The 30 reference contexts in paper G. Kuvyrkin N., I. Savelieva Yu., V. Zarubin S., В. Зарубин С., Г. Кувыркин Н., И. Савельева Ю. (2016) “Оценка методом самосогласования температурного коэффициента линейного расширения композита с дисперсными включениями // Self-Consistency Method to Evaluate a Linear Expansion Thermal Coefficient of Composite with Dispersed Inclusions” / spz:neicon:technomag:y:2015:i:2:p:197-215

  1. Start
    1870
    Prefix
    —Â‰Ë ÏÂı‡ÌË ̃ÂÒÍËı Ò‚ÓÈÒÚ‚, ÓÔ‰ÂΡ ̨ ̆Ëı ÍÓÌÍÂÚÌ ̊ ӷ·ÒÚË ÔËÏÂÌÂÌˡ ÍÓÏÔÓÁËÚÓ‚ ÔË Ì‡ÎË ̃ËË ÚÂÔÎÓ‚ ̊ı ‚ÓÁ‰ÂÈÒÚ‚ËÈ, ‚‡ÊÌÓ ÏÂÒÚÓ Á‡ÌËχ ̨Ú ÚÂÏÓÛÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË, ‚ ÚÓÏ ̃ËÒΠÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ŒˆÂÌÍÛ ̋ÚÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÔÓ ËÁ‚ÂÒÚÌ ̊Ï Ò‚ÓÈÒÚ‚‡Ï χÚˈ ̊ ÍÓÏÔÓÁËÚ‡ Ë ‡ÏËÛ ̨ ̆Ëı ‚ÍÎ ̨ ̃ÂÌËÈ ÏÓÊÌÓ ÔÓÎÛ ̃ËÚ ̧, ËÒÔÓÎ ̧ÁÛˇ ‡ÁÎË ̃Ì ̊ ÔÓ‰ıÓ‰ ̊
    Exact
    [1,2,3,4,5,6,7]
    Suffix
    . Œ‰ËÌ ËÁ Ú‡ÍËı ÔÓ‰ıÓ‰Ó‚, ̇Á ̊‚‡ÂÏ ̊È ÏÂÚÓ‰ÓÏ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ [8,9,10,11,12], ÒÓÒÚÓËÚ ‚ Û ̃ÂÚ ‚Á‡ËÏÓ‰ÂÈÒڂˡ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÓ„Ó ̋ÎÂÏÂÌÚ‡ ÌÂÓ‰ÌÓÓ‰ÌÓÒÚË Ï‡ÚÂˇ· (‚ÍÎ ̨ ̃ÂÌˡ ËÎË ̃‡ÒÚˈ ̊ χÚˈ ̊ ÍÓÏÔÓÁËÚ‡) Ò Ó‰ÌÓÓ‰ÌÓÈ ËÁÓÚÓÔÌÓÈ Ò‰ÓÈ, ı‡‡ÍÚÂËÒÚËÍË ÍÓÚÓÓÈ ÔÓ‰ÎÂÊ‡Ú ÓÔ‰ÂÎÂÌË ̨ [13]. œÓÒÎÂ‰Û ̨ ̆ ÓÒ‰ÌÂÌË ÔÓ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏÛ Ó· ̇ÂÏÛ Ï‡ÚÂˇ· ‚ÓÁÏÛ ̆ÂÌËÈ ‡ÒÔ‰ÂÎÂÌˡ Ô‡‡ÏÂÚÓ‚ ‚
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  2. Start
    1951
    Prefix
    ŒˆÂÌÍÛ ̋ÚÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÔÓ ËÁ‚ÂÒÚÌ ̊Ï Ò‚ÓÈÒÚ‚‡Ï χÚˈ ̊ ÍÓÏÔÓÁËÚ‡ Ë ‡ÏËÛ ̨ ̆Ëı ‚ÍÎ ̨ ̃ÂÌËÈ ÏÓÊÌÓ ÔÓÎÛ ̃ËÚ ̧, ËÒÔÓÎ ̧ÁÛˇ ‡ÁÎË ̃Ì ̊ ÔÓ‰ıÓ‰ ̊ [1,2,3,4,5,6,7]. Œ‰ËÌ ËÁ Ú‡ÍËı ÔÓ‰ıÓ‰Ó‚, ̇Á ̊‚‡ÂÏ ̊È ÏÂÚÓ‰ÓÏ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ
    Exact
    [8,9,10,11,12]
    Suffix
    , ÒÓÒÚÓËÚ ‚ Û ̃ÂÚ ‚Á‡ËÏÓ‰ÂÈÒڂˡ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÓ„Ó ̋ÎÂÏÂÌÚ‡ ÌÂÓ‰ÌÓÓ‰ÌÓÒÚË Ï‡ÚÂˇ· (‚ÍÎ ̨ ̃ÂÌˡ ËÎË ̃‡ÒÚˈ ̊ χÚˈ ̊ ÍÓÏÔÓÁËÚ‡) Ò Ó‰ÌÓÓ‰ÌÓÈ ËÁÓÚÓÔÌÓÈ Ò‰ÓÈ, ı‡‡ÍÚÂËÒÚËÍË ÍÓÚÓÓÈ ÔÓ‰ÎÂÊ‡Ú ÓÔ‰ÂÎÂÌË ̨ [13]. œÓÒÎÂ‰Û ̨ ̆ ÓÒ‰ÌÂÌË ÔÓ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏÛ Ó· ̇ÂÏÛ Ï‡ÚÂˇ· ‚ÓÁÏÛ ̆ÂÌËÈ ‡ÒÔ‰ÂÎÂÌˡ Ô‡‡ÏÂÚÓ‚ ‚ ̋ÚËı ̋ÎÂÏÂÌÚ‡ı ÔÓÁ‚ÓΡÂÚ ÔÓÎÛ ̃ËÚ ̧ ‡Ò ̃ÂÚÌ ̊ Á‡‚ËÒËÏÓÒÚË ‰Îˇ ÓˆÂÌÍË ËÒÍÓÏ
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  3. Start
    2176
    Prefix
    Œ‰ËÌ ËÁ Ú‡ÍËı ÔÓ‰ıÓ‰Ó‚, ̇Á ̊‚‡ÂÏ ̊È ÏÂÚÓ‰ÓÏ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ [8,9,10,11,12], ÒÓÒÚÓËÚ ‚ Û ̃ÂÚ ‚Á‡ËÏÓ‰ÂÈÒڂˡ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÓ„Ó ̋ÎÂÏÂÌÚ‡ ÌÂÓ‰ÌÓÓ‰ÌÓÒÚË Ï‡ÚÂˇ· (‚ÍÎ ̨ ̃ÂÌˡ ËÎË ̃‡ÒÚˈ ̊ χÚˈ ̊ ÍÓÏÔÓÁËÚ‡) Ò Ó‰ÌÓÓ‰ÌÓÈ ËÁÓÚÓÔÌÓÈ Ò‰ÓÈ, ı‡‡ÍÚÂËÒÚËÍË ÍÓÚÓÓÈ ÔÓ‰ÎÂÊ‡Ú ÓÔ‰ÂÎÂÌË ̨
    Exact
    [13]
    Suffix
    . œÓÒÎÂ‰Û ̨ ̆ ÓÒ‰ÌÂÌË ÔÓ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏÛ Ó· ̇ÂÏÛ Ï‡ÚÂˇ· ‚ÓÁÏÛ ̆ÂÌËÈ ‡ÒÔ‰ÂÎÂÌˡ Ô‡‡ÏÂÚÓ‚ ‚ ̋ÚËı ̋ÎÂÏÂÌÚ‡ı ÔÓÁ‚ÓΡÂÚ ÔÓÎÛ ̃ËÚ ̧ ‡Ò ̃ÂÚÌ ̊ Á‡‚ËÒËÏÓÒÚË ‰Îˇ ÓˆÂÌÍË ËÒÍÓÏ ̊ı ı‡‡ÍÚÂËÒÚËÍ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡.
