The 25 reference contexts in paper G. Kuvyrkin N., O. Pugachev V., V. Zarubin S., В. Зарубин С., Г. Кувыркин Н., О. Пугачёв В. (2016) “Двусторонние оценки термоупругих характеристик композита с дисперсными включениями // Two-Sided Estimates of Thermo-elastic Characteristics of Dispersed Inclusion Composites” / spz:neicon:technomag:y:2015:i:9:p:318-335

  1. Start
    1994
    Prefix
    Î ̨ ̃‚ ̊ ÒÎÓ‚‡:ÍÓÏÔÓÁËÚ; ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË; ‰ËÒÔÂÒÌ ̊ ‚ÍÎ ̨ ̃ÂÌˡ; ÚÂÏÓÛÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË ¬‚‰ÂÌË ÓÏÔÓÁËÚ ̊, ‡ÏËÓ‚‡ÌÌ ̊ ‚ÍÎ ̨ ̃ÂÌˡÏË ‡ÁÎË ̃ÌÓÈ ÙÓÏ ̊, ̇ıÓ‰ˇÚ ̄ËÓÍÓ ÔËÏÂÌÂÌË ‚ ÍÓÌÒÚÛÍˆËˇı, ÔÓ‰‚ÂÊÂÌÌ ̊ı Í‡Í ÏÂı‡ÌË ̃ÂÒÍËÏ, Ú‡Í Ë ÚÂÔÎÓ‚ ̊Ï ‚ÓÁ‰ÂÈÒڂˡÏ
    Exact
    [1,2,3]
    Suffix
    . ¬ÓÁÏÓÊÌÓÒÚ ̧ ËÒÔÓÎ ̧ÁÓ‚‡Ìˡ ÍÓÏÔÓÁËÚÓ‚ ‚ Ú‡ÍËı ÍÓÌÒÚÛÍˆËˇı ‚ Á̇ ̃ËÚÂÎ ̧ÌÓÈ ÒÚÂÔÂÌË Á‡‚ËÒËÚ ÓÚ ÍÓÏÔÎÂÍÒ‡ ÚÂÏÓÏÂı‡ÌË ̃ÂÒÍËı ı‡‡ÍÚÂËÒÚËÍ, ‚ ÚÓÏ ̃ËÒΠÓÚ Á̇ ̃ÂÌËÈ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË Ë ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ.
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  2. Start
    2430
    Prefix
    ‚ ‚ Ú‡ÍËı ÍÓÌÒÚÛÍˆËˇı ‚ Á̇ ̃ËÚÂÎ ̧ÌÓÈ ÒÚÂÔÂÌË Á‡‚ËÒËÚ ÓÚ ÍÓÏÔÎÂÍÒ‡ ÚÂÏÓÏÂı‡ÌË ̃ÂÒÍËı ı‡‡ÍÚÂËÒÚËÍ, ‚ ÚÓÏ ̃ËÒΠÓÚ Á̇ ̃ÂÌËÈ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË Ë ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. Œ‰Ì‡ÍÓ ÓÒÌÓ‚ÌÓ‚ÌÓ ‚ÌËχÌË ‚ ·ÓÎ ̧ ̄ËÌÒÚ‚Â ‡·ÓÚ, ÔÓÒ‚ˇ ̆ÂÌÌ ̊ı ÍÓÎË ̃ÂÒÚ‚ÂÌÌÓÏÛ ‡Ì‡ÎËÁÛ Ò‚ÓÈÒÚ‚ „ÂÚÂÓ„ÂÌÌ ̊ı ÚÂÎ, Í ÍÓÚÓ ̊Ï ÒΉÛÂÚ ÓÚÌÂÒÚË ÍÓÏÔÓÁËÚ ̊, Ë ÔӇ̇ÎËÁËÓ‚‡ÌÌ ̊ı, ̇ÔËÏÂ, ‚
    Exact
    [4,5,6,7]
    Suffix
    , Û‰ÂÎÂÌÓ ËÒÒΉӂ‡ÌË ̨ ÎË ̄ ̧ ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚÓ‚, ÔË ̃ÂÏ, ‚ ÓÒÌÓ‚ÌÓÏ, Ò ‚ÓÎÓÍÌËÒÚÓÈ ÒÚÛÍÚÛÓÈ, ‡ Ò‚ˇÁ ̧ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË Ò ÚÂÏÔÂ‡ÚÛÌ ̊Ï ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‡ÒÒÏÓÚÂ̇ ÏÂÌ ÔÓ‰Ó·ÌÓ.
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  3. Start
    2959
    Prefix
    ¬ ÚÂıÌËÍ ̇ˇ‰Û Ò ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ ‚ÓÎÓÍÌËÒÚ ̊ı ÍÓÏÔÓÁËÚÓ‚ ̄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
    [8,9,10,11]
    Suffix
    . œÓÒÍÓÎ ̧ÍÛ Ó· ̊ ̃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 ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ̄‡Ó‚Û ̨ [12,13,14]. —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃ÚÓ ‰ÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [15], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [1
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  4. Start
    3142
    Prefix
    ̊ı ÍÓÏÔÓÁËÚÓ‚ ̄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 ̊ [8,9,10,11]. œÓÒÍÓÎ ̧ÍÛ Ó· ̊ ̃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 ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ̄‡Ó‚Û ̨
    Exact
    [12,13,14]
    Suffix
    . —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃ÚÓ ‰ÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [15], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [16,17,18].
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  5. Start
    3267
    Prefix
    ̊ÒÓÍÓÔÓ ̃Ì ̊ı Ë ‚ ̊ÒÓÍÓÏÓ‰ÛÎ ̧Ì ̊ı χÚÂˇÎÓ‚, ‚ ÚÓÏ ̃ËÒΠ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊ [8,9,10,11]. œÓÒÍÓÎ ̧ÍÛ Ó· ̊ ̃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 ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ̄‡Ó‚Û ̨ [12,13,14]. —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃ÚÓ ‰ÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË
    Exact
    [15]
    Suffix
    , ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [16,17,18]. «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ҂ÓÈÒÚ‚ ÍÓÏÔÓÁËÚÓ‚ Ò ‰ËÒÔÂÒÌ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË ÔÓ‰Ú‚Âʉ‡ÂÚ ‡ÍÚۇΠ̧ÌÓÒÚ ̧ ËÒÒΉӂ‡ÌËÈ ‚ ̋ÚÓÏ Ì‡Ô‡‚ÎÂÌËË.
