The 22 references with contexts in paper O. Pugachev V., Z. Han T., З. Хан Т., О. Пугачёв В. (2016) “Эффективная теплопроводность композита с шаровыми включениями // Effective Heat Conductivity of Composite Materials with Ball Inclusions” / spz:neicon:technomag:y:2015:i:6:p:99-111

1
Dul'nev G.N., Zarichniak Iu.P.Teploprovodnost' smesei i kompozitsionnykh materialov[Heat conductivity of mixtures and composite materials]. Leningrad, Energiia Publ., 1974. 264 p. (in Russian).
Total in-text references: 1
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    Prefix
    ̧Ì ̊È ËÌÚÂ‚‡Î; ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊È ̋ÍÒÔÂËÏÂÌÚ; ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ
    Exact
    [1,2,3,4,5,6]
    Suffix
    . ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡.

2
Missenard A.Conductivite thermique des solides, liquides, gaz et de leurs melanges. Paris, Editions Eyrolles, 1965. (In French). (Russ. ed.: Missenard A.Teploprovodnost' tverdykh tel, zhidkostey, gazov i ikh kompozitsiy. Moscow, Mir Publ., 1968. 464 p.).
Total in-text references: 1
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    Prefix
    ̧Ì ̊È ËÌÚÂ‚‡Î; ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊È ̋ÍÒÔÂËÏÂÌÚ; ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ
    Exact
    [1,2,3,4,5,6]
    Suffix
    . ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡.

3
Shermergor T.D.Teoriia uprugosti mikroneodnorodnykh sred[Theory of elasticity of microheterogeneous media]. Moscow, Nauka Publ., 1977. 400 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=1923
    Prefix
    ̧Ì ̊È ËÌÚÂ‚‡Î; ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊È ̋ÍÒÔÂËÏÂÌÚ; ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ
    Exact
    [1,2,3,4,5,6]
    Suffix
    . ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡.

4
Zarubin V.S.Inzhenernye metody resheniia zadach teploprovodnosti[Engineering methods of solving problems of heat conductivity]. Moscow, Energoatomizdat Publ., 1983. 328 p. (in Russian).
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    Prefix
    ̧Ì ̊È ËÌÚÂ‚‡Î; ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊È ̋ÍÒÔÂËÏÂÌÚ; ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ
    Exact
    [1,2,3,4,5,6]
    Suffix
    . ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡.

5
Khoroshun L.P., Soltanov N.S.Termouprugost' dvukhkomponentnykh smesei[Thermoelasticity of two-component mixtures]. Kiev, Naukova dumka Publ., 1985. 109 p. (in Russian).
Total in-text references: 1
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    Prefix
    ̧Ì ̊È ËÌÚÂ‚‡Î; ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊È ̋ÍÒÔÂËÏÂÌÚ; ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ
    Exact
    [1,2,3,4,5,6]
    Suffix
    . ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡.

6
Isaev S.I., Kozhinov I.A., Kofanov V.I., Leont'ev A.I., et al.Teoriya teplomassoobmena [Heatmass exchange theory]. Moscow, Bauman MSTU Publ., 1997. 684 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=1923
    Prefix
    ̧Ì ̊È ËÌÚÂ‚‡Î; ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊È ̋ÍÒÔÂËÏÂÌÚ; ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ
    Exact
    [1,2,3,4,5,6]
    Suffix
    . ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡.

7
Zarubin V.S.Matematicheskoe modelirovanie v tekhnike[Mathematical modeling in engineering]. Moscow, Bauman MSTU Publ., 2001. 496 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=1971
    Prefix
    ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ [1,2,3,4,5,6]. ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË
    Exact
    [7,8]
    Suffix
    χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı [9,10,11,12,13,14,15] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·.

8
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: 1
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    Prefix
    ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧; ‰ËÙÙÛÁËÓÌÌ ̊È ÔÓˆÂÒÒ ¬‚‰ÂÌË ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË, Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÍÓÏÔÓÁËÚ ̊, ÒÓÒÚÓˇ ̆Ë ËÁ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ï‡ÚÂˇÎÓ‚ Ò ‡ÁÎË ̃Ì ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı ÚÂÎ ÔÓÒ‚ˇ ̆ÂÌÓ Á̇ ̃ËÚÂÎ ̧ÌÓ ÍÓÎË ̃ÂÒÚ‚Ó ‡·ÓÚ [1,2,3,4,5,6]. ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË
    Exact
    [7,8]
    Suffix
    χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı [9,10,11,12,13,14,15] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·.

