The 27 references with 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
Noton B.R., ed.Engineering applications of composites. New York, Academic Press, 1974. 538 p. (Russ. ed.: Noton B.R., ed.Primenenie compozitsionnykh materialov v tekhnike. Moscow, Mashinostroenie Publ., 1978. 511 p.).
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    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
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    . ¬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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    ‡;̂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
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    [1]
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    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.

2
Kalinchev V.A., Yagodnikov D.A.Tekhnologia proizvodstva raketnykh dvigatelei tverdogo topliva[Technology of production of rigid fuel rocket engines]. Moscow, Bauman MSTU Publ., 2011. 688 p. (in Russian).
Total in-text references: 1
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    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
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    . ¬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.

3
Komkov M.A., Tarasov V.A.Tekhnologia namotki kompozitnykh konstruktsii raket i sredstv porajenia[Technology of winding of composite constructions of rockets and defeat facilities]. Moscow, Bauman MSTU Publ., 2011. 432 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=1994
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    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
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    . ¬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.

4
Shermergor T.D.Teoria uprugisti mikroneodnorodykh sred[Theory of elasticity of microunhomogeneous media]. Moscow, Nauka Publ., 1977. 400 p. (in Russian).
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    ‚ ‚ 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, ‚
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    , 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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    ‡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
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    . »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 ‡

5
Sendeckyj G.P., ed.Mechanics of Composite Materials. New York, Academic Press, 1974. 520 p. (Russ. ed.: Sendeckyj G.P., ed.Mekhanika kompozitsionnykh materialov. Moscow, Mir Publ., 1978. 564 p.).
Total in-text references: 1
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    ‚ ‚ 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, ‚
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    , 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.

6
Christensen R.M.Mechanics of composite materials. New York, Wiley-Interscience publication, 1979. 348 p. (Russ. ed.: Christensen R.M.Vvedenie v mekhaniku kompozitov. Moscow, Mir Publ., 1982. 336 p.).
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    ‚ ‚ 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, ‚
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    , 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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    —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, .

7
Vanin G.A.Mikromekhanika kompozitsionnykh materialov[Micromechanics of composites]. Kiev, Naukova dumka Publ., 1985. 302 p. (in Russian).
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    ‚ ‚ 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]
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    , 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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Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Estimate of effective elastic characterics of materials modified of fullerene.Kompozity i nanostruktury=Composites and nanostructures, 2011, no. 4, pp. 21{31. (in Russian).
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    ¬ 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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9.Lur'e S.A., Mironov Yu.M., Nelyub V.A., Borodulin A.S., Chudnov I.V., Buianov I.A., Soliaev Yu.O. Modeling of dependences of physical-mechanical properties on parameters of micro- and nanostructure polymer composite materials.Nauka i obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2012, no. 6, pp. 37{60. DOI:
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    ¬ 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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7463/0612.0431339(in Russian). 10.Lehmann B., Schlarb A.K., Friedrich K., Zhang M.Q., Rong M.Z. Modelling of Mechanical Properties of Nanoparticle-Filled Polyethylene.International Journal of Polymeric Materials, 2008, vol. 57, no. 1, pp. 81{100. DOI:10.1080/00914030701337232
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    ¬ 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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Ivanisenko Y., Darbandi A., Dasgupta S., Kruk R., Hahn H. Bulk Nanostructured Materials: Non-Mechanical Synthesis.Advanced Engineering Materials, 2010, vol. 12, no. 8, pp. 666{ 676. DOI:10.1002/adem.201000131
Total in-text references: 1
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    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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12.Lur'e S.A., Soliaev Iu.O. Modified Eshelby method in the problem of definition of effective properties with spherical micro- and nanoincludes.Vestnik PGTU. Mekhanika= PNRPU Mechanics Bulletin, 2010, no. 1, pp. 80{90. (in Russian).
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    ̊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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Zaitsev A.V., Fukalov A.A. Effective Bulk Modules of 3D Matrix-Inclusion Composites with Continuous and Hollow Anisotropic Spherical Particles.Vestnik PGTU. Mekhanika=PNRPU Mechanics Bulletin, 2010, no. 4, pp. 46{54. (in Russian).
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    ̊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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Pruger S., Mehlhorn L., Muhlich U., Kuna M. Study of Reinforcing Mechanisms in TRIP-Matrix Composites under Compressive Loading by Means of Micromechanical Simulations.Advanced Engineering Materials, 2013, vol. 15, no. 7, pp. 542{549. DOI: 10.1002/adem.201200323
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    ̊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 ̨
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    [12,13,14]
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    . —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].

