Vol 52 Iss. 3

On September 4, 1969, the oldest professor of the Leningrad Mining Institute, Doctor of Technical Sciences, head of the Department of Higher Mathematics Andrey Mitrofanovich Zhuravsky died.

The arithmetic-geometric mean B (a, b) is the common limit of sequences defined by recurrent relations. ...

The issues of calculating the coordinates of the points of the borehole axis and the accuracy of determining its spatial position are presented in the works of A. M. Zhuravsky and A. A. Krzhizhanovskaya.

Some geological formations with increased radioactivity, owing to the release of emanations in them, create emanation halos around themselves. The main mechanisms of dispersion in this case are diffusion and convection. The use of radioactive prospecting methods requires studying the concentration distribution in such halos. For the case of emanation propagation in unconsolidated sediments covering an infinite radioactive half-space, there are methods for calculating the concentration under the combined action of diffusion and convection and under their separate action. For local objects such as veins and beds extending beneath sediments, there exists only the theory of diffusion halos developed by Yu. P. Bulashevich.

To obtain some estimates of the coefficients of functions regular and univalent in the circle, let us use the Grunsky condition: for a function univalent in the circle and regular in it, it is necessary and sufficient that inequality (1) be satisfied for any sequence {xₙ} for which the series on the right-hand side of the inequality converges, and the coefficients aₘₙ are determined by the expansion...

Fluctuations in the characteristics of ore qualitative composition, which create significant difficulties in processing ores and, in particular, in choosing the optimal operating modes of beneficiation units, require special measures for averaging the qualitative composition of ores.

The study of the stress state in roof pillars and the related issue of determining their safe dimensions are still relevant in the mining industry. As is known, the stability of a roof pillar is determined by the tensile stresses arising in it, the greatest value of which is reached at the contour of the working. The magnitude of these stresses depends on the thickness of the roof pillar, on the elastic properties of the roof rocks, on the depth of the working, and on other factors."

When a charge is exploded on a solid deformable medium with the aim of compaction, the formation of depressions or destruction, care is intuitively taken to ensure significant values of vertical displacements or particle displacement velocities in the corresponding areas of the surface. Maximum displacements (or velocities) are expected in those areas of the boundary surface where the greatest compressive normal stresses are created. Shear stresses during free explosion of a charge on a surface are considered significantly less than normal ones, and they are often neglected. Horizontal displacements are also neglected, which naturally decrease away from the point of explosion according to the principle of radiation, and at the point of explosion, under symmetry, should be zero.

Preparatory mine workings are usually subjected to the action of support pressure caused by stoping operations. For solving a number of practical problems, a qualitative and quantitative assessment of this effect on the stress state of rocks near them is of great importance. For the first time, the effect of a stoping face on the stress distribution in the vicinity of a working of square shape with a smooth contour was studied by A. S. Kosmodamiansky. In practice, however, they occur in various shapes with smooth and irregular contours.

Let us introduce the necessary notation in connection with the formulation of the biharmonic problem for a circular sector...

To establish the relations between strains and stresses of a viscoelastic body based on its statistical micro-inhomogeneity, a system of equations was constructed...

During the motion of a body in a gas at a high supersonic speed, the gas located in the region between the surface of the body and the shock wave is heated to a temperature of several thousand degrees. At such a temperature, the flow parameters can be significantly affected by radiative heat exchange between the gas particles, as well as between the gas and the surface of the body in the flow. The radiative emission of the gas in the shock layer leads to a decrease in its temperature and an increase in density.

The solution of problems associated with the study of kinematics, dynamics, and energy of free, unsubmerged liquid jets is associated with a number of specific difficulties. These jets differ from many other types of motion of a continuous medium in the presence of a free surface, the shape of which changes with time according to some previously unknown law.

Let us consider a horizontal, fairly wide channel; the influence of the vertical walls can be neglected. Then we can assume that there is motion of a two-component medium between two parallel horizontal infinite planes. We shall neglect the weight of the gas, but take into account the weight of the particles. Considering the motion as steady, and taking into account the interaction between the components of the medium according to Stokes' law, we write the following differential equations of motion and continuity in vector form.

In nonlinear problems of mechanics, the method of small perturbations is widely used; it consists in finding solutions close to those already known. ...

Let us consider elastic transverse (bending) free vibrations of a plate in the shape of a circular ring, clamped along the inner contour of radius B, with a free outer contour of radius C. ...

In the theory of inertial cone crushers, the crushing cone and the bowl are considered round. However, in the manufacture of crusher assemblies there are errors, and during operation the linings of the cone and bowl wear unevenly. As a result, the cone and bowl of the crusher cease to be strictly geometrically round. The question arises of the effect of such a violation of the shapes of the crusher units on its operating mode.

A study of the regularities of mineral raw material averaging processes shows that the use of the apparatus of the theory of random functions is the most promising for research. The practical use of this apparatus has a number of features both in processing the initial information and in solving specific quality control tasks.

Let us consider the problem of forcedsymmetric vibrations of a thin hemisphere of radius R with a mass of M, rigidly fixed along the equator, under the action of a normal load of constant surface density P. The front of the load wave propagates at a constant velocity v. ...

The gyrotachometer is designed to measure the angular velocity of rotation of a movable base around one of the axes, which is called the input or measuring axis. The problem is reduced to solving a linear differential equation with constant coefficients. However, the gyrotachometer reacts to rotation around other axes of the base, the so-called extraneous ones. At the same time, constant, or rather, slowly changing deviations or drifts are observed, which cannot be explained in any way by the properties of a linear equation with constant coefficients.

The accuracy of the solutions obtained by any of the known approximate methods depends on how well the functions approximating the solution are chosen. It is natural to expect that, of even minimum number of terms of the series (and it is this case that is of the greatest interest for practical calculations), the approximate solution will differ insignificantly from the exact one if the approximating functions satisfy all boundary conditions. ...

To predict the places of greatest wear on the walls of the ore pass, to determine the kinetic energy of falling pieces of ore, the possible degree of crushing of the material during transfer, and to solve some other problems, it is necessary to know the kinematics of the movement of an individual piece of ore in the ore pass.

The law of motion of the driven link of the mechanism should be chosen based on the requirements for the operation of the mechanism: general (for lifting and lowering sections, displacement, speed and acceleration at the beginning and end of the interval correspond to the set values); due to the nature of the diagram of movement of the driven link and closure of the highest kinematic pair cam — roller; determining the type of functions of ideal movements, speeds and accelerations, as well as the technological load and its derivatives, not at the boundaries of the interval of displacements, but at its individual sections.

In the works, the dynamic constants of displacement Ag, velocity Bg, acceleration Cg, and kinetic power Dg are used as criteria when choosing the law of motion. These dynamic constants are introduced for the run-up period Cg1 and Dg1, the run-out Cg2 and Dg2, and at the end of the forced displacement interval Ag1, Bg3, Cg3, Dg3. Additionally, on the interval of displacement of the driven link from 0 to Ymax dynamic constants (Ag1, Bg1) are introduced, and on the interval of displacement from Ymax to Y, the constant Bga is introduced.