53 research outputs found
Star products made (somewhat) easier
We develop an approach to the deformation quantization on the real plane with
an arbitrary Poisson structure which based on Weyl symmetrically ordered
operator products. By using a polydifferential representation for deformed
coordinates we are able to formulate a simple and effective
iterative procedure which allowed us to calculate the fourth order star product
(and may be extended to the fifth order at the expense of tedious but otherwise
straightforward calculations). Modulo some cohomology issues which we do not
consider here, the method gives an explicit and physics-friendly description of
the star products.Comment: 20 pages, v2, v3: comments and references adde
ΠΠΎΠ»ΠΈΠΌΠΎΡΡΠΈΠ·ΠΌ Π³ΡΡΠΏΠΏ ΠΊΡΠΎΠ²ΠΈ ΡΠΊΠΎΠ² Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ ΠΎΠΊΡΠ°ΡΠ° ΡΠ΅ΡΡΡΠΈ ΠΈ ΠΊΠΎΠΌΠΎΠ»ΠΎΡΡΠΈ
Yaks of the Republic of Tyva are characterised by high biological diversity, expressed by a wide range of body colours and polymorphism of blood groups. According to the distribution of colour and polymorphic blood systems in bulls and yak dams, the most characteristic colours are black, black-and-white, and brown; their frequency in the population is 0.403, 0.148 and 0.118, respectively. Animals of other colour patterns were encountered with a frequency ranging from 0.004 to 0.091. Differentiation of yak bulls and dams by the presence or absence of horns showed that in polled bulls and dams, the frequency of markers Q, L', F of the blood systems B, C, F-V is higher (from 0.250 to 0.846) than in horned ones (0.100β0.500). Blood markers R2, W, X1, U' systems C, and S were identified in polled bulls and dams with a frequency of 0.018β0.143, not found in horned bulls and dams. The frequency of blood antigens G2, T2, I2, E'2, Y', J2 of systems B, J is higher in horned bulls and dams (from 0.200 to 0.800) than in polled individuals (0.054β0.464), and S1 of blood system S was detected only in horned queens. Blood markers I1, Y2, R2, W, X1, and U' systems B, C, and S were undetected in horned bulls and dams. In polled and horned bulls, the frequency of genes E'2, E, X2, V, Z