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  4. Start
    2737
    Prefix
    ¬ ÚÂıÌËÍ ̇ˇ‰Û Ò ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ ÍÓÏÔÓÁËÚÓ‚, ‡ÏËÓ‚‡ÌÌ ̊ı ‚ÓÎÓÍÌËÒÚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË, ̄ËÓÍÓ ÔËÏÂÌˇ ̨Ú ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ ÍÓÏÔÓÁËÚ ̊, ‚ ÍÓÚÓ ̊ı ‚ÍÎ ̨ ̃ÂÌˡÏË ˇ‚Ρ ̨ÚÒˇ ̃‡ÒÚˈ ̊ ËÁ ‚ ̊ÒÓÍÓÔÓ ̃Ì ̊ı Ë ‚ ̊ÒÓÍÓÏÓ‰ÛÎ ̧Ì ̊ı χÚÂˇÎÓ‚, ‚ ÚÓÏ ̃ËÒΠ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊
    Exact
    [14,15,16,17]
    Suffix
    . Œ· ̊ ̃ÌÓ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ò ̃ËÚ‡Ú ̧ ̄‡Ó‚ÓÈ [18,19,20]. ƒÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [21], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [22,23,24].
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  5. Start
    2904
    Prefix
    Ó‚‡ÌÌ ̊ı ‚ÓÎÓÍÌËÒÚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË, ̄ËÓÍÓ ÔËÏÂÌˇ ̨Ú ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ ÍÓÏÔÓÁËÚ ̊, ‚ ÍÓÚÓ ̊ı ‚ÍÎ ̨ ̃ÂÌˡÏË ˇ‚Ρ ̨ÚÒˇ ̃‡ÒÚˈ ̊ ËÁ ‚ ̊ÒÓÍÓÔÓ ̃Ì ̊ı Ë ‚ ̊ÒÓÍÓÏÓ‰ÛÎ ̧Ì ̊ı χÚÂˇÎÓ‚, ‚ ÚÓÏ ̃ËÒΠ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊ [14,15,16,17]. Œ· ̊ ̃ÌÓ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ò ̃ËÚ‡Ú ̧ ̄‡Ó‚ÓÈ
    Exact
    [18,19,20]
    Suffix
    . ƒÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [21], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [22,23,24]. ¡ÎËÁÍËÏË ÔÓ ÚÂχÚËÍ ˇ‚Ρ ̨ÚÒˇ ‡·ÓÚ ̊ [25,26,27,28,29,30,31,32], ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ÚÂÏÓÛÔÛ„ËÏ Ò‚ÓÈÒÚ‚‡Ï ÔÓËÒÚ ̊ı ÏÂÚ‡ÎÎÓ‚, ÏÂÚ‡ÎÎÓÍÂ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚, Ú‡Í Í‡Í ÓÚ‰ÂÎ ̧ÌÓ ‚Á
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  6. Start
    3003
    Prefix
    Œ· ̊ ̃ÌÓ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ò ̃ËÚ‡Ú ̧ ̄‡Ó‚ÓÈ [18,19,20]. ƒÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË
    Exact
    [21]
    Suffix
    , ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [22,23,24]. ¡ÎËÁÍËÏË ÔÓ ÚÂχÚËÍ ˇ‚Ρ ̨ÚÒˇ ‡·ÓÚ ̊ [25,26,27,28,29,30,31,32], ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ÚÂÏÓÛÔÛ„ËÏ Ò‚ÓÈÒÚ‚‡Ï ÔÓËÒÚ ̊ı ÏÂÚ‡ÎÎÓ‚, ÏÂÚ‡ÎÎÓÍÂ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚, Ú‡Í Í‡Í ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÛ ̨ ÔÓÛ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ‡·ÒÓÎ ̨ÚÌÓ ÔÓ‰‡ÚÎË‚Ó ‚ÍÎ ̨ ̃ÂÌËÂ Ò ÌÛ΂ ̊Ï ÚÂÏÔÂ‡ÚÛ
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  7. Start
    3101
    Prefix
    Œ· ̊ ̃ÌÓ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ò ̃ËÚ‡Ú ̧ ̄‡Ó‚ÓÈ [18,19,20]. ƒÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [21], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊
    Exact
    [22,23,24]
    Suffix
    . ¡ÎËÁÍËÏË ÔÓ ÚÂχÚËÍ ˇ‚Ρ ̨ÚÒˇ ‡·ÓÚ ̊ [25,26,27,28,29,30,31,32], ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ÚÂÏÓÛÔÛ„ËÏ Ò‚ÓÈÒÚ‚‡Ï ÔÓËÒÚ ̊ı ÏÂÚ‡ÎÎÓ‚, ÏÂÚ‡ÎÎÓÍÂ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚, Ú‡Í Í‡Í ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÛ ̨ ÔÓÛ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ‡·ÒÓÎ ̨ÚÌÓ ÔÓ‰‡ÚÎË‚Ó ‚ÍÎ ̨ ̃ÂÌËÂ Ò ÌÛ΂ ̊Ï ÚÂÏÔÂ‡ÚÛÌ ̊Ï ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ƒÓÒÚÓ‚ÂÌ ̊ ӈÂÌÍË ÚÂÔÎÓ‚Ó„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ ÓÒÓ·ÂÌÌÓ
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  8. Start
    3151
    Prefix
    ̊ ̃ÌÓ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ò ̃ËÚ‡Ú ̧ ̄‡Ó‚ÓÈ [18,19,20]. ƒÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [21], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [22,23,24]. ¡ÎËÁÍËÏË ÔÓ ÚÂχÚËÍ ˇ‚Ρ ̨ÚÒˇ ‡·ÓÚ ̊
    Exact
    [25,26,27,28,29,30,31,32]
    Suffix
    , ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ÚÂÏÓÛÔÛ„ËÏ Ò‚ÓÈÒÚ‚‡Ï ÔÓËÒÚ ̊ı ÏÂÚ‡ÎÎÓ‚, ÏÂÚ‡ÎÎÓÍÂ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚, Ú‡Í Í‡Í ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÛ ̨ ÔÓÛ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ‡·ÒÓÎ ̨ÚÌÓ ÔÓ‰‡ÚÎË‚Ó ‚ÍÎ ̨ ̃ÂÌËÂ Ò ÌÛ΂ ̊Ï ÚÂÏÔÂ‡ÚÛÌ ̊Ï ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ƒÓÒÚÓ‚ÂÌ ̊ ӈÂÌÍË ÚÂÔÎÓ‚Ó„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ ÓÒÓ·ÂÌÌÓ ‚‡ÊÌ ̊ ÔË Â„Ó ËÒÔÓÎ ̧ÁÓ‚‡ÌËË ‚ ÚÂıÌË ̃ÂÒÍËı ÛÒÚÓÈÒÚ‚‡ı, Í ÍÓÚÓ
    (check this in PDF content)

  9. Start
    3642
    Prefix
    ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚, Ú‡Í Í‡Í ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÛ ̨ ÔÓÛ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ‡·ÒÓÎ ̨ÚÌÓ ÔÓ‰‡ÚÎË‚Ó ‚ÍÎ ̨ ̃ÂÌËÂ Ò ÌÛ΂ ̊Ï ÚÂÏÔÂ‡ÚÛÌ ̊Ï ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ƒÓÒÚÓ‚ÂÌ ̊ ӈÂÌÍË ÚÂÔÎÓ‚Ó„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ ÓÒÓ·ÂÌÌÓ ‚‡ÊÌ ̊ ÔË Â„Ó ËÒÔÓÎ ̧ÁÓ‚‡ÌËË ‚ ÚÂıÌË ̃ÂÒÍËı ÛÒÚÓÈÒÚ‚‡ı, Í ÍÓÚÓ ̊Ï Ô‰ ̇ˇ‚Ρ ̨ÚÒˇ ‚ ̊ÒÓÍË Ú·ӂ‡Ìˡ ÔÓ ‡ÁÏÂÌÓÈ ÒÚ‡·ËÎ ̧ÌÓÒÚË
    Exact
    [33]
    Suffix
    Ë ‚ ÍÓÚÓ ̊ı ËÒÔÓÎ ̧ÁÛÂÏ ̊È Ï‡ÚÂˇΠ‚ÍÎ ̨ ̃‡ÂÚ ‡ÁÌÓÓ‰Ì ̊ ÍÓÏÔÓÌÂÌÚ ̊ [34]. «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ÚÂÏÓÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚÓ‚ Ò ‰ËÒÔÂÒÌ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË ÔÓ‰Ú‚Âʉ‡ÂÚ ‡ÍÚۇΠ̧ÌÓÒÚ ̧ ËÒÒΉӂ‡ÌËÈ ‚ ̋ÚÓÏ Ì‡Ô‡‚ÎÂÌËË.
