Type Of Functional Dependence Research Articles

ДОСЛІДЖЕННЯ ДЕФОРМАЦІЙНИХ ВЛАСТИВОСТЕЙ ОХОРОННИХ СПОРУД ІЗ ПОДРІБНЕНОЇ ПОРОДИ В УМОВАХ СТАТИЧНОГО НАВАНТАЖЕННЯ

Purpose. Investigate the deformation properties of structures made of ground rock under static load conditions to preserve the integrity of the side rocks in the produced space of the coal massif and the operational state of the preparatory mine workings along the length of the excavation site. Methodology. In laboratory conditions, experimental samples of protective structures made of ground rock of heterogeneous granulometric composition were subjected to static loading under conditions of uniaxial and compression compression. Results. It was experimentally established that under the conditions of uniaxial compression of protective structures made of ground rock with the possibility of its lateral expansion, the effect of forming the bearing capacity is manifested in the relative change of the volume of the embedded material in the range of values , when, after increasing the relative deformation, the resistance reaches the maximum compaction of the rock . In such conditions, it is necessary to ensure the stability of the bearing pillar of the embedded material. During compressive compression of crushed rock, such an effect is achieved in conditions where the relative change in the volume of the embedded material is . After maximum compaction , the resistance of protective structures increases. Scientific novelty. The type of functional dependence between the relative deformation is established protective structures made of crushed rock and relative volume of the embedded material under static load under uniaxial and compressive compression, which allows to evaluate the bearing capacity of flexible supports. Practical significance. In order to assess the stability of protective structures made of crushed rock, which are in different compression conditions during the unloading of coal massif, it is necessary to take into account the compaction coefficient of the original material and the longitudinal deformation of the support under load. Keywords: coal massif, guard building, ground rock, uniaxial compression, compressive compression.

STUDY OF DEFORMATION PROPERTIES OF PROTECTIVE STRUCTURES OF PREPARATORY MINING WORKS

Purpose. To study the stability of the security structures of the preparatory mine roadways of steep seams while unloading the coal-rock massif to prevent the collapse of side rocks in the excavation areas of the coal mine and create safe working conditions for miners. Method. In order to achieve the aim of the research, the study of the stability of security structures was carried out at the laboratory of mountain pressure by using experimental samples in the form of whole coal and structures consisted of crushed rock, which were subjected to uniaxial compression. Results. Under the conditions of uniaxial compression of whole coal or constructions consisted of crushed rock, with the ratio of length to width a/b= (1-2) and an increase in the cross-sectional area S (m2) of the experimental samples, a relative change of their volume δV was observed. For whole coal, the steady state is ensured by the relative volume change δV ≤ 0,1. Beyond the set value of δV, the whole coals lose their stability and collapse, which results in the collapse of the side rocks. For the crushed rock structures, with an increase in the cross-sectional area of the compressible specimens, the relative volume change decreases from δV = 0,2 to δV = 0,35. At the same time, the crushed rock is compacted in the whole volume of the used material, the bearing capacity of protective structures is increased, which enables limiting the movement of lateral rocks and ensures their integrity. Scientific novelty Within the limits of the deformation resource of protective structures consisting of crushed rock of different granulometric composition, with their uniaxial compression, a type of functional dependence was established, which enables us to estimate the relative change in the volume of flexible supports from stiffness, which is necessary for assessing their bearing capacity. Practical significance. In order to create safe working conditions for miners in the excavation areas of a deep coal mine and prevent the collapse of side rocks in the coal massif, it is advisable to use flexible protective structures for the protection of preparatory coal mine roadways, when the ratio of their linear dimensions corresponds to the ratio of length to width of a/b>(1-2).

Determination of the residual life of an automobile engine according

The article discusses a method for determining the residual life of an automobile engine by the parameters of pressure in the lubrication system and oil consumption for carbon monoxide. The obtained experimental statistical data of public joint stock company "KAMAZ" on wear and macrogeometry of the bearing parts of the crankshaft of KAMAZ engines and parts of the cylinder piston group are described. According to experimental data, graphs of changes in structural and diagnostic parameters from the wear of engine parts are constructed. The methods of mathematical statistics (the least squares method, the method of assessing the adequacy of the model according to the Fisher criterion) were used to approximate various types of functional dependencies. The reliability of functional dependences of forecasting the residual life of automotive engines has been confirmed. Keywords: reliability, failure rate, structural parameter, diagnostic parameter, prediction of residual engine life, experimental data, exponential dependence

