Vol 37 Iss. 3

A broad generalization of theta functions is given by the solution of the differential equation ...

The well-known Gulden theorem, which establishes the relation between the volume of a body formed by the rotation of a plane figure, the area of this figure, and the length of the circle circumscribed by its center of gravity, is a special case of a much more general statement.

The questions considered in the present paper are related to the method of D-partitions for investigating the distribution of roots of equations,Let us give the main known results related to the method of D-partitions. Let it be required to investigate the distribution of roots of some equation with respect to the imaginary axis of the root plane. Let us introduce two real parameters α and β into the equation, after which it will take the form ...

The creation of highly sensitive measuring equipment made it possible to determine small concentrations and fluxes of radioactive impurities in the atmosphere. Due to this, an important from a practical point of view, the task of determining the position and power of sources of impurity located underground, based on observations in the surface layer of the atmosphere has arisen. The solution to this problem must be based on a theory that explains the propagation of radioactive impurities in the two-layer earth-atmosphere medium.

In many studies it is necessary to have information on the distribution laws of the geometrical characteristics (size, shape, etc.) of the phenocrysts contained in a mass of solid matter. However, it is often not possible to measure directly the grains representing the inclusions, because their mechanical separation from the binding medium without significant damage is impossible (e.g., for electrocorundum). Meanwhile, it is possible to make an indirect judgment about the distribution of the geometrical parameter of the grain from the experimentally found distributions of some parameters of the plane cross sections of inclusions observed in the slip.

Determination of the sizes of inclusions and the function of their size distribution in the mineral volume is an important task for practice. Since in the vast majority of minerals containing inclusions are opaque, it is not possible to experimentally measure the sizes of inclusions. Usually the sizes of inclusions cross-sections are measured on the slip, and by the picture on the slip we have to judge about the true sizes of inclusions in the mineral and about the size distribution of inclusions.

Parameters determining the results of gravity concentration of finely crushed coals. Disclosure of minerals, yields and compositions of fractions, quality of the obtained concentrate depend on the degree of crushing. The finer the coal is crushed, the greater the disclosure of minerals during crushing, the greater the amount of pyrite and mineral impurities (or rich in their aggregates) are extracted from the coal, the better the quality of coal obtained by gravity concentration of the crushed mass.

The aim of the paper is to study the flowing of some algebraic curves by a plane potential fluid flow, as well as to find aeroplane-type profiles with a return point and to indicate the method of their construction.

According to Einstein's gravitational equation, in the absence of an electromagnetic field, the metric tensor gμν, is related to the mass tensor Tμν by the relation …

As is known, secondary electron emission is characterized by: 1) the secondary electron emission coefficient; 2) the energy distribution of secondary electrons.The energy spectrum of secondary electrons mainly consists of two parts: slow secondary electrons with energies 0-50 eV; inelastically and elastically scattered primary electrons.

Mica is an extensive group of minerals characterized by perfect {001} cleavage, i.e. the ability to easily split into very thin sheets with a flat surface parallel to the face of the third pinacoid. Muscovite and phlogopite have the most important industrial value. Mica have high electrical characteristics, incombustibility and great mechanical strength, they are also thermally and chemically stable, and are not very hygroscopic. Mica crystallize in a monoclinic system, approaching hexagonal . forms. Under the influence of mechanical effects mica deform, lose their properties and become unsuitable for industrial purposes, so, of course, the study of deformed mica is paid much attention.

Free fall of spherical particles in a viscous fluid has been studied by many researchers in connection with mineral processing, chemical technology, metallurgy, etc. By changing the diameters of balls, density and viscosity of the fluid, it was possible to trace the motion of particles in the region of small and large values of the Reynolds and Archimedes criteria, i.e. in laminar, transitional and turbulent regimes.

Suppose that there is a moving medium - a liquid or a gas - under conditions where the gas can be considered an incompressible liquid. In this medium there is a large number of small particles. The particles will be considered as approximate perfectly equal in weight and volume solid bodies having a spherical shape. The trajectories, velocities and accelerations of the particles are different from the motion of the medium at any point of space.