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.     

Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).     

Effects of citrate on the different phases of calcium oxalate crystallization

Urinary citrate appears to be an important factor in the crystallization process of calcium oxalate and calcium phosphate. The urinary excretion of citrate was found to be significantly lower in patients with calcium oxalate stone disease as compared with normal subjects, and about 30 per cent of the calcium stone formers can be considered as hypocitraturic. The lowest excretion of citrate was recorded in urine collected during the night. Citrate has significant effects on supersaturation with respect to both calcium oxalate and calcium phosphate, it also inhibits the growth of these crystals. In addition, citrate appears to be capable of inhibiting the aggregation of crystals composed of calcium oxalate, brushite, and hydroxyapatite. The heterogenous growth of calcium oxalate on calcium phosphate is also counteracted by citrate. As a consequence of the crucial role of citrate in these processes, stone prevention with alkaline citrate has become an attractive form of treatment in patients with recurrent stone formation. Single evening dose administration of sodium potassium citrate resulted in an of sodium potassium citrate resulted in an increased excretion of citrate, reduced levels of the calcium/citrate ratio as well as supersaturation with respect to calcium oxalate and a decreased rate of stone formation. However, conflicting results of stone preventive treatment with alkaline citrate have been reported by different groups, and long-term follow-up of patients treated in a randomized way is necessary to definitely assess the efficacy of alkaline citrate.     

Investigations of delamination criticality and the transferability of growth criteria

This article describes a study of delamination growth along 0 °/0 °, 0 °/ 5 °, ± 5 °, and 0 °/90 ° interfaces sandwiched between unidirectional carbon fibre/epoxy composite material. Relationships between damage criticality, growth rate and acoustic emission activity for delamination growth have been studied and the transferability of results from laboratory coupons to composite structural elements has been examined. Two types of coupon tests, conventional delamination beams and rigidly loaded single edge notched strips, have been compared for different mode ratios. Comparative tests have been made on buckling-induced delamination in plates. A graphite crack gauge has been used to measure delamination length and growth rate, ranging from 0.05–2000 m/s. Damage growth was also followed using visual, ultrasonic C-scan, X-ray radiography, macro-video and acoustic emission measurements. Empirical evaluations of interlaminar toughness for delamination beams are made using the Irwin-Kies relation. Unstable growth is analysed using elasto-dynamic moving finite elements. Bucklinginduced delamination is analysed using plate/shell FE methods with growth/remeshing algorithms.     

Finite-element grid improvement by minimization of stiffness matrix trace

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.     

Comparison of copper emission rates from wood treated with different preservatives to the environment

This study describes a laboratory method for the estimation of emission from preservative-treated wood in the different situations where emissions could enter the environment for use classes 3 (not in contact with ground) and 4 and 5 (in contact with the ground, fresh water or sea water) according to OECD Guidelines. Samples of scotch pine sapwood (Pinus sylvestris L.) were treated with CCA (1% and 2%), ACQ-1900 (3% and 7%), ACQ-2200 (2%), Tanalith E 3491 (2% and 2.8%), and Wolmanit CX-8 (2%).     

Inhibition of Listeria monocytogenes on cold-smoked salmon by nisin and carbon dioxide atmosphere

The heat-stable enterotoxin of Escherichia coli binds to an intestinal receptor, guanylyl cyclase-C, and produces cGMP to induce diarrhea. Guanylin is an endogenous ligand of this receptor. In the present in vivo study, the intestinal water and ion secretion induced by mucosal application of 2 nmol/ml guanylin or 5 or 10 units/ml heat-stable enterotoxin into closed loops was compared in the rat. The characteristics of secretion induced by cAMP following intravenous perfusion of 1.2 nmol/100 g per h vasoactive intestinal peptide were compared to those induced by cGMP. Unidirectional Na+ and Cl- fluxes were estimated by addition of 22Na into the loop and i.v. injection of 36Cl. Guanylin induced less water and ion secretion than that produced by heat-stable enterotoxin in the colon, confirming the results of in vitro studies, and also in duodenum and ileum. The cAMP- or cGMP-mediated response had a similar pattern, i.e., an inhibition of Na+ absorption and an increase in anion secretion.