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.     

面积比较与上调和函数及其应用

本文研究了无穷远处具非负截曲率的完备非紧流形的几何和解析性质,并将 它应用于调和映照.     

Annealing behavior of gel‐spun polyethylene fibers at temperatures lower than needed for significant shrinkage

The annealing at 373 K of ultrastrong, gel‐spun polyethylene (PE) has been studied. At this temperature, the fibers show no significant shrinkage. Still, a significant decrease in the mechanical properties is observed. The fibers have been analyzed with differential scanning calorimetry (DSC), temperature‐modulated differential scanning calorimetry (TMDSC), atomic force microscopy (AFM), and small‐angle X‐ray scattering (SAXS). During the annealing, the glass transition of the intermediate phase is exceeded, as shown by DSC. When split for structure analysis by AFM, the annealed fibers undergo plastic deformation around the base fibrils instead of brittle fracture. The quasi‐isothermal TMDSC experiments are compared to the minor structural changes seen with SAXS and AFM. The loss of performance of the PE fibers at 373 K is suggested to be caused by the oriented intermediate phase, and not by major changes in the structure or morphology. The overall metastable, semicrystalline structure is shown by TMDSC to posses local regions that can melt reversibly. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 403–417, 2003     

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.     

Synthesis, Spectroscopy, and Electrochemistry of Metallophthalocyanines Substituted by Propylenedithiotetrathiafulvalene Derivatives

Zinc(II) and magnesium(II) phthalocyanines bearing four substituted propylenedithiotetrathiafulvalene (PDT-TTF) units were synthesized and characterized by NMR, MS, EA, and UV/VIS spectra. The absorption peaks of two target molecules were hypsochromically shifted compared with the phthalocyanine parent compound. Studies using cyclic voltammetry indicated that introduction of Zn and Mg as central metals enhanced the electronwithdrawing between the phthalocyanine core and the PDT-TTF unit, thus losing one electron to form (PDT-TTF)⁺ becomes more difficult.     

谈谈电磁污染

由于无线电广播、电视、通讯、及微波技术的迅猛普及,射频设备的功率成倍提高,地面上的电磁辐射已大幅度增加,电磁波已成为一种新型污染.1 电磁污染的特点 电磁污染是继水质污染、大气污染、噪声污染之后的第四大污染,前三种污染可看、可闻、可听,而电磁波的污染则是看不见、摸不着、闻不到,却又是无处不在的污染.     

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.

     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

Investigation on nonradiative decay of I13/2→I15/2 transition of Er-doped oxide glasses

Nonradiative decay of ⁴I_13/2→⁴I_15/2 transition of Er³⁺ has been investigated in a series of oxide glasses. For Er³⁺-doped glass samples, the Judd-Ofelt analysis on absorption spectra was performed and the fluorescence lifetime was determined by extrapolating to zero Er³⁺ concentration limit. Infrared spectra were measured in order to investigate the influence of OH⁻ groups in different glasses. The effects of glass matrix on the decay rate were discussed from the viewpoint of phonon energy, variations of effective fields, and OH⁻ groups. Compared to other glasses, phosphate glass presents low quantum efficiency and large nonradiative decay rate due to its high phonon energy and hygroscopic behavior.     

The Asymmetric Avalanche Process

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar–Parisi–Zhang universality class.