9 research outputs found
Evolution of the spatial models of the economic growth in the analysis of urbanization in Russian regions
Β© Medwell Journals, 2016.The researchers analyzed the evolution of models of economic growth with the spatial factor. Based on panel data shows the influence of the geographic factor including urbanization and economic potential for the growth of the differences in labor productivity in the cities of Russian regions. The researchers found that urbanization affects the growth of labor productivity in the cities with the power of 13% is higher than the Western European and close to Eastern European and Asian trends. On the spatial model of conditional beta-convergence shows that the less-developed and urbanized regions of Russia closer together among themselves on productivity under the influence of urbanization and Moran's index explains convergence only between them while the most developed regions diverge from the rest. The Russian regions are growing disparities in the level of urbanization due to excessive agglomeration of several cores, who take inputs from the entire periphery
Π‘ΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½ΠΈΠ΅ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ ΠΏΠΎΡΠ΅ΡΡ ΠΎΡ ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ (Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ Π‘Π°ΡΠ°ΡΠΎΠ²ΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ)
This paper presents experimental calculations of the economic losses caused by mortality of rural population of the Saratov region. An alternative approach to analyzing and quantifying the degree of the economic damage caused by rural mortality in the region, which estimates the economic losses as a shortfall of gross value added, less under consumption, taking into account age, gender and class of diseases, is proposed. Based on the official statistics on gross value added size and structure of employed in the economy of Saratov region and the number and pattern of the unemployed, the levels of the regional labor productivity and per capita real consumption were calculated. These calculations helped develop some options to quantify the economic damage from mortality among different social-demographic groups of the rural population. The results of this study can be used to design preventive measures aiming to reduce population mortality in rural areas, increase life expectancy and draw up regional strategies of social-economic development of the countryside.Π Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΠ΅ΡΠ±Π° ΠΎΡ ΠΏΠΎΡΠ΅ΡΡ, Π²ΡΠ·Π²Π°Π½Π½ΡΡ
ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΡΡ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ Π‘Π°ΡΠ°ΡΠΎΠ²ΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ ΠΏΠΎ ΠΎΡΠ½ΠΎΠ²Π½ΡΠΌ ΠΏΡΠΈΡΠΈΠ½Π°ΠΌ ΡΠΌΠ΅ΡΡΠΈ. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π°Π»ΡΡΠ΅ΡΠ½Π°ΡΠΈΠ²Π½ΡΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΊ Π°Π½Π°Π»ΠΈΠ·Ρ ΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΌΡ ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½ΠΈΡ ΠΌΠ°ΡΡΡΠ°Π±ΠΎΠ² ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΠ΅ΡΠ±Π° ΠΎΡ ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π³ΠΈΠΎΠ½Π°, ΠΎΡΠ΅Π½ΠΈΠ²Π°ΡΡΠΈΠΉ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΠΎΡΠ΅ΡΠΈ ΠΊΠ°ΠΊ Π½Π΅Π΄ΠΎΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²ΠΎ Π²Π°Π»ΠΎΠ²ΠΎΠΉ Π΄ΠΎΠ±Π°Π²Π»Π΅Π½Π½ΠΎΠΉ ΡΡΠΎΠΈΠΌΠΎΡΡΠΈ Π·Π° Π²ΡΡΠ΅ΡΠΎΠΌ Π½Π΅Π΄ΠΎΠΏΠΎΡΡΠ΅Π±Π»Π΅Π½ΠΈΡ, Ρ ΡΡΠ΅ΡΠΎΠΌ Π²ΠΎΠ·ΡΠ°ΡΡΠ°, ΠΏΠΎΠ»Π°, ΠΊΠ»Π°ΡΡΠ° Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π½ΠΈΠΉ. ΠΠΎ ΠΎΡΠΈΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΎ Π²Π°Π»ΠΎΠ²ΠΎΠΉ Π΄ΠΎΠ±Π°Π²Π»Π΅Π½Π½ΠΎΠΉ ΡΡΠΎΠΈΠΌΠΎΡΡΠΈ, ΡΠΈΡΠ»Π΅Π½Π½ΠΎΡΡΠΈ ΠΈ ΡΡΡΡΠΊΡΡΡΠ΅ Π·Π°Π½ΡΡΡΡ