    (check this in PDF content)

  10. Start
    3721
    Prefix
    ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ‡·ÒÓÎ ̨ÚÌÓ ÔÓ‰‡ÚÎË‚Ó ‚ÍÎ ̨ ̃ÂÌËÂ Ò ÌÛ΂ ̊Ï ÚÂÏÔÂ‡ÚÛÌ ̊Ï ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ƒÓÒÚÓ‚ÂÌ ̊ ӈÂÌÍË ÚÂÔÎÓ‚Ó„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ ÓÒÓ·ÂÌÌÓ ‚‡ÊÌ ̊ ÔË Â„Ó ËÒÔÓÎ ̧ÁÓ‚‡ÌËË ‚ ÚÂıÌË ̃ÂÒÍËı ÛÒÚÓÈÒÚ‚‡ı, Í ÍÓÚÓ ̊Ï Ô‰ ̇ˇ‚Ρ ̨ÚÒˇ ‚ ̊ÒÓÍË Ú·ӂ‡Ìˡ ÔÓ ‡ÁÏÂÌÓÈ ÒÚ‡·ËÎ ̧ÌÓÒÚË [33] Ë ‚ ÍÓÚÓ ̊ı ËÒÔÓÎ ̧ÁÛÂÏ ̊È Ï‡ÚÂˇΠ‚ÍÎ ̨ ̃‡ÂÚ ‡ÁÌÓÓ‰Ì ̊ ÍÓÏÔÓÌÂÌÚ ̊
    Exact
    [34]
    Suffix
    . «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ÚÂÏÓÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚÓ‚ Ò ‰ËÒÔÂÒÌ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË ÔÓ‰Ú‚Âʉ‡ÂÚ ‡ÍÚۇΠ̧ÌÓÒÚ ̧ ËÒÒΉӂ‡ÌËÈ ‚ ̋ÚÓÏ Ì‡Ô‡‚ÎÂÌËË. “‡ÍË ËÒÒΉӂ‡Ìˡ ÚÂ·Û ̨Ú ÍÓÏÔÎÂÍÒÌÓ„Ó ÔÓ‰ıÓ‰‡ Ë ËÒÔÓÎ ̧ÁÓ‚‡Ìˡ ÏÂÚÓ‰Ó‚ ÍÓÏÔ ̧ ̨ÚÂÌÓ„Ó ÏÓ‰ÂÎËÓ‚‡Ìˡ, ÔÓÒÍÓÎ ̧ÍÛ ÔÓÒÚÓÂÌË χÚÂχÚË ̃ÂÒÍÓÈ ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆ÂÈ ÚÂÔÎÓ‚Ó ‡Ò ̄ËÂÌË ÍÓÏÔÓÁËÚ‡, ÌÂ‡Á ̊‚ÌÓ Ò‚ˇÁ‡ÌÓ
    (check this in PDF content)

  11. Start
    4179
    Prefix
    “‡ÍË ËÒÒΉӂ‡Ìˡ ÚÂ·Û ̨Ú ÍÓÏÔÎÂÍÒÌÓ„Ó ÔÓ‰ıÓ‰‡ Ë ËÒÔÓÎ ̧ÁÓ‚‡Ìˡ ÏÂÚÓ‰Ó‚ ÍÓÏÔ ̧ ̨ÚÂÌÓ„Ó ÏÓ‰ÂÎËÓ‚‡Ìˡ, ÔÓÒÍÓÎ ̧ÍÛ ÔÓÒÚÓÂÌË χÚÂχÚË ̃ÂÒÍÓÈ ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆ÂÈ ÚÂÔÎÓ‚Ó ‡Ò ̄ËÂÌË ÍÓÏÔÓÁËÚ‡, ÌÂ‡Á ̊‚ÌÓ Ò‚ˇÁ‡ÌÓ Ò ‡Ì‡ÎËÁÓÏ Â„Ó Ì‡ÔˇÊÂÌÌÓ‰ÂÙÓÏËÓ‚‡ÌÌÓ„Ó ÒÓÒÚÓˇÌˡ
    Exact
    [35,36,37]
    Suffix
    . ¬ ‰‡ÌÌÓÈ ‡·ÓÚ ÔËÏÂÌÂÌË ÏÂÚÓ‰‡ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ ÔÓÁ‚ÓÎËÎÓ ‡ÎËÁÓ‚‡Ú ̧ Ú‡ÍÓÈ ÔÓ‰ıÓ‰ Ë ÔÓÎÛ ̃ËÚ ̧ ‡Ò ̃ÂÚÌ ̊ Á‡‚ËÒËÏÓÒÚË, Ò‚ˇÁ ̊‚‡ ̨ ̆Ë ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌÓ„Ó ÍÓÏÔÓÁËÚ‡ Ò ÚÂÏÓÛÔÛ„ËÏË ı‡‡ÍÚÂËÒÚË͇ÏË Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ëı Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËÂÈ. ƒÎˇ ÔÓ‚ÂÍË ‰ÓÒÚÓ‚ÂÌÓÒÚË ̋ÚËı Á‡‚ËÒËÏÓÒÚÂÈ ÔÓÒÚÓÂÌ ̊ ‰‚ÛÒÚÓÓÌÌË „‡Ìˈ ̊ ӷ·ÒÚË
    (check this in PDF content)

  12. Start
    5074
    Prefix
    ŒÒÌÓ‚Ì ̊ ÒÓÓÚÌÓ ̄ÂÌˡ ¬ ÒÎÛ ̃‡Â ̄‡Ó‚ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ Ó‰Ë̇ÍÓ‚Ó„Ó ‡ÁÏÂ‡ ÔË Ëı ̇˷ÓΠÔÎÓÚÌÓÈ ÛÔ‡ÍÓ‚ÍÂ, ÍÓ„‰‡ ‚ ͇ʉÓÏ ÒÎÓ ˆÂÌÚ ̊ ÍÓÌÚ‡ÍÚËÛ ̨ ̆Ëı ÏÂÊ‰Û ÒÓ·ÓÈ ̄‡Ó‚ ̇ıÓ‰ˇÚÒˇ ‚ ‚Â ̄Ë̇ı Ô‡‚ËÎ ̧Ì ̊ı ÚÂÛ„ÓÎ ̧ÌËÍÓ‚, Ó· ̇ÂÏ̇ˇ ÍÓ̈ÂÌÚ‡ˆËˇCVÚ‡ÍËı ‚ÍÎ ̨ ̃ÂÌËÈ ÔËÌËχÂÚ Ì‡Ë·ÓÎ ̧ ̄ Á̇ ̃ÂÌËÂC◦V= π 3 √ 2 ≈0,7405
    Exact
    [38]
    Suffix
    . ≈ÒÎË ÌÂ Û ̃ËÚ ̊‚‡Ú ̧ ÍÓÌÍÂÚÌ ̊È ‡ÁÏÂ ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ò ̃ËÚ‡Ú ̧, ̃ÚÓ Ëı ‰Ë‡ÏÂÚ ÏÓÊÂÚ ÔËÌËÏ‡Ú ̧ Á̇ ̃ÂÌˡ ÓÚ ÌÂÍÓÚÓÓ„Ó ÍÓÌ ̃ÌÓ„Ó ‰Ó ·ÂÒÍÓÌ ̃ÌÓ Ï‡ÎÓ„Ó, Ú. Â. ‚ÓÁÏÓÊÌÓ Á‡ÔÓÎÌÂÌË ‚ÒÂı ÔÛÒÚÓÚ ÏÂÊ‰Û ÍÛÔÌ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË, ÚÓ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Á̇ ̃ÂÌˡCV∈[0,1].
