RIGIDITY DIAPHRAGM OF HIGH-RISE BUILDINGS WITH ASYMMETRICALLY POSITIONED DOORWAYS

To increase the strength of the stiffness diaphragm, the doorways are not arranged symmetrically in height, i.e. in staggered order. Thus, excessive flexibility of the diaphragm is partially eliminated. To perform the calculation of such an irregular system relative to the openings causes a certain difficulty and from that we have implemented an elementary calculation. The design scheme was considered as a multi-story frame, for the action of horizontal wind load and floor-by-floor two-span beams with variable cross-sections on hinged supports for the action of vertical loads. The tasks were solved by the force method and graphoanalytically. Methods for determining the bending stiffness of the diaphragm from various loads are considered.

A Gyrogeometric Mean in the Einstein Gyrogroup

In this paper, we define a gyrogeometric mean on the Einstein gyrovector space. It satisfies several properties one would expect for means. For example, it is permutation-invariant and left-translation invariant. It is already known that the Einstein gyrogroup is a gyrocommutative gyrogroup. We give an alternative proof which depends only on an elementary calculation.

METHODOLOGICAL PRINCIPLES OF EVALUATION OF INVESTMENT ATTRACTIVENESS OF THE ENTERPRISE

The purpose of the research is a complex of theoretical and applied provisions on the formation, evaluation, and improvement of the methodology of evaluation of the investment attractiveness of enterprises. Methodology. In the process of research, the following methods were used: methods of comparison, analysis and synthesis is used in determining the features of conceptual approaches to the concept of investment attractiveness of an enterprise and the formation of the author’s definition of this category; method of diagnostic evaluation is used in the evaluation of existing models for analysing the investment attractiveness of enterprises; method of expert evaluation is used for the building of flexible limits of levels of investment attractiveness of the enterprise; methods of system and structural analysis is used for developing the basic elements and the general structure of the model of interpretation of the method of graphical integration; the method of graphic integration is used within the construction of graphs of investment attractiveness of enterprises A and B. The aim of the study is to justify of the approach to create a model that can justify of the feasibility of investing and determine the factors and conditions of investment attractiveness of the enterprise for different participants of the investment process. The findings of the study. The results of the research suggested an improved definition of the concept of investment attractiveness of the enterprise, which took into account the following disadvantages of existing approaches to the present essence of the concept: the investment attractiveness of the enterprise is often associated with the system of financial and economic indicators of the activity of enterprise, while not taking into account also an important social and psychological factor, since the very name of the term “investment attractiveness of the enterprise” includes the social-psychological element in the form of the concept of “attractiveness”, which is widely used in economic literature; the subjective view of the potential investor on the fact that the object being considered for investing to satisfy the investor’s expectations regarding the economic or social effect is significant. This aspect is key in determining of concept of investment attractiveness of the enterprise, when choosing an investor of an enterprise to invest its capital for the purpose of investing; it is necessary to achieve consistency and symbiosis between the evaluation of financial and economic, socio-psychological, industrial, innovative, environmental and other factors, which in the complex form the investment attractiveness of the enterprise; using the expression “high level of profitability on investment with minimal risks” is partially incorrect in some definitions of the investment attractiveness of the enterprise since obtaining high profits involves a certain level of risk and each investor knows about this; the importance of increasing the investment attractiveness of the enterprise has the level of involvement of innovation in the activities of the enterprise in the frames of use of investment capital; the targeting of almost all definitions only on high financial and economic indicators, which, depending on the situation, are not always correct. A complex system of indicators for evaluation of the investment attractiveness of an enterprise is proposed, consisting of six groups of indicators (market position, property complex, profitability, financial stability, risks, innovative potential), each of which includes six coefficients determining the level of investment attractiveness for this group. The features and advantages of this system of indicators are: complexity and complementary to standard methods with indicators of the level of investment risk and innovative potential of enterprises; standardization of indicators; unidirectionality of indicators; Flexibility of the recommended limits for each coefficient. The method of graphical integration of the investment attractiveness of the enterprise, which has several advantages over other methods, proposed in the scientific literature, is offered because: it is a combination that includes the advantages of an integral method, as well as a market, and partially matrix method; it allows quantifying various aspects of economic activity of the enterprise by the elementary calculation of a certain number of coefficients; it does not require significant time to spend on the evaluation; it has a mathematical justification since the final indicators for comparing the investment attractiveness of several enterprises are calculated using the numerical integration method; it has the flexibility of determining the level of investment attractiveness of an enterprise by incorporating into the methodology in accordance with the socio-psychological component of the concept of investment attractiveness and the interests of the investor; gives a visual interpretation of the results of investment attractiveness assessment.

Storm-water treatment in oil-separators and sedimentation tanks at fuel stations

The article presents the techniques of wastewater treatment from the area of fuel stations. The types of separators and devices cooperating with them are described, including their choice in terms of the applicable regulations. For this purpose, an elementary calculation example was used.

On the significands of uniform random variables

For all α > 0 and real random variables X, we establish sharp bounds for the smallest and the largest deviation of αX from the logarithmic distribution also known as Benford's law. In the case of uniform X, the value of the smallest possible deviation is determined explicitly. Our elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford's law, at least approximately, whenever it has large spread.

Migration of Nanoparticles in Operating Media of Heat Exchange Systems

The paper presents a scheme of elementary calculation of thermophoresis of shaped nanoparticles (nanotubes, fullerenes, graphenes), based on the molecule direct paths model and the theorem on variation of momentum for the system: nanoparticle-molecule in λ-layer. It has been found that there is relation of thermophoresis dimensionless velocity and parameters of the task.

Unified Impact Theory for Velocity-Changing Effects and Speed Dependencies in Neutral Species Lineshapes

A dipole correlation function which incorporates velocity-changing (motional narrowing) effects and the effects of speed-dependent Lorentz relaxation rates into otherwise Voigt profile correlation functions is developed, based partly upon previous work by the author. For the first time simple closed expressions, which lend themselves to elementary calculation beginning only with the relevant parts of intermolecular interaction energies, are developed for the cubic time-dependent term within the exponent describing the decay of the correlation function. This term is of first order in perturber number density, as are the Lorentz parameters, and is complex, thereby allowing for narrowing, changing in shape and asymmetry in the line profile. “Soft” and “hard” collisions play no explicit role, though both are variously present for each line. Quartic time dependencies are also discussed, though they are thought to be negligible in nonhydrogen molecular spectroscopy. Finally, some comments are added about a relevant technique for hydrogen spectra.

DISTRIBUTION OF TWISTED KLOOSTERMAN SUMS MODULO PRIME POWERS

In this paper, we study Kloosterman sums twisted by multiplicative characters modulo a prime power. We show, by an elementary calculation, that these sums become equidistributed on the real line with respect to a suitable measure.