Vol 52 Iss. 3

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

The arithmetic-geometric mean B (a, B) is the general limit of sequences defined by recurrence relations...

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

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

To obtain some estimates of the coefficients of regular and single-leaf functions in a circle, we use the Grunsky condition: for a single-leaf function in a circle that is regular in it, it is necessary and sufficient that the inequality be fulfilled...

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

The study of the stress state in the ceilings and the related issue of determining their durable dimensions are still relevant in the mining industry. As is known, the stability of the ceiling is determined by the tensile stresses that occur in it, the greatest value of which is achieved on the production circuit. The magnitude of these stresses depends on the thickness of the ceiling, on the elastic properties of the roofing rocks, on the depth of the excavation, and other reasons...

When a charge explodes on any solid deformable medium for the purpose of compaction, formation of depressions or destruction, intuitively care is taken to ensure significant amounts 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. Tangential stresses during the free explosion of a charge on a surface are considered significantly less than normal, 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, with symmetry, they should be zero.

Preparatory mining operations are usually affected by pressure pressure caused by cleaning operations. To solve a number of practical issues, 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 sewage treatment plant on the stress distribution in the vicinity of a square-shaped mine with a smooth contour was studied by A. S. Kosmodamiansky. In practice, however, they come in various shapes with smooth and uneven contours.

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

To establish the relationship between deformations and stresses of a viscoelastic body based on its statistical microuniformity , a system of equations was constructed...

When a body moves in a gas at high supersonic speed, the gas located in the area between the surface of the body and the shock wave heats up to a temperature of several thousand degrees. At such a temperature, the flow parameters can be significantly affected by the heat exchange of radiation between the gas particles, as well as between the gas and the surface of the streamlined body. The heat emission of the gas in the shock layer leads to a decrease in its temperature and an increase in density.

Solving problems related to the study of kinematics, dynamics, and energy of free, non-flooded liquid jets is fraught with a number of specific difficulties. These jets differ from many other types of motion of a continuous medium by the presence of a free surface, the shape of which changes over time according to some unknown law.

Consider a horizontal, fairly wide channel; the influence of vertical walls can be ignored. Then we can assume that there is a movement of a two-component medium between two parallel horizontal infinite planes. The weight of the gas will be neglected, and the weight of the particles will be taken into account...

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

Let us consider elastic transverse (bending) free vibrations of a plate having the shape of a circular ring, pinched 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, there are errors in the manufacture of crusher assemblies, and during its operation, the cone and bowl linings wear out unevenly. As a result, the cone and the bowl of the crusher cease to be geometrically strictly round. The question arises about the impact of such a violation of the shapes of the crusher units on its operating mode.

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

Let us consider the problem of forced symmetrical oscillations of a thin hemisphere of radius R with a mass of M, rigidly fixed along the equator, under the influence of a normal load of constant surface density R. The front of the load wave propagates at a constant velocity ѵ...

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 bases, the so-called extraneous ones. At the same time, constant, or rather, slowly changing deviations or deviations 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 this solution are chosen. It is natural to expect that, while maintaining the desired solution in the expansion series, even the 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 intake, to find the kinetic energy of falling pieces of ore, the possible degree of crushing of the material during bypass, and to solve some other issues, it is necessary to know the kinematics of the movement of a single piece of ore in the ore intake.

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 single-digit displacements, but at its individual sections.

In the works, the dynamic constants of displacement A_g, velocity B_g, acceleration C_g, and kinetic power D_g are used as criteria for choosing the law of motion.These dynamic constants are introduced for the run-up period C_g1 and D_g1 of the run-out C_g2, and D_g2 and at the end of the forced displacement interval A_g1, B_g3, C_g3, D_g3. Additionally, dynamic constants (A_g and B_g1) are introduced in the range of movement of the driven link from 0 to Ymax, and the constant Bg1 is introduced in the range of movement from U_max to Y.