    (check this in PDF content)

  13. Start
    6140
    Prefix
    –‡ÒÔÓÎÓÊÂÌË ‚ÍÎ ̨ ̃ÂÌËÈ ÔËÏÂÏ ÒÎÛ ̃‡ÈÌ ̊Ï, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ Ò ̃ËÚ‡Ú ̧ ÍÓÏÔÓÁËÚ Ï‡ÍÓÒÍÓÔË ̃ÂÒÍË ËÁÓÚÓÔÌ ̊Ï Ò Ó· ̇ÂÏÌ ̊Ï ÏÓ‰ÛÎÂÏ ÛÔÛ„ÓÒÚËKË ÏÓ‰ÛÎÂÏ Ò‰‚Ë„‡G. ◊ÂÂÁ ̋ÚË ÏÓ‰ÛÎË ÏÓÊÌÓ ‚ ̊‡ÁËÚ ̧ ÔÓ‰ÓÎ ̧Ì ̊È ÏÓ‰ÛÎ ̧ ÛÔÛ„ÓÒÚË (ÏÓ‰ÛÎ ̧ fiÌ„‡)E= 9KG 3K+G Ë ÍÓ ̋ÙÙˈËÂÌÚ œÛ‡ÒÒÓ̇ν= 1 2 − 3G 6K+ 2G ÍÓÏÔÓÁËÚ‡
    Exact
    [39]
    Suffix
    . »ÒÍÓÏ ̊È ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ Ó·ÓÁ̇ ̃ËÏα. ”ÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË ‚ÍÎ ̨ ̃ÂÌËÈ, χÚˈ ̊ Ë ÍÓÏÔÓÁËÚ‡ ‚ ˆÂÎÓÏ ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ Ó‰Ë̇ÍÓ‚ÓÈ ÚÂÌÁÓÌÓÈ ÙÓÏ [1,40] (̇ ÔËÏÂ ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡) Cˆ= 3KˆV+ 2GˆD,(2) „‰ÂˆC| ÚÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË, ‡ˆVˈD| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡, ˇ‚Ρ ̨ ̆ËÂÒˇ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ó· ̇ÂÏÌÓÈ Ë ‰Â‚ˇÚ
    (check this in PDF content)

  14. Start
    6338
    Prefix
    ◊ÂÂÁ ̋ÚË ÏÓ‰ÛÎË ÏÓÊÌÓ ‚ ̊‡ÁËÚ ̧ ÔÓ‰ÓÎ ̧Ì ̊È ÏÓ‰ÛÎ ̧ ÛÔÛ„ÓÒÚË (ÏÓ‰ÛÎ ̧ fiÌ„‡)E= 9KG 3K+G Ë ÍÓ ̋ÙÙˈËÂÌÚ œÛ‡ÒÒÓ̇ν= 1 2 − 3G 6K+ 2G ÍÓÏÔÓÁËÚ‡ [39]. »ÒÍÓÏ ̊È ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ Ó·ÓÁ̇ ̃ËÏα. ”ÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË ‚ÍÎ ̨ ̃ÂÌËÈ, χÚˈ ̊ Ë ÍÓÏÔÓÁËÚ‡ ‚ ˆÂÎÓÏ ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ Ó‰Ë̇ÍÓ‚ÓÈ ÚÂÌÁÓÌÓÈ ÙÓÏÂ
    Exact
    [1,40]
    Suffix
    (̇ ÔËÏÂ ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡) Cˆ= 3KˆV+ 2GˆD,(2) „‰ÂˆC| ÚÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË, ‡ˆVˈD| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡, ˇ‚Ρ ̨ ̆ËÂÒˇ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ó· ̇ÂÏÌÓÈ Ë ‰Â‚ˇÚÓÌÓÈ ÒÓÒÚ‡‚Ρ ̨ ̆ËÏË Â‰ËÌË ̃ÌÓ„Ó ÚÂÌÁÓ‡ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ˆI=ˆV+ˆD.
    (check this in PDF content)

  15. Start
    7015
    Prefix
    ‰ËÌË ̃Ì ̊È ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ Ò ÍÓÏÔÓÌÂÌÚ‡ÏËδij,i, j= 1,2,3(δij= 1ÔËi=jËδij= 0ÔËi6=j), ÚÓ ÍÓÏÔÓÌÂÌÚ ̊ ̋ÚËı ÒÓÒÚ‡‚Ρ ̨ ̆Ëı, ÓÔ‰ÂÎÂÌÌ ̊ ‚ ‚ ̊·‡ÌÌÓÈ ÔˇÏÓÛ„ÓÎ ̧ÌÓÈ ‰Â͇ÚÓ‚ÓÈ ÒËÒÚÂÏ ÍÓÓ‰ËÌ‡Ú Ox1x2x3, ÔËÏÛÚ ‚ˉ Vijmn= 1 3 δijδmn, Dijmn= 1 2 (δimδjn+δinδjm)−Vijmn, m, n= 1,2,3. — Û ̃ÂÚÓÏ ̋ÚËı ÙÓÏÛÎ, Ô‡‚Ë· ÒÛÏÏËÓ‚‡Ìˡ Ò·„‡ÂÏ ̊ı ÔÓ ÔÓ‚ÚÓˇ ̨ ̆ËÏÒˇ ‚ ÒÓÏÌÓÊËÚÂΡı ·ÚËÌÒÍËÏ Ë̉ÂÍÒ‡Ï
    Exact
    [41]
    Suffix
    Ë ‡‚ÂÌÒÚ‚‡δii= 3ÏÓÊÌÓ ÛÒÚ‡ÌÓ‚ËÚ ̧, ̃ÚÓVijklδkl=δij, Dijklδkl= 0,k, l= 1,2,3, ‡ Ú‡ÍÊ [1] VijmnVmnkl=Vijkl, DijmnDmnkl=Dijkl, VijmnDmnkl= 0,(3) “ÂÌÁÓ ̊ˆVˈDË Ô‰ÒÚ‡‚ÎÂÌÌ ̊È ̃ÂÂÁ ÌËı ‚ ÙÓÏÛΠ(2) ÚÂÌÁÓˆCˇ‚Ρ ̨ÚÒˇ ËÁÓÚÓÔÌ ̊ÏË, Ú.
    (check this in PDF content)

  16. Start
    7106
    Prefix
    — Û ̃ÂÚÓÏ ̋ÚËı ÙÓÏÛÎ, Ô‡‚Ë· ÒÛÏÏËÓ‚‡Ìˡ Ò·„‡ÂÏ ̊ı ÔÓ ÔÓ‚ÚÓˇ ̨ ̆ËÏÒˇ ‚ ÒÓÏÌÓÊËÚÂΡı ·ÚËÌÒÍËÏ Ë̉ÂÍÒ‡Ï [41] Ë ‡‚ÂÌÒÚ‚‡δii= 3ÏÓÊÌÓ ÛÒÚ‡ÌÓ‚ËÚ ̧, ̃ÚÓVijklδkl=δij, Dijklδkl= 0,k, l= 1,2,3, ‡ Ú‡ÍÊÂ
    Exact
    [1]
    Suffix
    VijmnVmnkl=Vijkl, DijmnDmnkl=Dijkl, VijmnDmnkl= 0,(3) “ÂÌÁÓ ̊ˆVˈDË Ô‰ÒÚ‡‚ÎÂÌÌ ̊È ̃ÂÂÁ ÌËı ‚ ÙÓÏÛΠ(2) ÚÂÌÁÓˆCˇ‚Ρ ̨ÚÒˇ ËÁÓÚÓÔÌ ̊ÏË, Ú. Â. Ëı ÍÓÏÔÓÌÂÌÚ ̊ Ì Á‡‚ËÒˇÚ ÓÚ ÓËÂÌÚ‡ˆËË ÓÒÂÈ ‚ ̊·‡ÌÌÓÈ ÒËÒÚÂÏ ̊ ÔˇÏÓÛ„ÓÎ ̧Ì ̊ı ‰Â͇ÚÓ‚ ̊ı ÍÓÓ‰Ë̇Ú. 2.
