41 research outputs found
Minimal non-1-planar graphs
AbstractA graph is 1-planar if it can be drawn on the plane so that each edge is crossed by no more than one other edge. A non-1-planar graph G is minimal if the graph G-e is 1-planar for every edge e of G. We prove that there are infinitely many minimal non-1-planar graphs (MN-graphs). It is known that every 6-vertex graph is 1-planar. We show that the graph K7-K3 is the unique 7-vertex MN-graph
Realizing the chromatic numbers of triangulations of surfaces
AbstractGiven an orientable or nonorientable closed surface S and an integer n not less than 3 and not greater than the chromatic number of S, we construct a graph admitting a triangular embedding in S and having chromatic number n
Advance in Keyless Cryptography
The term βkeyless cryptographyβ as it is commonly adopted, applies to secure message transmission either directly without any key distribution in advance or as key sharing protocol between communicating users, based on physical layer security, before ordinary encryption/decryption procedures. In the current chapter the results are presented concerning to keyless cryptography that have been obtained by authors recently. Firstly Shamirβs protocol of secure communication is considered where commutative encryption procedure is executed. It has been found out which of the public key algorithms can be used with such protocol. Next item of consideration concerns Deanβs and Goldsmithβs cryptosystem based on multiple-input, multiple-output (MIMO) technology. It has been established under which conditions this cryptosystem is in fact secure. The third example under consideration is EVSkey scheme proposed recently by D. Qin and Z. Ding. It has been proven that such key distribution method is in fact insecure, in spite of the authorsβ claims. Our main result is a description of a key sharing protocol executing over public noiseless channels (like internet) that provides a key sharing reliability and security without any cryptographic assumptions
ΠΠΈΡΠ²Π»Π΅Π½Π½Ρ Π²ΠΏΠ»ΠΈΠ²Ρ ΡΠΈΠΏΡ ΠΏΠΎΠ»ΡΠΌΠ΅ΡΠ½ΠΎΡ ΠΌΠ°ΡΡΠΈΡΡ Π½Π° ΡΡΡΡΠΊΡΡΡΠΎΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ ΠΌΡΠΊΡΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ² ΠΏΡΠΈ ΡΡ Π½Π°ΠΏΠΎΠ²Π½Π΅Π½Π½Ρ ΡΠ°ΡΡΠΈΠ½ΠΊΠ°ΠΌΠΈ ΠΌΡΠ΄Ρ
Studies were carried out to establish the mechanisms of structure formation during crystallization of polymer composites based on polyethylene, polypropylene or polycarbonate filled with copper microparticles. The researches were executed using a technique, the first stage of which consisted in the experimental determination of crystallization exotherms of composites, and the second β in the theoretical analysis based on the obtained exotherms of the structure formation characteristics. A complex of studies on determination of crystallization exotherms for investigated microcomposites was carried out. The regularities of the cooling rate influence of composites, the method of their production and the mass fraction of filler on the temperature level of the beginning and ending of crystallization, the maximum value of the reduced heat flux, etc. were established. It is shown that for the applied methods of obtaining composites the increase of their cooling rate causes the decrease of the indicated temperatures and heat flux. It