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).     

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 two methods of surfactant administration and the effect on dosing-associated hypoxemia

OBJECTIVE: The purpose of our study was to test the hypothesis that surfactant dosing through a proximal sideport adapter on an endotracheal tube leads to more dosing-associated hypoxemia compared with a method of dosing that uses a double-lumen endotracheal tube. STUDY DESIGN: Using adequate sample size to compare significant changes in O2 saturation (power > 0.8, alpha < 0.05) we enrolled 36 infants with respiratory distress syndrome in this randomized trial. A 10% change in O2 saturation was considered clinically significant. Nineteen infants received 38 doses of surfactant through the sideport adapter. Seventeen infants received 31 doses of surfactant through the nonventilation lumen of a double-lumen endotracheal tube. Two main outcome measures were assessed: time-averaged O2 saturation values 30 minutes after dosing and the largest absolute fall in O2 saturation for each patient. RESULTS AND CONCLUSIONS: Time-averaged O2 saturation measures were higher in the proximal sideport group (p = 0.02), but the magnitude of difference was probably not clinically significant. No significant difference was detected between groups when we compared largest absolute drop in O2 saturation. Secondary analyses found no effect of birth weight or dose number (second vs third dose) on either outcome measure.     

Screening demand-side management programs with a value-based test

A value-based test is presented for economic screening of electric utility demand-side management (DSM) programs. The widely used least cost test is valid if the programs do not alter the amount or value of energy services provided to customers. But, in general, DSM programs have such effects and, as a result, the value consumers receive is changed. A more general economic efficiency test, the most value test, provides a practical method for considering the effects of DSM on customer value. The version presented allows for multiple load periods and can account for rate impacts on several customer classes. Four typical DSM programs are evaluated as illustrations     

Pentacene-based organic thin-film transistors

Organic thin-film transistors using the fused-ring polycyclic aromatic hydrocarbon pentacene as the active electronic material have shown mobility as large as 0.7 cm²/V-s and on/off current ratio larger than 10⁸; both values are comparable to hydrogenated amorphous silicon devices. On the other hand, these and most other organic TFT's have an undesirably large subthreshold slope. We show here that the large subthreshold slope typically observed is not an intrinsic property of the organic semiconducting material and that devices with subthreshold slope similar to amorphous silicon devices are possible     

Nonlinear self-guiding and switching in an all-fiber device

We study the nonlinear propagation of light in optical fibers in the strong nonlinearity limit. In this limit, the transverse guiding properties are altered and cannot be decoupled from the longitudinal part of the wave equation. We consider a refractive index profile with no bound modes at low intensities and show that stable self-guiding occurs at a critical intensity. This critical intensity is a property of the guide and can be made much lower than the threshold for unstable self-focusing. We consider a particular design for which self-guiding occurs at three orders of magnitude lower than the self-focusing threshold.     

Category Norms as a Function of Culture and Age: Comparisons of Item Responses to 105 Categories by American and Chinese Adults.

Understanding how aging influences cognition across different cultures has been hindered by a lack of standardized, cross-referenced verbal stimuli. This study introduces a database of such item-level stimuli for both younger and older adults, in China and the United States, and makes 3 distinct contributions. First, the authors specify which item categories generalize across age and/or cultural groups, rigorously quantifying differences among them. Second, they introduce novel, powerful methods to measure between-group differences in freely generated ranked data, the rank-ordered logit model and Hellinger Affinity. Finally, a broad archive of tested, cross-linguistic stimuli is now freely available to researchers: data, similarity measures, and all stimulus materials for 105 categories and 4 culture-by-age groups, comprising over 10,000 fully translated unique item responses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)