of blood systems B, C, F-V, and Z is higher; they are detected with a frequency of 0.333 to 1.000, regardless of colour. Polled bulls of grey colour do not have markers A2, G2, I1, O2, Y', Y2, Q', Y', X1 blood systems A, B, C, and brown colour - A2, O2, Q', F, U, U' blood systems A, B, F-V, S. Still, in polled bulls with black and brown colours, blood antigens I1, X1 were identified, which are absent in horned individuals of different colours. In yaks, statistically significant differences were noted in colour, polledness and antigens A2, G2, I1, I2, Q, T2, E'2, I', Y', R2, W, X1, X2, L', F, V, J2, H', U, U', Z.Π―ΠΊΠΈ Π Π΅ΡΠΏΡΠ±Π»ΠΈΠΊΠΈ Π’ΡΠ²Π° Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΡΡ Π²ΡΡΠΎΠΊΠΈΠΌ Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΌ ΡΠ°Π·Π½ΠΎΠΎΠ±ΡΠ°Π·ΠΈΠ΅ΠΌ, Π²ΡΡΠ°ΠΆΠ΅Π½Π½ΡΠΌ ΡΠΈΡΠΎΠΊΠΎΠΉ Π³Π°ΠΌΠΌΠΎΠΉ ΠΎΠΊΡΠ°ΡΠΊΠΈ ΡΡΠ»ΠΎΠ²ΠΈΡΠ° ΠΈ ΠΏΠΎΠ»ΠΈΠΌΠΎΡΡΠΈΠ·ΠΌΠΎΠΌ Π³ΡΡΠΏΠΏ ΠΊΡΠΎΠ²ΠΈ. ΠΠΎ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΌΠ°ΡΡΠΈ ΠΈ ΠΏΠΎΠ»ΠΈΠΌΠΎΡΡΠ½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ ΠΊΡΠΎΠ²ΠΈ Ρ Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ ΡΠΊΠΎΠ² Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ½ΡΠΌΠΈ ΠΎΠΊΡΠ°ΡΠΊΠ°ΠΌΠΈ ΡΠ²Π»ΡΡΡΡΡ ΡΠ΅ΡΠ½Π°Ρ, ΡΠ΅ΡΠ½ΠΎΠΏΠ΅ΡΡΡΠ°Ρ, ΠΊΠΎΡΠΈΡΠ½Π΅Π²Π°Ρ, ΠΈΡ
ΡΠ°ΡΡΠΎΡΠ° Π² ΠΏΠΎΠΏΡΠ»ΡΡΠΈΠΈ ΡΠΎΡΡΠ°Π²Π»ΡΠ΅Ρ 0,403; 0,148 ΠΈ 0,118 ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²Π΅Π½Π½ΠΎ. ΠΠΈΠ²ΠΎΡΠ½ΡΠ΅ Π΄ΡΡΠ³ΠΈΡ
ΡΠ°ΡΡΠ²Π΅ΡΠΎΠΊ ΠΎΠΊΡΠ°ΡΠΊΠΈ Π²ΡΡΡΠ΅ΡΠ°Π»ΠΈΡΡ Ρ ΡΠ°ΡΡΠΎΡΠΎΠΉ ΠΎΡ 0,004 Π΄ΠΎ 0,091. ΠΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°ΡΠΈΡ ΡΠΊΠΎΠ²-Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ ΠΏΠΎ Π½Π°Π»ΠΈΡΠΈΡ ΡΠΎΠ³ΠΎΠ² ΠΈΠ»ΠΈ ΠΈΡ
ΠΎΡΡΡΡΡΡΠ²ΠΈΡ ΠΏΠΎΠΊΠ°Π·Π°Π»Π°, ΡΡΠΎ Ρ ΠΊΠΎΠΌΠΎΠ»ΡΡ
Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ ΡΠ°ΡΡΠΎΡΠ° ΠΌΠ°ΡΠΊΠ΅ΡΠΎΠ² Q, L', F ΡΠΈΡΡΠ΅ΠΌ ΠΊΡΠΎΠ²ΠΈ B, C, F-V Π²ΡΡΠ΅ (ΠΎΡ 0,250 Π΄ΠΎ 0,846), ΡΠ΅ΠΌ Ρ ΡΠΎΠ³Π°ΡΡΡ
(0,100β0,500). ΠΠ°ΡΠΊΡΡΡ ΠΊΡΠΎΠ²ΠΈ R2, W, Π₯1, U' ΡΠΈΡΡΠ΅ΠΌ C, S Π²ΡΡΠ²Π»Π΅Π½Ρ Ρ ΠΊΠΎΠΌΠΎΠ»ΡΡ
Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ Ρ ΡΠ°ΡΡΠΎΡΠΎΠΉ 0,018β0,143, ΠΊΠΎΡΠΎΡΡΡ
Π½Π΅ ΠΎΠΊΠ°Π·Π°Π»ΠΎΡΡ Ρ ΡΠΎΠ³Π°ΡΡΡ
Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ. Π§Π°ΡΡΠΎΡΠ° Π°Π½ΡΠΈΠ³Π΅Π½ΠΎΠ² ΠΊΡΠΎΠ²ΠΈ G2, Π’2, I2, Π'2, Y', J2 ΡΠΈΡΡΠ΅ΠΌ B, J Π²ΡΡΠ΅ Ρ ΡΠΎΠ³Π°ΡΡΡ
Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ (ΠΎΡ 0,200 Π΄ΠΎ 0,800), ΡΠ΅ΠΌ Ρ ΠΊΠΎΠΌΠΎΠ»ΡΡ
ΠΎΡΠΎΠ±Π΅ΠΉ (0,054β0,464), Π° S1 ΡΠΈΡΡΠ΅ΠΌΡ ΠΊΡΠΎΠ²ΠΈ S Π²ΡΡΠ²Π»Π΅Π½ ΡΠΎΠ»ΡΠΊΠΎ Ρ ΡΠΎΠ³Π°ΡΡΡ
ΠΌΠ°ΡΠΎΠΊ. ΠΠ°ΡΠΊΠ΅ΡΡ ΠΊΡΠΎΠ²ΠΈ I1, Y2, R2, W, Π₯1, U' ΡΠΈΡΡΠ΅ΠΌ B, C, S Π½Π΅ Π²ΡΡΠ²Π»Π΅Π½Ρ Ρ ΡΠΎΠ³Π°ΡΡΡ
Π±ΡΠΊΠΎΠ² ΠΈ ΠΌΠ°ΡΠΎΠΊ. Π£ ΠΊΠΎΠΌΠΎΠ»ΡΡ
ΠΈ ΡΠΎΠ³Π°ΡΡΡ
Π±ΡΠΊΠΎΠ² Π²ΡΡΠ΅ ΡΠ°ΡΡΠΎΡΠ° Π³Π΅Π½ΠΎΠ² Π'2, Π, Π₯2, V, Z ΡΠΈΡΡΠ΅ΠΌ ΠΊΡΠΎΠ²ΠΈ B, C, F-V, Z, ΠΎΠ½ΠΈ Π²ΡΡΠ²Π»Π΅Π½Ρ Ρ ΡΠ°ΡΡΠΎΡΠΎΠΉ ΠΎΡ 0,333 Π΄ΠΎ 1,000 Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΠΎ ΠΎΡ ΠΌΠ°ΡΡΠΈ. ΠΠΎΠΌΠΎΠ»ΡΠ΅ Π±ΡΠΊΠΈ ΡΠ΅ΡΠΎΠΉ ΠΌΠ°ΡΡΠΈ Π½Π΅ ΠΈΠΌΠ΅ΡΡ ΠΌΠ°ΡΠΊΠ΅ΡΠΎΠ² Π2, G2, I1, Π2, Y', Y2, Q', Y', Π₯1 ΡΠΈΡΡΠ΅ΠΌ ΠΊΡΠΎΠ²ΠΈ Π, Π, Π‘, Π° ΠΊΠΎΡΠΈΡΠ½Π΅Π²ΠΎΠΉ ΠΎΠΊΡΠ°ΡΠΊΠΈ β Π2, Π2, Q', F, U, U' ΡΠΈΡΡΠ΅ΠΌ ΠΊΡΠΎΠ²ΠΈ Π, Π, F-V, S, Π½ΠΎ Ρ ΠΊΠΎΠΌΠΎΠ»ΡΡ
Π±ΡΠΊΠΎΠ² Ρ ΡΠ΅ΡΠ½ΠΎΠΉ ΠΈ ΠΊΠΎΡΠΈΡΠ½Π΅Π²ΠΎΠΉ ΠΎΠΊΡΠ°ΡΠΊΠΎΠΉ Π²ΡΡΠ²Π»Π΅Π½Ρ Π°Π½ΡΠΈΠ³Π΅Π½Ρ ΠΊΡΠΎΠ²ΠΈ I1, Π₯1, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΎΡΡΡΡΡΡΠ²ΡΡΡ Ρ ΡΠΎΠ³Π°ΡΡΡ
ΠΎΡΠΎΠ±Π΅ΠΉ Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΠΎΠΉ ΠΌΠ°ΡΡΡΡ. Π£ ΡΠΊΠΎΠ² ΠΎΡΠΌΠ΅ΡΠ΅Π½Ρ ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈ Π·Π½Π°ΡΠΈΠΌΡΠ΅ ΠΎΡΠ»ΠΈΡΠΈΡ ΠΏΠΎ ΠΎΠΊΡΠ°ΡΠΊΠ΅, ΠΊΠΎΠΌΠΎΠ»ΠΎΡΡΠΈ ΠΈ Π°Π½ΡΠΈΠ³Π΅Π½Π°ΠΌ A2, G2, I1, I2, Q, T2, Π'2, I', Y', R2, W, X1, X2, L',Β F, V,Β J2,Β H', U, U',Β Z
ΠΡΠ΅Π½ΠΊΠ° ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½ΡΡ Π³ΡΡΠΏΠΏ ΠΏΠΎΠ»Π½ΠΎΠ²ΠΎΠ·ΡΠ°ΡΡΠ½ΡΡ ΠΊΠΎΡΠΎΠ² ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ ΠΏΠΎΡΠΎΠ΄, Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ
The assessment of black-and-white, red steppe, and Simmental cattle, differentiated by milk fat was carried out. Three groups were formed: selection, production and marriage. The selection parameters are calculated using the standard deviation. The calculated parameters of selection of animals of the breeding group for milk fat in adult black-and-white cows are at least 179 kg, red steppe - 186, Simmental breed from the Novosibirsk region - 143, the Republic of Khakassia - 176 kg. Cows of