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  6. Start
    3365
    Prefix
    —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃ÚÓ ‰ÓÒÚ‡ÚÓ ̃ÌÓ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ÔÓÎÛ ̃ËÎË ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [15], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊, ̇ÔËÏÂ ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊
    Exact
    [16,17,18]
    Suffix
    . «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ҂ÓÈÒÚ‚ 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 ÔËÏÂÌÂÌˡ ÏÂÚÓ‰Ó‚ χÚÂχÚË ̃ÂÒÍÓ„Ó ÏÓ‰ÂÎËÓ‚‡Ìˡ ÚÂÏÔÂ‡ÚÛÌÓ„Ó Ë Ì‡ÔˇÊÂÌÌÓ-‰ÂÙÓÏËÓ‚‡ÌÌÓ„Ó ÒÓÒÚÓˇÌËÈ ÍÓÏÔÓÁËÚ‡ [19,20,21].
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  7. Start
    3704
    Prefix
    «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ҂ÓÈÒÚ‚ 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 ÔËÏÂÌÂÌˡ ÏÂÚÓ‰Ó‚ χÚÂχÚË ̃ÂÒÍÓ„Ó ÏÓ‰ÂÎËÓ‚‡Ìˡ ÚÂÏÔÂ‡ÚÛÌÓ„Ó Ë Ì‡ÔˇÊÂÌÌÓ-‰ÂÙÓÏËÓ‚‡ÌÌÓ„Ó ÒÓÒÚÓˇÌËÈ ÍÓÏÔÓÁËÚ‡
    Exact
    [19,20,21]
    Suffix
    . ¬ÏÂÒÚÂ Ò ÚÂÏ Ì‡ˇ‰Û Ò ‡Á‡·ÓÚÍÓÈ Ë ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ ‡ÁÎË ̃Ì ̊ı χÚÂχÚË ̃ÂÒÍËı ÏÓ‰ÂÎÂÈ, ÓÔËÒ ̊‚‡ ̨ ̆Ëı Ò‚ÓÈÒÚ‚‡ ÍÓÏÔÓÁËÚÓ‚, ˆÂÎÂÒÓÓ·‡ÁÌÓ ‡ÒÔÓ·„‡Ú ̧ ‡Ò ̃ÂÚÌ ̊ÏË Á‡‚ËÒËÏÓÒÚˇÏË, ÔÓÁ‚ÓΡ ̨ ̆ËÏË ÔÓÎÛ ̃ËÚ ̧ „‡‡ÌÚËÓ‚‡ÌÌ ̊ ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË, Óı‚‡Ú ̊‚‡ ̨ ̆Ë ËÌÚÂ‚‡Î ̊ ‚ÓÁÏÓÊÌ ̊ı ËÒÚËÌÌ ̊ı Á̇ ̃ÂÌËÈ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË Ë ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ÍÓÌÍÂÚÌÓ„Ó ÍÓ
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  8. Start
    4485
    Prefix
    ≈ÒÎË ‚ ͇ ̃ÂÒÚ‚Â Â„Ó ÚÂÏÓÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ‚ ̊·‡Ú ̧ ÔÓÎÛÒÛÏÏ ̊ „‡ÌË ̃Ì ̊ı Á̇ ̃ÂÌËÈ Û͇Á‡ÌÌ ̊ı Ô‡‡ÏÂÚÓ‚, ÚÓ ÌÂÒÎÓÊÌÓ ÛÒÚ‡ÌÓ‚ËÚ ̧ ̇˷ÓÎ ̧ ̄Û ̨ ‚ÓÁÏÓÊÌÛ ̨ ÔÓ„ ̄ÌÓÒÚ ̧, ‚ÓÁÌË͇ ̨ ̆Û ̨ ÔË Ú‡ÍÓÏ ‚ ̊·ÓÂ. ¬ ‰‡ÌÌÓÈ ‡·ÓÚ Û͇Á‡ÌÌ ̊ Á‡‚ËÒËÏÓÒÚË ÔÓÒÚÓÂÌ ̊ ̇ ÓÒÌÓ‚Â ‰‚ÓÈÒÚ‚ÂÌÌÓÈ ‚‡ˇˆËÓÌÌÓÈ ÙÓÏÛÎËÓ‚ÍË Á‡‰‡ ̃Ë ÚÂÏÓÛÔÛ„ÓÒÚË ‚ ÌÂÓ‰ÌÓÓ‰ÌÓÏ Ú‚Â‰ÓÏ ÚÂÎÂ
    Exact
    [22]
    Suffix
    . 1. ŒÒÌÓ‚Ì ̊ ÒÓÓÚÌÓ ̄ÂÌˡ œÛÒÚ ̧ ÍÓÏÔÓÁËÚ ÒÓÒÚÓËÚ ËÁ ËÁÓÚÓÔÌÓÈ ÎËÌÂÈÌÓ ÛÔÛ„ÓÈ Ï‡Úˈ ̊, ÚÂÏÓÛÔÛ„Ë ҂ÓÈÒÚ‚‡ ÍÓÚÓÓÈ ı‡‡ÍÚÂËÁÛ ̨Ú Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧K◦, ÏÓ‰ÛÎ ̧ Ò‰‚Ë„‡G◦Ë ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚα◦ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ, Ë ÎËÌÂÈÌÓ ÛÔÛ„Ëı ËÁÓÚÓÔÌ ̊ı ‰ËÒÔÂÒÌ ̊ı ̄‡Ó‚ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈN‚ˉӂ.
