Kolmogorov and Linear Widths of Weighted Sobolev-Type Classes on a Finite Interval, II

AbstractLet I be a finite interval, r∈N and ρ(t)=dist{t, ∂I}, t∈I. Denote by Δs+Wrp, α, 0⩽α<∞, the class of functions x on I with the seminorm ‖x(r)ρα‖Lp⩽1 for which Δsτx, τ>0, is nonnegative on I. We obtain two-sided estimates of the Kolmogorov widths dn(Δs+Wrp, α)Lq and of the linear widths dn(Δs+Wrp, α)linLq, s=0, 1, …, r+1

Estimating mass of harvested Asian seabass Lates calcarifer from images

Total of 1072 Asian seabass or barramundi (Lates calcarifer) were harvested at two different locations in Queensland, Australia. Each fish was digitally photographed and weighed. A subsample of 200 images (100 from each location) were manually segmented to extract the fish-body area (S in cm2), excluding all fins. After scaling the segmented images to 1mm per pixel, the fish mass values (M in grams) were fitted by a single-factor model ( M=aS1.5 , a=0.1695 ) achieving the coefficient of determination (R2) and the Mean Absolute Relative Error (MARE) of R2=0.9819 and MARE=5.1% , respectively. A segmentation Convolutional Neural Network (CNN) was trained on the 200 hand-segmented images, and then applied to the rest of the available images. The CNN predicted fish-body areas were used to fit the mass-area estimation models: the single-factor model, M=aS1.5 , a=0.170 , R2=0.9819 , MARE=5.1% ; and the two-factor model, M=aSb , a=0.124 , b=0.155 , R2=0.9834 , MARE=4.5

Cyclic and Acyclic NN Bonds in Reactions with Some Alkenes and Dienes

© 2017 Wiley Periodicals, Inc., A Wiley Company.The kinetics of the Diels-Alder (DA) reactions of 4-phenyl-1,2,4-triazoline-3,5-dione 1, trans-diethyl azodicarboxylate 2, and tetracyanoethene 3 with 1,3-cyclohexadiene 4, cycloheptatriene 5, 1,3-cycloheptadiene 6, cyclooctatetraene 7, and 1,3-cyclooctadiene 8 in a range of temperatures and pressures has been studied. Values of the enthalpy, entropy, and volume of activation, as well as the enthalpy and volume of reaction have been obtained. Observed reaction rates of 5+1 and 7+1 have been compared with the known rate of norcaradiene 17 formation in the equilibrium 5⇌17, and that of bicyclo[4,2,0]-octa-2,4,7-triene 20 in the equilibrium 7⇌20. The kinetic data show that the rate of formation of 17 from 5 is much greater than the loss rate of dienophile 1 in reaction of 5+1. In contrast, the formation rate of tautomer 20 is less than the loss rate of dienophile 1 in reaction of 7+1. This reflects that the consecutive reaction of 5 → 17 (+1) → 15 is possible whereas the consecutive reaction of 7 → 20 (+1) → 22 does not occur as the only way

Treatment of petroleum-contaminated water resources: modern techniques

The article deals with the issue of petroleum-contaminated water resources. The authors have analyzed the dynamics of oil spills, including the world's largest ones, and claimed the issue to be global. The modern methods of mitigating oil spill effects have been studied, as well as the modern techniques of water resource treatment. The particular attention is paid to peat sorbent production, which is considered a promising trend of petroleum- contaminated water treatment