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  17. Start
    8426
    Prefix
    ≈ÒÎË Ï ̊ÒÎÂÌÌÓ ËÁ‚Π̃ ̧ ‚ÍÎ ̨ ̃ÂÌË ËÁ ÓÍÛʇ ̨ ̆ÂÈ Ò‰ ̊ Ë ÒÓÁ‰‡Ú ̧ ‚ ÌÂÏ Ó‰ÌÓÓ‰ÌÛ ̨ ‰ÂÙÓχˆË ̨, ÓÔ‰ÂΡÂÏÛ ̨ ÚÂÌÁÓÓψe′′, ÚÓ ÔÓÒΠ‚ÓÁ‚‡ ̆ÂÌˡ ‚ÍÎ ̨ ̃ÂÌˡ ̇ ÔÂÊÌ ÏÂÒÚÓ ‰ÂÙÓÏËÓ‚‡ÌÌÓ ÒÓÒÚÓˇÌË ̋ÚÓ„Ó ‚ÍÎ ̨ ̃ÂÌˡ Ú‡ÍÊ ·Û‰ÂÚ Ó‰ÌÓÓ‰Ì ̊Ï
    Exact
    [13]
    Suffix
    , ÓÔ‰ÂΡÂÏ ̊Ï ÚÂÌÁÓÓψe•. ›ÚÓÚ ÚÂÌÁÓ Ò‚ˇÁ‡Ì Ò ÚÂÌÁÓÓÏ ˆe′′ÒÓÓÚÌÓ ̄ÂÌËÂÏ [1,13]ˆe′′=ˆW··ˆe•, „‰Â Wˆ= 31−ν 1 +ν Vˆ+15 2 1−ν 4−5ν Dˆ.(4) œË ̋ÚÓÏ Ì‡ÔˇÊÂÌÌÓ ÒÓÒÚÓˇÌË ‚ÍÎ ̨ ̃ÂÌˡ ·Û‰ÂÚ ı‡‡ÍÚÂËÁÓ‚‡Ú ̧ ÚÂÌÁÓ ˆs•=ˆC··(ˆe•−ˆe′′) =ˆC··ˆe•−ˆC··ˆW··ˆe•.(5) «‰ÂÒ ̧ ͇ʉ‡ˇ ËÁ ÚÓ ̃ÂÍ ÏÂÊ‰Û ÒÓÏÌÓÊËÚÂΡÏË ‚ ÔÓËÁ‚‰ÂÌËË ÚÂÌÁÓÓ‚ ÓÁ̇ ̃‡ÂÚ Ò‚ÂÚ ̊‚‡ÌË ÔÓ Ë̉ÂÍÒÛ, Ó‰Ë̇ÍÓ‚ÓÏÛ ‚ Ó·ÓËı ÒÓÏÌÓÊËÚÂΡı [41].
    (check this in PDF content)

  18. Start
    8506
    Prefix
    ≈ÒÎË Ï ̊ÒÎÂÌÌÓ ËÁ‚Π̃ ̧ ‚ÍÎ ̨ ̃ÂÌË ËÁ ÓÍÛʇ ̨ ̆ÂÈ Ò‰ ̊ Ë ÒÓÁ‰‡Ú ̧ ‚ ÌÂÏ Ó‰ÌÓÓ‰ÌÛ ̨ ‰ÂÙÓχˆË ̨, ÓÔ‰ÂΡÂÏÛ ̨ ÚÂÌÁÓÓψe′′, ÚÓ ÔÓÒΠ‚ÓÁ‚‡ ̆ÂÌˡ ‚ÍÎ ̨ ̃ÂÌˡ ̇ ÔÂÊÌ ÏÂÒÚÓ ‰ÂÙÓÏËÓ‚‡ÌÌÓ ÒÓÒÚÓˇÌË ̋ÚÓ„Ó ‚ÍÎ ̨ ̃ÂÌˡ Ú‡ÍÊ ·Û‰ÂÚ Ó‰ÌÓÓ‰Ì ̊Ï [13], ÓÔ‰ÂΡÂÏ ̊Ï ÚÂÌÁÓÓψe•. ›ÚÓÚ ÚÂÌÁÓ Ò‚ˇÁ‡Ì Ò ÚÂÌÁÓÓÏ ˆe′′ÒÓÓÚÌÓ ̄ÂÌËÂÏ
    Exact
    [1,13]
    Suffix
    ˆe′′=ˆW··ˆe•, „‰Â Wˆ= 31−ν 1 +ν Vˆ+15 2 1−ν 4−5ν Dˆ.(4) œË ̋ÚÓÏ Ì‡ÔˇÊÂÌÌÓ ÒÓÒÚÓˇÌË ‚ÍÎ ̨ ̃ÂÌˡ ·Û‰ÂÚ ı‡‡ÍÚÂËÁÓ‚‡Ú ̧ ÚÂÌÁÓ ˆs•=ˆC··(ˆe•−ˆe′′) =ˆC··ˆe•−ˆC··ˆW··ˆe•.(5) «‰ÂÒ ̧ ͇ʉ‡ˇ ËÁ ÚÓ ̃ÂÍ ÏÂÊ‰Û ÒÓÏÌÓÊËÚÂΡÏË ‚ ÔÓËÁ‚‰ÂÌËË ÚÂÌÁÓÓ‚ ÓÁ̇ ̃‡ÂÚ Ò‚ÂÚ ̊‚‡ÌË ÔÓ Ë̉ÂÍÒÛ, Ó‰Ë̇ÍÓ‚ÓÏÛ ‚ Ó·ÓËı ÒÓÏÌÓÊËÚÂΡı [41].
    (check this in PDF content)

  19. Start
    8811
    Prefix
    ›ÚÓÚ ÚÂÌÁÓ Ò‚ˇÁ‡Ì Ò ÚÂÌÁÓÓÏ ˆe′′ÒÓÓÚÌÓ ̄ÂÌËÂÏ [1,13]ˆe′′=ˆW··ˆe•, „‰Â Wˆ= 31−ν 1 +ν Vˆ+15 2 1−ν 4−5ν Dˆ.(4) œË ̋ÚÓÏ Ì‡ÔˇÊÂÌÌÓ ÒÓÒÚÓˇÌË ‚ÍÎ ̨ ̃ÂÌˡ ·Û‰ÂÚ ı‡‡ÍÚÂËÁÓ‚‡Ú ̧ ÚÂÌÁÓ ˆs•=ˆC··(ˆe•−ˆe′′) =ˆC··ˆe•−ˆC··ˆW··ˆe•.(5) «‰ÂÒ ̧ ͇ʉ‡ˇ ËÁ ÚÓ ̃ÂÍ ÏÂÊ‰Û ÒÓÏÌÓÊËÚÂΡÏË ‚ ÔÓËÁ‚‰ÂÌËË ÚÂÌÁÓÓ‚ ÓÁ̇ ̃‡ÂÚ Ò‚ÂÚ ̊‚‡ÌË ÔÓ Ë̉ÂÍÒÛ, Ó‰Ë̇ÍÓ‚ÓÏÛ ‚ Ó·ÓËı ÒÓÏÌÓÊËÚÂΡı
    Exact
    [41]
    Suffix
    . ¬ ÒÓÓÚÌÓ ̄ÂÌË (5) ‚ıÓ‰ËÚ ‚ÌÛÚÂÌÌ ÔÓËÁ‚‰ÂÌË ËÁÓÚÓÔÌ ̊ı ÚÂÌÁÓÓ‚ˆCˈW. — Û ̃ÂÚÓÏ ÙÓÏÛÎ (2){(4) Ë Ô‰ÒÚ‡‚ÎÂÌˡ ÍÓ ̋ÙÙˈËÂÌÚ‡ œÛ‡ÒÒÓ̇ ̃ÂÂÁ ÏÓ‰ÛÎËKËGÔÓÎÛ ̃ËÏ Cˆ··ˆW= (3K+ 4G)ˆV+5 3 3K+ 4G K+ 2G Dˆ.(6) Õ‡ ‚ÚÓÓÏ ̋Ú‡Ô ÔÓ‚ ̊ÒËÏ ÚÂÏÔÂ‡ÚÛÛ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓ„Ó Ó· ̇Âχ ̇ ‚ÂÎË ̃ËÌÛ∆T, ̃ÚÓ Ô˂‰ÂÚ Í ‚ÓÁÌËÍÌÓ‚ÂÌˡ Ó‰ÌÓÓ‰ÌÓÈ ÔÓ ̋ÚÓÏÛ Ó· ̇ÂÏÛ ÚÂÏÔÂ‡ÚÛÌÓÈ ‰ÂÙÓχˆËË, ÓÔ‰ÂΡÂÏÓÈ ÚÂÌÁÓÓψ
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  20. Start
    11735
    Prefix
    ̊È ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡα‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡, ˇ‚ΡÂÚÒˇ ÓÒ‰ÌÂÌË ÔÓ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏÛ Ó· ̇ÂÏÛ ‚ÓÁÏÛ ̆ÂÌËÈ Ì‡ÔˇÊÂÌÌÓ„Ó ÒÓÒÚÓˇÌˡ ‚Ó ‚ÒÂı ‚ÍÎ ̨ ̃ÂÌˡı Ë ̃‡ÒÚˈ‡ı χÚˈ ̊. ƒÎˇ ÚÂÌÁÓ‡ ̇ÔˇÊÂÌËÈ Í‡Í ÚÂÌÁÓ‡ ‚ÚÓÓ„Ó ‡Ì„‡ Ú‡ÍÓ ÓÒ‰ÌÂÌË ̋Í‚Ë‚‡ÎÂÌÚÌÓ ‚ ̊ ̃ËÒÎÂÌË ̨ Â„Ó ÔÂ‚Ó„Ó ËÌ‚‡ˇÌÚ‡, Ú. Â. ÛÏÌÓÊÂÌË ̨ ̋ÚÓ„Ó ÚÂÌÁÓ‡ ̇ ‰ËÌË ̃Ì ̊È ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ ˆI2
    Exact
    [41,42]
    Suffix
    . “Ó„‰‡ ‰Îˇ ‚ÍÎ ̨ ̃ÂÌËÈ ËÁ χÚÂˇ· Ò ÌÓÏÂÓÏς, Û ̃ËÚ ̊‚‡ˇ ÙÓÏÛÎ ̊ (2), (3), (6) Ë (8), ÔÓÎÛ ̃‡ÂÏ ˆsς··ˆI2= 12GKς(ας−α) 3Kς+ 4G . ¿Ì‡ÎÓ„Ë ̃ÌÓ, ËÒÔÓÎ ̧ÁÛˇ ÙÓÏÛÎ ̊ (2), (3), (6) Ë (9), ̇ıÓ‰ËÏ ˆsm··ˆI2= 12GKm(αm−α) 3Km+ 4G .