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  9. Start
    5139
    Prefix
    ‡Ê‰ ̊È ‚ˉ ‚ÍÎ ̨ ̃ÂÌËÈ Ò ÌÓÏÂÓÏς∈1, NË Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËÂÈCςËÏÂÂÚ Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧Kς, ÏÓ‰ÛÎ ̧ Ò‰‚Ë„‡GςË ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚÓÏας ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. Œ· ̇ÂÏ̇ˇ ÍÓ̈ÂÌÚ‡ˆËˇ ‚ÒÂı ‚ÍÎ ̨ ̃ÂÌËÈ ‚ ÍÓÏÔÓÁËÚ ‡‚̇ CV= ∑N ς=1 Cς. œË ı‡ÓÚË ̃ÂÒÍÓÏ ‡ÒÔÓÎÓÊÂÌËË ‚ÍÎ ̨ ̃ÂÌËÈ ‚ ÍÓÏÔÓÁËÚ ÓÌ Ì ӷ·‰‡ÂÚ ÚÂÍÒÚÛÓÈ Ë Â„Ó ‰ÓÔÛÒÚËÏÓ Ò ̃ËÚ‡Ú ̧ ËÁÓÚÓÔÌ ̊Ï
    Exact
    [4,23]
    Suffix
    . »ÒÍÓÏ ̊ÏË ÚÂÏÓÛÔÛ„ËÏË ı‡‡ÍÚÂËÒÚË͇ÏË ÍÓÏÔÓÁËÚ‡ ˇ‚Ρ ̨ÚÒˇ Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧K, ÏÓ‰ÛÎ ̧ Ò‰‚Ë„‡GË ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚα ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ›ÚË ı‡‡ÍÚÂËÒÚËÍË Ô‰ÒÚ‡‚ËÏ ‚ ÚÂÌÁÓÌÓÈ ÙÓÏ ÒÓÓÚÌÓ ̄ÂÌˡÏË [24] Ĉ= 3K̂V+2ĜD,̂S= ̂V 3K + ̂D 2G D̂,α=α̂I 2,(1) „‰Â̂CË̂S| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË Ë ÔÓ‰‡ÚÎË‚ÓÒÚË ÍÓÏÔÓÁËÚ‡;̂VË̂D| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡
    (check this in PDF content)

  10. Start
    5407
    Prefix
    »ÒÍÓÏ ̊ÏË ÚÂÏÓÛÔÛ„ËÏË ı‡‡ÍÚÂËÒÚË͇ÏË ÍÓÏÔÓÁËÚ‡ ˇ‚Ρ ̨ÚÒˇ Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧K, ÏÓ‰ÛÎ ̧ Ò‰‚Ë„‡GË ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚα ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ. ›ÚË ı‡‡ÍÚÂËÒÚËÍË Ô‰ÒÚ‡‚ËÏ ‚ ÚÂÌÁÓÌÓÈ ÙÓÏ ÒÓÓÚÌÓ ̄ÂÌˡÏË
    Exact
    [24]
    Suffix
    Ĉ= 3K̂V+2ĜD,̂S= ̂V 3K + ̂D 2G D̂,α=α̂I 2,(1) „‰Â̂CË̂S| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË Ë ÔÓ‰‡ÚÎË‚ÓÒÚË ÍÓÏÔÓÁËÚ‡;̂VË̂D| 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„‡̂I=̂V+̂D;α| ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÚÂÏÔÂ‡ÚÛÌÓÈ ‰ÂÙÓχˆËË;̂I2| ‰ËÌË ̃Ì ̊È ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡
    (check this in PDF content)

  11. Start
    5944
    Prefix
    ‡;̂VË̂D| 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„‡̂I=̂V+̂D;α| ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÚÂÏÔÂ‡ÚÛÌÓÈ ‰ÂÙÓχˆËË;̂I2| ‰ËÌË ̃Ì ̊È ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ Ò ÍÓÏÔÓÌÂÌÚ‡ÏËδij= 1ÔËi=jËδij= 0ÔËi6=j(i, j= 1,2,3) ‚ ÔˇÏÓÛ„ÓÎ ̧ÌÓÈ ‰Â͇ÚÓ‚ÓÈ ÒËÒÚÂÏ ÍÓÓ‰Ë̇ÚOx1x2x3. ÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓÓ‚̂VË̂DËÏ ̨Ú ‚ˉ
    Exact
    [1]
    Suffix
    Vijmn= δijδmn 3 , Dijmn= δimδjn+δinδjm 2 −Vijmn, m, n= 1,2,3. »Á ̋ÚËı ÙÓÏÛÎ Ë ‡‚ÂÌÒÚ‚‡δii= 3(Ò Û ̃ÂÚÓÏ Ô‡‚Ë· ÒÛÏÏËÓ‚‡Ìˡ Ò·„‡ÂÏ ̊ı ÔÓ ÔÓ‚ÚÓˇ ̨ ̆ËÏÒˇ ‚ ÒÓÏÌÓÊËÚÂΡı ·ÚËÌÒÍËÏ Ë̉ÂÍÒ‡Ï [20], ËÒÔÓÎ ̧ÁÛÂÏÓ„Ó Ë ‚ ‰‡Î ̧ÌÂÈ ̄ÂÏ) ÒΉÛÂÚ VijmnVmnkl=Vijkl(k, l= 1,2,3),DijmnDmnkl=DijklËVijmnDmnkl= 0, Ú.
    (check this in PDF content)

  12. Start
    6136
    Prefix
    ÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓÓ‚̂VË̂DËÏ ̨Ú ‚ˉ [1] Vijmn= δijδmn 3 , Dijmn= δimδjn+δinδjm 2 −Vijmn, m, n= 1,2,3. »Á ̋ÚËı ÙÓÏÛÎ Ë ‡‚ÂÌÒÚ‚‡δii= 3(Ò Û ̃ÂÚÓÏ Ô‡‚Ë· ÒÛÏÏËÓ‚‡Ìˡ Ò·„‡ÂÏ ̊ı ÔÓ ÔÓ‚ÚÓˇ ̨ ̆ËÏÒˇ ‚ ÒÓÏÌÓÊËÚÂΡı ·ÚËÌÒÍËÏ Ë̉ÂÍÒ‡Ï
    Exact
    [20]
    Suffix
    , ËÒÔÓÎ ̧ÁÛÂÏÓ„Ó Ë ‚ ‰‡Î ̧ÌÂÈ ̄ÂÏ) ÒΉÛÂÚ VijmnVmnkl=Vijkl(k, l= 1,2,3),DijmnDmnkl=DijklËVijmnDmnkl= 0, Ú. Â. ̂V··̂V=̂V,̂D··̂D=̂D,̂V··̂D=̂O4,(2) „‰Â̂O4| ÚÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ Ò ÌÛ΂ ̊ÏË ÍÓÏÔÓÌÂÌÚ‡ÏË, ‡ ͇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 [20].
