Solvolysis of 2-Amino-2-thiazoline Derivatives by Aliphatic Amino Alcohols

The opening of the thiazoline ring upon the action of amino alcohols was studied. The effects of the reagent ratio and structures of the heterocycles and amino alcohols on aminolysis were investigated. A new method was developed for the preparative synthesis of a series of N'-(hydroxyalkyl)-2-guanidinoalkanethiols.     

Reduction of Vector Boundary Value Problems on Riemann Surfaces to One-Dimensional Problems

Siberian Mathematical Journal - This article lays foundations for the theory of vector conjugation boundary value problems on a compact Riemann surface of arbitrary positive genus. The main...     

Linear instability of the state of rest for an incompressible polymer liquid upon injection from the cathode and heating from the top

The existence of partial solutions, increasing with time, of the linearized equations of a nonisothermal incompressible polymer liquid is established.     

New Method for the Synthesis of N'-Monoderivatives of 2(3)-Guanidinoalkanethiols by the Aminolysis of Heterocycles

A study of the solvolysis of heterocycles under the influence of amines uncovered a new ring-opening reaction of heterocyclic rings to give N'-monoderivatives of 2(3)-guanidinoalkanethiols. A new preparative method for N'-monoderivatives of 2(3)-guanidinoalkanethiols is developed.     

Magnetohydrodynamic Vortex Motion of an Incompressible Polymeric Fluid

Journal of Applied and Industrial Mathematics - Under consideration is some mathematical model describing magnetohydrodynamic motion of viscoelastic polymeric fluid in the cylindrical near-axial...     

Vortex Motion of an Incompressible Polymer Liquid in the Cylindrical Near-Axial Zone

The time-dependent mathematical model describing the vortex motion of an incompressible polymeric liquid is discussed. In the steady-state case certain particular solutions are found. In the case of the steady-state pressure along the axis of cylinder, a version of deriving this model for both fixed and free boundaries is given.     

Connection between holomorphic vector bundles and cohomology on a Riemann surface and conjugation boundary value problems

This paper studies interconnections between holomorphic vector bundles on compact Riemann surfaces and the solution of the homogeneous conjugation boundary value problem for analytic functions on the one hand, and cohomology and the solution of the inhomogeneous problem on the other. We establish that constructing the general solution to the homogeneous problem with arbitrary coefficients in the boundary conditions is equivalent to classifying holomorphic vector bundles. Solving the inhomogeneous problem is equivalent to checking the solvability of 1-cocycles with coefficients in the sheaf of sections of a bundle; in particular, the solvability conditions in the inhomogeneous problem determine obstructions to the solvability of 1-cocycles, i.e. the first cohomology group. Using this connection, we can apply the methods of boundary value problems to vector bundles. The results enable us to elucidate the role of boundary value problems in the general theory of Riemann surfaces.     

Inverse problem of hydrodynamics for doubly connected domain

We consider an inverse problem of hydrodynamics for flow past pair of aerofoils. We find a general form of its solution. The key part of problem’s solving is to determine numerical parameters defining flow domain and complex velocity in it up to conformal mapping (the parameters problem). The solvability of parameters problem is proved for various flow schemes. For that we essentially use the interpretation of the problem in terms of Riemann surface and the Riemann surfaces theory.     

Noise-induced coupling and phase transition in initially homogeneous bistable system

We show that a colored spatial noise induces a heterogeneous behavior and coupling of initially uncoupled single bistable units. A formal approximation reduces a non-Markovian stochastic process described by the initial set of equations into Markovian process in terms of Langevin equation, for which a simple piecewise linear emulation was used to represent the nonlinear deterministic force. It turned out that the coupling leads to a phase transition due to the noise-induced diffusive term. As an example, a typical bistable noisy system with symmetric double-well potential was studied.