The plasma oscillations spectrum of a periodically inhomogeneous 2D electron system near the perforation threshold

The transformation of the spectrum of plasma oscillations with the zero reduced wave vector in the spatially modulated two-dimensional electron system moving to the regime of isolated quasi-one-dimensional electron channels is theoretically investigated. The results provide an explanation of the well-known experimental observations of the plasma resonance transformation when a two-dimensional electron system crosses the continuity violation threshold.     

Calculation of diatomic van der Waals systems inert gas atom-halogen type inert gas ion in the ground state

Interatomic potentials are calculated for the systems inert gas ion in the ground state-inert gas atom Ne⁺, Xe⁺-Ne, Ar, Kr, Xe, Fr. The calculation is performed by the effective pseudopotential method using the new form of the polarization interaction potential obtained by calculating the most important polarization diagrams of perturbation theory in the Thomas-Fermi approximation. The quasimolecular states of these van der Waals systems are calculated to refine the available data; some data are obtained for the first time. Translated from ZhurnalStrukturnoi Khimii, Vol. 39, No. 4, pp. 591–595, July–August, 1998     

<Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">∞</Emphasis></Subscript>-Structures on an Elliptic Curve

The main result of this paper is the proof of the transversal part of the homological mirror symmetry conjecture for an elliptic curve that states an equivalence of two A-categories: one is built using holomorphic vector bundles on an elliptic curve and another is a subcategory in the Fukaya A-category of a torus. The proof is based on the study of A-structures on the category of line bundles over an elliptic curve satisfying some natural restrictions (in particular, m₁ should be zero, m₂ should coincide with the usual composition). The key observation is that such a structure is uniquely determined up to equivalence by certain triple products.This work is partially supported by NSF grant     

Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. I

In this paper we construct and study the actions of certain deformations of the Lie algebra of Hamiltonians on the plane on the Chow groups (resp., cohomology) of the relative symmetric powers and the relative Jacobian of a family of curves . As one of the applications, we show that in the case of a single curve C this action induces a -form of a Lefschetz sl₂- action on the Chow groups of C ^[N]. Another application gives a new grading on the ring CH ₀(J) of 0-cycles on the Jacobian J of C (with respect to the Pontryagin product) and equips it with an action of the Lie algebra of vector fields on the line. We also define the groups of tautological classes in CH and in CH and prove for them analogs of the properties established in the case of the Jacobian of a single curve by Beauville in [5]. We show that our algebras of operators preserve the subrings of tautological cycles and act on them as some explicit differential operators. This work was partially supported by the NSF grant DMS-0601034.     

A modified projection-iterative method for solution of a singular integral equation with parameters and small nonlinearity

We suggest a modified version of the projection-iterative method of solving a singular integral equation with parameters and small nonlinearity. Kiev Polytechnic Institute, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 418–422, March, 1999.     

Photochemical behavior of levofloxacin

The effect of intermolecular proton transfer on the spectral properties of levofloxacin in the ground and excited electronic states was studied. The preferred direction of possible protolytic reactions induced by UV irradiation in this compound was studied. It was found that the proton transfer processes have a considerable effect on the capability of the compound to emit light and occur on the nanosecond time scale.     

Low-supersaturation nucleation kinetics in beryllium electrocrystallization

Classical electrocrystallization theory has been used to estimate the beryllium nucleation rate in electroplating on tungsten from molten chloride in the galvanostatic mode. Details of the process have been identified, and satisfactory agreement is obtained between the observed and calculated values.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 2, pp. 245–249, March–April, 1987.