On Euclidean Norm Approximations

Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches were based on minimizing the maximum error. Recently, Seol and Cheun proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.Comment: 9 pages, 1 figure, Pattern Recognitio

Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"

Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in $\mathbb{Z}^n$. In this note we compare this approximation to two previously proposed Euclidean norm approximations and demonstrate that the empirical average errors given by Mukherjee are significantly optimistic in $\mathbb{R}^n$. We also propose a simple normalization scheme that improves the accuracy of his approximation substantially with respect to both average and maximum relative errors.Comment: 7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.487

Effect of Ag2O addition on the intergranular properties of the superconducting Bi–(Pb)–Sr–Ca–Cu–O system

The effect of Ag2O addition on the Bi–(Pb)–Sr–Ca–Cu–O system has been investigated in terms of ac susceptibility, phase evolution, critical current density and critical temperature. It was found that as the amount of Ag2O addition increases, the intergranular critical current density decreases in our samples (Bi1.84Pb0.34Sr1.91Ca2.03Cu3.06O10) fabricated by ammonium nitrate technique. The analysis for comparison is based on the suppression degree of the diamagnetic behaviour with respect to fields, rapid or slow shift of the summit in χ'(T) to lower temperature with increasing field amplitude and the sharpness of the transition of χ'(T) for intergranular component for the same field amplitude. We also qualitatively discuss experimental results in the framework of the critical state model. The room temperature XRD diagram indicates the presence of large amount of high-Tc (2223) phase. The percentage of Bi-2223 phase in the phase mixture was estimated from the intensities of high-Tc (2223) and low-Tc (2212) phase peaks as 78% for the pure BSCCO sample. Among the Ag2O-added BSCCO samples studied, the one in which 5 wt%Ag2O was added shows the highest rate of Bi-2223 formation as 92%. The SEM analysis reveals some morphological changes induced by silver addition

Effects of the weed density on grass yield of Alfalfa (Medicago sativa L.) in different row spacing applications

This study, in which the effects of different row spacing applications on weed density and on grass yield of Medicago sativa L. were investigated, was carried out in Van-Turkey from 2006 - 2008. Randomized blocks design was adopted with three replications. Row spacing applications of 20, 30, 40, 50, 60 and 70 cm were tested. The alfalfa plant height, yield of green herbage yield, dry matter yield, crude protein rate and crude protein yield were investigated. In addition, the weed densities at different row spacing distances were determined. The highest plant heights were obtained in 40 cm row spacing application in the first year and in 20 cm row spacing application in the second year. The highest dry matter and crude protein yields were obtained in 20, 30 and 40 cm row spacings in the first year and in 20 cm row spacing applications in the second year. The most intense weed was Alopecurus myosuroides Huds in 2007 and Amaranthus retroflexus L. in 2008. The least weed density was found in 20 cm row spacing during all three before cutting periods in the first year of study and this was found in 30 cm row spacing application in first before cutting period and in 20 cm row spacing application in the second and third before cutting periods in the second year.Key words: Alfalfa, weed, row distance, yield

Test beam studies of the TRD prototype filled with different gas mixtures based on Xe, Kr, and Ar

Towards the end of LHC Run1, gas leaks were observed in some parts of the Transition Radiation Tracker (TRT) of ATLAS. Due to these leaks, primary Xenon based gas mixture was replaced with Argon based mixture in various parts. Test-beam studies with a dedicated Transition Radiation Detector (TRD) prototype were carried out in 2015 in order to understand transition radiation performance with mixtures based on Argon and Krypton. We present and discuss the results of these test-beam studies with different active gas compositions.Comment: 5 pages,12 figures, The 2nd International Conference on Particle Physics and Astrophysics (ICPPA-2016); Acknowledgments section correcte