<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     

Lag of the front of the polymer behind the carrier liquid with the filtration of a polymer through a porous medium

The fact of the lag of the front of a polymer solution behind the carrying water has been established experimentally. A study has been made of the dependence of the size of this zone on the length of a linear homogeneous porous sample, on the volume of the liquid pumped through it, and on the gradients of the thermodynamic pressure.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 149–151, July–August, 1976.     

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.     

Hermite transformation and the expansion of normalized convolution

The article focuses on the computation of the coefficients of infinite-dimensional Edgeworth expansion. A method based on the Hermite transformation leads to explicit expressions for these coefficients in some cases.     

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     

Anomalous Bloch oscillations in arrays of coupled waveguides

Anomalous Bloch oscillations in arrays of coupled waveguides have been investigated using two different approaches: multiple scattering formalism and coupled-mode model. Both approaches are shown to yield identical results. Formulas for the parameters of the coupled-mode model are derived. An analytical expression for the optical beam path is obtained, and the condition for the existence of anomalous Bloch oscillations is found.