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¤ Ʉɨɪɨɥɟɜ ɋ. Ⱥ., Ɋɭɫɹɤ ɂ. Ƚ., ɋɭɮɢɹɧɨɜ ȼ. Ƚ., 2016 1 ɇɢɠɟ ɜ ɤɚɱɟɫɬɜɟ ɨɛɴɟɤɬɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɜɵɫɬɪɟɥ ɫɧɚɪɹɞɚ ɢɡ ɨɪɭɞɢɹ. Ɉɫɨɛɟɧɧɨɫɬɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɫɜɹɡɚɧɧɵɟ ɫ ɩɭɫ-ɤɨɦ ɪɚɤɟɬ, ɜ ɬɟɤɫɬɟ ɨɬɦɟɱɟɧɵ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ. Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɜɧɟɲɧɹɹ ɛɚɥɥɢɫɬɢɤɚ, ɬɪɚɟɤɬɨɪɢɹ, ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ, ɩɨɞɜɢɠɧɵɣ ɧɨɫɢɬɟɥɶ, ɧɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɫɬɪɟɥɶɛɵ, ɧɟɫɭɳɢɣ ɜɢɧɬ ɜɟɪɬɨɥɟɬɚ, ɢɧɞɭɤɬɢɜɧɚɹ ɫɤɨɪɨɫɬɶ. ȼɜɟɞɟɧɢɟ ɉɪɢ ɫɬɪɟɥɶɛɟ ɫ ɩɨɞɜɢɠɧɨɝɨ ɧɨɫɢɬɟɥɹ (ɉɇ) ɧɟɨɛ-ɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɦɧɨɠɟɫɬɜɨ ɮɚɤɬɨɪɨɜ, ɜɥɢɹɸɳɢɯ ɧɚ ɧɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɫɬɪɟɥɶɛɵ ɢ ɧɚɱɚɥɶɧɵɣ ɭɱɚɫɬɨɤ ɬɪɚɟɤɬɨɪɢɢ ɫɧɚɪɹɞɨɜ ɢ ɪɚɤɟɬ. Ɉɫɧɨɜɧɵɦɢ ɜɨɡɦɭ-ɳɚɸɳɢɦɢ ɮɚɤɬɨɪɚɦɢ ɩɪɢ ɫɬɪɟɥɶɛɟ ɫ ɜɟɪɬɨɥɟɬɚ ɹɜ-ɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɞɜɢɠɟɧɢɹ ɜɟɪɬɨɥɟɬɚ ɢ ɩɨɬɨɤ ɜɨɡ-ɞɭɯɚ, ɫɨɡɞɚɜɚɟɦɵɣ ɧɟɫɭɳɢɦ ɜɢɧɬɨɦ. Ⱦɥɹ ɢɫɫɥɟɞɨɜɚ-ɧɢɹ ɩɪɢɜɟɞɟɧɧɵɯ ɮɚɤɬɨɪɨɜ ɪɚɡɪɚɛɨɬɚɧɚ ɦɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ ɬɪɚɟɤɬɨɪɢɢ ɞɜɢɠɟɧɢɹ ɫɧɚɪɹɞɨɜ ɢ ɪɚɤɟɬ ɩɪɢ ɫɬɪɟɥɶɛɟ ɫ ɩɨɞɜɢɠɧɨɝɨ ɧɨɫɢɬɟɥɹ.Ɋɚɫɱɟɬ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɫɬɪɟɥɶɛɵ ɫ ɩɨɞɜɢɠɧɨɝɨ ɧɨɫɢɬɟɥɹ Ox y z ɫ ɧɚɱɚɥɨɦ ɜ ɰɟɧɬɪɟ ɦɚɫɫ ɉɇ ɢ ɨɫɹɦɢ ɜ ɜ ɜ , , x y z , ɫɨɪɢɟɧɬɢɪɨɜɚɧ-ɧɵɦɢ ɜɞɨɥɶ ɩɪɨɞɨɥɶɧɨɣ, ɜɟɪɬɢɤɚɥɶɧɨɣ ɢ ɩɨɩɟɪɟɱɧɨɣ ɨɫɟɣ ɉɇ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ɉɪɢɟɧɬɚɰɢɹ ɫɜɹɡɚɧɧɨɣ ɫɢɫ-ɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɨɪɦɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɝɥɚɦɢ ɬɚɧɝɚɠɚɊɢɫ. 1. Ɉɪɢɟɧɬɚɰɢɹ ɩɨɞɜɢɠɧɨɝɨ ɧɨɫɢɬɟɥɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ Ʉɨɦɩɨɧɟɧɬɵ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɜ ɧɨɪɦɚɥɶɧɨɣ ɫɢɫ-ɬɟɦɟ ɤɨɨɪɞɢɧɚɬɄɨɦɩɨɧɟɧɬɵ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɜ ɫɜɹɡɚɧɧɨɣ ɫɢɫ-ɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɭɬɟɦ ɩɨɜɨɪɨɬɚ ɧɚ ɭɝɥɵ, , 0, , 0 , 0, .(4) ȼ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɧɟɲɧɟɣ ɛɚɥɥɢɫɬɢɤɢ ɡɚɞɚɸɬɫɹ ɦɨɞɭɥɶ ɜɟɤɬɨɪɚ ɧɚ-ɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɫɧɚɪɹɞɚ ɫ ɭɱɟɬɨɦ ɞɜɢɠɟɧɢɹ ɉɇ:ɧɨɣ ɫɤɨɪɨɫɬɢ ɜ ɫɬɚɪɬɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɨɩɪɟ-ɞɟɥɹɟɦɵɟ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ (4). ɉɨɫɤɨɥɶɤɭ ɩɪɢ ɞɜɢɠɟɧɢɢ ɉɇ ɨɫɶ ɨɪɭɞɢɹ ɢ, ɫɨɨɬ-ɜɟɬɫɬɜɟɧɧɨ, ɨɫɶ ɫɢɦɦɟɬɪɢɢ ɫɧɚɪɹɞɚ ɧɟ ɫɨɜɩɚɞɚɸɬ ɫ ɫɭɦɦɚɪɧɵɦ ɜɟɤɬɨɪɨɦ ɫɤɨɪɨɫɬɢ ɫɧɚɪɹɞɚ, ɬɨ ɜɨɡɧɢɤɚ-ɸɬ ɭɝɥɵ ɧɭɬɚɰɢɢ, ɤɨɬɨɪɵɟ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟ-ɦɟɧɢ ɪɚɜɧɵ:ɇɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɢ ɜɟɪɬɢ-ɤɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɢɯ ɷɤɜɚɬɨɪɢɚɥɶɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨ-ɪɨɫɬɢ ɫɧɚɪɹɞɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɱɟɪɟɡ ɤɨɦɩɨɧɟɧɬɵ ɭɝɥɨ-ɜɨɣ ɫɤɨɪɨɫɬɢ ɉɇ: Ɋɚɫɱɟɬ ɬɪɚɟɤɬɨɪɢɢ ɞɜɢɠɟɧɢɹ ɫɧɚɪɹɞɚ (ɪɚɤɟɬɵ)Ʉɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɚ ɦɚɫɫ ɫɧɚɪɹɞɚ ɜ ɫɬɚɪɬɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɨɩɪɟɞɟɥɹɸɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ [2]:ɝɞɟ ɫ x -ɞɚɥɶɧɨɫɬɶ; ɫ y -ɜɵɫɨɬɚ ɩɨɥɟɬɚ; ɫ z -ɛɨɤɨ-ɜɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɫɬɚɪɬɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ; ɤ V -ɫɤɨɪɨɫɬɶ ɰɟɧɬɪɚ ɦɚɫɫ ɫɧɚɪɹɞɚ (ɪɢɫ. 2). ɇɚɱɚɥɶɧɵɟ Ox y z , ɫɜɹɡɚɧɧɨɣ ɫ ɰɟɧɬɪɨɦ ɦɚɫɫ ɫɧɚɪɹɞɚ ɢ ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɣ ɩɨ ɜɟɤ-ɬɨɪɭ ɫɤɨɪɨɫɬɢ (ɫɦ. ɪɢɫ. 2):Ɂɞɟɫɶ g -ɭɫɤɨɪɟɧɢɟ ɫɢɥɵ ɬɹɠɟɫɬɢ; (10)- (12) ɡɚɞɚ-ɸɬɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (5)-(6).Ⱦɥɹ ɜɪɚɳɚɸɳɟɝɨɫɹ ɫɧɚɪɹɞɚ ɚɤɫɢɚɥɶɧɚɹ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹɝɞɟ x m -ɤɨɷɮɮɢɰɢɟɧɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɚɤɫɢɚɥɶ-ɧɨɝɨ ɞɟɦɩɮɢɪɭɸɳɟɝɨ ɦɨɦɟɧɬɚ (ɦɨɦɟɧɬɚ ɬɪɟɧɢɹ) ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ Oxyz , ɫɜɹɡɚɧɧɨɣ ɫ ɰɟɧɬɪɨɦ ɦɚɫɫ ɫɧɚɪɹɞɚ, ɝɞɟ ɨɫɢ , ,x y z ɧɚɩɪɚɜɥɟɧɵ ɜɞɨɥɶ ɩɪɨɞɨɥɶ-ɧɨɣ, ɜɟɪɬɢɤɚɥɶɧɨɣ ɢ ɩɨɩɟɪɟɱɧɨɣ ɨɫɟɣ ɫɧɚɪɹɞɚ, ɫɨɨɬ-ɜɟɬɫɬɜɟɧɧɨ; l -ɞɥɢɧɚ ɫɧɚɪɹɞɚ; x I -ɚɤɫɢɚɥɶɧɵɣ ɦɨ-ɦɟɧɬ ɢɧɟɪɰɢɢ; 0 x Z -ɚɤɫɢɚɥɶɧɚɹ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜ ɦɨɦɟɧɬ ɜɵɫɬɪɟɥɚ.Ƚɨɪɢɡɨɧɬɚɥɶɧɚɹ ɢ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɢɟ ɭɝɥɚ ɧɭɬɚɰɢɢ ɫɧɚɪɹɞɚ 1 2 , G G ɨɩɪɟɞɟɥɹɸɬɫɹ ɢɡ ɫɢɫɬɟ-ɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ:ɝɞɟ 1 2 , Z Z -ɫɨɫɬɚɜɥɹɸɳɢɟ ɷɤɜɚɬɨɪɢɚɥɶɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɫɧɚɪɹɞɚ.Ⱦɥɹ ɨɩɪɟ...

The problem of the impact of the mathematical model dimension on the calculated intraballistic characteristics of a shot for the charges made of granulated powder is considered. Mathematical models of the shot are studied using the spatial (axisymmetric), one-dimensional, and zero-dimensional (thermodynamic) formulations. The thermodynamic model takes into account the distribution of the pressure and velocity of a gas-powder mixture behind the shot for a channel of variable cross-section. Comparison of simulation results is carried out in a wide range of loading parameters. It is shown that there is a range of the loading parameters for a thermodynamic approach to give satisfactory approximation to the parameters obtained using the gas-dynamic approach, which describes the flow of a heterogeneous reacting mixture with a separate consideration of phases and intergranular interactions between them. Notably that in the entire range of the charging parameters studied in this work, the one-dimensional and twodimensional gas-dynamic models only slightly differ from each other. Therefore, in the main pyrodynamic period, the actuation of the charge, made of granulated powder, can be simulated using a one-dimensional gas-dynamic model or a zero-dimensional thermodynamic model with allowance for spatial distribution of the pressure and velocity of the gas-powder mixture.

