The special case of industrial investment which is the equipment rent by the enterprises of city building and economy is investigated. The necessity in the quantitative financial analysis of the equipment lease arises both for the owner of the equipment and for the lessee. For the owner it is important to correctly determine the amount of rent and financial efficiency of leasing the equipment. The lessee, if there is an alternative, must decide whether to lease the equipment or buy it. These problems can be solved on the basis of purely financial principles, and any method of their solution is based on the concept of the present value of financial flows. There are ratios, which allow you to determine the size of payments for the lease of equipment, the effectiveness of leasing equipment for the owner. The problem (to rent or buy equipment?), which is a special case of the problem of measuring efficiency, is solved. Numerical examples of solving the above problems are also given. Particular attention is paid to the analysis of the effect of risk and inflation on the rate of interest on which the discounting of cash flows, rent payments are made. The estimation of the market value of urban construction and economy enterprises with different types of risks taken into account has been carried out. The modification of I. Fisher's formula which allows, in conditions of uncertainty, using appropriate methods to predict the real rate of inflation (as well as using the model of capital market equilibrium - in particular beta coefficient) to determine the expected value of inflation rates, inflation risk premium has been substantiated.

This paper develops an approach to solving problems about the excitation of vibrations/vibrations by sources of waves in linear-viscous-elastic media modeling compacted concrete/building mixtures with depth-variable mechanical characteristics. An analysis of contact stresses and forces occurring under the oscillating stamp, the types of waves generated in the medium and on its surface, and the energy carried by each type of wave for different vibration sources are discussed. The previously described but unspecified for such problems, phenomena of resonance in deep layers of the medium of great thickness and the eigenmovement of the vibration stamps themselves are proposed. We present the technique of reducing the problem of dynamic interaction of finite-dimensional surface vibrosources with compacted linear-viscous-elastic medium to the possible ways of its solution. It is important to comprehensively investigate the peculiarities of vibrations of the stamp-elastic/linear-viscous-elastic medium system, but the integral equations arising here are a serious obstacle to research. Attempts to circumvent these difficulties give rise to a number of approximate, "engineering" approaches, within which the response of the medium (compacted by the vibrating field of the concrete/concrete mixture) is modeled by elastic and viscoelastic (damping) links with some "attached mass". The characteristics of elastic elements and the value of the attached mass are selected, as a rule, from experimental data. The oscillations of the finite-dimensional system resulting from this approach are determined by the usual theoretical methods of mechanics. Such an approach is especially widely used in construction calculations. It gives the possibility to determine the static settlement of structures with a sufficient accuracy and provides satisfactory results at a certain, fixed frequency. When analyzing vibrations in a wide range of frequencies, the linear-viscous-elastic medium is substantially infinitely measurable system with its own resonances and complex dispersion properties, and therefore cannot be approximated by a finite set of springs. In order to identify the characteristic features of the dynamics of massive stamps on a linear viscoelastic basis in this paper we carried out: calculations using methods of solving integral equations; analysis of numerical results and identified qualitative effects.

Substantiated mathematical model for non-stationary thermoelastic deformed media during their laser processing by short waves pulses fields analysis is proposed . Precise analytical solutions of the thermal conductivity equations  which simulate the short laser pulses interaction and allow to further determine their components thermally stress-strain state of the processed materials, in particular, thin porous films, capillary-porous bodies are obtained. Two analysis methods were used: 1) traditional separating variables method (Fourier method), 2) non-Fourier analysis of the non-stationary thermal fields that described by the telegraphic equation known in the literature. The results obtained in this work can be used further to establish the thermo stress-strain state of materials interacting with short waves laser radiation pulses parameters. Such approach is used at the modern building process for the rising of the reliability, durability and strength of the metal construction elements.

In the study, an analysis of the dynamic model of construction cranes’ load lifting mechanism, proposed by professor Loveikyn V.S. and others, was carried out. In order to determine the dynamic loads in the elastic rope, a dynamic model is used, in which all sections of the shafts are considered rigid, and only the cable is elastic. Bringing the engine rotor masses, brake pulley, gears, drum and load to the rope branchers that are wound on the drum, allows the original complex multi-mass tech-nical system to be reduced to a simplified (two-mass) crane lifting mechanism dynamic model, which is comprehensively and in detail analyzed in transition-type modes (for example, in the start-up mode).  An established and substantiated criterion for the movement quality of the hoisting crane load mechanism, at which rope system dynamic stresses are minimized in the starting mode, as well as the dynamic coefficient for different ways of lifting the load: 1) “from the weight”; 2) “with a pick up”/ “from the base” − typical during cranes real work in cargo lifting/lowering operations (loading and unloading).  Classical variational calculus methods usage (Euler-Poisson equation) allows to determine the conditions, according to which the above-mentioned criterion for the movement quality of the load lifting mechanism can be implemented. The movements laws of the load cargo and the drive crane mechanism are also defined, as well as law of dynamic coefficient change in time, for which there is no oscillation nature of time dependence, and the specified time functions have a mono-tonically growing character over time. The results obtained in the work allow (when using mechatronic control systems for the cargo lifting process) prevent overloading of the crane rope system and possible emergency situations, which lead to breaks in the elastic elements of the load lifting mechanisms (i.e. ropes), and also clarify and improve the existing engineering methods of similar complex technical systems calculations in their real operation modes.