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.     

模糊层次分析法在腐蚀影响因素分析中的应用

结合国内外对碳钢CO2腐蚀影响因素的研究成果,采用模糊层次分析法对影响输油管道 CO2腐蚀的因素进行定量分析,明确界定出这些因素对二氧化碳腐蚀影响的相对重要性(权重),为后续制定经济有效的管道内腐蚀防护措施提供了客观依据。     

电力系统谐波检测的现状与发展

准确、实时地对电力系统谐波进行检测有着重要的意义。本文根据电力系统谐波测量的基本方法，对近年来电力系统谐波检测的新方法进行了分析和评述。最后对电力系统的谐波测量进行了总结并提出了看法。     

A stochastic model for localized disturbances and its applications

A stochastic model for local disturbances, particularly for a temporal harmonic with random modulations in amplitude and/or phase, is proposed in this paper. Results for the second moment responses of a linear single-degree-of-freedom system to this type of stochastic loading demonstrate a significant change in response characteristics due to a small uncertainty. A local phenomenon may last much longer and resonance may be smeared to a broad range. Integrated with wavelet transform, the proposed approach may be used to model a random process with non-stationary frequency content. Especially, it can be effectively used for Monte Carlo simulation to generate large size of samples that have similar characteristics in time and frequency domains as a pre-selected mother sample has. The technique has a great potential for the case where uncertainty study is warranted but the available samples are limited.     

套保稠油油田火烧油层可行性分析

从火烧油层的筛选标准、实际地质条件及室内物理模拟实验入手，对该油田火烧可行性进行了分析。分析结果认为，套保油田进行火烧总体上是可行的，在实际火烧时应避开底水的影响，火烧区域应选在构造高部位或仅烧其主力层。     

Anthocyanin composition of the red wine Babić affected by maceration treatment

Identification of anthocyanins in the wine made of the Croatian autochthonous grape variety of Babić (Vitis vinifera L.) was carried out and their profile was determined by means of high-performance liquid chromatography with diode array and mass spectrometric detection. Dependence of anthocyanins content and profile on maceration treatment conditions was investigated. Statistically significant differences of anthocyanins concentration in wines Babić produced by various maceration treatments were confirmed by the use of multivariate analysis of variances. The investigation results indicated that the maceration temperature exerts higher influence on anthocyanins concentration than the duration of maceration. In addition, on the basis of anthocyanin composition and using different multivariate statistical analyses, differentiation of wines Babić according to maceration treatments was procured.     

加油站油品损耗的管理问题分析及解决办法

针对加油站在油品进、销、存方面因管理和人为作弊而产生的损耗大问题，提出了解决办法：各环节交接手续要严密完备；发货方实施保量运输，选择信誉好的承运方；在销售、储存方面应加强管理，推行加油站计量员、账务员集中管理，主要账表电子表格化，及时上报主管部门，执行责任追究制并与效益工资挂钩。     

试论循环水装置的经济性及其成本分析

通过对循环水装置的投资和成本分析，阐述了建设该装置的经济性和社会意义。     

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.     

Failure analysis of a broken tooth

Several days after heart surgery, a patient discovered his upper right canine tooth had broken at the root. Such tooth damage, recognized post-operatively, is usually assumed to be caused by blunt mechanical force from an instrument used by the anesthesiologist during placement of a breathing tube at the start of surgery. In this case, the patient had saved the crown portion of the broken tooth, and it was possible to examine the root fracture characteristics. The curvature and direction of the crack path and natural tooth situation suggested that failure could be described through a cantilever beam model. This was confirmed when a whole extracted sample tooth was embedded and broken by a measured force in a manner consistent with the model. The resulting fracture surface matched that of the patient’s broken canine tooth. However, the high load and force direction necessary to fracture the root was inconsistent with forces applied during the anesthesia procedure. The failure analysis and further investigation indicated tooth clenching on the breathing tube during recovery was the likely cause of fracture. This paper presents an alternate explanation for intubation-related dental injury, demonstrates the practicality of fractographic analysis of biological materials, and introduces a methodology for simulating in vitro tooth settings for mechanical testing.