A note on balance vertices in trees

The notion of balanced bipartitions of the vertices in a tree T was introduced and studied by Reid (Networks 34 (1999) 264). Reid proved that the set of balance vertices of a tree T consists of a single vertex or two adjacent vertices. In this note, we give a simple proof of that result.     

Lattice parameter and luminescence properties of europium activated yttrium oxide

Samples of yttrium oxide doped with trivalent europium have been prepared by ceramic techniques, under different synthesis conditions; barium chloride (BaCl₂) and sodium tetraborate (Na₂B₄O₇) were tested as flux. The improvement of luminescence properties in dependence on substitution of Eu³⁺ for Y³⁺ in the host lattice, under electron and UV excitations is demonstrated. The lattice parameter as a quantitative assessment of activator incorporation degree is proposed. The obtained results are discussed with respect to the employed processing method.     

Backward extensions of subnormal operators

The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.

     

Determination of carbamazepine by chemiluminescence detection using chemically prepared tris(2,2'-bipyridine)ruthenium(III) as oxidant.

A new chemiluminescence method for the determination of carbamazepine (CBZ) has been developed. The method is based on the chemiluminescence produced in the reaction of tris(2,2'-bipyridine)ruthenium(III) and CBZ in an acidic medium. The chemiluminescence intensity was enhanced by organic solvents in the reaction system. Under the optimum experimental conditions, the calibration curve was linear over the range 4.0 x 10(-3)-8.6 x 10(-7) mol/L for CBZ. The detection limit (S/N = 3) was 2.5 x 10(-7) mol/L and the relative standard deviation of six replicate measurements was 2.6% for 4.0 x 10(-4) mol/L of CBZ. The possible reaction mechanism were also discussed. The chemiluminescence method was successfully applied to assay the CBZ contents in pharmaceutical tablets.     

On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R 2

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain the asymptotic rate of convergence. Finally, we also give a numerical example.

     

Metallization of U3O8via catalytic electrochemical reduction with Li2O in LiCl molten salt

The concept of a novel electrochemical reduction process for the treatment of spent nuclear fuels in Li₂O-LiCl molten salt was proposed and fresh tests using U₃O₈ powder were carried out to elucidate the reaction mechanism and verify the feasibility of the process. Electrolysis of Li₂O and reduction of U₃O₈ powder took place simultaneously at the cathode part of the electrolysis cell via a catalytic EC mechanism and the conversion of U₃O₈ to U metal was more than 99%. This revised version was published online in June 2006 with corrections to the Cover Date.     

Brightness and decay time of Zn2SiO4:Mn phosphor particles with spherical shape and fine size

Green-light-emitting Zn₂SiO₄:Mn phosphor particles were synthesized by modified large-scale spray pyrolysis using a colloidal solution containing fumed silica particles. The particles had a fine size, filled morphology, spherical shape and non-aggregation characteristics even after post-treatment at 1150 °C. The luminescence characteristics of Zn₂SiO₄:Mn phosphor particles having spherical shape, such as brightness and decay time under VUV excitation light, were investigated as a function of Mn content. The luminescence intensity exhibits a maximum at 5 mol% Mn-doped powder. The decay time increases consistently with decreasing Mn content and more saturated color coordinates are obtained with the composition having 12 mol% Mn. As a consequence, the 10 mol% Mn-doped powder proved to provide a good combination of favorable luminance and acceptable decay time. The influence of post-treatment temperature on the decay time and photoluminescence characteristics of Zn₂SiO₄:Mn particles was also investigated. Particles post-treated at 1155 °C had the maximum photoluminescence intensity, which was identical to 113% that of the commercial product, and a comparable decay time of 5.8 ms. PACS 81.20.Rg; 78. 55.Hx; 78.40.Ha; 81.05.Hd; 81.40.Tv     

Synthesis and adsorption properties of gold nanoparticles within pores of surface‐functional porous polymer microspheres

Mesoporous polymer microspheres with gold (Au) nanoparticles inside their pores were prepared considering their surface functionality and porosity. The Au/polymer composite microspheres prepared were characterized by transmission electron microscope (TEM), X‐ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) techniques. The results showed that the adsorption of Au nanoparticles could be increased by imparting the pore structure and surface‐functional groups into the supporting polymer microspheres (in this study, poly (ethylene glycol dimethacrylate‐co‐acrylonitrile) and poly (EGDMA‐co‐AN) system). Above all, from this study, it was established that the porosity of the polymer microspheres is the most important factor that determines the distribution and adsorption amount of face‐centered cubic (fcc) Au nanoparticles in the final products. Our study showed that the continuous adsorption of Au nanoparticles with the aid of the large surface area and surface interaction sites formed more favorably the Au/polymer composite microspheres. The BET measurements of Au/poly(EGDMA‐co‐AN) composite microspheres reveals that the adsorption of Au nanoparticles into the pores kept the pore structure intact and made it more porous. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5627–5635, 2004     

系综分布和它的小涨落近似

由“从正则分布出发，在小涨落近似下得出的能量涨落分布公式”求得的能量涨落的二次矩与直接由正则分布求得的二次矩完全相同，但分别由二求得的高次矩并不完全相同。     

Preparation of enantiomerically pure (R)-2-butyryloxymethylglycidol by lipase-catalyzed asymmetric hydrolysis

Optically active epoxy alcohol, (R)-2-butyryloxymethylglycidol3 which is the precursor of a tert-alcohol chiral building block was obtained in high enantiomeric purity, 98.7% e.e., by lipase-catalyzed asymmetric hydrolysis using a phosphate buffer and organic co-solvent system in 95% of chemical yield.