9
Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Estimation of effective heat conductivity coefficient of fullerene-modified composite material.Kompozity i nanostruktury=Composites and Nanostructures, 2012, no. 4, pp. 15{22. (in Russian).
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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
    Exact
    [9,10,11,12,13,14,15]
    Suffix
    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

10
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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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

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    “ ‡ · Î Ë ˆ ‡ 5 rPˆa/a=ˆλ/λ 0,20,632...0,6611,01...1,07 0,30,662...0,6901,07...1,14 0,40,752...0,7771,33...1,41 “ ‡ · Î Ë ˆ ‡ 6 rPˆa/a=ˆλ/λ 0,20,614...0,6440,97...1,03 0,30,578...0,6070,90...0,95 0,40,518...0,5480,79...0,84 —‡‚ÌËÏ ÔÓÎÛ ̃ÂÌÌ ̊ ̇ÏË ÂÁÛÎ ̧Ú‡Ú ̊ Ò ÂÁÛÎ ̧Ú‡Ú‡ÏË ‡·ÓÚ ̊
    Exact
    [10]
    Suffix
    , „‰Â · ̊· ‚ ̊‚‰Â̇ ÙÓÏÛ· λˆ λ1 = 1−2bα 1 +bα ,b= 1−λ2/λ1 2 +λ2/λ1 ,(6) (Á‰ÂÒ ̧ ̃ÂÂÁαÓ·ÓÁ̇ ̃Â̇ Ó· ̇ÂÏ̇ˇ ÍÓ̈ÂÌÚ‡ˆËˇ ‚ÍÎ ̨ ̃ÂÌËÈ). ¬ Ú‡·Î.7,8‚ÂÎË ̃ËÌ ̊ˆλ/λ, Ô‰ÒÚ‡‚ÎÂÌÌ ̊ ‚ Ú‡·Î.1‰Îˇ ÛÔÓˇ‰Ó ̃ÂÌÌ ̊ı Ë ‚2‰Îˇ ı‡ÓÚË ̃ÂÒÍËı ‚ÍÎ ̨ ̃ÂÌËÈ, ÒÓÔÓÒÚ‡‚ÎÂÌ ̊ Ò Ì‡È‰ÂÌÌ ̊ÏË ÔÓ ÙÓÏÛΠ(6).

11
Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Thermal Conductivity of Composite Reinforced with Fibers.Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie=Proceedings of Higher Educational Institutions. Machine Building, 2013, no. 5, pp. 75{81. (in Russian).
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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

12
Zarubin V.S., Kuvyrkin G.N. Effective Coefficients of Thermal Conductivity of a Composite with Ellipsoidal Inclusions.Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki= Herald of the Bauman Moscow State Technical University. Ser. Natural science, 2012, no. 3, pp. 76{85. (in Russian).
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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

13
Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Comparative analysis of estimations of heat conduction of a composite with ball inclusions.Nauka i obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2013, no. 7, pp. 299{318. DOI: 10.7463/0713.0569319(in Russian).
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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

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Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Evaluation of effective thermal conductivity of composites with ball inclusions by the method of self-consistency.Nauka i obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2013, no. 9, pp. 435{444. DOI:10.7463/0913.0601512(in Russian).
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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

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Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Effective Thermal Conductivity Coefficient of the Composite with Continuous Change in Heat Conduction of the Intermediate Layer between Spherical Inclusions and Matrix.Inzhenernyy zhurnal: nauka i innovatsii=Engineering Journal:Science and Innovation, 2012, no. 4. Available at: http://engjournal.ru/catalog/mathmodel/hidden/145.html, accessed 01.05.2015. (in Russian).
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    ¬ ÒËÎÛ ̋ÎÂÍÚÓÚÂÔÎÓ‚ÓÈ ‡Ì‡ÎÓ„ËË [7,8] χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ÓÔËÒ ̊‚‡ ̨ ̆Ë ÔÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ‚ ÍÓÏÔÓÁËÚÂ, ÏÓ„ÛÚ · ̊Ú ̧ ÔËÏÂÌÂÌ ̊ ‰Îˇ ÓˆÂÌÍË ̋ÎÂÍÚÓÔÓ‚Ó‰ÌÓÒÚË, ‰Ë ̋ÎÂÍÚË ̃ÂÒÍÓÈ Ë Ï‡„ÌËÚÌÓÈ ÔÓÌˈ‡ÂÏÓÒÚË ÍÓÏÔÓÁËÚ‡. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