МОДЕЛЮВАННЯ ТА ОПТИМІЗАЦІЯ ПРОЦЕСУ ОЧИЩЕННЯ ПОВІТРЯ ВІД ЗЕРНОВОГО ПИЛУ ЗАСОБАМИ ОБЧИСЛЮВАЛЬНОЇ ГІДРОГАЗОДИНАМІКИ

The article is dedicated to the development of generalized methods of calculation, modeling and optimization of the cyclones’ parameters that are used to clean the air from the grain dust. The basis of the developed methods is the usage of computational hydraulic gas dynamics, in particular the SOLIDWORKS software package and the integrated CFD-package SOLIDWORKS Flow Simulation, as well as the principles of theory of similarity and dimensions. The deposition efficiency coefficient was chosen as the optimization criterion that can be calculated as the ratio of the mass of deposited particles to the total mass of grain dust particles entering the working volume of the cyclone. By means of SOLIDWORKS, a parametrized solid model of cyclone with the necessary elements of adaptation for further study of gas-dynamic processes was created. The dependence of the deposition efficiency on various parameters that can be optimized, in particular, on the pressure at the inlet and outlet nozzles of the cyclone was studied; volumetric flow rate of air to be purified; design dimensions of the working chamber of the cyclone etc. The usage of the simulation methods allowed to obtain an extended database of optimization parameters and values of the objective function that correspond to them. The generalization of the obtained data set in the form of dimensionless criteria was enabled by the analysis of the dimensions of the quantities that affect the deposition efficiency. Using the basics of similarity theory, the type of functional dependence between similarity criteria was established. The constant parameters of the mentioned power function are determined using a two-dimensional approximation using a software package for mathematical calculations – Mathcad 15. The obtained mathematical model allows to select the optimal operating modes (volumetric air flow, inlet and outlet pressures of cyclone etc.) depending on the design and the size of the cyclone that allows to maximize the efficiency of grain dust deposition.

Influence of external factors on the process of hydrates development in laboratory conditions

The object of research is the influence of various factors on the process of synthesis of propane hydrate in laboratory conditions. It is known that a synthesized gas hydrate can contain a significant amount of ice, which reduces its gas content. The quality of the hydrate is affected by: gas pressure, water temperature, time of the experiment and the concentration of surfactants.To study the complex effect of these factors on the quality of the hydrate obtained, an experimental setup is developed. After synthesis of the gas hydrate, its gas content is determined using a specially designed stand. In the course of the research, various measuring instruments were used: manometers, thermometers, measuring utensils, electronic scales, etc., which made it possible to obtain reliable information on the thermophysical characteristics of the synthesis and dissociation of gas hydrate.As a result of the multivariate experiment, an array of data for analysis by mathematical statistics methods is obtained. Correlation coefficients are determined and found that the dominant factors are the gas pressure and concentration of surfactants. The water temperature should be within the operating range of 1–5 °C. The formation time of the hydrate in the bubbling regime within 0.5–5 h also does not significantly affect the quality of the obtained hydrate. For all factors, regression dependencies and graphs are constructed. It is established that for standard regression dependencies (linear, exponential, logarithmic and polynomial), the coefficients of multiple correlation are in the range 0.19–0.46. This means that the standard regression relationships do not allow to take into account all the features of the obtained results. Therefore, the selection of the optimal dependence is carried out by the method of variation of the coefficients and types of functional dependencies and an approximate formula is obtained for determining the predicted gas content of the hydrate.The research results show that due to the complex consideration of various factors, it is possible to determine the range of optimum values of pressure, temperature and concentration of surfactants, which makes it possible to quickly produce a high-quality hydrate.

Rationally Functional Dependence

Two different types of functional dependencies are compared: dependencies that are functional due to the laws of nature and dependencies that are functional if all involved agents behave rationally. The first type of dependencies was axiomatized by Armstrong. This article gives a formal definition of the second type of functional dependencies in terms of strategic games and describes a sound and complete axiomatization of their properties. The axiomatization is significantly different from the Armstrong’s axioms.

Mодель прогноза коэффициентов накопления137Cs в растениях

The forecasting model of the concentration ratio (CR) of 137Cs in the plants taking into consideration organic carbon, pH, mobile and total content of potassium in soil has been developed on the basis of the radioecological investigations in the valleys of the Resseta and Vytebet rivers. The type of functional dependence of CR from soil characteristics can be used for an estimation of the content of radionuclides in various species and productive parts of plants.

Determination of Functional Dependence Between Parameters of Lattice in Ferroelastics and Multiaxial Ferroelectrics

The method of determination of functional dependence between parameters of crystalline lattice in ferroelastics and multiaxial ferroelectrics based on the condition of orientation matching of domains is offered. The analytical type of functional dependence has been found for phase transitions m3m-F4mm and 4/m-F2/m. We have compared theoretical results with experimental data for BaTiO3 and BiVO4.

