On solvability of homogeneous Riemann–Hilbert problem with discontinuities of coefficients and two-sided curling at infinity of a logarithmic order

We consider a homogeneous Riemann–Hilbert boundary-value problem for upper halfplane in the situation where its coefficients have countable set of discontinuities of jump type and two-side curling at infinity of a logarithmic order. We obtain general solution and describe completely its solvability in a special class of functions for the case where the index of the problem has power singularity of a logarithmic order.     

Current density distribution at the periphery of submicron probes

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 3–9, November–December, 1992.     

Resonance chiral theory for low-energy ππ scattering

The scattering of a pion on a pion in the energy region $\sqrt s $ ≤1 GeV is successfully described on the basis of pole diagrams featuring spinless, spin-1, and spin-2 intermediate particles, provided that the properties of these particles and of their interactions are deduced from the basic principles of QCD and from the requirements of chiral theory.     

On validity of the weak interaction renormalizable theory of Tanikawa-Watanabe

It is shown that the weak interaction renormalizable theory of Tanikawa-Watanabe, which in its simple formulation predicts essential effects in (e^±p) scattering, contradicts the experimental data on elastic scattering of electrons and positrons on protons if the existing concepts on the role of the two-photon exchange in these processes are valid.     

Sorption of cesium ions by nanostructured calcium aluminosilicates

Data on the sorption properties of synthetic calcium aluminosilicates (CASes) with Al: Si ratios of 2: 2, 2: 6, and 2: 10, fabricated within the multicomponent system CaCl₂–AlCl₃–KОН–SiO₂–H₂O, are presented. Isotherms of the sorption of Cs⁺ ions from aqueous solutions with Cs⁺ concentrations of 0.2 to 6.0 mmol L^–1 are analyzed. The CAS maximum sorption capacity and the Langmuir constants are determined. Kinetic data are obtained, and the energy of cation-exchange activation upon the sorption of Cs⁺ ions is determined. The effect of a salt background (1% KCl + 6% NaCl) has on the values of distribution coefficient (K_d) and the degree of Cs⁺ ion removal is established.     

EVOLUTION OF A SHORT COMPRESSION PULSE IN A HETEROGENEOUS ELASTOPLASTIC MEDIUM

Journal of Applied Mechanics and Technical Physics - The propagation of a short compression pulse in heterogeneous targets containing ceramic inclusions of different sizes is studied numerically....     

Mapping of a half-plane onto a polygon with infinitely many vertices

In this paper we generalize the Schwarz—Christoffel formula for a conformal mapping of a half-plane onto a certain polygon with infinitely many vertices. We assume that the interior angles of the polygon (at unknown vertices) and the points of the real axis that are images of unknown vertices under the mentioned mapping are given.     

The influence of the nature of phosphine ligand on palladium catalysts for cross-coupling of weakly nucleophilic potassium pentafluorophenyltrifluoroborate with ArHal and PhCH2Hal (Hal=Br,Cl)

The influence of the ligand nature on catalytic activity of palladium catalysts for cross-coupling of weakly nucleophilic potassium pentafluorophenyltrifluoroborate, which imitates the behavior of electron-deficient organoboron reagents, with aryl halides, ArHal (Hal=Br, Cl) was studied. The activity of the catalysts generated in situ from Pd(OAc)₂ and appropriate phosphorous containing ligands and the reaction selectivity was found to depend on the nature of bulky phosphines used as ligands. As a result, conditions for involving the electron-deficient organoboron reagent—potassium pentafluorophenyltrifluoroborate—in the palladium-catalyzed cross-coupling with aryl bromides and aryl chlorides were identified. It was demonstrated that the chosen conditions are appropriate for the reaction of K[C₆F₅BF₃] with benzyl chloride and benzyl bromide deriving pentafluorophenylarylmethanes, C₆F₅CH₂Ar.