Boundary conditions of Sturm-Liouville operators with mixed spectra

We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.     

若干具有[(PO4)2Mo5O15]簇骼的化合物的光谱研究

本文对所合成的具有 [(PO4 ) 2 Mo5O1 5]簇骼的 3种新颖的有机 磷钼酸盐簇合物(NH3CH2 CH2 NH3) 2 5[(PO4 ) (HPO4 )Mo5O1 5]·7 5H2 O (Ⅰ ) ,(H3NCH2 CH2 NH3) 3·[(PO4 ) 2 Mo5O1 5]·3H2 O (Ⅱ )和(H3NCH2 CH2 NH3) 2 ·[Cu(en) ][(PO4 ) 2 Mo5O1 5]·5H2 O (Ⅲ )用FTIR ,NIR Raman ,紫外 可见漫反射光谱 (UV VisDRS)和荧光光谱等研究手段 ,对其进行光谱研究 ,探讨其结构和性能的关系。在这些化合物中 ,化合物Ⅰ和Ⅱ具有孤立的 [(PO4 ) 2 Mo5O1 5]簇骼基元 ,而化合物Ⅲ的 [(PO4 ) 2 Mo5O1 5]簇骼基元是由 [Cuen]基团桥联成链 ;磷钼酸盐的特征振动频率和这些化合物的结构相关 ;UV VisDRS显示 ,在 2 0 0和 2 6 0nm左右有两个杂多化合物的特征吸收谱带 ;化合物的稳态荧光光谱中 ,观察到以 2 4 0nm激发 ,在大约 4 0 0nm附近出现的由金属氧簇Oμ→Mo跃迁激发所引起的较强的发射峰 ,在化合物 (Ⅲ )中 ,还观察到通过 [Cuen]的荷移跃迁的以 5 70nm激发所产生的 6 0 4nm的发射峰。     

A statistical study of the analysis of congested spectra by total spectrum fitting

Heavily overlapped, or congested spectra often display much structure but few individual “lines.” Methods have been devised for analyzing such spectra through nonlinear least-squares fitting of the intensity as a function of wavelength or wavenumber. Such total spectrum fitting (TSF) methods are examined statistically for a simple diatomic model and compared with the standard “measure-assign-fit” (MAF) approach in use since the dawn of spectroscopy. Monte Carlo computations on typically 1000 synthetic spectra at a time verify that the predictions of the variance-covariance matrix are reliable under many circumstances. However in regions where the P and R branches double up, the predicted standard errors in the key spectroscopic constants rise sharply and greatly exceed estimates from the Monte Carlo ensemble statistics. In the same regions, the MAF method actually gives better precision. However, for imperfectly overlapped R and P branches, the MAF standard errors are typically three times larger than the TSF values; moreover, the MAF statistical errors are dwarfed by bias. The TSF approach, while clearly superior in these tests, has a practical drawback: it, too, can give significant bias if the spectra are analyzed with an incorrect model, as illustrated here through calculations employing the wrong function to describe the spectral lineshape.     

The opacity coefficient method—nongray determination of inhomogeneous atmospheric extinction

The computation of radiation transmittance in nongray, inhomogeneous atmospheric models is frequently complicated by complex bands of line spectra which range in value over many orders of magnitudes and depend strongly on either or both of pressure and temperature. We present here a new opacity sampling technique which is shown to determine correctly the wavelength-averaged extinction due to path-dependent realizations of banded line spectra. The technique is easy to implement computationally and is applicable to a wide variety of atmospheric problems in which frequent iteration of the radiative transfer model is required. We consider two such instances: modeling of solar flux attenuation for use in a time-dependent planetary ionosphere model and retrieval from nadir measurements of backscattered solar irradiance. The power of the new method lies in its straightforward analytical treatment of both atmospheric inhomogeneity and spectral complexity. It is thus relevant for both retrieval and radiative transfer modeling purposes.     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.

     

消色差谱相位延迟器的光谱特性测试研究

本文应用归一化偏振调制原理建立的测试系统，对常规菲涅耳菱体，改进型菲涅菱体，斜入射型以及直角棱镜组合型的消色差相位延迟的光谱特性进行了测试研究，得到了各延迟器的消色差特性曲线，并对测试结果进行了分析。结果表明改进型菲涅耳菱体以及直色棱镜组合型型消色差相位延迟器，是目前较理想的实用型消色相位延迟器。     

Behavior of zirconium in the ZrOW(100) system at high temperature, studied by ISS, AES and work-function measurements

The behavior of zirconium atoms at the W(100) surface associated with oxygen adsorption at different sample temperatures has been studied by Auger electron spectroscopy (AES), ion scattering spectroscopy (ISS), and the relative change of the work function (Δф) measured by the onset of the secondary electron energy distribution. The results have revealed: (i) adsorption of zirconium onto the W(100) surface followed by the elevation of the sample temperature up to 1710 K in an oxygen partial pressure of 2.7 × 10⁻⁴ induces complete diffusion of zirconium atoms into the W(100) substrate; (ii) further exposure of oxygen induces co-existence of oxygen and tungsten on the surface at 1710 K, resulting in a work function of 4.37 eV; (iii) keeping the sample temperature at 1710 K, simple evacuation of the system has resulted in surface segregation of zirconium atoms to the surface to form a zirconium atomic layer on the top-most surface, reducing the work function to 2.7 eV. The results have revealed that this specific behavior of zirconium atoms at high temperature assures, with very good reproducibility, the highly stable performance and long service life of Zr---O/W(100)-emitters in practical use, even in a low vacuum of 10⁻⁶ Pa.     

Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.