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Yankovskii A.P. Numerically-Analytical Modelling of Processes of Thermal Conductivity in Spatially Reinforced Composites at Intensive Thermal Action.Teplovye protsessy v tekhnike =Thermal Processes in Engineering, 2011, no. 11, pp. 500{516. (in Russian ).
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    ¬ ‡·ÓÚ‡ı [9,10,11,12,13,14,15] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Pugachev O.V., Han Z.T. Heat Conductivity of Composite Materials with Included Balls of Zero Heat Conductivity.Nauka i obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2015, no. 5, pp. 205{217. DOI:10.7463/0515.0776224(in Russian).
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    »‰Âˇ ÒÓÒÚÓËÚ ‚ ÚÓÏ, ̃ÚÓ· ̊ ÒÙÓÏÛÎËÓ‚‡Ú ̧ Û‰Ó·ÌÓ ‚ ̊ ̃ËÒΡÂÏÛ ̨ ÓˆÂÌÍÛ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚË, ÍÓÚÓ‡ˇ ÚÂÓÂÚË ̃ÂÒÍË ËÁ‚ÂÒÚ̇ ‰Îˇ Ó‰ÌÓÓ‰ÌÓ„Ó Ï‡ÚÂˇ·, Ë ÒÚ‡ÚËÒÚË ̃ÂÒÍË ÓˆÂÌË‚‡Ú ̧  ‰Îˇ ÍÓÏÔÓÁËÚ‡. ¬ Ô‰ ̊‰Û ̆ÂÈ ‡·ÓÚÂ
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    ‡ÒÒχÚË‚‡Î‡Ò ̧ Á‡‰‡ ̃‡ ÓˆÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ËÁ χÚÂˇ· Ò ÌÛ΂ÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧ ̨. –‡Á‡·ÓÚ‡ÌÌ ̊È Ú‡Ï ÏÂÚÓ‰ ̇ıÓʉÂÌˡ ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÍÓÏÔÓÁËÚÓ‚ ÔËÏÂÌËÏ ‰Îˇ ‚ÍÎ ̨ ̃ÂÌËÈ ÔÓËÁ‚ÓÎ ̧ÌÓ„Ó ‡ÁÏÂ‡ Ë ÙÓÏ ̊.

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    –‡ÒÒ ̃ËÚ‡ÂÏ ̋ÚÛ ‚ÂÓˇÚÌÓÒÚ ̧ ‰Îˇ Ó‰ÌÓÓ‰ÌÓ„Ó Ï‡ÚÂˇ· Ò ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚËa. œÛÒÚ ̧{wt}t>0| Òڇ̉‡ÚÌ ̊È ‚ËÌÂÓ‚ÒÍËÈ ÒÎÛ ̃‡ÈÌ ̊È ÔÓˆÂÒÒ. —ËÏ‚ÓÎÓÏΦ(x)·Û‰ÂÏ Ó·ÓÁ̇ ̃‡Ú ̧ ÙÛÌÍˆË ̨ Òڇ̉‡ÚÌÓ„Ó ÌÓχΠ̧ÌÓ„Ó ‡ÒÔ‰ÂÎÂÌˡ. ‘ÛÌÍˆËˇ ‡ÒÔ‰ÂÎÂÌˡ ÒÎÛ ̃‡ÈÌÓ„Ó ÏÓÏÂÌÚ‡ Tb= min{t>0:|wt|=b},b>0, ‡‚̇
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    [17]
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    P{Tb<T}=F1(T/b2),„‰Â ÙÛÌÍˆËˇF1Á‡‰‡Ì‡ ÙÓÏÛÎÓÈ F1(t) = 4 ∑∞ k=0 (−1)kΦ ( − 2k+ 1 √ t ) ,  „‡ÙËÍ ÔÓ͇Á‡Ì ̇ ËÒ.1. ƒÎˇ ÒÎÓˇ{(x,y,z): 0<x<b}ËÁ Ó‰ÌÓÓ‰ÌÓ„Ó Ï‡ÚÂˇ· Ò ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚËa, ‚ ÍÓÚÓÓÏ Ï ̊ ‡ÒÒχÚË‚‡ÂÏ ‰‚ËÊÂÌË ̃‡ÒÚˈ ̊ ‰Ó ÔÂ‚Ó„Ó ÔÓÔ‡‰‡Ìˡ ̇ ÔÓ‚ÂıÌÓÒÚ ̧{x=b}, ‚‡ÊÌÓ ÎË ̄ ̧ ÓÚ‡ÊÂÌË ÓÚ ÔÓ‚ÂıÌÓÒÚË{x= 0}. œÓÒÍÓÎ ̧ÍÛ Xt∼N(0,2at), ÔÓÎÛ ̃‡ÂÏ P=P { min{t:|Xt|=b}<T }