the red steppe breeding group are leading in productivity. Their milk fat index is 216.8 kg (P β₯ 0.95). In animals of the black-and-white breed, the milk fat productivity is 193.2 kg. In the Simmental Republic of Khakassia it is 193.8, in the Novosibirsk region - 163.5 kg. Analysis of interbreed differences in cows of breeding groups shows that animals of the black-and-white breed surpass their peers in chest width behind the shoulder blades, milk yield and milk production index. Animals of the red steppe breed are the best in milk fat, live weight, width in shanks, oblique body length, oblique rear length, chest girth, milk fat content. Simmental cows bred in the Novosibirsk region lead over their peers in height at the withers, and Simmental cows in Khakassia - in height at the sacrum, chest depth, cannon girth, assessment of the exterior. Evaluation of the production groups of animals for milk fat allows to note that the selection group of the black-and-white breed, despite the superiority in milk yield, is inferior to the peers of the red steppe and Simmental in terms of the evaluated character. However, the cows of the black-and-white breed of the production group surpass their peers in milk fat and most other signs. The formation of breeding groups for milk fat enables to note the consolidation of the black-and-white breed in terms of productive and exterior characteristics. The Red Steppe and Simmental breeds have a high potential for improvement. These breeding groups are worthy of competing with the contemporaries of the black-andwhite breed in milk fat productivity.ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π° ΠΎΡΠ΅Π½ΠΊΠ° ΠΊΡΡΠΏΠ½ΠΎΠ³ΠΎ ΡΠΎΠ³Π°ΡΠΎΠ³ΠΎ ΡΠΊΠΎΡΠ° ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ, ΠΊΡΠ°ΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ½ΠΎΠΉ, ΡΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»ΡΡΠΊΠΎΠΉ ΠΏΠΎΡΠΎΠ΄, Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ. Π‘ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΎ ΡΡΠΈ Π³ΡΡΠΏΠΏΡ: ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½Π°Ρ, ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½Π°Ρ, Π±ΡΠ°ΠΊ. ΠΠ°ΡΠ°ΠΌΠ΅ΡΡΡ ΠΎΡΠ±ΠΎΡΠ° Π²ΡΡΠΈΡΠ»Π΅Π½Ρ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΡΠ΅Π΄Π½Π΅ΠΊΠ²Π°Π΄ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΎΡΠΊΠ»ΠΎΠ½Π΅Π½ΠΈΡ. Π Π°ΡΡΡΡΠ½ΡΠ΅ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ ΠΎΡΠ±ΠΎΡΠ° ΠΆΠΈΠ²ΠΎΡΠ½ΡΡ
ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½ΠΎΠΉ Π³ΡΡΠΏΠΏΡ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ Ρ ΠΏΠΎΠ»Π½ΠΎΠ²ΠΎΠ·ΡΠ°ΡΡΠ½ΡΡ
ΠΊΠΎΡΠΎΠ² ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΡΠΎΡΡΠ°Π²Π»ΡΡΡ Π½Π΅ ΠΌΠ΅Π½Π΅Π΅ 179 ΠΊΠ³, ΠΊΡΠ°ΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ½ΠΎΠΉ β 186, ΡΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»ΡΡΠΊΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΠΈΠ· ΠΠΎΠ²ΠΎΡΠΈΠ±ΠΈΡΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ β 143, Π Π΅ΡΠΏΡΠ±Π»ΠΈΠΊΠΈ Π₯Π°ΠΊΠ°ΡΠΈΡ β 176 ΠΊΠ³, ΠΏΡΠΈ ΡΡΠΎΠΌ ΠΏΠΎ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π»ΠΈΠ΄ΠΈΡΡΡΡ ΠΊΠΎΡΠΎΠ²Ρ ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½ΠΎΠΉ Π³ΡΡΠΏΠΏΡ ΠΊΡΠ°ΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ½ΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ, ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠ³ΠΎ ΠΆΠΈΡΠ° ΠΊΠΎΡΠΎΡΡΡ
ΡΠΎΡΡΠ°Π²Π»ΡΠ΅Ρ 216,8 ΠΊΠ³ (P β₯ 0,95). Π£ ΠΆΠΈΠ²ΠΎΡΠ½ΡΡ
ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ ΡΠ°Π²Π½Π° 193,2 ΠΊΠ³, ΡΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»ΡΡΠΊΠΎΠΉ Π Π΅ΡΠΏΡΠ±Π»ΠΈΠΊΠΈ Π₯Π°ΠΊΠ°ΡΠΈΡ β 193,8, ΠΠΎΠ²ΠΎΡΠΈΠ±ΠΈΡΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ β 163,5 ΠΊΠ³. ΠΠ½Π°Π»ΠΈΠ· ΠΌΠ΅ΠΆΠΏΠΎΡΠΎΠ΄Π½ΡΡ
ΡΠ°Π·Π»ΠΈΡΠΈΠΉ ΠΊΠΎΡΠΎΠ² ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½ΡΡ
Π³ΡΡΠΏΠΏ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Π΅Ρ, ΡΡΠΎ ΠΆΠΈΠ²ΠΎΡΠ½ΡΠ΅ ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΠΏΡΠ΅Π²ΠΎΡΡ
ΠΎΠ΄ΡΡ ΡΠ²Π΅ΡΡΡΠ½ΠΈΡ ΠΏΠΎ ΡΠΈΡΠΈΠ½Π΅ Π³ΡΡΠ΄ΠΈ Π·Π° Π»ΠΎΠΏΠ°ΡΠΊΠ°ΠΌΠΈ, ΡΠ΄ΠΎΡ ΠΈ ΠΈΠ½Π΄Π΅ΠΊΡΡ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΡΡΠΈ. ΠΠΈΠ²ΠΎΡΠ½ΡΠ΅ ΠΊΡΠ°ΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ½ΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΡΠ²Π»ΡΡΡΡΡ Π»ΡΡΡΠΈΠΌΠΈ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ, ΠΆΠΈΠ²ΠΎΠΉ ΠΌΠ°ΡΡΠ΅, ΡΠΈΡΠΈΠ½Π΅ Π² ΠΌΠ°ΠΊΠ»ΠΎΠΊΠ°Ρ