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  21. Start
    12072
    Prefix
    ¿Ì‡ÎÓ„Ë ̃ÌÓ, ËÒÔÓÎ ̧ÁÛˇ ÙÓÏÛÎ ̊ (2), (3), (6) Ë (9), ̇ıÓ‰ËÏ ˆsm··ˆI2= 12GKm(αm−α) 3Km+ 4G . »ÚÓ„Ó‚ ̊È ÂÁÛÎ ̧Ú‡Ú ÓÒ‰ÌÂÌˡ ÔÓ ‚ÒÂÏ ‚ÍÎ ̨ ̃ÂÌËˇÏ Ë ̃‡ÒÚˈ‡Ï χÚˈ ̊ ‚ ÒÓÓÚ‚ÂÚÒÚ‚ËË Ò ÏÂÚÓ‰ÓÏ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ
    Exact
    [10]
    Suffix
    ‰ÓÎÊÂÌ · ̊Ú ̧ ‡‚ÂÌ ÌÛÎ ̨, Ú. Â. Ò Û ̃ÂÚÓÏ ‰‚Ûı ÔÓÒΉÌËı ‡‚ÂÌÒÚ‚ Ë ÙÓÏÛÎ ̊ (1) 12GKm αm−α 3Km+ 4G (1−CV) + 12G ∑N ς=1 Kς ας−α 3Kς+ 4G Cς= 0. –‡Á ̄Ë‚ ̋ÚÓ ‡‚ÂÌÒÚ‚Ó ÓÚÌÓÒËÚÂÎ ̧ÌÓ ËÒÍÓÏÓ„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡, Á‡ÔË ̄ÂÏ α= ( Km 1−CV 3Km+ 4G + ∑N ς=1 KςCς 3Kς+ 4G )−1( αmKm 1−CV 3Km+ 4G + ∑N ς=1 αςKςCς 3Kς+ 4G ) .(10) —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃
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  22. Start
    12907
    Prefix
    ÔË‚Ó‰ËÚ ÓÒ‰ÌÂÌË ÔÓ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏÛ Ó· ̇ÂÏÛ ÚÂÌÁÓÓ‚ ‰ÂÙÓχˆËË ‚Ó ‚ÒÂı ‚ÍÎ ̨ ̃ÂÌˡı Ë ̃‡ÒÚˈ‡ı χÚˈ ̊ ÍÓÏÔÓÁËÚ‡. 3. ƒ‚ÛÒÚÓÓÌÌË ӈÂÌÍË ƒÎˇ ÔÓÒÚÓÂÌˡ ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡ ËÒÔÓÎ ̧ÁÛÂÏ ‰‚ÓÈÒÚ‚ÂÌÌÛ ̨ ‚‡ˇˆËÓÌÌÛ ̨ ÙÓÏÛ ÏÓ‰ÂÎË ÎËÌÂÈÌÓÈ ÚÂÏÓÛÔÛ„ÓÒÚË ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ÌÂÓ‰ÌÓÓ‰ÌÓÏÛ ÎËÌÂÈÌÓ ÛÔÛ„ÓÏÛ Ú‚Â‰ÓÏÛ ÚÂÎÛ
    Exact
    [36,38]
    Suffix
    . ›Ú‡ ÙÓχ ÒÓ‰ÂÊËÚ ‰‚‡ ‡Î ̧ÚÂ̇ÚË‚Ì ̊ı ÙÛÌ͈ËÓ̇· (ÏËÌËÏËÁËÛÂÏ ̊È Ë Ï‡ÍÒËÏËÁËÛÂÏ ̊È), ÍÓÚÓ ̊ ̇ ËÒÚËÌÌ ̊ı ‡ÒÔ‰ÂÎÂÌˡı ÔÂÂÏ ̆ÂÌËÈ Ë Ì‡ÔˇÊÂÌËÈ ‰ÓÒÚË„‡ ̨Ú ‡‚Ì ̊ı ÔÓ Á̇ ̃ÂÌË ̨ ̋ÍÒÚÂÏÛÏÓ‚.
    (check this in PDF content)

  23. Start
    13492
    Prefix
    –‡ÒÒÏÓÚËÏ Ô‰ÒÚ‡‚ËÚÂÎ ̧Ì ̊È Ó· ̇ÂÏVÍÓÏÔÓÁËÚ‡, Á‡ÍÎ ̨ ̃ÂÌÌ ̊È ‚ ‡·ÒÓÎ ̨ÚÌÓ ÊÂÒÚÍÛ ̨ Ó·ÓÎÓ ̃ÍÛ, Ó·ÂÒÔ ̃Ë‚‡ ̨ ̆Û ̨ ÔË Ó‰ÌÓÓ‰ÌÓÏ ÔË‡ ̆ÂÌËË ÚÂÏÔÂ‡ÚÛ ̊ ÍÓÏÔÓÁËÚ‡ ̇ ‚ÂÎË ̃ËÌÛ∆TÓÚÒÛÚÒÚ‚Ë ÔÂÂÏ ̆ÂÌËÈ Ì‡ ÔÓ‚ÂıÌÓÒÚË, Ó„‡ÌË ̃Ë‚‡ ̨ ̆ÂÈ ̋ÚÓÚ Ó· ̇ÂÏ. ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â ̇ ‰ÓÔÛÒÚËÏÓÏ ‰Îˇ ÏËÌËÏËÁËÛÂÏÓ„Ó ÙÛÌ͈ËÓ̇· Ó‰ÌÓÓ‰ÌÓÏ ‡ÒÔ‰ÂÎÂÌËË u(M) = 0(M∈V) ÔÂÂÏ ̆ÂÌËÈ ÓÌ ÔËÏÂÚ ‚ˉ
    Exact
    [43]
    Suffix
    J1= 9 2 ∫ V K′(M) ( α′(M)∆T )2 dV(M) = 9V 2 (∆T)2 ( Kmα2m(1−CV) + ∑N ς=1 Kςα2ςCς ) ,(11) „‰ÂK′(M)Ëα′(M)| Á‡‚ËÒˇ ̆Ë ÓÚ ÔÓÎÓÊÂÌˡ ÚÓ ̃ÍËM∈VÁ̇ ̃ÂÌˡ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚË Ë ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‚ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏ Ó· ̇ÂÏ ÍÓÏÔÓÁËÚ‡. ƒÎˇ χÍÒËÏËÁËÛÂÏÓ„Ó ÙÛÌ͈ËÓ̇· Ó‰ÌËÏ ËÁ ‰ÓÔÛÒÚËÏ ̊ı ‡ÒÔ‰ÂÎÂÌËÈ Ì‡ÔˇÊÂÌËÈ ˇ‚ΡÂÚÒˇ Ó‰ÌÓÓ‰ÌÓ ÔÓ Ó· ̇ÂÏÛV, ÓÔ‰ÂΡÂÏÓ ̄‡Ó‚
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  24. Start
