Technical progress is impossible without the creation of new devices, the quantitative and qualitative indicators of which radically differ from the known ones, which in turn requires new technologies and materials. In the creation of new materials, rare and rare-earth metals are increasingly used, the reserves of which are very limited. Therefore, the development and implementation of new methods of mining such metals are a timely and urgent task.

Prospective methods of mining mineral deposits from volcanic gases are considered. The proposed model makes it possible to reveal the composition of volcanic gas, to experimentally prove its dynamic properties, to develop a model that allows one to trace the behavior of gas, on its basis to develop a principle scheme for extracting rare-earth elements (REE) and to present the hardwaretechnological scheme for obtaining REE from fumaroles (types of gas) in the form fumarolic metallurgical plant.

On the basis of a model system with heavy metal solutions in a liquid, the possibility of studying the behavior of gas particles is shown. Such a model system is converted to volcanic gas and allows interpretation of the results for a fumarolic metallurgical unit (FMU) by determining the critical dimensions of the elements of such an installation (dome sizes, parameters of connecting hoses).

The processes occurring during the geodetic excavation of underground excavations are characterized by the interaction of the elements of the geokhod with each other and with the geo-environment. The interaction process can be investigated in mathematical modeling, solving the problems of justifying the parameters of the drives and interacting forces, ensuring sufficient strength of the machine elements and the bearing capacity of the contour array. The proposed block-modular principles of constructing a mathematical model allow solving particular problems of the system and its individual elements. From the solution of particular problems, it is now necessary to proceed to the solution of the generalized model, using equivalent loads and reduced total moments (forces). The construction of a generalized model requires a number of assumptions, but its solution will reveal the interaction between the elements of the geokhod and the geo-environment, which is very relevant.

As an example, the solution of a particular problem is given-the determination of the value of the forces arising from the interaction of the blade of an external engine with the medium.

A list of assumptions is formulated that allow us to describe a general mathematical model of the interaction between the geo-environment and the geokhod, as well as the processes occurring during geodetic excavation of mine workings.

Addressing urban transport is a very timely matter, especially in the capital Hanoi and Ho Chi Minh City. In order to solve this problem, a solution has been proposed for the construction of overhead tram and subway lines. In fact, when constructing subway lines through historical sites, high population density, many surface structures, etc., the method of open construction is not feasible, it is necessary to use the method Underground construction. These areas are often weak soil, the physical parameters of the soil detrimental to the tunnel construction work; Such as small stickiness, small internal friction angle, high porosity, high permeability coefficient, high water saturation, short shear strength etc. These factors create complex geological conditions in Construction tunnel. With that in mind, the calculation of the selection of the tunnel casing structure is necessary, which is timely.

This paper provides a solution to the problem of stress state of multilayer lining supporting the tunnel of circular cross-section, constructed in a technologically heterogeneous array. The tunnel lining and surrounding soil mass are considered as elements of a united deformable system. 

For continuous rolling mills one of the most important technical issues is to configure the speed interrelated stands line. The basic law when setting speed rolling of the group of sequentially connected mill stands is the constancy of the volume of rolled metal S1*V1=S2*V2=S3*V3=...=SiVi . Setting the desired coherent frequencies of rotation of the rolls carried by the mill operator with the drive control specific panel. The electric drive system driven Converter (TP) – DC motor (D) with independent excitation allows operation in two zones (nн>n>n0), which gives the possibility of rapid adjustment of speed of rolling, in violation of the law of constancy of volume rolled. Construction properties of different groups of stands (roughing, intermediate, finishing) can have a considerable effect on the dynamic interaction and, as a consequence, loads on the interconnected Electromechanical systems stands. To assess the interaction of Electromechanical systems of interconnected mill stands it is recommended to first conduct a research on mathematical models to identify the most loaded units with their further study on a real mill using the methods of thermal and vibration field.