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Chen Y.-M., Ting J.-M. Ultra high thermal conductivity polymer composites.Carbon, 2002, vol. 40, no. 3, pp. 359{362. DOI:10.1016/S0008-6223(01)00112-9
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    ¬ ‡·ÓÚ‡ı [9,10,11,12,13,14,15] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Nan C.-W., Birringer R., Clarke D.R., Gleiter H. Effective thermal conductivity of particulate composites with interfacial thermal resistance.Journal of Applied Physics, 1997, vol. 81, no. 10, pp. 6692{6699. DOI:10.1063/1.365209
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    ¬ ‡·ÓÚ‡ı [9,10,11,12,13,14,15] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Tikhonov A.N., Samarskii A.A.Uravneniia matematicheskoi fiziki[Equations of mathematical physics]. Moscow, MSU Publ., 1999. 799 p. (in Russian).
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    ̨C (ƒÊ/Ï3 ) Ë ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚËλ(¬Ú/Ï ), ÚÓ Û‡‚ÌÂÌË ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ËÏÂÂÚ ‚ˉ u ̇=a∇2u, „‰Âu=u(t,x,y,z)| ÚÂÏÔÂ‡ÚÛ‡ (ÓÚÒ ̃ËÚ ̊‚‡Âχˇ ÓÚ ÌÂÍÓÚÓÓ„Ó ‚ ̊·‡ÌÌÓ„Ó ÌÛΡ, Ì ӷˇÁ‡ÚÂÎ ̧ÌÓ ‡·ÒÓÎ ̨ÚÌÓ„Ó);a=λ/C(Ï2/Ò) | ÍÓ ̋ÙÙˈËÂÌÚ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚË. ≈ÒÎË ËÁ‚ÂÒÚÌÓ Ì‡ ̃‡Î ̧ÌÓ ‡ÒÔ‰ÂÎÂÌË ÚÂÏÔÂ‡ÚÛ ̊u0(x,y,z), ÚÓ ÏÓÊÌÓ ÔÓÎÛ ̃ËÚ ̧ ‡ÒÔ‰ÂÎÂÌË ÚÂÏÔÂ‡ÚÛ ̊ ̃ÂÂÁ ‚ÂÏˇtÔÓ ÙÓÏÛÎÂ
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    u(t,x,y,z) =u0∗pt(x,y,z),(1) „‰Â ÒËÏ‚ÓÎÓÏ∗Ó·ÓÁ̇ ̃Â̇ Ò‚ÂÚ͇ ÙÛÌ͈ËÈ: f∗g(x,y,z) = ∫∫∫ f(x−u,y−v,z−w)g(u,v,w)dudvdw, Ë ÙÛÌÍˆËˇ pt(x,y,z) = 1 (√ 4πat )3exp ( − x2+y2+z2 4at ) (2) ÂÒÚ ̧ ÔÎÓÚÌÓÒÚ ̧ ÌÓχΠ̧ÌÓ„Ó ‡ÒÔ‰ÂÎÂÌˡ Ò ÌÛ΂ ̊Ï Ò‰ÌËÏ, ‰ËÒÔÂÒˡÏË2atË ÌÛ΂ ̊ÏË ÍÓÂΡˆËˇÏË.