    13953
    Prefix
    11) „‰ÂK′(M)Ëα′(M)| Á‡‚ËÒˇ ̆Ë ÓÚ ÔÓÎÓÊÂÌˡ ÚÓ ̃ÍËM∈VÁ̇ ̃ÂÌˡ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚË Ë ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‚ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏ Ó· ̇ÂÏ ÍÓÏÔÓÁËÚ‡. ƒÎˇ χÍÒËÏËÁËÛÂÏÓ„Ó ÙÛÌ͈ËÓ̇· Ó‰ÌËÏ ËÁ ‰ÓÔÛÒÚËÏ ̊ı ‡ÒÔ‰ÂÎÂÌËÈ Ì‡ÔˇÊÂÌËÈ ˇ‚ΡÂÚÒˇ Ó‰ÌÓÓ‰ÌÓ ÔÓ Ó· ̇ÂÏÛV, ÓÔ‰ÂΡÂÏÓ ̄‡Ó‚ ̊Ï ÚÂÌÁÓÓψs′=σδij,σ= const. Õ‡ Ú‡ÍÓÏ ‡ÒÔ‰ÂÎÂÌËË ̋ÚÓÚ ÙÛÌ͈ËÓ̇ΠËÏÂÂÚ ‚ˉ
    Exact
    [43]
    Suffix
    J2=− ∫ V ( σ2 18K′(M) +σα′(M)∆T ) dV(M). «Ì‡ ̃ÂÌËÂσ̇ȉÂÏ ËÁ ÌÂÓ·ıÓ‰ËÏÓ„Ó ÛÒÎӂˡ ÒÛ ̆ÂÒÚ‚Ó‚‡Ìˡ ̋ÍÒÚÂÏÛχ ̋ÚÓ„Ó ÙÛÌ͈ËÓ̇· dJ2 dσ =− ∫ V ( σ 9K′(M) +α′(M)∆T ) dV(M) = 0. ŒÚÒ ̨‰‡ ÒΉÛÂÚ σ=−9∆T ( 1−CV Km + ∑N ς=1 Cς Kς )−1( αm(1−CV) + ∑N ς=1 αςCς ) . œÓÒΠÔÓ‰ÒÚ‡ÌÓ‚ÍËσ‚ ÙÛÌ͈ËÓ̇ÎJ2ÔÓÎÛ ̃ËÏ J2= 9V 2 (∆T)2 ( 1−CV Km + ∑N ς=1 Cς Kς )−1( αm(1−CV) + ∑N ς=1 αςCς )2 .(12) ƒÎˇ Ò‰ ̊, ËÏ ̨ ̆ÂÈ ËÒÍÓ
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  25. Start
    14886
    Prefix
    N ς=1 KςCς ) = 9V 2 (α∆T)2KV,(13) ‡ χÍÒËÏËÒÁËÛÂÏ ̊È ÙÛÌ͈ËÓ̇Π̇ ‰ÓÔÛÒÚËÏÓÏ Ó‰ÌÓÓ‰ÌÓÏ ‡ÒÔ‰ÂÎÂÌËË Ì‡ÔˇÊÂÌËÈ σ∗=−9α∆T ( 1−CV Km + ∑N ς=1 Cς Kς )−1 ÔËÏÂÚ Á̇ ̃ÂÌË J∗2= 9V 2 (α∆T)2 ( 1−CV Km + ∑N ς=1 Cς Kς )−1 = 9V 2 (α∆T)2KR.(14) ŒÚÏÂÚËÏ, ̃ÚÓ ËÁ Ò‡‚ÌÂÌˡσ∗ÒσË ÒÓÔÓÒÚ‡‚ÎÂÌˡ ÙÓÏÛÎ (14) Ë (12) ÏÓÊÌÓ ÔÓÎÛ ̃ËÚ ̧ ÓˆÂÌÍÛ α∗=αm(1−CV) + ∑N ς=1 αςCς,(15) ÍÓÚÓ‡ˇ Ú‡ÍÊ ÒΉÛÂÚ ËÁ ÚÂÓËË ÒÏÂÒÂÈ
    Exact
    [44]
    Suffix
    . »Á Ò‚ÓÈÒÚ‚ ‰‚ÓÈÒÚ‚ÂÌÌÓÈ ‚‡ˇˆËÓÌÌÓÈ ÙÓÏ ̊ ÏÓ‰ÂÎË ÎËÌÂÈÌÓÈ ÚÂÏÓÛÔÛ„ÓÒÚË ‰Îˇ Á̇ ̃ÂÌËÈ ‡Î ̧ÚÂ̇ÚË‚Ì ̊ı ÙÛÌ͈ËÓ̇ÎÓ‚ ̇ ‰ÓÔÛÒÚËÏ ̊ı ‡ÒÔ‰ÂÎÂÌˡı ÔÂÂÏ ̆ÂÌËÈ Ë Ì‡ÔˇÊÂÌËÈ ÒÎÂ‰Û ̨Ú Ì ÚÓÎ ̧ÍÓ ÌÂ‡‚ÂÌÒÚ‚‡J1>J2,J∗1>J∗2, ÌÓ ËJ1>J∗2,J∗1>J2.
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  26. Start
    16148
    Prefix
    “Ó„‰‡ ËÁ ÙÓÏÛÎ ̊ (15) ÔÓÎÛ ̃ËÏ α ̃∗= α∗ αm = 1−CV+ ̄α,(17) ËÁ ÙÓÏÛÎ ̊ (10) | α ̃= ̃α∗+ ( ̄α−1)( ̄K−1)CV(1−CV) K ̄V+3 K ̄ 4 ̄G ,(18) „‰Â ̄KV= 1−CV+ ̄KCV, ‡ ÒÓÓÚÌÓ ̄ÂÌË (16) ÔËÏÂÚ ‚ˉ α ̃+= √ √ √ √1−CV+ K ̄ ̄α2CV K ̄R ≥ ̃α≥ ̃α∗ √ √ √ √ K ̄R K ̄V = ̃α−,(19) „‰Â K ̄R=1 1−CV+CV/ ̄K . œÓÒÍÓÎ ̧ÍÛ ̄KR/ ̄KV>1Í‡Í ÓÚÌÓ ̄ÂÌË ÌËÊÌÂÈ Ë ‚ÂıÌÂÈ ÓˆÂÌÓÍ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚ‡
    Exact
    [39]
    Suffix
    , ËÁ ÒÓÓÚÌÓ ̄ÂÌˡ (19) ÒΉÛÂÚ, ̃ÚÓ ̃α−6 ̃α∗. œË Ó‰Ë̇ÍÓ‚ ̊ı Á̇ ̃ÂÌˡı Ó· ̇ÂÏÌ ̊ı ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ï‡Úˈ ̊ ( ̄K= 1) ËÏÂÂÏ ̄KR/ ̄KV= 1 Ë ̃α−= ̃α∗, ‡ ‚ÂıÌˇˇ ÓˆÂÌ͇ ̃α+= √ 1−CV+ ̄α2CV> ̃α∗ÔË ̄α6= 1ËCV∈(0,1). ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â, Òӄ·ÒÌÓ ÙÓÏÛΠ(18), ̃α= ̃α∗.