15
Sokolov I.I., Dolmatovskii M.G. Spheroplasts.Polimernye materialy=Polymeric materials, 2005, no. 9, pp. 20{21. (in Russian).
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    ̊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
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    [15]
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    , 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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Sokolov I.I., Dolmatovskii M.G., Deev I.S., Stetsenko V.Ia. Influence of the physicomechanical characteristics of hollow glass microspheres on the properties of sphere-filled plastics.Plasticheskie massy, 2005, no. 7, pp. 16{18. (English version of journal:International Polymer Science and Technology, 2006, vol. 33, no. 3, pp. 31{35.).
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    —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]
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    . «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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Weise J., Salk N., Jehring U., Baumeister J., Lehmhus D., Bayoumi M.A. Influence of Powder Size on Production Parameters and Properties of Syntactic Invar Foams Produced by Means of Metal Powder Injection Moulding.Advanced Engineering Materials, 2013, vol. 15, no. 3, pp. 118{122. DOI:10.1002/adem.201200129
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    —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 ̊
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    [16,17,18]
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    . «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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Cunha S., Aguiar J.B., Ferreira V.M., Tadeu A. Influence of the Type of Phase Change Materials Microcapsules on the Properties of Lime-Gypsum Thermal Mortars.Advanced Engineering Materials, 2014, vol. 16, no. 4, pp. 433{441. DOI:10.1002/adem.201300278
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    —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 ̊
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    [16,17,18]
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    . «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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Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. The Effective Coefficients of Thermal Conductivity of Composites with Spherical Inclusions.Teplovye protsessy v tekhnike=Thermal Processes in Engineering, 2012, no. 10, pp. 470{474. (in Russian).
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    «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‡
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    . ¬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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Dimitrienko Yu.I., Sbortshikov S.V., Egoleva E.S., Matveeva A.A. Modeling of thermo-elastic properties of composites with alumino-chromic phosphate matrices.Nauka I obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2013, no. 11, pp. 497{518. DOI:10.7463/1113.0623564(in Russian).
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    «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‡
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    . ¬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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    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
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    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].

  3. In-text reference with the coordinate start=6471
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    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
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    [20]
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    . “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.

  4. In-text reference with the coordinate start=7407
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    ‡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
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    . “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

  5. In-text reference with the coordinate 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]
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    : 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.

21
Zarubin V.S., Kuvyrkin G.N. Special features of mathematical modeling of technical instruments.Matematicheskoe modelirovanie i chislennye metody=Mathematical modeling and numerical method, 2014, no. 1, pp. 5{17. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate 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‡
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    [19,20,21]
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    . ¬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

22
Zarubin V.S., Kuvyrkin G.N.Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoi sredy[Mathematical models of mechanics and electrodynamics of continuous media]. Moscow, Bauman MSTU Publ., 2008. 512 p. (in Russian).
Total in-text references: 6
  1. In-text reference with the coordinate 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]
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    . 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.

  2. In-text reference with the coordinate start=9062
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    «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]
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    . 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).

  3. In-text reference with the coordinate start=9578
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    ≈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
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    [22]
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    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.

  4. In-text reference with the coordinate start=11050
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    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
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    [22]
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    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

  5. In-text reference with the coordinate start=13050
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    ‡ 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]
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    . ›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‚.

  6. In-text reference with the coordinate start=14910
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    ‰ ̊, 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
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    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=

23
Ageev N.V., ed.Teoria obrazovania tekstur in metallakh i splavakh[Theory of forming textures in metals and alloys]. Moscow, Nauka Publ., 1979. 344 p. (in Russian).
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  1. In-text reference with the coordinate start=5139
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    ‡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
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    . »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 ‡

24
Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Yu. Comparative Analysis Estimates of Elastic Moduli for Composite. Isotropic Spherical Inclusions.Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie=Herald of the Bauman Moscow State Technical University. Ser. Mechanical Engineering, 2014, no. 5, pp. 53-69. (in Russian).
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  1. In-text reference with the coordinate start=5407
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    »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
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    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„‡

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    »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
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    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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Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Mixture Models of Composite Mechanics. P. 1. Thermal Mechanics and Thermoelasticity of Multicomponent Mixture.Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki=Herald of the Bauman Moscow State Technical University. Ser. Natural science, 2009, no. 3, pp. 36{49. (in Russian).
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  1. In-text reference with the coordinate start=12279
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    ‚ ̋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
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    , 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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    «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
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    . 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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Zarubin V.S., Stankevich I.V.Raschet teplonapriajennykh konstruktsii[Calculation of heat strained constructions]. Moscow, Mashinostroenie Publ., 2005. 352 p. (in Russian).
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  1. In-text reference with the coordinate start=13050
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    ‡ 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·
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    . ›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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    )··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
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    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

27
Hashin Z., Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials.Journal of the Mechanics and Physics of Solids, 1963., vol. 11, no. 2, pp. 127{140. DOI:10.1016/0022-5096(63)90060-7
Total in-text references: 1
  1. In-text reference with the coordinate 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, .