    (check this in PDF content)

  13. Start
    6471
    Prefix
    Â. ̂V··̂V=̂V,̂D··̂D=̂D,̂V··̂D=̂O4,(2) „‰Â̂O4| ÚÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ Ò ÌÛ΂ ̊ÏË ÍÓÏÔÓÌÂÌÚ‡ÏË, ‡ ͇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
    [20]
    Suffix
    . “ÂÌÁÓ ̊̂V,̂DËT I2ˇ‚Ρ ̨ÚÒˇ ËÁÓÚÓÔÌ ̊ÏË, Ú.Â. Ëı ÍÓÏÔÓÌÂÌÚ ̊ Ì Á‡‚ËÒˇÚ ÓÚ ÓËÂÌÚ‡ˆËË ‚ ̊·‡ÌÌÓÈ ÒËÒÚÂÏ ̊ ÍÓÓ‰Ë̇Ú. ‘ÓÏÛÎ ̊ (1) ÒÓı‡Ìˇ ̨Ú Ò‚ÓÈ ‚ˉ ÔËÏÂÌËÚÂÎ ̧ÌÓ Í Ï‡ÚËˆÂ Ë Ô·ÒÚËÌ ̃‡Ú ̊Ï ‚ÍÎ ̨ ̃ÂÌËˇÏ ÔË Á‡ÏÂÌ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚËKËGË ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡αÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ÍÓÏÔÓÁËÚ‡ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ì‡K◦,G◦,α◦‰Îˇ χÚˈ ̊ Ë Ì‡Kς,ς,ας‰Îˇ ‚ÍÎ ̨ ̃ÂÌËÈ.
    (check this in PDF content)

  14. Start
    7407
    Prefix
    ‡ÏË ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓCijmnËSijmn, Òӄ·ÒÌÓ ÙÓÏÛÎ‡Ï (1), ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ÒÓÓÚÌÓ ̄ÂÌˡÏË Ĉ····̂V=C iimm= 9K, Ĉ····̂D=C imim− Ciimm 3 = 10G,(3) Ŝ····̂V=S iimm= 1 K ,̂S····̂D=Simim− Siimm 3 = 5 2G .(4) “‡ÍËÏ Ó·‡ÁÓÏ, ÎËÌÂÈÌ ̊ ËÌ‚‡ˇÌÚ ̊ ÚÂÌÁÓ‡ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ˇ‚Ρ ̨ÚÒˇ ‚ÌÛÚÂÌÌËÏË ÔÓËÁ‚‰ÂÌˡÏË ̋ÚÓ„Ó ÚÂÌÁÓ‡ Ë ÚÂÌÁÓÓ‚̂VË̂DÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ÔË Ò‚ÂÚ ̊‚‡ÌËË ÔÓ ‚ÒÂÏ ̃ÂÚ ̊ÂÏ Ë̉ÂÍÒ‡Ï
    Exact
    [20]
    Suffix
    . “ÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ ËÏÂÂÚ Â‰ËÌÒÚ‚ÂÌÌ ̊È ÎËÌÂÈÌ ̊È ËÌ‚‡ˇÌÚ, ÍÓÚÓ ̊È ‰Îˇ ÚÂÌÁÓ‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÚÂÏÔÂ‡ÚÛÌÓÈ ‰ÂÙÓχˆËË ËÏÂÂÚ ‚Ë‰α··̂I2= 3α. ÃÓ‰ÛÎË ÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚ‡, Ò‚ˇÁ ̊‚‡ ̨ ̆Ë ÏÂÊ‰Û ÒÓ·ÓÈ ÓÒ‰ÌÂÌÌ ̊ ÔÓ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏÛ Ó· ̇ÂÏÛVÍÓÏÔÓÁËÚ‡ ÚÂÌÁÓ ̊ ‚ÚÓÓ„Ó ‡Ì„‡ ̇ÔˇÊÂÌËÈ Ë ‰ÂÙÓχˆËË ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ 〈ˆs〉= 1 V ∫ V ˆs(M)dV(M)и〈ˆe〉= 1 V ∫ V eˆ(M)dV(M), „‰Âˆs(M)ˈe(M)| ÚÂÌÁÓ ̊, ÓÔ‰ÂÎ
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  15. Start
    8448
    Prefix
    ˆs〉, „‰Â Ò Û ̃ÂÚÓÏ ÙÓÏÛÎ (1)̂C∗= 3K∗̂V+2G∗̂DË̂S∗= 1/(3K∗)̂V+1/(2G∗)̂D| ̇Á ̊‚‡ÂÏ ̊ ̋ÙÙÂÍÚË‚Ì ̊ÏË ÚÂÌÁÓ ̊ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ÛÔÛ„ÓÒÚË Ë ÔÓ‰‡ÚÎË‚ÓÒÚË ÍÓÏÔÓÁËÚ‡, Ô‰ÒÚ‡‚ÎÂÌÌ ̊ ̃ÂÂÁ ̋ÙÙÂÍÚË‚Ì ̊ Á̇ ̃ÂÌˡ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡK∗Ë ÏÓ‰ÛΡ Ò‰‚Ë„‡ G∗ÍÓÏÔÓÁËÚ‡, ‚‚Ó‰ËÏ ̊ ËÁ ÛÒÎӂˡ ‡‚ÂÌÒÚ‚‡ Ó· ̇ÂÏÌÓÈ ÔÎÓÚÌÓÒÚË ÔÓÚÂ̈ˇΠ̧ÌÓÈ ̋ÌÂ„ËË ‰ÂÙÓχˆËË ‚ ËÁÓÚÓÔÌÓÈ ÒÂ‰Â Ë ‚ ‡Π̧ÌÓÏ ÍÓÏÔÓÁËÚÂ
    Exact
    [20]
    Suffix
    : 1 2 〈ˆe〉··̂C∗··〈ˆe〉= 1 2 〈ˆs〉··̂S∗··〈ˆs〉= 1 2V ∫ V eˆ∗(M)··ˆs∗(M)dV(M).(5) «‰ÂÒ ̧ˆs∗ˈe∗| ÚÂÌÁÓ ̊ ̇ÔˇÊÂÌËÈ Ë ‰ÂÙÓχˆËË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ËÒÚËÌÌÓ ̇ÔˇÊÂÌÌÓ-‰ÂÙÓÏËÓ‚‡ÌÌÓ ÒÓÒÚÓˇÌË ‚ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏ Ó· ̇ÂÏ ÍÓÏÔÓÁËÚ‡, Û‰Ó‚ÎÂÚ‚Óˇ ̨ ̆ ÛÒÎÓ‚ËˇÏ ‡‚ÌÓ‚ÂÒˡ Ë ÒÓ‚ÏÂÒÚÌÓÒÚË ‰ÂÙÓχˆËÈ.
