Vol 43 Iss. 3

The solution of the general biharmonic problem by the method of G. A. Greenberg is as follows.

The arithmetic-geometric mean algorithm introduced by Gauss is a remarkable example of approximation of a multivalued transcendental function by means of an algebraic function. In Gauss's works published during his lifetime and in the remaining posthumous materials, almost no attention is paid to the convergence of the algorithm and the branching of its terms is not considered at all.

In 1954, in co-authorship with O. V. Sarmanov and R. E. Soloveichik, the author posed the following stochastic problem.

The W. Borchardt algorithm, which is a generalization of the arithmetic‑geometric mean algorithm, was first introduced by Borchardt and then studied by I. Hettner. In these works, the Borchardt mean was studied for real positive initial arguments. The study of the Borchardt mean for complex initial elements is devoted to the work of G. Genpert. The proof of convergence of the Borchardt algorithm is carried out by Genpert on the basis of geometric considerations. In the present paper we give an analytical proof of convergence of the Borchardt algorithm and consider cases of degeneracy of the algorithm.

In questions related to the approximate determination of a function, one encounters the problem of constructing an approximate expression of a function from its mean values given for a number of intervals. An example of this may be constructing the equation of a distribution curve or constructing the equation of a regression line of one of two random variables on the other. The same problem is encountered in determining the distribution of a mineral in a well on the basis of readings obtained from core analyses, and in a number of other sampling problems.

К. Begl formulates the definitions of continuity and directional derivative in the space Rn in such a way that they respectively have a unified general form for all n and coincide at n=1 with the corresponding definitions for functions of one variable. In addition to the concept of continuity, the concepts of derivative, integral, convergence, semicontinuity, and limit, expressed in a unified and general form, are introduced successively.

Let there be a function f(x), which is a realization of some stationary random function. It is required to find an approximate value of the integral ...

The paper considers the solution of the laminar boundary layer equations on a semi‑infinite body of revolution streamlined by a binary mixture of gases at zero angle of attack. In the flow and on the surface of the streamlined body a reaction of the type X₂ = 2X is possible. Basic equations and boundary conditions. Consider a high‑temperature boundary layer on a body of revolution with an axis having the direction of the velocity of the oncoming flow. The gas motion in this case is obviously axisymmetric and is completely determined by the flow pattern in the meridional plane.

Consider a flat laminar boundary layer in an incompressible fluid in the presence of a longitudinal pressure drop. We assume the physical characteristics of the fluid to be constant for all points of the flow field, and the flow parameters to be independent of time.

At the end of the XIX century researchers pointed out the internal instability of a free jet caused by capillary forces applied to its surface.

Over the last 20 years, new methods have been introduced in geodesy, allowing us to solve all the main problems of geodesy from the values characterizing the external gravitational field and the figure of the Earth's physical surface. Within the irregular and complex physical surface of the Earth, a smooth surface close to Listing's geoid, called the quasigeoid, is distinguished.

Seventy years since his birth and forty‑five years of scientific and teaching activity of the Head of the Department of Higher Mathematics of the Mining Institute, Doctor of Technical Sciences, Professor Andrei M. Zhuravsky were marked.