四元数体上λ-多项式的线性因式分解

本文证明了实四元数体上任一次数大于１的λ－多项式可分解作一次因式的乘积给出了这样分解的若干性质及其在矩阵论中的应用。     

A hierarchical method for obtaining eigenvalue enclosures

We introduce a new method of obtaining guaranteed enclosures of the eigenvalues of a variety of self-adjoint differential and difference operators with discrete spectrum. The method is based upon subdividing the region into a number of simpler regions for which eigenvalue enclosures are already available.

     

A sampling theorem on homogeneous manifolds

We consider a generalization of entire functions of spherical exponential type and Lagrangian splines on manifolds. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a manifold is uniquely determined by its values on some discrete sets of points.

The main result of the paper is a formula for reconstruction of spectral entire functions from their values on discrete sets using Lagrangian splines.

     

A Kuznetsov Formula for Kloosterman Sums on GLn

We prove a Kuznetsov sum formula for Kloosterman sums on GL _n corresponding to the big Bruhat cell. Using this formula, a weighted sum of Kloosterman sums can be expressed in spectral decomposition. A non-trivial estimate of the spectral side might lead to a proof of cancellations in sums of Kloosterman sums on GL _n.     

Surface-enhanced resonance Raman scattering spectroscopy of single R6G molecules

Surface-enhanced resonance Raman scattering (SERRS) of Rhodamine 6G (R6G) adsorbed on colloidal silver clusters has been studied. Based on the great enhancement of the Raman signal and the quench of the fluorescence, the SERRS spectra of R6G were recorded for the samples of dye colloidal solution with different concentrations. Spectral inhomogeneity behaviours from single molecules in the dried sample films were observed with complementary evidences, such as spectral polarization, spectral diffusion, intensity fluctuation of vibrational lines and even ``breathing' of the molecules. Sequential spectra observed from a liquid sample with an average of 0.3 dye molecules in the probed volume exhibited the expected Poisson distribution for actually measuring 0, 1 or 2 molecules. Difference between the SERRS spectra of R6G excited by linearly and circularly polarized light were experimentally measured.     

润滑油中添加剂元素光谱分析研究

以船用内燃机油为研究对象,利用原子发射光谱对润滑油中的添加剂成分进行量化确定。根据MOA原子发射光谱仪的工作原理,选择校正曲线法定量,提出对不在测量精度范围内的添加剂元素含量用0 μg·g-1的空白标油进行稀释测量的方法,并进行误差计算。试验结果表明,添加剂各元素钙、磷和锌的测量相对标准偏差分别为1.6%,4.8%和4.6%,样品稀释前后的测量误差结果分别为4.21％,6.99％和5.09％。     

矩阵Hadamard积和Fan积的特征值界的一些新估计式

本文研究了非奇异M-矩阵A与B的Fan积的最小特征值下界和非负矩阵A与B的Hadamard积 的谱半径上界的估计问题.利用Brauer定理,得到了一些只依赖于矩阵的元素且易于计算的新估计式,改进 了文献[4]现有的一些结果.     

Crystal growth and spectral analysis of Dy3+ and Er3+ doped KPb2Cl5 as a mid‐infrared laser crystal

This paper reports crystal growth and optical characteristics of dysprosium (Dy³⁺) and erbium (Er³⁺) doped mid‐infrared laser crystal ternary‐potassium‐lead‐chloride (KPb₂Cl₅). Two transparent crystals with good optical quality have been grown successfully by using the Bridgman technique,the largest crystal size reaches up to ∅︁10×60mm². Measurements of X‐ray diffraction(XRD) and absorption spectra were carried out. Based on Judd‐Ofelt theory, the intensity parameters Ω_t(t=2,4,6), the experimental and theoretical oscillator strengths have been obtained.The intensity parameters Ω_t(t=2,4,6) of Er³⁺:KPb₂Cl₅ were calculated to be Ω₂=5.10×10^‐20 cm², Ω₄=1.25×10^‐20 cm², Ω₆=0.83×10^‐20 cm², and the values for Dy³⁺:KPb₂Cl₅ were calculated to be Ω₂=6.26×10^‐20 cm², Ω₄=2.45×10^‐20 cm², Ω₆=0.04×10^‐20 cm² respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exponential convergence rate in entropy

The exponential convergence rate in entroy is studied for symmetric forms, with a special attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.      

A Simple Closed-Loop Active Control of Electrodynamic Shakers by Acceleration Power Spectral Density for Environmental Vibration Tests

This work presents the main results of a simple closed-loop active control for an electrodynamic shaker in order to generate acceleration Power Spectral Densities (PSD) according to prescribed Standards used in environmental vibration tests. The main idea is to start generating acceleration pseudo-signals obeying the prescribed Power Spectral Density and then to acquire acceleration data from the electrodynamic shaker’s table behaviour. So the Power Spectral Density of the acquired acceleration is computed and compared with the required PSD and then the time-varying pseudo-acceleration is updated to reflect this corrected PSD. It was noticed that for piecewise narrow bands frequencies, the electrodynamic shaker acceleration behaves near linearly, both in frequency and voltage, for the input signals. A code in AgilentVee 7.5 software to acquire, send and process signals for the active control in a closed-loop scheme was developed. The used A/D D/A hardware was a single PC sound card with specific characteristics. The control could be accomplished sending and acquiring at the same time with a range of input/output of ±1.5 V with 16 bits of resolution, at 48 kHz and assistance of an external sound amplifier.