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  16. Start
    9062
    Prefix
    «Ì‡ ̃ÂÌˡK∗,̂S∗Ëα∗ÔÓ‰ÎÂÊ‡Ú ÓˆÂÌÍ ̇ ÓÒÌÓ‚Â ÚÓ„Ó ËÎË ËÌÓ„Ó ÔÓ‰ıÓ‰‡. Œ‰ËÌ ËÁ ‚ÓÁÏÓÊÌ ̊ı ÔÓ‰ıÓ‰Ó‚ Ò‚ˇÁ‡Ì Ò ÔËÏÂÌÂÌËÂÏ ‰‚ÓÈÒÚ‚ÂÌÌÓÈ ‚‡ˇˆËÓÌÌÓÈ ÙÓÏÛÎËÓ‚ÍË ÎËÌÂÈÌÓÈ Á‡‰‡ ̃Ë ÚÂÏÓÛÔÛ„ÓÒÚË ‚ ÌÂÓ‰ÌÓÓ‰ÌÓÏ Ú‚Â‰ÓÏ ÚÂÎÂ
    Exact
    [22]
    Suffix
    . 2. œÓÒÚÓÂÌË ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ œË ÓÚÒÛÚÒÚËË ÚÂÔÎÓ‚ ̊ı ‚ÓÁ‰ÂÈÒÚ‚ËÈ ‚ ‰‚ÓÈÒÚ‚ÂÌÌÛ ̨ ‚‡ˇˆËÓÌÌÛ ̨ ÙÓÏÛÎËÓ‚ÍÛ ÎËÌÂÈÌÓÈ Á‡‰‡ ̃Ë ÛÔÛ„ÓÒÚË ‚ıÓ‰ˇÚ ‰‚‡ ‡Î ̧ÚÂ̇ÚË‚Ì ̊ı ÙÛÌ͈ËÓ̇· (ÏËÌËÏËÁËÛÂÏ ̊È ÙÛÌ͈ËÓ̇ΠÀ‡„‡Ìʇ Ë Ï‡ÍÒËÏËÁËÛÂÏ ̊È ÙÛÌ͈ËÓ̇Π‡ÒÚËΡÌÓ).
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  17. Start
    9578
    Prefix
    ≈ÒÎË ÓÚÒÛÚÒÚ‚Û ̨Ú Ó· ̇ÂÏÌ ̊ ÒËÎ ̊, ‡ ̇ ÔÓ‚ÂıÌÓÒÚËS, Ó„‡ÌË ̃Ë‚‡ ̨ ̆ÂÈ Ó· ̇ÂÏV, Á‡‰‡Ì ̊ ÍËÌÂχÚË ̃ÂÒÍË „‡ÌË ̃Ì ̊ ÛÒÎӂˡ, ÚÓ ÙÛÌ͈ËÓ̇ΠÀ‡„‡Ìʇ, ‰ÓÒÚË„‡ ̨ ̆ËÈ ÏËÌËÏÛχ ̇ ËÒÚËÌÌÓÏ ‡ÒÔ‰ÂÎÂÌËË ÔÂÂÏ ̆ÂÌËÈ ‚ Á‡ÏÍÌÛÚÓÈ Ó·Î‡ÒÚËV=V∪S, ËÏÂÂÚ ‚ˉ
    Exact
    [22]
    Suffix
    J1= 1 2 ∫ V ˆe(M)··̂C ∗ (M)··ˆe(M)dV(M), M∈V,(6) „‰Â̂C ∗ | ÚÂÌÁÓ, ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ËÈ ÎÓ͇Π̧Ì ̊Ï Á̇ ̃ÂÌËˇÏ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ ‚ Ó· ̇ÂÏÂV. ›ÚÓÚ ÙÛÌ͈ËÓ̇Π‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ ̇ ÌÂÔÂ ̊‚Ì ̊ı Ë ÍÛÒÓ ̃ÌÓ ‰ËÙÙÂÂ̈ËÛÂÏ ̊ı ÔÓ ÔÓÒÚ‡ÌÒÚ‚ÂÌÌ ̊Ï ÍÓÓ‰ËÌ‡Ú‡Ï ‡ÒÔ‰ÂÎÂÌˡı ÔÂÂÏ ̆ÂÌËÈ, Û‰Ó‚ÎÂÚ‚Óˇ ̨ ̆Ëı ÍËÌÂχÚË ̃ÂÒÍËÏ „‡ÌË ̃Ì ̊Ï ÛÒÎӂˡÏ.
