The Two-Dimensional Clifford-Fourier Transform

Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced, including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued kernel. In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained, leading to further properties, both in the L ₁ and in the L ₂ context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced. AMS subject classification numbers: 42B10, 30G35 Fred Brackx received a diploma degree in mathematics from Ghent University, Belgium, in 1970 and a Ph.D. degree in mathematics from the same university in 1973. Since 1984 he is professor for mathematical analysis at Ghent University and currently he is leading the Clifford Research Group. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets. Nele De Schepper received a diploma degree in mathematics from Ghent University, Belgium, in 2001. Since then she holds an assistantship at the Department of Mathematical Analysis of Ghent University and is a member of the Clifford Research Group. Her main interests are function theory and functional analysis for functions with values in Clifford algebras. The research covers generalized Fourier transforms, orthogonal polynomials and multi-dimensional wavelets. Frank Sommen received a diploma degree in mathematics from Ghent University, Belgium, in 1978, a Ph.D. degree in mathematics from the same university in 1980, and a habilitation degree in mathematical analysis in 1984. From 1978 until 1999 he was at the National Fund for Scientific Research (Flanders). Since 2000 he holds a Research professorship at Ghent University. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets, algebraic analysis, hyperfunctions and radial algebra.     

Chemische Zusammensetzung und Mikrostruktur polymerabgeleiteter Gläser und Keramiken im System Si–C–O. Teil 2: Charakterisierung der Gefügeausbildung mittels hochauflösender Durchstrahlungselektronenmikroskopie und Feinbereichsbeugung

Chemical Composition and Microstructure of Polymer‐Derived Glasses and Ceramics in the Si–C–O System. Part 2: Characterization of microstructure formation by means of high‐resolution transmission electron microscopy and selected area diffraction Liquid or solid silicone resins represent the economically most interesting class of organic precursors for the pyrolytic production of glass and ceramics materials on silicon basis. As dense, dimensionally stable components can be cost‐effectively achieved by admixing reactive filler powders, chemical composition and microstructure development of the polymer‐derived residues must be exactly known during thermal decomposition. Thus, in the present work, glasses and ceramics produced by pyrolysis of the model precursor polymethylsiloxane at temperatures from 525 to 1550 °C are investigated. In part 1, by means of analytical electron microscopy, the bonding state of silicon was determined on a nanometre scale and the phase separation of the metastable Si–C–O matrix into SiO₂, C and SiC was proved. The in‐situ crystallization could be considerably accelerated by adding fine‐grained powder of inert fillers, such as Al₂O₃ or SiC, which permits effective process control. In part 2, the microstructure is characterized by high‐resolution transmission electron microscopy and selected area diffraction. Turbostratic carbon and cubic β‐SiC precipitate as crystallization products. Theses phases are embedded in an amorphous matrix. Inert fillers reduce the crystallization temperature by several hundred °C. In this case, the polymer‐derived Si–C–O material acts as a binding agent between the powder particles. Reaction layer formation does not occur. On the investigated pyrolysis conditions, no crystallization of SiO₂ was observed.     

基于WVD的防空雷达直升机信号特征分析

基于直升机目标旋转部件的调制模型，本文针对防空雷达提出了分析直升机信号特征的一种新方法——WVD法，并对直升机目标旋转部件调制回波信号在不同噪声情况下加以仿真分析，结果表明：用WVD分析雷达回波中直升机信号特征是一种非常有效的方法。     

具有阻力特性材料的σ_f－σ关系及一种新的阻力曲线测定方法

通过对相变增韧陶瓷及一种可切削玻璃－陶瓷动态疲劳（恒应力速率）试验中高应力速率区断裂应力下降现象的理论分析，发现这种现象与材料的阻力特性（Ｒ－ｃｕｒｖｅ）密切相关。确立的σ_ｆ－σ理论关系能够很好地描述整个应力速率区间内的动态疲劳试验结果。高应力速率区σ_ｆ－σ在双对数坐标下为负斜率直线，直线斜率为（ｍ为阻力曲线ＫＲ＝ｋ（△ａ）~ｍ的指数），断裂主要由材料阻力行为控制；低应力速率区，σ_ｆ－σ在双对数坐标下为正斜率直线，直线斜率为　（ｎ为应力腐蚀指数），断裂主要由材料应力腐蚀行为控制。建立了测定材料阻力特性的一种新方法，分别用这种方法及压痕／弯曲方法对一种可切削玻璃－陶瓷的阻力特性进行了实验测定，两种方法所得结果有很好的一致性。     

一种基于三次样条函数求离子浓度的自动算法

本文提出了一种用三次样条函数模拟双次标准加入法测量方程，直接求解离子浓度的自动算法。比较了三咱不同边界条件下用要池数计算离子浓度的结果。造出节点区间两极端点的二阶导数为零时的三次样条函数为最佳模拟函数。并讨论了该方法在实际分析中误差的来源及消除办法。经对一系列文献数据的验算对比，表明本法完全可代替传统的迭代法和查图法，且能方便地设置在智能化的电位分析系统中。     

中国古典园林三维造型研究

论述了采用层次结构化及参数化三维造型方法，建立一个以造型函数库为核心，从而构造各类、各级园林景观构件表面模型的方法和过程。对于某些非建筑类的园林配景构件，采用了Ｆｒａｃｔａｌ方法进行造型。     

心电地图仪中工频干扰的一种滤除方法

在心电地图仪中记录到的体表心电信号往往由于电磁的影响而引进工频干扰．基于体表心电信号中工频干扰的特点，作者提出了一种滤除工频干扰的方法，即就单独—胸导联信号通过提高频谱的分辨率来估计工频干扰的频率；基于最小均方误差准则来估计各导联信号中工频干扰的幅度和相位。文中还给出了该算法的流程图和滤波性能分析。模拟结果表明了该算法的有效性。应用该算法对心电地图仪中的工频干扰进行对消，取得了满意的结果。     

A method of identifying latent human errors in work systems

Work system improvements are implemented in various manufacturing processes to prevent problems caused by human errors. However, they are almost always applied to problems which have already occurred. This paper examines a method of identifying latent human errors existing within the work systems beforehand. A procedure for applying failure mode and effect analysis to this identification problem was defined based on over 1000 empirical errors: a work system decomposition criterion and fundamental error modes for listing latent human errors, and then applied to three practical manufacturing processes in order to evaluate its effectiveness.     

Control strategies for reactive batch distillation

A batch reactor may be combined directly with a distillation column by distilling off the light component product in order to increase the reactor temperature or to improve the product yield of an equilibrium reaction. The same amount of the light product should be removed as the amount being formed by the reaction at any time. A linearized model has been developed which describes the process behaviour satisfactorily for control analysis purposes. The controllability of a combined batch reactor/batch distillation column is found to depend strongly on the operating conditions and on the time during the run. In general, controlling only the reactor temperature (one-point bottom control) is difficult since the set-point has to be specified below a maximum value in order to avoid break-through of an intermediate component in the ditillate. This maximum value may be difficult to know a priori. For the example considered in this study, control of both reactor temperature and distillate composition (two-point control) is also found to be difficult due to large interactions in the column. As with one-point bottom control, the reactor temperature has to be specified below a maximum value. However, energy can be saved since the heat duty can be decreased with time. Controlling the temperature on a tray in the column (one-point column control) is found to give good performance for the given process with no loss of reactant and a high reactor temperature, although no direct control of the reactor temperature is obtained.