Methods of Text Analysis as University Subject: Cognitive and Discursive Aspect

The article explores the principles of studying the methods of text analysis at the university.В статье рассматриваются принципы изучения методов анализа текста в вузе

On the approximate conformal mapping of the unit disk on a simply connected domain

We present a method of constructing the analytic function realizing an approximate conformal mapping of the unit disk on an arbitrary simply connected domain with the given smooth parametrically defined boundary. The method is based on a new boundary parameterization. Solution of the problem is reduced to the Fredholm integral equation of the second kind. We present the examples of three ways to solve the integral equation. © 2014 Allerton Press, Inc

Reconstruction of the velocities and pressures for a viscous fluid in a hollow cylinder

We find the continuous velocities and pressures at all points of an incompressible viscous fluid flowing in a hollow cylinder from the given velocities at the points of some closed curves on the inner sides of the cylinder and the given pressures at two points on the inner sides of the cylinder. This solution can be named the interpolation solution. The solution is reduced to a succession of plane boundary problems for the elliptic differential equations. The method of solution is programmable and applicable for problems of piping, for example, for modelling a blood flow in a vessel with a fibrin on its inner surface. This method is illustrated by application to flow in a hollow circular cylinder with a rotation on the central level. The interpolation solution is the basis for the method of restoration of continuous velocities and pressures in the flow of an incompressible viscous fluid from the given velocities at a finite number of points on the inner surface of the cylinder and given pressures at two points on the same surface. © 2007 Elsevier Ltd. All rights reserved

The boundary value problems for thin coats

The boundary value problems for the coats of finite and infinite domain in the plane were discussed. The problems were applicable to the 'soft' elastic layers of a 'sandwich'. The conformal mapping was applied with the help of the analytic in the disk function on D. Analysis shows that the third problem with the additional data was solvable and had six-parameter set of solutions within the assumption

Elastic solutions for a pressurised tube with given exterior displacements

We find the particular solution of the following problem for an elastic tube: given the displacements at n+1 levels of the exterior surface and a constant pressure and the 'sliding condition' on the interior surface of the tube it should be possible to find the displacements at any point of the tube. The solution is reduced to a succession of plane boundary problems for the elliptic differential equations. Each boundary value problem is reduced to a system of linear equations. The method is programmable and applicable for problems of tubing. It is illustrated by application to a pressurised tube subjected to bending and compression. © 2004 Elsevier Ltd. All rights reserved

On 3-d analog of the second basic problem of the theory of elasticity for a cylindrical solid

We formulate and solve the 3-d analog of the second basic problem for a cylindrical elastic solid

The analogues of the basic problems of the theory of elasticity for the special 3-d strain in the plates

The analogues of the basic boundary problems of the theory of elasticity for the special three-dimensional strain in thin symmetric plates were formulated. The exact solution was obtained of the problems for the plate with the symmetric drop-like cut with cusp. The problems were found to be applicable to the coats of the plane unbounded domains with cuts

On 3-d strains in a thin coat of a plane domain

Three-dimensional strains in a thin coat of a plane domain was investigated. The problem for the coat of the unite disk was solved when the horizontal layer of the constant thickness is pressed so that the points of the boundary of the plane base of the layer and the points of its upper edge was displaced. The boundary value problem for the thin coat of a plane domain was formulated and solved

Some questions on the univalence of functions of the class Σ

In this paper we give an example of two convex functions in | ζ| > 1 whose arithmetic mean is nonconvex. We calculate the radius of convexity of the sum of two convex functions; it is equal to {Mathematical expression}. For functions F(ζ)=ζ+b1/ζ+..., where F′(ζ)=f(ζ)/ζ, if f(ζ) = ζ + a1/ζ+... is univalent |ζ| > 1, then the radius of univalence is the root of the equation 4E· (1/r)/K(1/r)+1/r2=3. © 1976 Plenum Publishing Corporation