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  18. Start
    11050
    Prefix
    ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË K∗ËG∗ÍÓÏÔÓÁËÚ‡ Ô‰ÒÚ‡‚ËÚ ̧ ‚ÂıÌË ӈÂÌÍËK+ËG+c Û ̃ÂÚÓÏ ÙÓÏÛÎ (3) Ë (4) ‚ ‚ˉ K ̃+=K+ K◦ = 1−CV+ ∑N ς=1 Kς K◦ Cς, ̃G+= G+ G◦ = 1−CV+ ∑N ς=1 Gς G◦ Cς.(7) œË ÓÚÒÛÚÒÚ‚ËË Ó· ̇ÂÏÌ ̊ı ÒËÎ Ë Á‡‰‡ÌËË ÒËÎÓ‚ ̊ı „‡ÌË ̃Ì ̊ı ÛÒÎÓ‚ËÈ Ì‡ ÔÓ‚ÂıÌÓÒÚË, Ó„‡ÌË ̃Ë‚‡ ̨ ̆ÂÈ Ó· ̇ÂÏV, ÙÛÌ͈ËÓ̇Π‡ÒÚËΡÌÓ, χÍÒËÏËÁËÛÂÏ ̊È Ì‡ ËÒÚËÌÌÓÏ ‡ÒÔ‰ÂÎÂÌËË Ì‡ÔˇÊÂÌËÈ ‚ Á‡ÏÍÌÛÚÓÈ Ó·Î‡ÒÚËV, ËÏÂÂÚ ‚ˉ
    Exact
    [22]
    Suffix
    J2=− 1 2 ∫ V ˆs(M)··̂S ∗ (M)··ˆs(M)dV(M), M∈V,(8) „‰Â̂S ∗ | ÚÂÌÁÓ, ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ËÈ ÎÓ͇Π̧Ì ̊Ï Á̇ ̃ÂÌËˇÏ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÔÓ‰‡ÚÎË‚ÓÒÚË Ï‡Úˈ ̊ Ë ÒÙÂÓ‰‡Î ̧Ì ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ ‚ Ó· ̇ÂÏÂV. ›ÚÓÚ ÙÛÌ͈ËÓ̇Π‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ ̇ ÒÚ‡ÚË ̃ÂÒÍË ‚ÓÁÏÓÊÌ ̊ı ‡ÒÔ‰ÂÎÂÌˡı ̇ÔˇÊÂÌËÈ. œË ‰ÓÔÛÒÚËÏÓÏ Ó‰ÌÓÓ‰ÌÓÏ Ì‡ÔˇÊÂÌÌÓÏ ÒÓÒÚÓˇÌËË, ÓÔ‰ÂΡÂÏÓÏ ÚÂÌÁÓÓψs0=〈ˆs〉Ò ÍÓÏÔÓÌÂÌÚ‡ÏËσij= const, Ò Û ̃ÂÚÓÏ ÙÓ
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  19. Start
    12279
    Prefix
    ‚ ̋ÚËı ÌÂ‡‚ÂÌÒÚ‚‡ı ÍÛÒÓ ̃ÌÓ ÔÓÒÚÓˇÌÌ ̊ ‚ Ô‰Â·ı ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ Ë ‚ χÚˈÂ, ̃ÚÓ ‰‡ÂÚ ‚ÓÁÏÓÊÌÓÒÚ ̧ ‰Îˇ ̋ÙÙÂÍÚË‚Ì ̊ı Á̇ ̃ÂÌËÈ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚËK∗ËG∗ÍÓÏÔÓÁËÚ‡ Ô‰ÒÚ‡‚ËÚ ̧ ÌËÊÌË ӈÂÌÍËK−ËG−c Û ̃ÂÚÓÏ ÙÓÏÛÎ (3) Ë (4) ‚ ‚ˉ 1 K ̃ − = K◦ K− = 1−CV+K◦ ∑N ς=1 Cς Kς , 1 G ̃− = G◦ G− = 1−CV+G◦ ∑N ς=1 Cς Gς .(9) ŒˆÂÌÍË (7) Ë (9) ÏÓÊÌÓ Ú‡ÍÊ ÔÓÎÛ ̃ËÚ ̧ Ò Ô˂Π̃ÂÌËÂÏ ÚÂÓËË ÒÏÂÒÂÈ
    Exact
    [25]
    Suffix
    , ÌÓ ËÁ ̋ÚÓÈ ÚÂÓËË Ì ÒΉÛÂÚ, ̃ÚÓ ̋ÚË ÓˆÂÌÍË ˇ‚Ρ ̨ÚÒˇ ‰‚ÛÒÚÓÓÌÌËÏË ÔÓ ÓÚÌÓ ̄ÂÌË ̨ Í ËÒÚËÌÌ ̊Ï Á̇ ̃ÂÌËˇÏ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚ‡. œÓÒÚÓÂÌÌ ̊ ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ Ë ÏÓ‰ÛΡ Ò‰‚Ë„‡ ÍÓÏÔÓÁËÚ‡ ÔÓÁ‚ÓΡ ̨Ú ÔÓÎÛ ̃ËÚ ̧ ‚ÂıÌ ̨ ̨ Ë ÌËÊÌ ̨ ̨ ÓˆÂÌÍË Â„Ó ÔÓ‰ÓÎ ̧ÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚË (ÏÓ‰ÛΡ fiÌ„‡)E: E+= 9K+G+ 3K++G+ , E−= 9K−G− 3K−+G− ,(10) ‡ Ú‡ÍÊ ӈÂÌÍË ÍÓ ̋ÙÙˈËÂÌÚ‡ œÛ‡ÒÒÓ̇
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  20. Start
    13050
    Prefix
    ‡ œÛ‡ÒÒÓ̇νÍÓÏÔÓÁËÚ‡: ν1= 3K+/2−G+ 3K++G+ , ν2= 3K−/2−G− 3K−+G− ,(11) ÔË ̃ÂÏ ‡ÁÌÓÒÚ ̧ Á̇ ̃ÂÌËÈν1Ëν2ÏÓÊÂÚ · ̊Ú ̧ Í‡Í ÔÓÎÓÊËÚÂÎ ̧ÌÓÈ, Ú‡Í Ë ÓÚˈ‡ÚÂÎ ̧ÌÓÈ. ƒÎˇ ÔÓÒÚÓÂÌˡ ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡ ÏÓÊÌÓ ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ ‰‚ÓÈÒÚ‚ÂÌÌÛ ̨ ‚‡ˇˆËÓÌÌÛ ̨ ÙÓÏÛÎËÓ‚ÍÛ ÎËÌÂÈÌÓÈ Á‡‰‡ ̃Ë ÚÂÏÓÛÔÛ„ÓÒÚË ‰Îˇ ÌÂÓ‰ÌÓÓ‰ÌÓ„Ó Ú‚Â‰Ó„Ó Ú·
    Exact
    [22,26]
    Suffix
    . ›Ú‡ ÙÓÏÛÎËӂ͇ ‚ÍÎ ̨ ̃‡ÂÚ ‰‚‡ ‡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‚.
