非线性方程组的不精确仿射牛顿法

1 引言众所周知,对于非线性方程组问题 F(x)=0 F:Rn→Rn (1) 经典的牛顿法从给出一个初始点x0之后,计算第k步迭代点xk及步长sk:     

Improvement of 1D off-axis computer-generated holograms

Creation of Fresnel off-axis computer-generated holograms and improvement of images reconstructed from the holograms are described. To improve the reconstructed images, we have created the holograms with high construct diffraction patterns by using a histogram method. From reconstruction experiments of the holograms, clear images have been obtained and 3D images have been seen directly with eyes.     

具有特定非零Walsh谱值个数的布尔函数的研究及构造

布尔函数与其变元的相关性与流密码的相关攻击有紧密联系，Walsh变换则是研究布尔函数相关特性的主要工具，本文研究了非零Walsh谱值个数k=9，10的布尔函数，证明了k=9的函数的不存在性，并构造了所有k=10的函数。     

Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform

New filtering scheme is investigated and implemented on digital speckle pattern interferometric fringes to enhance the signal-to-noise ratio (SNR) in the speckle interferograms. To establish the potential of new filtering scheme the experiment was conducted on the vibrating cantilever beam. Experimental results revealed that the new filtering scheme is more powerful than other known filtering schemes (Kumar et al. Opt Laser Eng 2004;41:81–93. Kumar et al. Opt Laser Technol 2001;33:567–571. Shakher et al. Opt Eng 2002;41:176–180. Shakher et al. Proceedings ICICS, Singapore, 9–12 September 1997, p. 953–956. Bowler et al. Proceedings of IEE second international conference on image processing, London, 1986, p. 24–26. Lim. Opt Eng 1981;20:670–678. Devila et al. J Mod Opt 1995;42:1795–1804; Kaufmann et al. Opt Eng 1996;35:9–14). The new scheme reduced the speckle noise and improved SNR in speckle interferograms. Further, the new investigated filtering scheme is implemented to study the mode shapes of square plates under two different boundary conditions. In the first condition all the edges of the square plate were fixed while in the second condition two adjacent edges were fixed and the remaining two edges were free. From the experimental results it is clear that the mode shapes are more distinctly visible with the implementation of the new filtering scheme as compared to other known schemes. Under both the boundary conditions the recorded resonance frequencies were compared with the calculated values of resonance frequencies based on classical theory. The results obtained form DSPI show good agreement with classical theory.     

加热模型及其最优控制

本文应用Pontryagin最大值原理研究加热过程,提出一个在加热过程中节能的最优控制方案。     

Data handling in HPLC-diode array UV-spectrometry

Summary The mathematical resolution of overlapped chromatographic peaks obtained in HPLC with a diode array UV detector has received considerable attention recently. The purpose of the proposed methods is the quantitation and identification of unknown solutes in complex mixtures by an efficient use of all available data. Basically two approaches have been proposed: the first one resolves the concentration profiles and calculates the pure spectra by applying a minimal number of assumptions, which is denoted self-modeling-curve resolution. The second one is based on a match of pure spectra available in a spectral library with the measured mixture spectra. In this paper both approaches are evaluated with respect to their performance to provide the pure spectra and an accurate quantitation of the concentrations.     

Simulation of certain multivariate generalized Pareto distributions

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page .      

Optimizing thermography depth probing with a dynamic thermal point spread function

Derivation of two point spread functions PSFs suitable for infrared thermograms analysis is illustrated, based on two unique approaches, one based on depth decaying limit and one on diffusion limit. Experimental work using PMMA sample with back drilled holes and pulsed thermographic routine is utilized to show the effectiveness of deconvoluting pixel temperature transient history with suggested PSF’s. Synthetic second time derivative thermograms are utilized for comparison and the signal to noise ratio is used as a figure of merit for quantification.     

有限局部环上对称矩阵的计数定理(I)

设$A_{n}(R)$是有限局部环$Z/p^{k}Z$上$n$阶对称矩阵的集合, 这里$n\geq 2$. $p$是大于$2$素数, $p\equiv1({\rm mod}4)$ 且$k>1$. 通过确定有限局部环$Z/p^{k}Z$上对称矩阵的标准型, 计算出$A_{n}(R)$在线性群${\rm GL}_{n}(R)$作用下的轨道数, 从而计算出由特定对称矩阵确定的正交群的阶以及与特定对称矩阵在同一轨道的对称矩阵的阶.     

矢算变换在重矢积和重矢混合积积分中的应用

应用重矢积的矢算变换计算稳恒磁场中载流导线回路的磁力和导线回路定轴转动所产生的感应电动势。