is established that the value of the mass fraction of the filler has a less significant effect on the characteristics of the crystallization process.The regularities of structure formation of polymer composites at the initial stage of crystallization with the involvement of data on crystallization exotherms and nucleation equations are investigated. The presence of planar and three-dimensional mechanisms of structure formation at this stage has been established. It is shown that the ratio of these mechanisms is influenced by the type of polymer matrix and the method of obtaining composites.For the second stage of crystallization, which occurs in the entire volume of the composite, the results of experiments on crystallization exotherms were analyzed on the basis of the Kolmogorov-Avrami equation. It is shown that the structure formation of polyethylene-based composites occurs by the three-dimensional mechanism, and on the basis of polypropylene and polycarbonate β by the mechanism of the stressed matrixΠΡΠΏΠΎΠ»Π½Π΅Π½Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎ ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠ² ΡΡΡΡΠΊΡΡΡΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΠ»ΠΈΠΌΠ΅ΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΠΎΠ»ΠΈΡΡΠΈΠ»Π΅Π½Π°, ΠΏΠΎΠ»ΠΈΠΏΡΠΎΠΏΠΈΠ»Π΅Π½Π° ΠΈΠ»ΠΈ ΠΏΠΎΠ»ΠΈΠΊΠ°ΡΠ±ΠΎΠ½Π°ΡΠ°, Π½Π°ΠΏΠΎΠ»Π½Π΅Π½Π½ΡΡ
ΠΌΠΈΠΊΡΠΎΡΠ°ΡΡΠΈΡΠ°ΠΌΠΈ ΠΌΠ΅Π΄ΠΈ. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ Ρ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ, ΠΏΠ΅ΡΠ²ΡΠΉ ΡΡΠ°ΠΏ ΠΊΠΎΡΠΎΡΠΎΠΉ Π·Π°ΠΊΠ»ΡΡΠ°Π»ΡΡ Π² ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠΌ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ ΡΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ², Π° Π²ΡΠΎΡΠΎΠΉ β Π² ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΌ Π°Π½Π°Π»ΠΈΠ·Π΅ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠΊΠ·ΠΎΡΠ΅ΡΠΌ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΡΡΡΡΠΊΡΡΡΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΏΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ Π΄Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΡΡ
ΠΌΠΈΠΊΡΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ². Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½Ρ Π·Π°ΠΊΠΎΠ½ΠΎΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ Π²Π»ΠΈΡΠ½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΎΡ
Π»Π°ΠΆΠ΄Π΅Π½ΠΈΡ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ², ΠΌΠ΅ΡΠΎΠ΄Π° ΠΈΡ
ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΈ ΠΌΠ°ΡΡΠΎΠ²ΠΎΠΉ Π΄ΠΎΠ»ΠΈ Π½Π°ΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»Ρ Π½Π° ΡΡΠΎΠ²Π΅Π½Ρ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ Π½Π°ΡΠ°Π»Π° ΠΈ ΠΊΠΎΠ½ΡΠ° ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ, ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠ³ΠΎ ΠΏΠΎΡΠΎΠΊΠ° ΠΈ Π΄Ρ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π΄Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ² ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΈΡ
ΠΎΡ
Π»Π°ΠΆΠ΄Π΅Π½ΠΈΡ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΠΊΠ°Π·Π°Π½Π½ΡΡ
ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ ΠΈ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠ³ΠΎ ΠΏΠΎΡΠΎΠΊΠ°. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π²Π΅Π»ΠΈΡΠΈΠ½Π° ΠΌΠ°ΡΡΠΎΠ²ΠΎΠΉ Π΄ΠΎΠ»ΠΈ Π½Π°ΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»Ρ ΠΌΠ΅Π½Π΅Π΅ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ Π²Π»ΠΈΡΠ΅Ρ Π½Π° Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ.ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ Π·Π°ΠΊΠΎΠ½ΠΎΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ ΡΡΡΡΠΊΡΡΡΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠ»ΠΈΠΌΠ΅ΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ² Π½Π° Π½Π°ΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠ°Π΄ΠΈΠΈ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ Ρ ΠΏΡΠΈΠ²Π»Π΅ΡΠ΅Π½ΠΈΠ΅ΠΌ Π΄Π°Π½Π½ΡΡ
ΠΏΠΎ ΡΠΊΠ·ΠΎΡΠ΅ΡΠΌΠ°ΠΌ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Π½ΡΠΊΠ»Π΅Π°ΡΠΈΠΈ. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ Π½Π°Π»ΠΈΡΠΈΠ΅ Π½Π° ΡΡΠΎΠΉ ΡΡΠ°Π΄ΠΈΠΈ ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠ½ΠΎΠ³ΠΎ ΠΈ ΠΎΠ±ΡΠ΅ΠΌΠ½ΠΎΠ³ΠΎ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠ² ΡΡΡΡΠΊΡΡΡΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π½Π° ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ Π΄Π°Π½Π½ΡΡ
ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠ² Π²Π»ΠΈΡΠ΅Ρ ΡΠΈΠΏ ΠΏΠΎΠ»ΠΈΠΌΠ΅ΡΠ½ΠΎΠΉ ΠΌΠ°ΡΡΠΈΡΡ ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ².ΠΠ»Ρ Π²ΡΠΎΡΠΎΠΉ ΡΡΠ°Π΄ΠΈΠΈ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π²ΠΎ Π²ΡΠ΅ΠΌ ΠΎΠ±ΡΠ΅ΠΌΠ΅ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ°, Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΠΎΠ»ΠΌΠΎΠ³ΠΎΡΠΎΠ²Π°-ΠΠ²ΡΠ°ΠΌΠΈ ΠΏΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΡΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΠ·Π°ΡΠΈΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΡΡΠΊΡΡΡΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠ΅ Π΄Π»Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΠΎΠ»ΠΈΡΡΠΈΠ»Π΅Π½Π° ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ ΠΏΠΎ ΠΎΠ±ΡΠ΅ΠΌΠ½ΠΎΠΌΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΡ, Π° Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΠΎΠ»ΠΈΠΏΡΠΎΠΏΠΈΠ»Π΅Π½Π° ΠΈ ΠΏΠΎΠ»ΠΈΠΊΠ°ΡΠ±ΠΎΠ½Π°ΡΠ° - ΠΏΠΎ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΡ Π½Π°ΠΏΡΡΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠ°ΡΡΠΈΡΡΠΠΈΠΊΠΎΠ½Π°Π½ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΡΠΎΠ΄ΠΎ Π²ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡΠ² ΡΡΡΡΠΊΡΡΡΠΎΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ ΠΏΡΠΈ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ ΠΏΠΎΠ»ΡΠΌΠ΅ΡΠ½ΠΈΡ
ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΠΏΠΎΠ»ΡΠ΅ΡΠΈΠ»Π΅Π½Ρ, ΠΏΠΎΠ»ΡΠΏΡΠΎΠΏΡΠ»Π΅Π½Ρ Π°Π±ΠΎ ΠΏΠΎΠ»ΡΠΊΠ°ΡΠ±ΠΎΠ½Π°ΡΡ, Π½Π°ΠΏΠΎΠ²Π½Π΅Π½ΠΈΡ
ΠΌΡΠΊΡΠΎΡΠ°ΡΡΠΈΠ½ΠΊΠ°ΠΌΠΈ ΠΌΡΠ΄Ρ. ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΡΠ· Π·Π°ΡΡΠΎΡΡΠ²Π°Π½Π½ΡΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ, ΠΏΠ΅ΡΡΠΈΠΉ Π΅ΡΠ°ΠΏ ΡΠΊΠΎΡ ΠΏΠΎΠ»ΡΠ³Π°Π² Ρ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠΌΡ Π²ΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ Π΅ΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ², Π° Π΄ΡΡΠ³ΠΈΠΉ β Ρ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ½ΠΎΠΌΡ Π°Π½Π°Π»ΡΠ·Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΠΎΡΡΠΈΠΌΠ°Π½ΠΈΡ
Π΅ΠΊΠ·ΠΎΡΠ΅ΡΠΌ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΡΡΡΡΠΊΡΡΡΠΎΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Ρ ΡΠΎΠ΄ΠΎ Π²ΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ Π΅ΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ Π΄Π»Ρ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΡΠ²Π°Π½ΠΈΡ
ΠΌΡΠΊΡΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ². ΠΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ Π·Π°ΠΊΠΎΠ½ΠΎΠΌΡΡΠ½ΠΎΡΡΡ Π²ΠΏΠ»ΠΈΠ²Ρ ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡ ΠΎΡ
ΠΎΠ»ΠΎΠ΄ΠΆΠ΅Π½Π½Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ², ΠΌΠ΅ΡΠΎΠ΄Ρ ΡΡ
ΠΎΠ΄Π΅ΡΠΆΠ°Π½Π½Ρ ΡΠ° ΠΌΠ°ΡΠΎΠ²ΠΎΡ ΡΠ°ΡΡΠΊΠΈ Π½Π°ΠΏΠΎΠ²Π½ΡΠ²Π°ΡΠ° Π½Π° ΡΡΠ²Π΅Π½Ρ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ ΠΏΠΎΡΠ°ΡΠΊΡ Ρ ΠΊΡΠ½ΡΡ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ, ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½Π΅ Π·Π½Π°ΡΠ΅Π½Π½Ρ ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½ΠΎΠ³ΠΎ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠ³ΠΎ ΠΏΠΎΡΠΎΠΊΡ ΡΠΎΡΠΎ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π΄Π»Ρ Π·Π°ΡΡΠΎΡΠΎΠ²ΡΠ²Π°Π½ΠΈΡ
ΠΌΠ΅ΡΠΎΠ΄ΡΠ² ΠΎΠ΄Π΅ΡΠΆΠ°Π½Π½Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ² ΠΏΡΠ΄Π²ΠΈΡΠ΅Π½Π½Ρ ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡ ΡΡ
ΠΎΡ
ΠΎΠ»ΠΎΠ΄ΠΆΠ΅Π½Π½Ρ ΡΠΏΡΠΈΡΠΈΠ½ΡΡ Π·Π½ΠΈΠΆΠ΅Π½Π½Ρ Π²ΠΊΠ°Π·Π°Π½ΠΈΡ
ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ ΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠ³ΠΎ ΠΏΠΎΡΠΎΠΊΡ. ΠΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΠΎ Π²Π΅Π»ΠΈΡΠΈΠ½Π° ΠΌΠ°ΡΠΎΠ²ΠΎΡ ΡΠ°ΡΡΠΊΠΈ Π½Π°ΠΏΠΎΠ²Π½ΡΠ²Π°ΡΠ° ΠΌΠ΅Π½Ρ ΡΡΡΡΡΠ²ΠΎ Π²ΠΏΠ»ΠΈΠ²Π°Ρ Π½Π° Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΏΡΠΎΡΠ΅ΡΡ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ.ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½ΠΎ Π·Π°ΠΊΠΎΠ½ΠΎΠΌΡΡΠ½ΠΎΡΡΡ ΡΡΡΡΠΊΡΡΡΠΎΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ ΠΏΠΎΠ»ΡΠΌΠ΅ΡΠ½ΠΈΡ
ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ² Π½Π° ΠΏΠΎΡΠ°ΡΠΊΠΎΠ²ΡΠΉ ΡΡΠ°Π΄ΡΡ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ ΡΠ· Π·Π°Π»ΡΡΠ΅Π½Π½ΡΠΌ Π΄Π°Π½ΠΈΡ
ΡΠΎΠ΄ΠΎ Π΅ΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ ΡΠ° ΡΡΠ²Π½ΡΠ½Π½Ρ Π½ΡΠΊΠ»Π΅Π°ΡΡΡ. ΠΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ Π½Π°ΡΠ²Π½ΡΡΡΡ Π½Π° ΡΡΠΉ ΡΡΠ°Π΄ΡΡ ΠΏΠ»ΠΎΡΠΈΠ½Π½ΠΎΠ³ΠΎ ΡΠ° ΠΎΠ±βΡΠΌΠ½ΠΎΠ³ΠΎ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡΠ² ΡΡΡΡΠΊΡΡΡΠΎΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π½Π° ΡΠΏΡΠ²Π²ΡΠ΄Π½ΠΎΡΠ΅Π½Π½Ρ Π΄Π°Π½ΠΈΡ
ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡΠ² Π²ΠΏΠ»ΠΈΠ²Π°Ρ ΡΠΈΠΏ ΠΏΠΎΠ»ΡΠΌΠ΅ΡΠ½ΠΎΡ ΠΌΠ°ΡΡΠΈΡΡ ΡΠ° ΠΌΠ΅ΡΠΎΠ΄ ΠΎΡΡΠΈΠΌΠ°Π½Π½Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ².ΠΠ»Ρ Π΄ΡΡΠ³ΠΎΡ ΡΡΠ°Π΄ΡΡ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ, ΡΠΎ Π²ΡΠ΄Π±ΡΠ²Π°ΡΡΡΡΡ Π² ΡΡΡΠΎΠΌΡ ΠΎΠ±βΡΠΌΡ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡ, Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΡΡΠ²Π½ΡΠ½Π½Ρ ΠΠΎΠ»ΠΌΠΎΠ³ΠΎΡΠΎΠ²Π°-ΠΠ²ΡΠ°ΠΌΡ ΠΏΡΠΎΠ°Π½Π°Π»ΡΠ·ΠΎΠ²Π°Π½ΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΡΠ² ΡΠΎΠ΄ΠΎ Π΅ΠΊΠ·ΠΎΡΠ΅ΡΠΌ ΠΊΡΠΈΡΡΠ°Π»ΡΠ·Π°ΡΡΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ ΡΡΡΡΠΊΡΡΡΠΎΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ Π΄Π»Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΠΏΠΎΠ»ΡΠ΅ΡΠΈΠ»Π΅Π½Ρ Π²ΡΠ΄Π±ΡΠ²Π°ΡΡΡΡΡ Π·Π° ΠΎΠ±βΡΠΌΠ½ΠΈΠΌ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΠΎΠΌ, Π° Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΠΏΠΎΠ»ΡΠΏΡΠΎΠΏΡΠ»Π΅Π½Ρ Ρ ΠΏΠΎΠ»ΡΠΊΠ°ΡΠ±ΠΎΠ½Π°ΡΡ β Π·Π° ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΠΎΠΌ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΎΡ ΠΌΠ°ΡΡΠΈΡ