Linear and nonlinear optical susceptibilities of orthorhombic rare earth molybdates RE2(MoO4)3

The dielectric responses (i.e. the refractive indices and the second order nonlinear susceptibilities) of all orthorhombic rare earth molybdates have been studied on the basis of the relationship between dielectric responses and the average atomic number of constituent atoms of crystals. Both the linear and second order nonlinear optical responses at 1.064 μm decrease with increasing atomic number from La to Lu.     

The Study of Primary Cosmic Ray Mass Composition Around the

The lg N_e-N_μ relationship has been studied from 4.4×10⁴ events (total observation time is 2.9×10⁶s)collected from Mt. Liang Wang Array (24.5°N, 102.9°E, 2720m above sea level). In order to study the mass composition at the knee, Monte-Carlo simulations for the EAS development and detection under same event selection criteria as used in the experimental data have been performed. The result shows that the mass composition of primary cosmic rays has no obvious change and the dominant component is light nuclei around the knee.     

Quenched phosphorescence as alternative detection mode in the chiral separation of methotrexate by electrokinetic chromatography

Quenched phosphorescence was used, for the first time, as detection mode in the chiral separation of methotrexate (MTX) enantiomers by electrokinetic chromatography. The detection is based on dynamic quenching of the strong emission of the phosphorophore 1-bromo-4-naphthalene sulfonic acid (BrNS) by MTX under deoxygenated conditions. The use of a background electrolyte with 3 mg/mL 2-hydroxypropyl-β-cyclodextrin and 20% MeOH in 25 mM phosphate buffer (pH 7.0) and an applied voltage of 30 kV allowed the separation of l-MTX and its enantiomeric impurity d-MTX with sufficient resolution. In the presence of 1 mM BrNS, a detection limit of 3.2 × 10⁻⁷ M was achieved, about an order of magnitude better than published techniques based on UV absorption. The potential of the method was demonstrated with a degradation study and an enantiomeric purity assessment of l-MTX. Furthermore, l-MTX was determined in a cell culture extract as a proof-of-principle experiment to show the applicability of the method to biological samples.     

2-（1,3-Diphenylpropen-1,3-diolato）-1,3,2-（5-formylbenzo）dioxaborol： A ＇Whole-molecule Disorder＇ Crystal Structure

The boron atom in C22H15BO5 is O,O’-chelated by the anions in a tetrahedral geometry, with the planar five-and six-membered chelate rings being orthogonal to each other. The molecule lies on a two-fold rotation axis. The molecule is disordered with respect to another molecule in a 93:7 ratio; the treatment of the ‘whole-molecule disorder’ by employing a large number of restraints is described. Crystal data: C22H15BO5, monoclinic C2/c, a = 17.1804(5), b = 12.9409(4), c = 9.8842(3) , β = 124.832(2)o, V = 1803.82(9) 3 at –173 K.     

The luminescence of α- and β-LaNb3O9

The luminescence of undoped and rare-earth-doped LaNb₃O₉ is reported. The two modifications (α and β) show striking differences. Whereas undoped β-LaNb₃O₉ does not luminesce at all (down to 4.2 K), α-LaNb₃O₉ emits efficiently with a quenching temperature of 250 K. Energy transfer from niobate to rare-earth dopants is observed for the α, but not for the β modification. The rare-earth dopant emission consists of sharp lines for the α modification, but is considerably broadened for the β modification. The luminescence properties are discussed in terms of the crystal structure. In addition results for α-NbPO₅ will be given.     

Nonabsolute Integral on Measure Spaces

We define a Henstock-type integral on measure spaces with metrictopologies, and give an example of a function which is integrablebut whose absolute value is not. 1991 Mathematics Subject Classification26A39, 46G12.     

Factorization of proper holomorphic maps on irreducible bounded symmetric domains of rank≥2

We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described.