基于室温脉冲量子级联激光器的NO气体检测中的光谱处理方法研究

报导了采用基于室温脉冲量子级联激光器的脉内光谱检测技术,利用中心波长为1904 cm^-1的量子级联激光器,在实验室对NO气体样品进行检测的研究结果. 针对单线直接吸收光谱反演算法进行了研究,介绍了基线拟合的最小二乘算法以获取其吸光度,根据HITRAN数据库中相应吸收谱线的吸收线强,采用扫描积分实现了气体浓度的反演,避免了标气标定造成的误差及污染;通过拟合残差分析得到了系统的检测限,达到34×10^-6 m.     

Nitrogen bonding in aluminum oxynitride films

Assignment of oxidation states of N_1s in XPS spectra of aluminum oxynitride by curve fitting is difficult. The XPS curve fitting was previously discussed in the paper published in J. Non-Cryst. Solids, 224 (1998) 31, in which O_1s photoelectrons from GeO₂ glass were used to illustrate how to fit the XPS spectra. Three different ways were pointed out to eliminate the ambiguity caused by curve fitting such as comparing the data to data from standard samples, investigating the continuous surface modifications caused by slowly sputtering the surface, and monitoring the continuous surface modifications due to gradual increases in surface species under heating, cooling, or irradiation. Our recent work in aluminum oxynitride films provides another example of how to fit the XPS spectra of N_1s by three different oxidation states of N⁺, N²⁺, and N³⁺, by comparison of the measured data to data from previously published results, and by the gradual changes of spectra as functions of the oxygen contents in the films. Three oxidation states in different nitrogen bonding in the aluminum oxynitride, AlO₂N, Al₂O₅N₂, and AlO₃N, were clearly deduced.     

ON ENERGY CONSERVATION BY TRIGONOMETRIC INTEGRATORS IN THE LINEAR CASE WITH APPLICATION TO WAVE EQUATIONS

Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on all-time near-conservation of energy. The extension can be applied to linear wave equations.     

On finitely generated module whose first nonzero fitting ideal is maximal

Let R be a Noetherian ring and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M. The main result of this paper asserts that when I(M) = Q is a regular maximal ideal of R, then M?R∕Q⊕P, for some projective R-module P of constant rank if and only if T(M)?QM. As a consequence, it is shown that if M is an Artinian R-module and I(M) = Q is a regular maximal ideal of R, then M?R∕Q.     

Richards模型参数估计及其模型应用

在非线性模型中,Richards模型是一个含有四参数的增长曲线模型,该模型对数据的拟合有较强的适应性,应用较为广泛.但其参数的估计较为复杂,给出简便易行的三种方法,实例应用表明拟合效果很好.     

Shape analysis of cubic trigonometric Bézier curves with a shape parameter

For the cubic trigonometric polynomial curves with a shape parameter (TB curves, for short), the effects of the shape parameter on the TB curve are made clear, the shape features of the TB curve are analyzed. The necessary and sufficient conditions are derived for these curves having single or double inflection points, a loop or a cusp, or be locally or globally convex. The results are summarized in a shape diagram of TB curves, which is useful when using TB curves for curve and surface modeling. Furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples, respectively.     

ON BLOCK MATRICES ASSOCIATED WITH DISCRETE TRIGONOMETRIC TRANSFORMS AND THEIR USE IN THE THEORY OF WAVE PROPAGATION

Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.     

基于条纹中心线的载波散斑条纹解调方法

针对传统傅里叶变换法在处理含有多突起的载波散斑条纹图时,由于存在频谱展宽会出现严重的解调相位失真,提出了一种基于条纹中心线的载波散斑条纹解调方法.根据载波调制时所采用平行调制方式和倾斜调制方式,分别从理论上对相关的中心线解调法进行数学推导,并进一步采用最小二乘三次曲面拟合法获得被测物面全场的离面位移信息.实验结果表明:利用上述中心线解调法和曲面拟合法能解调出复杂的载波条纹图,并获得具有亚像素定位准确度、连续光滑的全场离面位移信息.     

Influence of Sulfur on Cure Kinetics of Natural Rubber/Sulfur/N-t-butylbenzothiazole-2-sulfenamide (TBBS) System Studied by Rubber Processing Analyzer

Based on the cure characteristics of the Natural Rubber/Sulfur/N–t–butylbenzothiazole– 2–sulfenamide (NR/S/TBBS) system, a kinetic model with induction, curing, and overcure periods was chosen to simulate the cure reaction of this system. Cure-curves reflecting the development of torque were recorded as a function of cure time for NR compounds by a rubber processing analyzer. The cure curves were then non-linear fitted. The results show that the simulated curves fit well with the experimental curves. Rate constant K ₂ for formation of activated crosslink precursors is much higher than rate constant K ₆ for crosslink degradation under the same cure condition. Reaction activation energy E ₂ and E ₆ calculated from K ₂ and K ₆ through the Arrhenius equation showed that E ₆ is higher than E ₂. The increase of sulfur dosage led to the decrease of E ₆ and E ₂, but E ₆ decreased more evidently.     

On the Consistency of Prony's Method and Related Algorithms

Abstract

Modifications of Prony's classical technique for estimating rate constants in exponential fitting problems have many contemporary applications. In this article the consistency of Prony's method and of related algorithms based on maximum likelihood is discussed as the number of observations n → ∞ by considering the simplest possible models for fitting sums of exponentials to observed data. Two sampling regimes are relevant, corresponding to transient problems and problems of frequency estimation, each of which is associated with rather different kinds of behavior. The general pattern is that the stronger results are obtained for the frequency estimation problem. However, the algorithms considered are all scaling dependent and consistency is not automatic. A new feature that emerges is the importance of an appropriate choice of scale in order to ensure consistency of the estimates in certain cases. The tentative conclusion is that algorithms referred to as Objective function Reweighting Algorithms (ORA's) are superior to their exact maximum likelihood counterparts, referred to as Gradient condition Reweighting Algorithms (GRA's), especially in the frequency estimation problem. This conclusion does not extend to fitting other families of functions such as rational functions.