Spin-other-orbit interaction in highly excited configurations with p and g electrons in outer shells

The matrix of the operator of the spin-other-orbit interaction energy is constructed for npn’g and np ⁵ n’g configurations. The matrix elements of this operator are calculated in the single-configuration approximation with wave functions in the LSJM representation and in the representation of uncoupled angular momenta using the known general formulas. The spin-other-orbit interaction is represented by three direct and three exchange radial Marvin spin interaction integrals.     

Determination of the surface area of loose metal deposits by impedance spectroscopy

The surface area and fractal dimensions of the surface of loose copper and zinc deposits obtained within 30 and 300 s at direct current sixfold exceeding limiting diffusion current on a smooth electrode were in situ determined by impedance spectroscopy. Impedance measurements were performed in 0.5 M Na₂SO₄ solution. A constant phase element taking into account the distribution of double-layer capacitance over the fractal surface of the electrode was used in the equivalent impedance scheme. Specific surface calculated with regard to the weight of the released metal slightly varied within 300 s (from 6.16 to 6.55 and from 7.12 to 5.89 m²/g for copper and zinc deposits, respectively). Fractal dimensions estimated by chronopotentiometry were given for comparison. Fractal dimensions found by two methods for loose copper and zinc deposits agree with each other; their values (2.19–2.75) testify that the surface of the deposits densely fills the space.     

Supply function equilibria for uniform price auction in oligopolistic markets

We consider game-theoretic models related to the supply function auction for electricity markets. We determine the set of supply function equilibria (SFE), introduced by Klemperer and Mayer (Econometrica 57:1243–1277, 1989), for a symmetric oligopoly with linear demand, fixed marginal cost and capacity constraint. This set depends on the maximum random shock of the demand function. We also study the best response dynamics and show that in general it does not converge to any SFE. We find out sufficient conditions for the convergence and conclude on the optimal parameters of the auction.     

A semiempirical calculation of the fine and Zeeman structure of 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">f</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">f</Emphasis> configurations of Ge I. Gyromagnetic ratios

The gyromagnetic ratios (g-factors) belong to the most important characteristics of atoms. For the 4p4f configuration of a germanium atom experimental values of g-factors are available only for four levels, while similar experimental data on the 4p5f configuration of Ge I are absent. Therefore, a theoretical study of the fine and Zeeman structures is topical for determining the gyromagnetic ratios. All the calculations are performed in the one-configuration approximation with the energy-operator matrix containing a maximum possible number of interactions, including magnetic: spin-orbit (own and other), spin-spin, and also orbitorbit interaction. The fine structure has been examined in three (LS, LK, and jK) approximations in order to establish the nature of coupling in the systems studied and the reliability of g-factors. Apart from the g-factors, in studying the Zeeman splitting, its specific features—the crossing and anticrossing fields of magnetic components— have been determined. A comparative analysis of g-factors was performed that showed that our results are in agreement with the available, albeit few in number, experimental data. At all stages, the corresponding energy-operator matrices were numerically diagonalized, i.e., all the results presented in the paper were obtained in the intermediate coupling scheme.     

Kinetics of ethylbenzene oxy-chemiluminescence in the presence of antioxidants from tissues of the marine invertebrate Eupentacta fraudatrix: Estimating the concentration and reactivity of the natural antioxidants

Extracts from tissues of the holothuria Eupentacta fraudatrix suppress the oxy-chemiluminescence of ethylbenzene in chlorobenzene initiated by azobisisobutyronitrile thermolysis and enhanced by energy transfer to 9,10-dibromoanthracene. The decrease of the chemiexcitation rate in the reaction between peroxyl radicals is caused by radical interception by the antioxidants contained in the extracts. The concentrations of the antioxidants in the extracts and the rate constants of their reactions with peroxyl radicals have been estimated from chemiluminescence kinetics.     

Zeeman splitting,its specific features,and gyromagnetic ratios for configurations 1<Emphasis Type="Italic">snf</Emphasis> (<Emphasis Type="Italic">n</Emphasis> = 4–10) of the helium atom

The fine structure parameters of configurations 1snf (n = 4–10) with new refined energy values are calculated by the semiempirical method. The emphasis is on the study of the Zeeman structure in order to determine the gyromagnetic ratios of all four the levels of the configuration from the splitting. For this purpose, the matrices of an energy operator with allowance for the interaction between the atom and a magnetic field were diagonalized for all possible values of quantum number M. For each configuration, 17 values of crossing fields of the Zeeman sublevels with ΔМ = ±1, ±2 and the regions of anticrossings with ΔМ = 0 were determined. It is remarkable that, because the levels are closely spaced, anticrossings are observed for each pair of levels in these systems. The regions of linearity of a magnetic field, which are different for different configurations, and the levels in them are established. The g-factors are calculated from the coefficients of an intermediate coupling scheme in a magnetic field that is guaranteed to be linear. They are compared with the analogous values in the absence of a field.     

Sharp Jackson inequality with a special modulus of continuity

Best integral approximations of B-splines by trigonometric polynomials are found. A sharp Jackson type inequality with a special modulus of continuity is obtained.     

Optimization of transmission network for homogeneous good market

We examine a model of a perfect competitive homogeneous good market with a network structure. Such a structure is typically important for energy resources: natural gas, oil and electricity. Local markets are connected by transmission lines with limited capacities and given cost functions for capacity increments. We consider the total welfare optimization problem and provide a method that determines optimal investments in the transmission system expansion for some types of the networks. In particular, we study the case where the market is divided into two submarkets with binding transmission line flow constraints between the submarkets. We obtain efficient algorithms for determination of the transmission systems optimal expansion. We conclude with the impact of the results and the outlook to future studies.     

Specific features of Zeeman structure of configurations 2p55g of Ne I and 3p55g of Ar I

The energies of Zeeman sublevels of the 2p ⁵5g configuration of the neon atom and the 3p ⁵5g configuration of the argon atom are calculated for different values of the magnetic quantum number M (mainly for M = 0, ±1, and ±2) and magnetic field strength that vary in the range of 0–100 kOe. Values of the fields of crossings (ΔM = ±1 and ±2) and anticrossings (ΔM = 0) of magnetic components are determined. The regions of the strong nonlinearity of the dependence of Zeeman sublevel energies on the magnetic field strength are revealed. The gyromagnetic ratios are determined from the level splitting in the linear region (H ∼ 0.05 Oe).