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.     

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)     

Moving on and moving up: The experience of households who resell public sector dwellings

The long‐term consequences of the sale of public sector dwellings to sitting tenants are under‐researched; in particular, the experience of tenant purchasers in the housing market subsequent to purchase is little known. This paper reports research designed to fill this gap in knowledge. Over 200 tenants who had bought their dwelling from the Scottish Special Housing Association and subsequently resold on the open market were traced using the Register fo Sasines and the Land Register and interviewed. Most had made considerable capital gains on resale and had used some of the realised capital to trade up in the housing market. They were, on average, slightly more affluent and younger than sitting tenant purchasers generally; they represented a group of households who were privileged within the public sector through living as tenants in the best stock and who were enabled by the Right to Buy to convert that good luck into hard cash and move into mainstream owner occupation. This good luck compounded the advantaged position vis‐à‐vis other tenants that they enjoyed in the labour market.     

FRACTURE ASSESSMENT FOR SECONDARY LOADS

The fracture assessment of structures subjected to secondary loading systems was studied by FEM-analysis of a few illustrative two-dimensional examples. The first example is an edge-cracked plate with a thermal gradient. The FEM-calculations revealed that a purely elastic analysis yielded J-values that are in most cases considerably more conservative than the ones calculated from an elastic-plastic analysis. The results were further compared with different engineering type non-linear estimates. As a second example a crack emanating from a semi-circular notch in a rectangular plate was chosen. The plate was subjected to uniaxial tension along its boundaries. It turned out that for the cases considered the J-values were fairly close to those elastically predicted.     

Parental caregiving and child externalizing behavior in nonclinical samples: A meta-analysis.

A meta-analysis of 47 studies was used to shed light on inconsistencies in the concurrent association between parental caregiving and child externalizing behavior. Parent–child associations were strongest when the measure of caregiving relied on observations or interviews, as opposed to questionnaires, and when the measure tapped combinations of parent behaviors (patterns), as opposed to single behaviors. Stronger parent–child associations were also found for older than for younger children, and for mothers than for fathers. Finally, externalizing was more strongly linked to parental caregiving for boys than for girls, especially among preadolescents and their mothers. The meta-analysis helps account for inconsistencies in findings across previous studies and supports theories emphasizing reciprocity of parent and child behavior. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Faking behavior and gender differences on a new personality research instrument.

Faking behavior was studied by comparing the personality profiles of 161 job applicants (motivated to be hired) with those of a control group of 73 graduate and undergraduate business students (motivated to obtain personal information for their own enlightenment). 44% of the Ss were female. Both groups were instructed to describe themselves honestly while completing the Self-Perception Test. Applicants did "fake good," scoring significantly higher on 10 of 11 scales; variance was significantly lower among applicants on 7 scales. Gender differences, consistent with cultural stereotypes, occurred on 5 scales. Overall profile shapes were virtually identical for student and applicant groups, suggesting that faking may not have dramatically altered the essence of the personality constructs. The scales of the test were found to have high reliability. Scale independence is discussed in relation to the 5-factor model of personality. (PsycINFO Database Record (c) 2010 APA, all rights reserved)