Π² ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠ΅ Π‘Π°ΡΠ°ΡΠΎΠ²ΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠ°ΡΡΡΠΈΡΠ°Π½Ρ ΡΡΠΎΠ²Π½ΠΈ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΡΡΠ΄Π°, ΡΡΠ΅Π΄Π½Π΅Π΄ΡΡΠ΅Π²ΠΎΠ³ΠΎ ΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΅Π±Π»Π΅Π½ΠΈΡ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Π½ΡΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Ρ Π²Π°ΡΠΈΠ°Π½ΡΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΠΎΡΠ΅Π½ΠΊΠΈ ΠΌΠ°ΡΡΡΠ°Π±ΠΎΠ² ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΠ΅ΡΠ±Π° ΠΎΡ ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΡΠΎΡΠΈΠ°Π»ΡΠ½ΠΎΠ΄Π΅ΠΌΠΎΠ³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π³ΡΡΠΏΠΏ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½Ρ Π΄Π»Ρ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠΈ ΠΏΡΠ΅Π²Π΅Π½ΡΠΈΠ²Π½ΡΡ
ΠΌΠ΅Ρ, Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΡΡ
Π½Π° ΡΠΎΠΊΡΠ°ΡΠ΅Π½ΠΈΠ΅ ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ, ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΆΠΈΠ·Π½ΠΈ, ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
ΡΡΡΠ°ΡΠ΅Π³ΠΈΠΉ ΡΠΎΡΠΈΠ°Π»ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΡΠ΅Π»Π°
Evolution of the spatial models of the economic growth in the analysis of urbanization in Russian regions
Β© Medwell Journals, 2016.The researchers analyzed the evolution of models of economic growth with the spatial factor. Based on panel data shows the influence of the geographic factor including urbanization and economic potential for the growth of the differences in labor productivity in the cities of Russian regions. The researchers found that urbanization affects the growth of labor productivity in the cities with the power of 13% is higher than the Western European and close to Eastern European and Asian trends. On the spatial model of conditional beta-convergence shows that the less-developed and urbanized regions of Russia closer together among themselves on productivity under the influence of urbanization and Moran's index explains convergence only between them while the most developed regions diverge from the rest. The Russian regions are growing disparities in the level of urbanization due to excessive agglomeration of several cores, who take inputs from the entire periphery
Evolution of the spatial models of the economic growth in the analysis of urbanization in Russian regions
Β© Medwell Journals, 2016.The researchers analyzed the evolution of models of economic growth with the spatial factor. Based on panel data shows the influence of the geographic factor including urbanization and economic potential for the growth of the differences in labor productivity in the cities of Russian regions. The researchers found that urbanization affects the growth of labor productivity in the cities with the power of 13% is higher than the Western European and close to Eastern European and Asian trends. On the spatial model of conditional beta-convergence shows that the less-developed and urbanized regions of Russia closer together among themselves on productivity under the influence of urbanization and Moran's index explains convergence only between them while the most developed regions diverge from the rest. The Russian regions are growing disparities in the level of urbanization due to excessive agglomeration of several cores, who take inputs from the entire periphery
