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

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

Changes in permittivity and density of molecular liquids under high pressure

We collected and analyzed the density and permittivity of 57 nonpolar and dipolar molecular liquids at different temperatures (143 sets) and pressures (555 sets). No equation was found that could accurately predict the change to polar liquid permittivity by the change of its density in the range of the pressures and temperatures tested. Consequently, the influence of high hydrostatic pressure and temperature on liquid permittivity may be a more complicated process compared to density changes. The pressure and temperature coefficients of permittivity can be drastically larger than the pressure and temperature coefficients of density, indicating that pressure and particularly temperature significantly affect the structure of molecular liquids. These changes have less influence on the density change but can strongly affect the permittivity change. The clear relationship between the tangent and secant moduli of the permittivity curvatures under pressure for various molecular liquids at different temperatures was obtained, from which one can calculate the Tait equation coefficients from the experimental values of the pressure influence on the permittivity at ambient pressure. © 2014 American Chemical Society

Determination of the reaction acceleration effect at an elevated hydrostatic pressure

© 2017, Springer Science+Business Media, LLC. A method was proposed for the calculation of changes in the rate (k P /k P=0 ) and equilibrium constants (K P /K P=0 ) for chemical reactions under high hydrostatic pressure (10—20 kbar). The calculation based on the activation and reaction volume data makes it possible to select optimum conditions for slow and equilibrium chemical processes