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  21. Start
    14062
    Prefix
    )··α∗(M)dV= BαV 2 (∆T)2,(12) „‰Âα∗| Á‡‚ËÒˇ ̆ËÈ ÓÚ ÔÓÎÓÊÂÌˡ ÚÓ ̃ÍËM∈VÚÂÌÁÓ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÚÂÏÔÂ‡ÚÛÌÓÈ ‰ÂÙÓχˆËË, ‡ Bα= 9K◦(α◦)2(1−СV) + 9 ∑N ς=1 Kςα2ςCς. 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=σ̂I2,σ= const. Õ‡ Ú‡ÍÓÏ ‡ÒÔ‰ÂÎÂÌËË ̋ÚÓÚ ÙÛÌ͈ËÓÌ‡Î Ò Û ̃ÂÚÓÏ ÔÂ‚ÓÈ ÙÓÏÛÎ ̊ (9) ËÏÂÂÚ ‚ˉ
    Exact
    [26]
    Suffix
    J∗2=− σ2V 2K− −σ∆T ∫ V α∗(M)··̂I2dV(M). «Ì‡ ̃ÂÌËÂσÏÓÊÌÓ Ì‡ÈÚË ËÁ ÌÂÓ·ıÓ‰ËÏÓ„Ó ÛÒÎӂˡ ÒÛ ̆ÂÒÚ‚Ó‚‡Ìˡ ̋ÍÒÚÂÏÛχ ̋ÚÓ„Ó ÙÛÌ͈ËÓ̇· dJ∗2 dσ =− σ K− −∆T ∫ V α∗(M)··̂I2dV(M) = 0. ŒÚÒ ̨‰‡ ÒΉÛÂÚσ=−3K−α∗∆T, „‰Â α∗= (1−CV)α◦+ ∑N ς=1 αςCς,(13) ÔË ̃ÂÏ ̋Ú‡ ÙÓÏÛ· ÒÓ‚Ô‡‰‡ÂÚ Ò ÓˆÂÌÍÓÈ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ, ÍÓÚÓ‡ˇ ÒΉÛÂÚ ËÁ ÚÂÓËË ÒÏÂÒÂÈ [25]. œÓÒΠÔÓ‰ÒÚ‡ÌÓ‚ÍËσ‚ χÍÒËÏËÁ
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  22. Start
    14411
    Prefix
    «Ì‡ ̃ÂÌËÂσÏÓÊÌÓ Ì‡ÈÚË ËÁ ÌÂÓ·ıÓ‰ËÏÓ„Ó ÛÒÎӂˡ ÒÛ ̆ÂÒÚ‚Ó‚‡Ìˡ ̋ÍÒÚÂÏÛχ ̋ÚÓ„Ó ÙÛÌ͈ËÓ̇· dJ∗2 dσ =− σ K− −∆T ∫ V α∗(M)··̂I2dV(M) = 0. ŒÚÒ ̨‰‡ ÒΉÛÂÚσ=−3K−α∗∆T, „‰Â α∗= (1−CV)α◦+ ∑N ς=1 αςCς,(13) ÔË ̃ÂÏ ̋Ú‡ ÙÓÏÛ· ÒÓ‚Ô‡‰‡ÂÚ Ò ÓˆÂÌÍÓÈ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ, ÍÓÚÓ‡ˇ ÒΉÛÂÚ ËÁ ÚÂÓËË ÒÏÂÒÂÈ
    Exact
    [25]
    Suffix
    . œÓÒΠÔÓ‰ÒÚ‡ÌÓ‚ÍËσ‚ χÍÒËÏËÁËÛÂÏ ̊È ÙÛÌ͈ËÓ̇ΠÓÌ ÔËÏÂÚ ‚ˉ J◦2= 9 2 V K−(α∗∆T)2.(14) ƒÎˇ Ó‰ÌÓÓ‰ÌÓÈ Ò‰ ̊, ËÏ ̨ ̆ÂÈ Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧ ÛÔÛ„ÓÒÚËKË ËÒÍÓÏ ̊È ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚαÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡, ÏËÌËÏËÁËÛÂÏ ̊È ÙÛÌ͈ËÓ̇ΠÔË ÛÒÎÓ‚ËËu(M) = 0(M∈V) ‡‚ÂÌJ◦1= 9 2 V K(α∆T)2, ̃ÚÓ ÒÓ‚Ô‡‰‡ÂÚ ÒÓ Á̇ ̃ÂÌËÂÏJ∗2χÍÒËÏËÁËÛÂÏÓ„Ó ÙÛÌ͈ËÓ̇· ̇ ‰ÓÔÛÒÚËÏÓÏ Ó‰ÌÓÓ‰Ì
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  23. Start
    14910
    Prefix
    ‰ ̊, ËÏ ̨ ̆ÂÈ Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧ ÛÔÛ„ÓÒÚËKË ËÒÍÓÏ ̊È ÚÂÏÔÂ‡ÚÛÌ ̊È ÍÓ ̋ÙÙˈËÂÌÚαÎËÌÂÈÌÓ„Ó ‡Ò ̄ËÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡, ÏËÌËÏËÁËÛÂÏ ̊È ÙÛÌ͈ËÓ̇ΠÔË ÛÒÎÓ‚ËËu(M) = 0(M∈V) ‡‚ÂÌJ◦1= 9 2 V K(α∆T)2, ̃ÚÓ ÒÓ‚Ô‡‰‡ÂÚ ÒÓ Á̇ ̃ÂÌËÂÏJ∗2χÍÒËÏËÁËÛÂÏÓ„Ó ÙÛÌ͈ËÓ̇· ̇ ‰ÓÔÛÒÚËÏÓÏ Ó‰ÌÓÓ‰ÌÓÏ ‡ÒÔ‰ÂÎÂÌËË Ì‡ÔˇÊÂÌˡ, ‡‚ÌÓ„Óσ∗=−3Kα∆T. ƒÎˇ ‡Î ̧ÚÂ̇ÚË‚Ì ̊ı ÙÛÌ͈ËÓ̇ÎÓ‚ ÒÔ‡‚‰ÎË‚Ó ÌÂ‡‚ÂÌÒÚ‚Ó
    Exact
    [22]
    Suffix
