti(OH)4 gel from a comparison between the above equilibrium data and a kinetic study on the formation rate of the anatase TiO2 particles in the gel-sol system.     

Total synthesis of (-)-martinellic acid via radical addition-cyclization-elimination reaction

The asymmetric total synthesis of martinellic acid, the first pyrrolo[3,2-c]quinoline alkaloid found in nature, is described. Three key steps in our synthesis of (-)-martinellic acid are the Bu(3)SnH-promoted radical addition-cyclization-elimination (RACE) reaction of an oxime ether with an alpha,beta-unsaturated ester to generate the pyrrolo[3,2-c]quinoline core, a chemoselective lactam carbonyl reduction, and guanidinylation under Mitsunobu reaction conditions. The key radical cyclization has also been investigated by using SmI(2). (-)-Martinellic acid was synthesized from commercially available methyl 4-bromo-3-methylbenzoate in fewer steps than previous syntheses and in an improved overall yield.     

Unbounded generalizations of standard von Neumann algebras

The primary purpose of this paper is to study unbounded operator algebras called standard EW^#-algebras which are generalizations of standard von Neumann algebras to the unbounded case.The first part is an investigation of the weak, σ-weak, strong and σ-strong topologies on a standard EW^#-algebra. It is showed that the weak and σ-weak topologies on a standard EW^#-algebra coincide.The second part is a study of a locally convex topology called _∞L^ω₂-topology on a standard EW^#-algebra U. It is proved that U is a GB¹-algebra under the topology.The third part is an investigation of isomorphisms of standard EW^#-algebras. It is showed that if standard EW^#-algebras U and B are isomorphic then U and B are spatially isomorphic.     

New electron states that float on semiconductor and metal surfaces

We report first-principle electronic-structure calculations using the local density approximation in the density functional theory for Si(1 0 0) and Al(1 0 0) surfaces. We find a novel class of surface electron states that are distributed not near atomic arrays but float around with the maximum amplitudes being substantially separated from matters. We also find that the origin of the unusual character is quantum spill of electron density from matters and exchange-correlation effects among electrons.     

Hybrid textures in minimal seesaw mass matrices

In the context of the minimal seesaw framework, we discuss the implications of Dirac and Majorana mass matrices in which two properties coexist, namely, equalities among matrix elements and texture zeros. Among the large number of general possibilities, only 12 patterns are found to be consistent with the global neutrino oscillation data at the level of the most minimal number of free parameters. The predictions of the allowed textures for mass hierarchy, θ₁₃${\theta }_{13}$ and effective mass governing neutrino-less double beta decay are discussed. We also explore the possibility of having non-zero CP violation for each allowed solution. We find that only one allowed solution can accommodate both low and high energy CP violation. We discuss the prediction of this solution for leptogenesis and explore the correlation, between leptogenesis and low energy CP violation.     

Weak-field magnetoresistance anomaly and Shubnikov–de Haas oscillations in Sn-doped InSb thin films on GaAs (100) substrates

Distinctive magnetoresistance (MR) effects in weak magnetic fields before the appearance of Shubnikov–de Haas (SdH) oscillations at low temperatures in Sn-doped (7×10¹⁶ cm⁻³) InSb films grown on GaAs(100) substrates by MBE have been investigated with decreasing film thickness d from 1 μm. The negative MR found in weak magnetic fields for d0.5 μm can be broadly divided into two regimes: T-sensitive negative MR below B_c observed with anisotropy between parallel and perpendicular magnetic field and a T-insensitive parabolic one above B_c observable only under in-plane magnetic fields. The latter is ascribable to the skipping orbit effect due to surface boundary scattering. In vanishing magnetic fields far below B_c, the negative MR reduces with decreasing d and the different positive MR overlaps with it below 0.5 μm, eventually dominating the positive MR at d0.2 μm. These results have been analyzed using a two-layer model for the films, where the composition of the upper layer under the surface and the lower one adjacent to the InSb/GaAs interface is assumed. The MR data in the extremely weak magnetic fields below 100 G for each layer have been successfully fitted to the two-dimensional (2D) weak localization (WL) theory. These results explain that the crossover from the 2D WL to the weak anti-localization (WAL) occurs when the interface is approached with the increase of SO interaction in the layers caused by the increased influence of the asymmetric potential at the hetero interface (Rashba term) and the SO rate in the intrinsic InSb film due to the crystal field of the zinc-blende structure (Dresselhaus term) is as small as τ_so⁻¹3×10⁸ s⁻¹.     

A bound on the Castelnuovo-Mumford regularity for curves

Recall that a projective curve in with ideal sheaf is said to be n-regular if for every integer and that in this case, it is cut out scheme-theoretically by equations of degree at most n. The purpose here is to show that an irreducible, reduced, projective curve of degree d and large arithmetic genus satisfies a smaller regularity bound than the optimal one . For example, if then a curve is -regular unless it is embedded by a complete linear system of degree . Received: 29 May 2000 / Published online: 24 September 2001