一种低原子序数元素EDX RF的多次导-样条小波解析方法研究

能量色散X射线荧光（EDXRF）光谱分析待测元素的信息主要反映在能谱的特征峰峰位以及特征峰净峰面积中。对于特征峰的准确检测是EDXRF光谱分析的关键。特征X射线之间的能量在低原子序数元素中相差很小,在实际测量过程中由其他一些因素干扰会导致EDXRF光谱中特征峰产生严重重叠,以EDXRF光谱中低序列元素的重叠峰作为研究对象,提出一种四次导数结合三样条小波变换处理低序列元素重叠峰的新方法。通过数学模型模拟重叠峰检测了该方法的可行性,并仿真了实测X荧光光谱数据进行检测得到良好的效果,通过使用了CIT-3000SY X 荧光元素录井仪实测T铅黄铜数据和混合轻元素数据荧光光谱作为验证。首先,介绍导数法以及三样条小波法分解重叠的原理。导数法阶数越高信号越畸形但可以有效提高重峰分离度,而三样条小波变换对低分离度重峰处理较为无力但能有效的保持峰型。通过Tsallis峰信号模拟重叠峰,模拟出3个峰信号,第1个峰和第2个峰的分离度R=0.33,第2个峰和第3个峰的分离度R=0.67,导数处理后信号任仍具有一部分重叠,但是导数处理后不仅保留了信号的峰位值,且出现了分离度变大的现象,而三样条小波对低分离度重叠峰的分解较为无力,但是对于分离度较大的重叠峰具有较好的效果,信号通过四次导增加分离度再进行三样条小波变换,通过调节样条小波分解层次的次数,然后对分解出的高频信号采取适当的系数进行放大,最后进行信号重构。实验实现了对模拟信号的分解。验证了此方法针对重叠峰分解具有可行性。实验采用分解4层的三样条小波变换以及放大6倍的高频信号。然后,处理仿真K元素的重叠光谱,实现了重叠峰的分解,通过仿真实验表明新方法能准确的识别峰位,结果表明只有1%之内的误差,证明了新方法对X荧光光谱重叠峰分解的适用性。最后用此方法对CIT-3000SY X荧光元素录井仪实测T铅黄铜元素数据以及混合轻元素数据X荧光光谱进行处理,实现了对重叠峰的分解,且分解后的峰位误差控制在1%之内,具有较高的准确率。实验结果证明：四次导数结合三样条小波变换能有效分离重叠峰,并且在处理X荧光光谱的重叠峰分解上具有实用性。     

Integrating noisy data

Suppose the parametric form of a curve is not known, but only a set of observations. Quadrature formulae can be used to integrate a function only known from a set of data points. However, the results will be unreliable if the data contains measurement errors (noise). The method presented here fits an even degree piecewise polynomial to the data where all the data points are being used as knot points and the smoothing parameter is optimal for the indefinite integral of the curve which happens to be a smoothing spline. After the smoothing parameter has been chosen, this approach is less computationally expensive than fitting a smoothing spline and integrating.     

Two-scale symbol and autocorrelation symbol for B-splines with multiple knots

The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure of the corresponding autocorrelation symbol is investigated. In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions of degree 2m+1 and defectr, first considered by Lipow and Schoenberg [9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in [9] has a unique solution.     

Optimality conditions for strongly monotone variational inequalities

Necessary conditions for optimal controls have been obtained for strongly monotone variational inequalities by the penalty method, Ekeland's Variational Principle, and lower-semicontinuity of set-valued mappings. It has been shown that these conditions are easy to apply and can imply some known necessary conditions. They also yield new optimality conditions.     

A generalized approximation theory for quadratic forms II: Application to randomized spline type focal/conjugate point problems

This paper continues our earlier work on random quadratic forms. We show that if continuity conditions for a family of quadratic forms holds uniformly on an index set, generalized focal/conjugate point signature approximation results hold. We then apply these results to obtain continuity of thenth focal point in a random (robust) setting.     

A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications

This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.     

Scalarization and Kuhn-Tucker-Like Conditions for Weak Vector Generalized Quasivariational Inequalities

We consider a weak vector generalized quasivariational inequality. By introducing a method of scalarization which does not require any assumption on the data and by using previous results of the authors concerning scalar generalized quasivariational inequalities, we present Kuhn-Tucker-like conditions for this problem in the case in which the set-valued operator of the constraints is defined by a finite number of inequalities     

Kalman filter deconvolution after cubic splines background removal in the HPLC determination of Cr(III) and Al(III) as 8-hydroxyquinolines

Summary A procedure for the simultaneous quantitation of Al(III) and Cr(III) ions by reversed-phase HPLC, after pre-column complexation with 8-hydroxyquinoline, is described. The deconvolution of the partially overlapped peaks was by the Kalman filter method which yielded accurate and precise results. Background removal from the chromatograms was by a new approach employing cubic splines as interpolators between the peak valleys. Finally, it is shown that the Kalman filter deconvolution, after subtraction of the background by cubic spline interpolation, allowed quantitation of Al(III) and Cr(III) down to 25 ppb for each metal. These concentrations were not detectable by conventional integration methods due to a very low signal-to-noise ratio.     

Spline approximation method

A system of relations is presented for determining optimal coefficients for a set consisting of an arbitrary number of smoothly matched cubic polynomial dependences. As an example, the method is used to construct optimal approximating formulas for the viscosity of air in thermochemical equilibrium as a function of enthalpy.     

自共轭椭圆型方程的样条解法

本文从二元样条空间的理论出发,构造了一类新的差分格式,并利用它得到了一类自共轭椭圆型方程的样条解,并证明了这样的解的唯一性和收敛性问题.最后,给出了一个数值例子,说明了本方法是可行的.