Polynomial identities of bicommutative algebras,Lie and Jordan elements

ABSTRACT

An algebra with identities a(bc)?=?b(ac), (ab)c?=?(ac)b is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan.     

Erratum to: “Activated carbons of varied nature in recovery of gold”

Russian Journal of Applied Chemistry -     

The Kinetics of Indium Electroreduction from Chloride Solutions

The electroreduction of indium on indium electrode (99.98%) in perchlorate-containing chloride electrolytes is studied by the methods of linear sweep and cyclic voltammetry, impedance spectroscopy, and chronoamperometry. The indium electroreduction is limited by diffusion, the reaction rate constant is 1.3 10^–4 cm/s at the indium salt concentration of 0.1 M. The values of the apparent rate constant for the charge transfer stage found by linear sweep and cyclic voltammetry and also by impedance spectroscopy are 2.37 × 10^–3, 3.62 × 10^–3, 3.06 × 10^–3 cm/s, respectively. The values of diffusion coefficient of indium(III) ions calculated according to the Cottrell equation based on chronoamperametric measurements and from the Warburg impedance found by impedance spectroscopy are in good agreement. The presence of the Gerischer impedance is stated, which suggests that a homogeneous reaction of formation of indium chloride complexes proceeds and its mechanism is chemical-electrochemical.

     

Preparation and investigation of active carbons based on furfural copolymer

Active carbons were synthesized from a furfural copolymer using a polyester resin as an activator. The influence of the temperature of the thermal treatment of the carbon sorbents on the weights and ash contents of the obtained materials was established. The molecular structures of the carbons were studied by NMR spectroscopy.     

An Exact Order of Discrepancy of the Smolyak Grid and Some General Conclusions in the Theory of Numerical Integration

This paper examines the relationship between the degree of uniformity of distribution of grids, including Smolyak grids, with the intention of choosing weights to obtain efficient quadrature formulas.     

Approximative capabilities of “Smolyak type” computational aggregates with Dirichlet,Fejér and Valleé-Poussin kernels in the scale of Ul’yanov classes

In Ul’yanov classes, we compare computational aggregates constructed by the method of tensor products of functionals by means of trigonometric Fourier series.     

硫胺素-三维荧光法测定水中汞离子的研究

汞是一种具有显著积累效应和遗传毒性的重金属元素,对人体健康和生态环境危害极大。我国水环境中汞污染严重,开发快速、高效、经济的汞离子检测方法可以有效推动水环境中汞污染的源头治理。该研究创新性地提出利用硫胺素-三维荧光法来实现水环境中汞离子的检测。研究结果表明,硫胺素与汞离子发生氧化还原反应前后,其荧光峰的位置与数量发生了明显改变,可作为检测水中汞离子的特征性信号。此外,在利用该法检测水中汞离子时,硫胺素的浓度不宜过高,体系应保持碱性环境,反应温度与反应时间可由一级动力学模型来优化,以期降低检测成本,提高检测效率。在指定的检测条件（硫胺素浓度为10 μmol·L-1、pH为9.7、反应时间为120 min、温度为20 ℃）下,汞离子浓度的线性检测范围为4～15 μmol·L-1。硫胺素-三维荧光法与传统的水中汞离子的检测方法相比具有突出优势和良好的实际应用价值,可以有效助力水环境中汞污染的源头监管,极大提升环境执法效率。     

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Mañé action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of α.For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on α. We also show injectivity and stability for g and α in a generic class G including real analytic ones.For the nonlinear problem, we show rigidity for real analytic simple (g,α), rigidity for metrics in a given conformal class, and locally, near any (g,α)∈G. We also show that simple magnetic systems on two-dimensional manifolds are always rigid.