Π§ΠΈΡΠ»Π΅Π½Π½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΠΎΠ½ΡΠ΅-ΠΠ°ΡΠ»ΠΎ Π² Π·Π°Π΄Π°ΡΠ΅ Π°Π½Π°Π»ΠΈΠ·Π° ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΠΎΡΡΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ ΡΡΠ΅Π΄ΡΡΠ²
The problem of ensuring high temperature stability of parameters by reason of the characteristic
features inherent in the integral performance becomes especially urgent for microminiature
electronic devices. For the mathematical description of the electronic devicesβ temperature error
it is proposed to use the method of experimentβs statistical planning in combination with regression
analysis. There are classes of electrical circuits in which the output parameter depends mainly on
one-parameter electrical radio elements. In the article it is shown that the problem of obtaining the
temperature error equation for such electrical circuits can be reduced to the problem of effective
finding of the one-parameter electro radio elementsβ influence coefficients. A modification of the
Monte Carlo statistical method with the computational factor experimentβs scenario to find the
temperature error equation is considered. Approbation of the proposed modification is carried
out using the example of the electric circuit of the generator with the Wien bridgeΠΠ»Ρ ΠΌΠΈΠΊΡΠΎΠΌΠΈΠ½ΠΈΠ°ΡΡΡΠ½ΡΡ
ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ
ΡΡΠ΅Π΄ΡΡΠ² ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎ Π°ΠΊΡΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠ°Π½ΠΎΠ²ΠΈΡΡΡ Π·Π°Π΄Π°ΡΠ°
ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ Π²ΡΡΠΎΠΊΠΎΠΉ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² Π² ΡΠ²ΡΠ·ΠΈ Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ½ΡΠΌΠΈ
ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡΠΌΠΈ, ΠΏΡΠΈΡΡΡΠΈΠΌΠΈ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠΌΡ ΠΈΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ. ΠΠ»Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ
ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ
ΡΡΠ΅Π΄ΡΡΠ² ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅
ΠΌΠ΅ΡΠΎΠ΄Π° ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ° Π² ΡΠΎΡΠ΅ΡΠ°Π½ΠΈΠΈ Ρ ΡΠ΅Π³ΡΠ΅ΡΡΠΈΠΎΠ½Π½ΡΠΌ
Π°Π½Π°Π»ΠΈΠ·ΠΎΠΌ. Π‘ΡΡΠ΅ΡΡΠ²ΡΡΡ ΠΊΠ»Π°ΡΡΡ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡ
Π΅ΠΌ, Π² ΠΊΠΎΡΠΎΡΡΡ
Π²ΡΡ
ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡ
Π·Π°Π²ΠΈΡΠΈΡ Π² ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠΌ ΠΎΡ ΠΎΠ΄Π½ΠΎΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ»Π΅ΠΊΡΡΠΎΡΠ°Π΄ΠΈΠΎΠΈΠ·Π΄Π΅Π»ΠΈΠΉ. Π ΡΡΠ°ΡΡΠ΅
ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π·Π°Π΄Π°ΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΠΈ Π΄Π»Ρ ΡΠ°ΠΊΠΈΡ
ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡ
Π΅ΠΌ ΠΌΠΎΠΆΠ½ΠΎ ΡΠ²Π΅ΡΡΠΈ ΠΊ Π·Π°Π΄Π°ΡΠ΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½ΡΠΎΠ²
Π²Π»ΠΈΡΠ½ΠΈΡ ai ΠΎΠ΄Π½ΠΎΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ»Π΅ΠΊΡΡΠΎΡΠ°Π΄ΠΈΠΎΠΈΠ·Π΄Π΅Π»ΠΈΠΉ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΡ
ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΠΎΠ½ΡΠ΅-ΠΠ°ΡΠ»ΠΎ ΠΏΠΎ ΡΡΠ΅Π½Π°ΡΠΈΡ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΠΊΡΠΎΡΠ½ΠΎΠ³ΠΎ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ° Π΄Π»Ρ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΠΈ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π°
Π°ΠΏΡΠΎΠ±Π°ΡΠΈΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡ
Π΅ΠΌΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠ° Ρ
ΠΌΠΎΡΡΠΎΠΌ ΠΠΈΠ½