Activities and immiscibility in the system Cu-Rh

The thermodynamic activity of rhodium in solid Cu-Rh alloys is measured by the electromotive force method in the temperature range from 1050 to 1325 K with a solid-state cell: Rh, Cu 1 Cu2O//(Y2O3)ZrO2//Cu-Rh 1 Cu2O, Rh The activity of copper and the Gibbs energy, enthalpy, and entropy of mixing of the solid solution are derived. Activities exhibit large positive deviation from Raoult’s law. The mixing properties can be represented by a pseudo-subregular solution model in which excess entropy has the same type of functional dependence on composition as the enthalpy of mixing: DH 5 XRh(1 2 XRh)[41,340 1 12,670 XRh] J mol21 DSE 5 XRh(1 2 XRh)[15.46 1 4.72 XRh] J mol21 K21 The results predict a solid-state miscibility gap with Tc 5 1408 (65) K at XRh 5 0.59 (60.02). The computed critical temperature is 15 K lower than that reported in the literature. The coherent spinodal, calculated using Cahn’s model, is characterized by T8c 5 983 (65) K and X8Rh 5 0.43 (60.02). The large difference between the coherent and chemical spinodal is caused by the relatively large difference in lattice parameters of Cu and Rh and high Young’s modulus of the alloy. The positive enthalpy of mixing obtained in this study contrasts with the negative values predicted by Miedema’s model. Thermodynamic properties of liquid alloys are estimated from the data for solid alloys obtained in this study and the approximate location of the liquidus available in the literature.

Thermodynamic properties and phase equilibria for Pt-Rh alloys

The activity of rhodium in solid Pt-Rh alloys is measured in the temperature range from 900 to 1300 K using the solid-state cell $$Pt - Rh,Rh + Rh_2 O_3 /(Y_2 O_3 )ZrO_2 /Pt_{1 - x} Rh_x + Rh_2 O_3 ,Pt - Rh$$ The activity of platinum and the free energy, enthalpy, and entropy of mixing are derived. Activities exhibit moderate negative deviation from Raoult’s law. The mixing properties can be represented by a pseudosubregular solution model in which excess entropy has the same type of functional dependence on composition as the enthalpy of mixing, $$\begin{gathered} \Delta H = X_{Rh} (1 - X_{Rh} )[ - 10,970 + 45X_{Rh} ] {J \mathord{\left/ {\vphantom {J {mol}}} \right. \kern-\nulldelimiterspace} {mol}} \hfill \\ \Delta S^E = X_{Rh} (1 - X_{Rh} )[ - 3.80 + 1.55 \times 10^{ - 2} X_{Rh} ] {J \mathord{\left/ {\vphantom {J {mol}}} \right. \kern-\nulldelimiterspace} {mol}} \cdot K \hfill \\ \end{gathered} $$ The negative enthalpy of mixing obtained in this study is in qualitative agreement with predictions of semiempirical models of Miedema and co-workers and Colinet et al. The results of this study do not support the solid-state miscibility gap suggested in the literature, but are consistent with liquidus data within experimental uncertainty limits.

Estimation of the through porosity of cloth made of chemical fibres in a blend with natural fibres and its correlation with air permeability

The accuracy and reliability of experimental data are determined by the choice of the method of determining the structural characteristics of materials to a significant degree. The data on the level of correlation and the type of functional dependence of the properties on the structure of materials obtained by correlation and regression analysis are a function of the reliability of the experimental data to a significant degree. Of the three methods of estimating the through porosity of materials examined here, the simplest and most widely used method of calculation provides the least reliable results. The most reliable data on through porosity can be obtained by the projection method of indirect estimation of the through porosity and it is recommended for practical research, especially when processing of materials with defined properties is the final goal.

Application of the momentum translation method to multiphoton ionization of hydrogen by intense electromagnetic fields

A nonperturbative theory, the momentum translation method, is applied to multiphoton ionization of hydrogen by an intense electromagnetic field. Using an approximation depending on a large number of photons absorbed, analytical results are presented for transitions from a 1S state to Coulomb states in the continuum. Results not only show the characteristic perturbation theory dependence of the intensity raised to the Nth power for an Nth order process, but give an explicit expression for the transition as a function of the number of photons absorbed, and the final electron angular momentum and energy. This type of functional dependence is very obscure in perturbation theory by its very nature. In particular, transitions to states with angular momenta 2, 4, and 6 dominate the l=0 transition in the absorption of 12 photons with energy of 1.17 eV, while l=3, 5, 7 transitions dominate the l=1 transition when 13 photons are absorbed. Also for particular values of the field intensity and final angular momentum the transition matrix is larger for a larger number of photons absorbed.