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In relation to the computation of electromagnetic scattering in layered media by the Gabor-frame-based spatial spectral Maxwell solver, we present two methods to compute the Gabor coefficients of the transverse cross section of three-dimensional scattering objects with high accuracy and efficiency. The first method employs the analytically obtained two-dimensional Fourier transform of the cross section of a scattering object, which we describe by two-dimensional characteristic functions, in combination with the traditional discrete Gabor transform method for computing the Gabor coefficients. The second method concerns the expansion of the so-called dual window function to compute the Gabor coefficients by employing the divergence theorem. Both methods utilize (semi)-analytical approaches to overcome the heavy oversampling requirement of the traditional discrete Gabor transform method in the case of discontinuous functions. Numerical results show significant improvement in terms of accuracy and computation time for these two methods against the traditional discrete Gabor transform method.

Unlabelled: Background- Polymorphisms in the promoter (T-786C) and exon 7 (G894T) of the endothelial nitric oxide synthase (eNOS) gene were shown to be associated with reduced vascular NO production or increased proteolytic cleavage of eNOS. Therefore, we aimed to determine the effects of these polymorphisms on endothelial function and endothelial response to physical exercise in patients with coronary artery disease (CAD)., Methods and Results: Sixty-seven patients were randomized to either a training or a control group. At the beginning and after 4 weeks, acetylcholine-induced changes in average peak velocity (APV) of a coronary or mammary artery were invasively assessed by Doppler velocimetry. Polymorphisms were detected by polymerase chain reaction-restriction fragment length polymorphism. At the beginning, in subjects with the wild-type (WT) variant, APV increased by 88+/-7% in response to acetylcholine. This response was significantly blunted in patients who were positive for the promoter (44+/-7%) or the exon 7 (62+/-9%) polymorphism. Four weeks of exercise training resulted in augmentation of an endothelium-dependent increase in APV by +36+/-12% in promoter polymorphism-positive patients but by +81+/-18% and +91+/-15% in WT variant- and exon 7 polymorphism-positive subjects, respectively., Conclusions: These results suggest that the presence of either one of the polymorphisms attenuates endothelium-dependent vasodilatation in CAD patients. Only the promoter polymorphism might have an adverse effect on training-induced improvement in endothelial function.