Π§ΠΈΡΠ»Π΅Π½Π½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΠΎΠ½ΡΠ΅-ΠΠ°ΡΠ»ΠΎ Π² Π·Π°Π΄Π°ΡΠ΅ Π°Π½Π°Π»ΠΈΠ·Π° ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΠΎΡΡΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ ΡΡΠ΅Π΄ΡΡΠ²
The problem of ensuring high temperature stability of parameters by reason of the characteristic
features inherent in the integral performance becomes especially urgent for microminiature
electronic devices. For the mathematical description of the electronic devicesβ temperature error
it is proposed to use the method of experimentβs statistical planning in combination with regression
analysis. There are classes of electrical circuits in which the output parameter depends mainly on
one-parameter electrical radio elements. In the article it is shown that the problem of obtaining the
temperature error equation for such electrical circuits can be reduced to the problem of effective
finding of the one-parameter electro radio elementsβ influence coefficients. A modification of the
Monte Carlo statistical method with the computational factor experimentβs scenario to find the
temperature error equation is considered. Approbation of the proposed modification is carried
out using the example of the electric circuit of the generator with the Wien bridgeΠΠ»Ρ ΠΌΠΈΠΊΡΠΎΠΌΠΈΠ½ΠΈΠ°ΡΡΡΠ½ΡΡ
ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ
ΡΡΠ΅Π΄ΡΡΠ² ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎ Π°ΠΊΡΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠ°Π½ΠΎΠ²ΠΈΡΡΡ Π·Π°Π΄Π°ΡΠ°
ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ Π²ΡΡΠΎΠΊΠΎΠΉ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² Π² ΡΠ²ΡΠ·ΠΈ Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ½ΡΠΌΠΈ
ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡΠΌΠΈ, ΠΏΡΠΈΡΡΡΠΈΠΌΠΈ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠΌΡ ΠΈΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ. ΠΠ»Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ
ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ
ΡΡΠ΅Π΄ΡΡΠ² ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅
ΠΌΠ΅ΡΠΎΠ΄Π° ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ° Π² ΡΠΎΡΠ΅ΡΠ°Π½ΠΈΠΈ Ρ ΡΠ΅Π³ΡΠ΅ΡΡΠΈΠΎΠ½Π½ΡΠΌ
Π°Π½Π°Π»ΠΈΠ·ΠΎΠΌ. Π‘ΡΡΠ΅ΡΡΠ²ΡΡΡ ΠΊΠ»Π°ΡΡΡ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡ
Π΅ΠΌ, Π² ΠΊΠΎΡΠΎΡΡΡ
Π²ΡΡ
ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡ
Π·Π°Π²ΠΈΡΠΈΡ Π² ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠΌ ΠΎΡ ΠΎΠ΄Π½ΠΎΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ»Π΅ΠΊΡΡΠΎΡΠ°Π΄ΠΈΠΎΠΈΠ·Π΄Π΅Π»ΠΈΠΉ. Π ΡΡΠ°ΡΡΠ΅
ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π·Π°Π΄Π°ΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΠΈ Π΄Π»Ρ ΡΠ°ΠΊΠΈΡ
ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡ
Π΅ΠΌ ΠΌΠΎΠΆΠ½ΠΎ ΡΠ²Π΅ΡΡΠΈ ΠΊ Π·Π°Π΄Π°ΡΠ΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½ΡΠΎΠ²
Π²Π»ΠΈΡΠ½ΠΈΡ ai ΠΎΠ΄Π½ΠΎΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ»Π΅ΠΊΡΡΠΎΡΠ°Π΄ΠΈΠΎΠΈΠ·Π΄Π΅Π»ΠΈΠΉ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΡ
ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΠΎΠ½ΡΠ΅-ΠΠ°ΡΠ»ΠΎ ΠΏΠΎ ΡΡΠ΅Π½Π°ΡΠΈΡ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΠΊΡΠΎΡΠ½ΠΎΠ³ΠΎ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ° Π΄Π»Ρ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠΉ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΠΈ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π°
Π°ΠΏΡΠΎΠ±Π°ΡΠΈΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡ
Π΅ΠΌΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠ° Ρ
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