, ΠΊΠΎΡΠΎΠΉ Π΄Π»ΠΈΠ½Π΅ ΡΡΠ»ΠΎΠ²ΠΈΡΠ°, ΠΊΠΎΡΠΎΠΉ Π΄Π»ΠΈΠ½Π΅ Π·Π°Π΄Π°, ΠΎΠ±Ρ
Π²Π°ΡΡ Π³ΡΡΠ΄ΠΈ, ΠΆΠΈΡΠ½ΠΎΡΡΠΈ ΠΌΠΎΠ»ΠΎΠΊΠ°. Π‘ΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»ΡΡΠΊΠΈΠ΅ ΠΊΠΎΡΠΎΠ²Ρ, ΡΠ°Π·Π²ΠΎΠ΄ΠΈΠΌΡΠ΅ Π² ΠΠΎΠ²ΠΎΡΠΈΠ±ΠΈΡΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ, Π»ΠΈΠ΄ΠΈΡΡΡΡ Π½Π°Π΄ ΡΠ²Π΅ΡΡΡΠ½ΠΈΡΠ°ΠΌΠΈ ΠΏΠΎ Π²ΡΡΠΎΡΠ΅ Π² Ρ
ΠΎΠ»ΠΊΠ΅, Π° ΡΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»Ρ Π₯Π°ΠΊΠ°ΡΠΈΠΈ β ΠΏΠΎ Π²ΡΡΠΎΡΠ΅ Π² ΠΊΡΠ΅ΡΡΡΠ΅, Π³Π»ΡΠ±ΠΈΠ½Π΅ Π³ΡΡΠ΄ΠΈ, ΠΎΠ±Ρ
Π²Π°ΡΡ ΠΏΡΡΡΠΈ, ΠΎΡΠ΅Π½ΠΊΠ΅ ΡΠΊΡΡΠ΅ΡΡΠ΅ΡΠ°. ΠΡΠ΅Π½ΠΊΠ° ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
Π³ΡΡΠΏΠΏ ΠΆΠΈΠ²ΠΎΡΠ½ΡΡ
ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΡΠΌΠ΅ΡΠΈΡΡ, ΡΡΠΎ ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½Π°Ρ Π³ΡΡΠΏΠΏΠ° ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ, Π½Π΅ΡΠΌΠΎΡΡΡ Π½Π° ΠΏΡΠ΅Π²ΠΎΡΡ
ΠΎΠ΄ΡΡΠ²ΠΎ ΠΏΠΎ ΡΠ΄ΠΎΡ, ΡΡΡΡΠΏΠ°Π΅Ρ ΡΠ²Π΅ΡΡΡΠ½ΠΈΡΠ°ΠΌ ΠΊΡΠ°ΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ½ΠΎΠΉ ΠΈ ΡΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»ΡΡΠΊΠΎΠΉ ΠΏΠΎ ΠΎΡΠ΅Π½ΠΈΠ²Π°Π΅ΠΌΠΎΠΌΡ ΠΏΡΠΈΠ·Π½Π°ΠΊΡ, ΠΎΠ΄Π½Π°ΠΊΠΎ ΠΊΠΎΡΠΎΠ²Ρ ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎΠΉ Π³ΡΡΠΏΠΏΡ ΠΏΡΠ΅Π²ΠΎΡΡ
ΠΎΠ΄ΡΡ ΡΠ²ΠΎΠΈΡ
ΡΠ²Π΅ΡΡΡΠ½ΠΈΡ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ ΠΈ Π±ΠΎΠ»ΡΡΠΈΠ½ΡΡΠ²Ρ Π΄ΡΡΠ³ΠΈΡ
ΠΏΡΠΈΠ·Π½Π°ΠΊΠΎΠ². Π€ΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½ΡΡ
Π³ΡΡΠΏΠΏ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΡΠΌΠ΅ΡΠΈΡΡ ΠΊΠΎΠ½ΡΠΎΠ»ΠΈΠ΄Π°ΡΠΈΡ ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ ΠΏΠΎ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΡΠΌ ΠΈ ΡΠΊΡΡΠ΅ΡΡΠ΅ΡΠ½ΡΠΌ ΠΏΡΠΈΠ·Π½Π°ΠΊΠ°ΠΌ. ΠΡΡΠΎΠΊΠΈΠΉ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π» Π΄Π»Ρ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΡ ΠΈΠΌΠ΅ΡΡ ΠΊΡΠ°ΡΠ½Π°Ρ ΡΡΠ΅ΠΏΠ½Π°Ρ ΠΈ ΡΠΈΠΌΠΌΠ΅Π½ΡΠ°Π»ΡΡΠΊΠ°Ρ ΠΏΠΎΡΠΎΠ΄Ρ, ΠΈΡ
ΡΠ΅Π»Π΅ΠΊΡΠΈΠΎΠ½Π½ΡΠ΅ Π³ΡΡΠΏΠΏΡ ΡΠΎΡΡΠ°Π²Π»ΡΡΡ Π΄ΠΎΡΡΠΎΠΉΠ½ΡΡ ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΠΈΡ ΡΠ²Π΅ΡΡΡΠ½ΠΈΡΠ°ΠΌ ΡΡΡΠ½ΠΎ-ΠΏΡΡΡΡΠΎΠΉ ΠΏΠΎΡΠΎΠ΄Ρ Π² ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΠΎ ΠΌΠΎΠ»ΠΎΡΠ½ΠΎΠΌΡ ΠΆΠΈΡΡ
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