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Venttsel' A.D.Kurs teorii sluchainykh protsessov[Course of the theory of random processes]. Moscow, Nauka Publ., 1975. 320 p. (in Russian).
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    ‡ÚÛ ̊ ̃ÂÂÁ ‚ÂÏˇtÔÓ ÙÓÏÛΠ[20] u(t,x,y,z) =u0∗pt(x,y,z),(1) „‰Â ÒËÏ‚ÓÎÓÏ∗Ó·ÓÁ̇ ̃Â̇ Ò‚ÂÚ͇ ÙÛÌ͈ËÈ: f∗g(x,y,z) = ∫∫∫ f(x−u,y−v,z−w)g(u,v,w)dudvdw, Ë ÙÛÌÍˆËˇ pt(x,y,z) = 1 (√ 4πat )3exp ( − x2+y2+z2 4at ) (2) ÂÒÚ ̧ ÔÎÓÚÌÓÒÚ ̧ ÌÓχΠ̧ÌÓ„Ó ‡ÒÔ‰ÂÎÂÌˡ Ò ÌÛ΂ ̊Ï Ò‰ÌËÏ, ‰ËÒÔÂÒˡÏË2atË ÌÛ΂ ̊ÏË ÍÓÂΡˆËˇÏË. Œ‰ÌÓÏÂÌ ̊È ÒÎÛ ̃‡ÈÌ ̊È ÔÓˆÂÒÒ{wτ}τ>0̇Á ̊‚‡ÂÚÒˇ Òڇ̉‡ÚÌ ̊Ï ‚ËÌÂÓ‚ÒÍËÏ
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    , ÂÒÎËwτ∼N(0,τ), Ë Â„Ó ÔË‡ ̆ÂÌˡ wτ2−wτ1,...,wτk−wτk−1,quad06τ1<τ2<...<τk, ÌÂÁ‡‚ËÒËÏ ̊. œ‡‡ÏÂÚτËÏÂÂÚ ‡ÁÏÂÌÓÒÚ ̧ Í‚‡‰‡Ú‡ ‡ÒÒÚÓˇÌˡ. ¬ Ò‚ˇÁË Ò Á‡‰‡ ̃ÂÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ì‡Ï Ì‡‰Ó ·Û‰ÂÚ ‡ÒÒχÚË‚‡Ú ̧ ‚ËÌÂÓ‚ÒÍË ÔÓˆÂÒÒ ̊ Òτ= 2at, Ú.

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Pechinkin A.V., Teskin O.I., Tsvetkova G.M., Bocharov P.P., Kozlov N.E.Teoriia veroiatnostei[Probability theory]. Moscow, Bauman MSTU Publ., 2004. 456 p. (Ser.Matematika v tekhnicheskom universitete[Mathematics in Technical University], vol. 16). (in Russian ) .
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    ‘ËÁË ̃ÂÒÍËÈ ÒÏ ̊ÒÎ Ú‡ÍÓ„Ó ̋ÍÒÔÂËÏÂÌÚ‡ | ÔËÎÓÊË‚ Í ÔÓ‚ÂıÌÓÒÚË{x= 0}‡‚ÌÓÏÂÌ ̊È ËÒÚÓ ̃ÌËÍ ÚÂÔ·, ÓˆÂÌËÚ ̧, ̇ÒÍÓÎ ̧ÍÓ · ̊ÒÚÓ ÓÌÓ ‰ÓıÓ‰ËÚ ‰Ó ÔÓ‚ÂıÌÓÒÚË{x=b}. Œ·ÓÁ̇ ̃ËÏq=m/n. —ӄ·ÒÌÓ ˆÂÌÚ‡Î ̧ÌÓÈ Ô‰ÂÎ ̧ÌÓÈ ÚÂÓÂÏÂ
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    , ÔË ·ÓÎ ̧ ̄ÓÏn, 95%-‰Ó‚ÂËÚÂÎ ̧Ì ̊È ËÌÚÂ‚‡Î ‰ÎˇPËÏÂÂÚ ‚ˉ P1=q−1,96 √ q(1−q) n <P<q+ 1,96 √ q(1−q) n =P2, ÒΉӂ‡ÚÂÎ ̧ÌÓ, 95%-‰Ó‚ÂËÚÂÎ ̧Ì ̊È ËÌÚÂ‚‡Î ‰ÎˇˆaËÏÂÂÚ ‚ˉ b2 2T F−11(P1)<ˆa< b2 2T F−11(P2).