    J∗1>J◦1>J∗2. ŒÚÒ ̨‰‡ Ò Û ̃ÂÚÓÏ ÙÓÏÛÎ (12) Ë (14) ÒÎÂ‰Û ̨Ú ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË α2+= Bα 9K >α2> K− K α2∗=α2−.(15) ¬ ÒÓÓÚÌÓ ̄ÂÌËË (14) ‚ÏÂÒÚÓKÏÓÊÌÓ ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ Â„Ó ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË, ÓÔ‰ÂΡÂÏ ̊ ÔÂ‚ ̊ÏË ÙÓÏÛ·ÏË (8) Ë (10), ̃ÚÓ ÔË‚Ó‰ËÚ Í „‡‡ÌÚËÓ‚‡ÌÌ ̊Ï ‰‚ÛÒÚÓÓÌÌËÏ ÓˆÂÌÍ‡Ï α ̄2+= Bα 9K− >α2> K− K+ α2∗= ̄α2−.(16) »ÒÔÓÎ ̧ÁÓ‚‡ÌË ‚ ÒÓÓÚÌÓ ̄ÂÌËË (15) Á̇ ̃ÂÌˡ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ ÛÔÛ„ÓÒÚËK=
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  24. Start
    15805
    Prefix
    —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃ÚÓ ÔË ÒÛ ̆ÂÒÚ‚ÂÌÌÓÏ ‡ÁÎË ̃ËË ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ô‰ÒÚ‡‚ÎÂÌÌ ̊ ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË ÏÓ„ÛÚ ÔË‚ÂÒÚË Í Á̇ ̃ËÚÂÎ ̧ÌÓÏÛ ÓÚÎË ̃Ë ̨ Á̇ ̃ÂÌËÈ, ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı ‚ÂıÌÂÈ Ë ÌËÊÌÂÈ „‡Ìˈ‡Ï. ›ÚË „‡Ìˈ ̊ ÏÓÊÌÓ Ò·ÎËÁËÚ ̧, ÂÒÎË ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ ÛÚÓ ̃ÌÂÌÌ ̊È ‚‡ˇÌÚ ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ Í‡Í Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡ, Ú‡Í Ë ÏÓ‰ÛΡ Ò‰‚Ë„‡ ‚ ‚ˉÂ
    Exact
    [6,27]
    Suffix
    K∗+= ( 1−CV K◦+ 4Gmax/3 + ∑N ς=1 Cς Kς+ 4Gmax/3 )−1 − 4 3 Gmax, K∗−= ( 1−CV K◦+ 4Gmax/3 + ∑N ς=1 Cς Kς+ 4Gmin/3 )−1 − 4 3 Gmin, G∗+= ( 1−CV G◦+ 4Gmax/3 + ∑N ς=1 Cς Gς+G∗max/3 )−1 −G∗max,(17) G∗+= ( 1−CV G◦+ 4Gmax/3 + ∑N ς=1 Cς Gς+G∗min/3 )−1 −G∗min, „‰ÂGmax= max{G◦, G1, .
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  25. Start
    18950
    Prefix
    »ÒÔÓÎ ̧ÁÛÂÏ ‰Îˇ Ò‡‚ÌÂÌˡ ÛÚÓ ̃ÌÂÌÌ ̊È ‚‡ˇÌÚ (17) ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ Á̇ ̃ÂÌËÈ ÏÓ‰ÛÎÂÈ ÛÔÛ„ÓÒÚË. ƒÎˇ ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡ Ò Ó‰ÌËÏ ‚ˉÓÏ ‚ÍÎ ̨ ̃ÂÌËÈ ̋ÚÓÚ ‚‡ˇÌÚ ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ÒÓÓÚÌÓ ̄ÂÌˡÏË
    Exact
    [24]
    Suffix
    K ̃∗ += K ̃ +−min{∆ ̄K ′,∆ ̄K′′}, ̃K∗ −= K ̃ +−max{∆ ̄K ′,∆ ̄K′′}, G ̃∗ += G ̃ +−min{∆ ̄G ′,∆ ̄G′′}, ̃G∗ −= G ̃ +−max{∆ ̄G ′,∆ ̄G′′}, „‰Â ∆ ̄K′= ( ̄K−1)2CV(1−CV) K ̄(1−CV)+CV+4 ̄G◦/3,∆ K ̄′′=( K ̄−1)2CV(1−CV) K ̄(1−CV)+CV+4 ̄G ̄G◦/3, ∆ ̄G′= ( ̄G−1)2CV(1−CV) G ̄(1−CV)+CV+ ̄G′,∆ G ̄′′=( G ̄−1)2CV(1−CV) G ̄(1−CV)+CV+ ̄G′′, G ̄◦=G ◦ K◦ , ̄G′= 9 + 8 ̄G◦ 6 + 12 ̄G◦ , ̄G′′= G ̄(9 ̄K+ 8 ̄G ̄G◦) 6 ̄K+ 12
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