A new a posteriori error estimate for convection–reaction–diffusion problems

A new a posteriori error estimate is derived for the stationary convection–reaction–diffusion equation. In order to estimate the approximation error in the usual energy norm, the underlying bilinear form is decomposed into a computable integral and two other terms which can be estimated from above using elementary tools of functional analysis. Two auxiliary parameter-functions are introduced to construct such a splitting and tune the resulting bound. If these functions are chosen in an optimal way, the exact energy norm of the error is recovered, which proves that the estimate is sharp. The presented methodology is completely independent of the numerical technique used to compute the approximate solution. In particular, it is applicable to approximations which fail to satisfy the Galerkin orthogonality, e.g. due to an inconsistent stabilization, flux limiting, low-order quadrature rules, round-off and iteration errors, etc. Moreover, the only constant that appears in the proposed error estimate is global and stems from the Friedrichs–Poincaré inequality. Numerical experiments illustrate the potential of the proposed error estimation technique.     

Nilpotent fusion categories

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central series of C. For fusion categories with commutative Grothendieck rings (e.g., braided fusion categories) we also introduce the lower central series. We study arithmetic and structural properties of nilpotent fusion categories, and apply our theory to modular categories and to semisimple Hopf algebras. In particular, we show that in the modular case the two central series are centralizers of each other in the sense of M. Müger.     

On well-posedness classes of locally bounded generalized entropy solutions of the Cauchy problem for quasilinear first-order equations

We study scalar conservation laws with power-growth restriction on the flux vector. For such equations, we find correctness classes for the Cauchy problem among locally bounded generalized entropy solutions. These classes are determined by some exponents of admissible growth with respect to space variables. We give examples showing that increasing the growth exponent leads to failure of the well-posedness. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 175–188, 2006.     

Comparison of direct sampling and emulsion analysis using a filter furnace for the determination of lead in crude oil by graphite furnace atomic absorption spectrometry

The determination of trace elements in crude oil is difficult due to the complex nature of the sample and the various different chemical forms in which the metals can occur. The advantage of graphite furnace atomic absorption spectrometry is that only a minimum of sample pretreatment is required. In this work two techniques have been compared to establish a fast and reliable method for lead determination in crude oil. In the first one the crude oil samples were weighed directly onto solid sampling (SS) platforms and introduced into the graphite tube for analysis. In the second one the samples were prepared as oil-in-water emulsions and analyzed in a filter furnace (FF). Twenty μL of a mixture of 0.5 mg L^− 1 Pd + 0.3 mg L^− 1 Mg + Triton X-100 has been used as the modifier, and calibration against aqueous solutions has been used for both methods. The sensitivity obtained with the FF was more than a factor of two better than that with SS; however, as a larger sample mass could be introduced in the latter case, so that the limits of detection for both techniques were 0.004 mg kg^− 1. Seven crude oil samples were analyzed using the two procedures, and all results were in agreement at a 95% confidence level using a paired Student's t-test. For validation purposes, three crude oil samples have been mineralized using an open-vessel acid digestion, and the results were in agreement with those found with direct sampling and with emulsion sampling using FF according to ANOVA test. Both methods are simple, fast and reliable, being appropriated for routine analysis; however, the direct method using SS technology should be preferred because of its simplicity, speed and commercial availability.     

Determination of Silicon Carbide Structures Layer Thicknesses using Reflection Spectra Frequency Analysis

Technical Physics - The paper introduces a method of determining thicknesses of single- and multi-layer silicon carbide structures using infrared reflection spectrum frequency analysis. Spectrum...     

Reactivity of 3-formyl- and 3-cyanothiochromones toward some N- and C-nucleophiles. Novel synthesis of 3-substituted 2-aminothiochromones

The reactions of 3-formylthiochromone with o-phenylenediamines, o-aminobenzenethiol, and indoles proceeded at the aldehyde group to give 3-(benzimidazol-2-yl)thiochromone, 3-(benzothiazol-2-yl)thiochromone, and 3-di(indol-3-yl)methylthiochromones, respectively. 3-Formyl- and 3-cyanothiochromones react with primary aromatic amines and phenylhydrazine to give the corresponding anils and phenylhydrazones of 3-formyl- and 2-amino-3-formylthiochromones. The reaction of 3-cyanochromones with o-phenylenediamines gave 2-amino-3-[(2-aminophenyl)iminomethyl]-4H-chromen-4-ones.     

Experimental measurement of the van der Waals binding energy of X-O2 clusters (X=Xe, CH3I, C3H6, C6H12)

Van der Waals binding energies for the X-O(2) complexes (X=Xe, CH(3)I, C(3)H(6), C(6)H(12)) are determined by analysis of experimental velocity map imaging data for O((3)P(2)) atoms arising from UV-photodissociation of the complex [A. V. Baklanov et al., J. Chem. Phys. 126, 124316 (2007)]. Several dissociation pathways have been observed, we focus on the channel corresponding to prompt dissociation of X-O(2) into X+2O((3)P) fragments, which is present for complexes of O(2) with all partners X. Our method is based on analysis of the kinetic energy of all three photofragments, where the O atom kinetic energy was directly measured in the experiment and the kinetic energy of the X partner was calculated using momentum conservation, along with the measured angular anisotropy for O atom recoil. We exploit the fact that the clusters are all T-shaped or nearly T-shaped, which we also confirm by ab initio calculations, along with knowledge of the transition dipole governing radiative absorption by the complex. The effect of partitioning the kinetic energy between translation along the X-O(2) and O-O coordinates on the angular anisotropy of the O atom recoil direction is discussed. Van der Waals binding energies of 110±20 cm(-1), 280±20 cm(-1), 135±30 cm(-1), and 585±20 cm(-1) are determined for Xe-O(2), CH(3)I-O(2), C(3)H(6)-O(2), and C(6)H(12)-O(2) clusters, respectively.