In the conditions of the development of modern economy, human capital is one of the main factors of economic growth. The formation of human capital begins with the birth of a person and continues throughout life, so the value of human capital is inseparable from its carriers, which in turn makes it difficult to account for this factor. This has led to the fact that currently there are no generally accepted methods of calculating the value of human capital. There are only a few approaches to the measurement of human capital: the cost approach (by income or investment) and the index approach, of which the most well-known approach developed under the auspices of the UN. This paper presents the assigned task in conjunction with the task of demographic dynamics solved in the time-age plane, which allows to more fully take into account the temporary changes in the demographic structure on the dynamics of human capital. The task of demographic dynamics is posed within the framework of the Mac-Kendrick-von Foerster model on the basis of the equation of age structure dynamics. The form of distribution functions for births, deaths and migration of the population is determined on the basis of the available statistical information. The numerical solution of the problem is given. The analysis and forecast of demographic indicators are presented. The economic and mathematical model of human capital dynamics is formulated on the basis of the demographic dynamics problem. The problem of modeling the human capital dynamics considers three components of capital: educational, health and cultural (spiritual). Description of the evolution of human capital components uses an equation of the transfer equation type. Investments in human capital components are determined on the basis of budget expenditures and private expenditures, taking into account the characteristic time life cycle of demographic elements. A one-dimensional kinetic equation is used to predict the dynamics of the total human capital. The method of calculating the dynamics of this factor is given as a time function. The calculated data on the human capital dynamics are presented for the Russian Federation. As studies have shown, the value of human capital increased rapidly until 2008, in the future there was a period of stabilization, but after 2014 there is a negative dynamics of this value.

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