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  27. Start
    16564
    Prefix
    ) ÒΉÛÂÚ, ̃ÚÓ ̃α−6 ̃α∗. œË Ó‰Ë̇ÍÓ‚ ̊ı Á̇ ̃ÂÌˡı Ó· ̇ÂÏÌ ̊ı ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ï‡Úˈ ̊ ( ̄K= 1) ËÏÂÂÏ ̄KR/ ̄KV= 1 Ë ̃α−= ̃α∗, ‡ ‚ÂıÌˇˇ ÓˆÂÌ͇ ̃α+= √ 1−CV+ ̄α2CV> ̃α∗ÔË ̄α6= 1ËCV∈(0,1). ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â, Òӄ·ÒÌÓ ÙÓÏÛΠ(18), ̃α= ̃α∗. ≈ÒÎË ÒÓ‚Ô‡‰‡ ̨Ú ÏÓ‰ÛÎË Ò‰‚Ë„‡ ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ï‡Úˈ ̊ (G1=Gm=G), ÚÓ ‰Îˇ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚËK∗Ú‡ÍÓ„Ó ÍÓÏÔÓÁËÚ‡ ËÁ‚ÂÒÚ̇ ÚÓ ̃̇ˇ ÙÓÏÛ·
    Exact
    [2]
    Suffix
    K ̄∗=K ∗ Km = 3 ̄K+ 4 ̄G ̄KV 3 ̄K+ 4 ̄G ̄KR . ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â ÔÓÎÛ ̃Â̇ Ë ÚÓ ̃̇ˇ ÙÓÏÛ· ‰Îˇ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡α∗ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ [1,2]. ›ÚÛ ÙÓÏÛÎÛ ÏÓÊÌÓ ÔË‚ÂÒÚË Í ‚Ë‰Û α ̃∗= α∗ αm = ̃α∗+ α ̄−1 1−1/ ̄K ( 1 K ̄R − 1 K ̄∗ ) . œÓÒÍÓÎ ̧ÍÛ ÚÓ ̃ÌÓ Á̇ ̃ÂÌËÂK∗‚ Ó· ̆ÂÏ ÒÎÛ ̃‡Â Ì ËÁ‚ÂÒÚÌÓ, ÔÓÒÎÂ‰Ì ̨ ̨ ÙÓÏÛÎÛ ÏÓÊÌÓ ÔËÏÂÌËÚ ̧ ‰Îˇ ÔÓÒÚÓÂÌˡ ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ.
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  28. Start
    16715
    Prefix
    ≈ÒÎË ÒÓ‚Ô‡‰‡ ̨Ú ÏÓ‰ÛÎË Ò‰‚Ë„‡ ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ï‡Úˈ ̊ (G1=Gm=G), ÚÓ ‰Îˇ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚËK∗Ú‡ÍÓ„Ó ÍÓÏÔÓÁËÚ‡ ËÁ‚ÂÒÚ̇ ÚÓ ̃̇ˇ ÙÓÏÛ· [2] K ̄∗=K ∗ Km = 3 ̄K+ 4 ̄G ̄KV 3 ̄K+ 4 ̄G ̄KR . ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â ÔÓÎÛ ̃Â̇ Ë ÚÓ ̃̇ˇ ÙÓÏÛ· ‰Îˇ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡α∗ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡
    Exact
    [1,2]
    Suffix
    . ›ÚÛ ÙÓÏÛÎÛ ÏÓÊÌÓ ÔË‚ÂÒÚË Í ‚Ë‰Û α ̃∗= α∗ αm = ̃α∗+ α ̄−1 1−1/ ̄K ( 1 K ̄R − 1 K ̄∗ ) . œÓÒÍÓÎ ̧ÍÛ ÚÓ ̃ÌÓ Á̇ ̃ÂÌËÂK∗‚ Ó· ̆ÂÏ ÒÎÛ ̃‡Â Ì ËÁ‚ÂÒÚÌÓ, ÔÓÒÎÂ‰Ì ̨ ̨ ÙÓÏÛÎÛ ÏÓÊÌÓ ÔËÏÂÌËÚ ̧ ‰Îˇ ÔÓÒÚÓÂÌˡ ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ.
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  29. Start
    20454
    Prefix
    ˇ ̇ ‚ ̊ÔÓÎÌÂÌË ‡‚ÂÌÒÚ‚ ̃α+= ̃α+= 1ÔËCV= 0Ë α ̃+= ̃α+= ̄αÔËCV= 1‰Îˇ ÔÓÏÂÊÛÚÓ ̃Ì ̊ı Á̇ ̃ÂÌËÈ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ ̋ÚË ÓˆÂÌÍË ÏÓ„ÛÚ ‚ ̊ıÓ‰ËÚ Á‡ Ô‰ÂÎ ̊ ÔÓÏÂÊÛÚ͇, Ó„‡ÌË ̃ÂÌÌÓ„Ó Á̇ ̃ÂÌˡÏË 1 Ë ̄α. œÓ ̋ÚÓÏÛ ‚ ÒÎÛ ̃‡Â ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡ Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÚÓÎ ̧ÍÓ ËÁ Ó‰ÌÓ„Ó Ï‡ÚÂˇ· ˆÂÎÂÒÓÓ·‡ÁÌÓ ÓÚ‰‡Ú ̧ Ô‰ÔÓ ̃ÚÂÌË ӈÂÌ͇Ï, ÓÔ‰ÂΡÂÏ ̊Ï ÌÂ‡‚ÂÌÒÚ‚‡ÏË (20). ¬ ‡·ÓÚÂ
    Exact
    [1]
    Suffix
    ÔÓÎÛ ̃ÂÌÌÛ ̨ ̇ ÓÒÌÓ‚Â ÒËÌ„ÛΡÌÓ„Ó ÔË·ÎËÊÂÌˡ ÚÂÓËË ÒÎÛ ̃‡ÈÌ ̊ı ÙÛÌ͈ËÈ ÙÓÏÛÎÛ, ‡Ì‡ÎÓ„Ë ̃ÌÛ ̨ ÔÓ ÒÚÛÍÚÛ ÙÓÏÛΠ(18), Ô‰ÎÓÊÂÌÓ ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ ‰Îˇ ÔÓÒÚÓÂÌˡ ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ ÔÛÚÂÏ ÔÓ‰·Ó‡ Ô‡‡ÏÂÚ‡ ̄G.
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  30. Start
    20935
    Prefix
    Œ‰ËÌ ËÁ ‚‡ˇÌÚÓ‚ ÒÓÒÚÓËÚ ‚ ËÒÔÓÎ ̧ÁÓ‚‡ÌËË ‰‚Ûı Á̇ ̃ÂÌËÈ ̄GV= 1−CV+ ̄G1CVË ̄GR= (1−CV+CV/ ̄G1)−1, „‰Â G ̄1=G1/Gm,G1ËGm| ÏÓ‰ÛÎË Ò‰‚Ë„‡ ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ï‡ÚÂˇ· χÚˈ ̊ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ. œÂ‚Ó Á̇ ̃ÂÌË ˇ‚ΡÂÚÒˇ ‚ÂıÌÂÈ ÓˆÂÌÍÓÈ ·ÂÁ‡ÁÏÂÌÓ„Ó ÏÓ‰ÛΡ Ò‰‚Ë„‡ ÍÓÏÔÓÁËÚ‡
    Exact
    [34]
    Suffix
    Ë Â„Ó ËÒÔÓÎ ̧ÁÓ‚‡ÌË ‚ ÙÓÏÛΠ‚ˉ‡ (18) ‰ÓÎÊÌÓ ‰‡Ú ̧ ‚ÂıÌ ̨ ̨ ÓˆÂÌÍÛ ‰Îˇ ̄α, ‡ ‚ÚÓÓ Á̇ ̃ÂÌËÂ, ·Û‰Û ̃Ë ÌËÊÌÂÈ ÓˆÂÌÍÓÈ ̋ÚÓ„Ó ÏÓ‰ÛΡ, ‰ÓÎÊÌÓ ÔË‚ÂÒÚË Í ÌËÊÌÂÈ ÓˆÂÌÍ ‰Îˇ α ̄. œÓÒÍÓÎ ̧ÍÛ ‚ÚÓÓ Ò·„‡ÂÏÓ ‚ Ô‡‚ÓÈ ̃‡ÒÚË ÙÓÏÛÎ ̊ (18) ˇ‚ΡÂÚÒˇ ÒÚÓ„Ó ÏÓÌÓÚÓÌÌÓÈ ÙÛÌ͈ËÂÈ Ô‡‡ÏÂÚ‡ ̄G, ÔË Î ̨·ÓÏ Á̇ ̃ÂÌËË ̄G∈( ̄GR, ̄GV)ÂÁÛÎ ̧Ú‡Ú ‚ ̊ ̃ËÒÎÂÌËÈ ÔÓ ̋ÚÓÈ ÙÓÏÛΠ·Û‰ÂÚ Á‡ÍÎ ̨ ̃ÂÌ ÏÂÊ‰Û Û͇Á‡ÌÌ ̊ÏË ‰‚
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