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.     

A Novel Neurofilament Light Chain ELISA Validated in Patients with Alzheimer’s Disease,Frontotemporal Dementia,and Subjective Cognitive Decline,and the Evaluation of Candidate Proteins for Immunoassay Calibration

Neurofilament light chain (Nf-L) is a well-known biomarker for axonal damage; however, the corresponding circulating Nf-L analyte in cerebrospinal fluid (CSF) is poorly characterized. We therefore isolated new monoclonal antibodies against synthetic peptides, and these monoclonals were characterized for their specificity on brain-specific intermediate filament proteins. Two highly specific antibodies, ADx206 and ADx209, were analytically validated for CSF applications according to well-established criteria. Interestingly, using three different sources of purified Nf-L proteins, a significant impact on interpolated concentrations was observed. With a lower limit of analytical sensitivity of 100 pg/mL using bovine Nf-L as the calibrator, we were able to quantify the Nf-L analyte in each sample, and these Nf-L concentrations were highly correlated to the Uman diagnostics assay (Spearman rho = 0.97, p < 0.001). In the clinical diagnostic groups, the new Nf-L ELISA could discriminate patients with Alzheimer’s disease (AD, n = 20) from those with frontotemporal lobe dementia (FTD, n = 20) and control samples with subjective cognitive decline (SCD, n = 20). Henceforth, this novel Nf-L ELISA with well-defined specificity and epitopes can be used to enhance our understanding of harmonizing the use of Nf-L as a clinically relevant marker for neurodegeneration in CSF.     

Magnetic field-driven induction of ZENK in the trigeminal system of pigeons (Columba livia)

Magnetoreception remains one of the few unsolved mysteries in sensory biology. The upper beak, which is innervated by the ophthalmic branch of the trigeminal nerve (V1), has been suggested to contain magnetic sensors based on ferromagnetic structures. Recently, its existence in pigeons has been seriously challenged by studies suggesting that the previously described iron-accumulations are macrophages, not magnetosensitive nerve endings. This raised the fundamental question of whether V1 is involved in magnetoreception in pigeons at all. We exposed pigeons to either a constantly changing magnetic field (CMF), to a zero magnetic field providing no magnetic information, or to CMF conditions after V1 was cut bilaterally. Using immediate early genes as a marker of neuronal responsiveness, we report that the trigeminal brainstem nuclei of pigeons, which receive V1 input, are activated under CMF conditions and that this neuronal activation disappears if the magnetic stimuli are removed or if V1 is cut. Our data suggest that the trigeminal system in pigeons is involved in processing magnetic field information and that V1 transmits this information from currently unknown, V1-associated magnetosensors to the brain.     

Comparison of drilled hole quality evaluation in CFRP/CFRP stacks using optical and ultrasonic non-destructive inspection

In aeronautical industry, stringent requirements relate to the quality of drilled holes in carbon fiber reinforced plastic (CFRP) composite laminates as low hole quality determines poor assembly tolerance, structural properties reduction, and risk for long-term part performance. Non-destructive quality control techniques were applied to drilled CFRP laminate stacks for aeronautical applications to characterize the material damage induced by drilling in order to assess the hole quality for product acceptability. Experimental metrology procedures, including optical measurements and ultrasonic non-destructive evaluation, were employed to appraise both external and internal induced material damage in holes machined under diverse drilling conditions. The optical inspection procedure, comparable to the visual inspection method regularly utilized in industry, provided delaminated area evaluations that are underestimated in the case of severe drilling conditions by up to 7% for hole exit and up to 5% for hole entry. In the case of less severe drilling conditions, the underestimation was limited to <2.5% for both hole exit and hole entry, which can be considered a practically negligible disparity.     

Analysis of polyolefin compositions through near infrared spectroscopy

In this work, NIRS is employed to provide compositions of α‐olefin copolymers, allowing for evaluation of the effects of certain key process variables on the final NIR spectral responses of obtained polymer materials. This work also introduces a new temperature programmed analytical technique, which combines NIRS measurements with partial fractionation of α‐olefin copolymers. The new proposed technique can be used for evaluation of polyolefin compositions, as presented here for poly(propene/1‐butene) copolymers. Besides, preliminary results obtained from thermal fractionation experiments indicate that this new proposed experimental technique can be employed for characterization of comonomer sequence distributions of α‐olefin copolymers. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40127.     

Investigation of Origin of Attached Cu-Ag Droplets to Solid Particles During High-Temperature Slag/Copper/Spinel Interactions

Metallurgical and Materials Transactions B - This study investigates the origin of mechanically entrained metal droplets in liquid slag due to their interaction with solid spinel particles. Two...     

Thermal comfort of patients: Objective and subjective measurements in patient rooms of a Belgian healthcare facility

In healthcare facilities, the prediction of mean thermal comfort perception of patients and staff is necessary to formulate requirements for the architectural and building systems design and control, and for establishing guidelines for the use of clothing and bedding systems.     

Synthesis of spherical core‐shell poly(vinyl acetate)/poly(vinyl alcohol) particles for use in vascular embolization: Study of morphological and molecular modifications during shell formation

Transarterial vascular embolization and chemoembolization has become common medical procedures, where partially hydrolyzed poly(vinyl alcohol) (PVA) beads remains as one of the most used embolic agent materials. Although synthetic, PVA cannot be synthesized by direct polymerization and must be obtained by chemical modification of another polymer, usually poly(vinyl acetate) (PVAc). The aim of the present work is to synthesize spherical core‐shell PVAc/PVA particles and study the morphological and molecular modifications during shell formation. The polymer particles where produced in two stages, where first the PVAc core was obtained by suspension polymerization of vinyl acetate (VAc) and then the PVA shell synthesized through hydrolysis. Spherical PVAc particles were successfully produced and isolated using an optimized suspension polymerization process. During the shell formation, it was shown that none of the conditions used affected the overall morphology of the particles although changes in the final size distribution could be observed. However, it was possible to identify the process variables and reaction condition that affect the molecular weight averages and polydispersities of the final copolymer. POLYM. ENG. SCI., 55:2237–2244, 2015. © 2015 Society of Plastics Engineers     

Comparative Investigation of Hoveyda–Grubbs Catalysts bearing Modified N‐Heterocyclic Carbene Ligands

This paper reports the structural modification of Hoveyda–Grubbs complexes through the introduction of either an N‐alkyl‐N′‐mesityl heterocyclic carbene, an N‐alkyl‐N′‐(2,6‐diisopropylphenyl) heterocyclic carbene, or an N‐alkyl‐N′‐alkyl heterocyclic carbene. The effect of the modified N‐heterocyclic carbene (NHC) ligand was investigated in representative ring‐opening metathesis polymerization (ROMP), ring‐closing metathesis (RCM) and cross metathesis (CM) reactions. A pronounced influence on both catalyst activity and selectivity was found to be exerted by the NHC amino substituents, which emphasizes that a rigorously selected steric environment is critical in olefin metathesis catalyst design.