[en] The possible existence of quantum copies of classical soliton solutions is discussed, which don't exist when the effective Planck contant of the theory γ tends to zero. The analytic results concerning the shape functions, masses and stability properties of such escitations are given for φ⁴-kink theory

[en] This article is the first part of the work where the variant of defining such notations of the classical stochastic analysis as stochastic integral, random process, stochastic partial differential equation is considered for the case of Grassman's variables is some particular situation. Analogues of stochastic integral and random process are studied in the first part

[en] Odd and even Kahlerian structures on the supermanifolds, associated with tangent bundles of Kahlerian manifolds are constructed. Mechanics, that are bi-Hamiltonian with respect to the corresponding Poisson brackets are found. They define Killing vectors of the Kahlerian structures. On these supermanifolds operator Δ of the Batalin-Vilkovsky quantization method is globally defined. It corresponds to the divergency of the basis manifold

[en] For a six-dimensional model with the matter represented by a quantized scalar field the time-dependent isotropic perturbations of the internal space S² are investigated. Within the frames of the local vacuum corrections 'partial summation' the exact equation for the multidimensional Universe proper frequences is obtained, whose solvability is proved numerically. Some general properties of the spectrum and the details concerned with the vacuum nonlocality are discussed. The spontaneous compactification is found to be unstable independently of the nonminimal coupling constant values. The direct calculations confirm the invalidity of the weak non-stationary approximation used before, so we still have no one example of a semiclassically stable compactification

[en] The statistical mechanics and thermodynamics of two-dimensional system in thin-film superconductor is constructed. The long-range vortex interaction is taken into account in the framework of cycle approximation well known from the plasma theory

[en] Generalization of the Cauchy-Kovalevskaya theoreme is obtained for non-linear evolution equations with (1.1)-supersymmetric time. This theoreme provides for the existence and uniqueness of the solution for a wide group of superanalytic functions. A generalization for the case of Carthan technique is also obtained, using which the problem of equation system investigation in specific derivatives is transformed into the problem of finding the sequence of integral supermultiplicities of lower dimensions using a sequence of integrations based on the Cauchy-Kovalevskaya theoreme. 15 refs

[en] The interrelations between Calogero quantum problem and Knizhnik-Zamolodchikov equation are described following Matsuo, Cherednik, Felder and the author. As the basic tool of the considerations the Dunkl operator is used. The generalizations related to arbitrary Coxeter group and the applications to the Hadamard problem about the hyperboloc equations with the Huygens principle are discussed

[en] We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the N=2 superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner construction in terms of simple currents and introduce the so-called extended Poincare polynomial. We finally comment on the various equivalence arising between models of this class, which can be expressed as level rank dualities

[en] The spaces of Dotsenko-Fateev integrals are investigated. The structure of integral formulas is illustrated in terms of conformal field theory. Periods and dimensions of these spaces are calculated. A set of linear partial differential equations is derived

[en] To estimate path integral for a nonrelativistic particle with one degree of freedom moving in an arbitrary potential V(x) it is supposed to use the pass method, being an analog of the known pass method for finite-dimensional integrals, without transferring to the euclidean formulation of the theory. The notions of the functional Cauchy-Riemann conditions and the Cauchy theorem in a complex functional space are introduced. Given a contour of the most rapid descending the initial path integral is reduced to the one with the descending exponent. In principle, this result may serve as a base to construct a path integral measure. 9 refs