Hilbert空间上线性算子的Drazin可逆性

主要研究了Hilbert空间上两个Drazin可逆算子和的Drazin可逆性.同时,对上三角算子矩阵的Drazin可逆性也给出了详细的讨论.     

Hybrid organosilazane/organosilylamine telechelic oligomers—I. Two-dimensional NMR spectroscopy characterization of dimethylsilylethylenediamine oligomers

The detailed characterization of multifunctional hybrid organosilazane/organosilylamine telechelic oligomers by IR and ¹H, ¹³C and ²⁹Si NMR spectroscopy in one and two dimenions has been undertaken. The specific multifunctional oligomers, comprising NH/NH₂ or SiCl functionalities depending on the monomer feed-ratio, were prepared from mono- and di-functionally reacted dichlorodimethylsilane (DDS) and mono-, di-, tri- and tetra-functionally reacted ethylenediamine (EDA). Varying the feed-ratio afforded control of the microstructures of the oligomers and the preparation of oligomers with, in some cases, conterminously located silicon–chlorine (SiCl) groups. The combination of the NMR methods with the IR technique has enabled the detailed microstructural characterization of the oligomers and the identification of the functionalities therein. This approach and the knowledge gained from the DDS/EDA system has been applied to the microstructural characterization of other hybrid organosilazane/silylamine preceramic telechelic oligomers.     

Intra-cavity spectroscopy with diode lasers

A multi-mode diode laser with an external cavity is studied experimentally and theoretically for its application to intra-cavity spectroscopy. One facet of a typical Ga_0.89Al_0.11As laser diode was antireflection-coated by deposition of HfO₂ such that 10^–3 residual reflectivity was left over. This diode was placed in an external optical cavity. The emission spectrum of this diode laser is highly sensitive to any frequency-dependent loss in the cavity, and the detectivity of such a loss grows with the pump rate. Even close to threshold, the absorption at 780 nm of Rb atoms with a density of 5×10¹⁰ cm^–3 has been detected. An adequate model for diode lasers based on rate equations and including frequency-dependent gain saturation is developed and applied to the calculations of output spectra. The sensitivity of these spectra to intra-cavity absorption is determined by the overall cavity loss — which is rather high — and the fraction of spontaneous emission in the total emission, in contrast with dye lasers where it is limited by nonlinear mode coupling. Various criteria for the sensitivity are suggested. The smallest detectable absorption with a perfectly antireflection-coated laser is 10^–6 cm^–1. Improvement of the characteristics of the laser diode would increase the sensitivity.     

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     

影响产生均匀等离子体状态的几个因素

 用数值模拟方法研究利用辐射加热来产生均匀等离子体状态,它可被用来测量元素的辐射不透明度,校验辐射不透明度理论。研究了在辐射加热铁的“三明治”型靶时影响生成均匀等离子体状态的几个重要因素（样品厚度、CH膜厚度和辐射源）所起的作用，研究发现，当铁等离子体通过热传导达到均匀状态时，其尺度必须与此时的传热距离相当，从而定出铁样品的厚度；低Z介质CH膜对铁等离子体有明显的箍束作用，调整CH膜的厚度可以调节所产生的等离子体状态；调整不同方向上的CH膜厚度，可以控制铁等离子体的膨胀方向，使它尽可能地达到一维膨胀，使得反推出的等离子体密度可以更加准确；样品的种类、厚度以及外面的低Z介质厚度决定了在某时刻能获得的等离子体状态，以及为产生此等离子体状态所需的最低辐射能。     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

关于Landau不等式

本文给出Landau不等式的一种改进。     

Modulation of Spin Distribution and Spin Transport by a Magnetic Field in a Quasi-One-Dimensional System with Spin--Orbit Coupling

The distributions of spin and currents modulated by magnetic field in a transverse parabolic confined two-dimensional electronic system with a Rashba spin--orbit coupling have been studied numerically. It is shown that the spin accumulation and the spin related current are generated by magnetic field if the spin--orbit coupling is presented. The distributions of charge and spin currents are antisymmetrical along the cross-section of confined system. A transversely applied electric field does not influence the characteristic behaviour of charge- and spin-dependent properties.     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10