Constraints on the number of maximal independent sets in graphs

A maximal independent set of a graph G is an independent set that is not contained properly in any other independent set of G. Let i(G) denote the number of maximal independent sets of G. Here, we prove two conjectures, suggested by P. Erdös, that the maximum number of maximal independent sets among all graphs of order n in a family Φ is o(3^n/3) if Φ is either a family of connected graphs such that the largest value of maximum degrees among all graphs of order n in Φ is o(n) or a family of graphs such that the approaches infinity as n → ∞.     

四溴双酚A锑铝双金属化合物的合成及其阻燃性能

以四溴双酚Ａ（ＴＢＡ）合成了在水和空气中稳定的四溴双酚Ａ合锑铝双金属化合物（ＴＢＡＳＡ）．通过ＩＲ、１ＨＮＭＲ和元素分析予以表征，并研究了其对聚乙烯（ＰＥ）和聚环氧乙烷（ＰＥＯ）的阻燃性能．结果表明，这种分子中含有溴、锑和铝的化合物，对聚乙烯和聚环氧乙烷等高聚物材料有高的阻燃性能与消烟效果．     

氙灯泵浦的NYAB晶体调Q激光运转特性及实验研究

首次报道了氙灯泵浦的自激活自倍频NYAB复合功能晶体的BDN染料片调Q运转,获得了自倍频绿光单脉冲.测量了不同L和T_o情况下的绿光脉冲的能量、脉宽和峰值功率.文中还从理论上推导了自激活自倍频晶体调Q激光器的方程组.数值求解方程组,所得的理论数据与实验结果很好地相符.最后,讨论了进一步提高绿光脉冲峰值功率的途径.     

Millimeter wave beams diffracted from reflecting gratings

According to the angular-spectrum method, a radiation beam of an antenna horn in the Fresnal region is decomposed into the plane waves with the fast Fourier transform algorithm and the waves diffracted from a reflection grating are superposed as a diffracted beam. Compared with the reflected beam from the same size mirror, the radiation half width of the diffracted beam from a grating is narrower and its lateral shape is shift. These performances have been experimentally verified at Ka-band by: (1). The relative diffraction efficiencies in the first order with two triangular gratings which is put along propagating direction of a beam produced by a conical lens-horn. (2). H-plane lateral width with power—3dB lapsed of the focus beam from a grating and a mirror in a grating spectrometer for millimeter waves (25–100 GHz).     

一种新的$1/f$过程小波模型

给出了一种新的二进小波1/f过程模型,从理论上证明了一类谱指数为H的近似1/f过程可通过一簇平稳随机过程产生.由于所提方法利用了1/f过程小波系数的相关性,因而有效地减少了合成1/f过程的谱误差.数值实验结果表明,新模型很好地改进了已有模型.     

A trace class operator inequality

In this note, we generalize the inequality about the trace of positive semidefinite matrix trk(AB)?k(trA)k(trB) to Hilbert space, and obtain a relevant inequality about positive trace class operator.     

Synthesis,characterization, and micellization of an epoxy‐based amphiphilic diblock copolymer of ϵ‐caprolactone and glycidyl methacrylate by enzymatic ring‐opening polymerization and atom transfer radical polymerization

Amphiphilic diblock copolymer polycaprolactone‐block‐poly(glycidyl methacrylate) (PCL‐b‐PGMA) was synthesized via enzymatic ring‐opening polymerization (eROP) and atom transfer radical polymerization (ATRP). Methanol first initiated eROP of ?‐caprolactone (?‐CL) in the presence of biocatalyst Novozyme‐435 under anhydrous conditions. The resulting monohydroxyl‐terminated polycaprolactone (PCL–OH) was subsequently converted to a bromine‐ended macroinitiator (PCL–Br) for ATRP by esterification with α‐bromopropionyl bromide. PCL‐b‐PGMA diblock copolymers were synthesized in a subsequent ATRP of glycidyl methacrylate (GMA). A kinetic analysis of ATRP indicated a living/controlled radical process. The macromolecular structures were characterized for PCL–OH, PCL–Br, and the block copolymers by means of nuclear magnetic resonance, gel permeation chromatography, and infrared spectroscopy. Differential scanning calorimetry and wide‐angle X‐ray diffraction analyses indicated that the copolymer composition (?‐CL/GMA) had a great influence on the thermal properties. The well‐defined, amphiphilic diblock copolymer PCL‐b‐PGMA self‐assembled into nanoscale micelles in aqueous solutions, as investigated by dynamic light scattering and transmission electron microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5037–5049, 2007