Моделювання процесів теплопровідності при розрахунках термостійкості та визначенні теплофізичних характеристик кристалів складної форми: Автореф. дис.

1

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO IIIIE?ENOAE?A

Ia i?aaao ?oeiieno

Noaoi?eiaa Ia?eia Aieiaeeie??aia

OAeE 536.24:539.3

Iiaeaethaaiiy i?ioean?a oaieii?ia?aeiino? i?e ?ic?aooieao
oa?iino?eeino? oa aecia/aii? oaieio?ce/ieo

oa?aeoa?enoee e?enoae?a neeaaeii? oi?ie

05.02.01. — iaoa??aeiciaanoai

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy a/aiiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Oa?e?a — 1999 ?.

Aeena?oaoe?y ? ?oeiienii.

?iaioo aeeiiaii a ?inoeooo? iiiie?enoae?a IAI Oe?a?ie

Iaoeiaee ea??aiee:aeieoi? oaoi?/ieo iaoe, i?ioani?, /eai.-ei?. IAI
Oe?a?ie, aaia?aeueiee aee?aeoi? IOE “?inoeooo iiiie?enoae?a” IAI
Oe?a?ie, A?eiueia Ai?en A?eoi?iae/

Io?oe?ei? iiiiaioe:aeieoi? oaoi?/ieo iaoe, i?ioani? eaoaae?e oaoiieia??
iaoae?a oa iaoa??aeiciaanoaa Oa?e?anueeiai aea?aeaaiiai
aaoiiia?eueii-oeyoiaiai oaoi?/iiai oi?aa?neoaoo I?i?noa?noaa ina?oe
Oe?a?ie, Oeiioa?aa Ea?ena Aiae???aia

eaiaeeaeao oaoi?/ieo iaoe, aeioeaio eaoaae?e o?ceee Oa?e?anueei?
aea?aeaaii? aeaaeai?? cae?cie/iiai o?ainii?oo I?i?noa?noaa o?ainii?oo
Oe?a?ie Eao?e/ Na?a?e Ieaenaiae?iae/

I?ia?aeia onoaiiaa:Oa?e?anueeee aea?aeaaiee iie?oaoi?/iee oi?aa?neoao
I?i?noa?noaa ina?oe Oe?a?ie, eaoaae?a caaaeueii? oa aenia?eiaioaeueii?
o?ceee

Caoeno a?aeaoaeaoueny “16” “ethoiai” 2000 ?. i 14.00 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.169.01 i?e ?inoeooo?
iiiie?enoae?a IAI Oe?a?ie (310001, Oa?e?a, i?iniaeo Eai?ia, 60).

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? ?inoeoooo
iiiie?enoae?a IAI Oe?a?ie.

Aaoi?aoa?ao ?ic?neaiee “23” “a?oaeiy”1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii? ?aaee,

eaiaeeaeao oaoi?/ieo iaoe Ao?iuaiei E.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. E?enoae?/i? oaa?ae? o?ea, oe?iei aeei?enoiaoth/enue
o no/aniiio i?eeaaeiaoaeoaaii? (o oiio /ene? o aeaoaeoi?ao ?ii?coth/iai
aei?ii?ithaaiiy oa oaoiieia?/ieo eaca?ao), /anoi i?aoeththoue a oiiaao
a?aie/ieo oaieiaeo iaaaioaaeaiue oa ??ceeo ia?aiaae?a oaiia?aoo?. I?e
oeueiio iiaeooue noai?eoenue oae? oaiia?aoo?i? iiey, ye? aeeee/ooue
cia/i? ii aaee/ei? oa?iii?oaei? iai?oaeaiiy.

A oeeo aeiaaeeao eaaeooue i?i oa?iino?ee?noue, ?icoi?th/e iaeneiaeueiee
a?aae??io oaiia?aoo?e o o?e?, i?e yeiio aeieeath/? oa?iii?oaei?
iai?oaeaiiy i?eaiaeyoue aei ca?iaeaeaiiy oa iioe?aiiy o??ueie.

Oa?iino?ee?noue aeyaey?oueny iaeiith c aaaeeea?oeo oa?aeoa?enoee
iaoa??aea, yea iio?aao? aea/aiiy. Aeey ioe?iee oa?iino?eeino? o
oaia?aoi?e /an o e?oa?aoo?? ?nio? ?yae e?eoa???a: E?iaeaea??, Aaeaoeea,
Athnnaia oa ?ioeo. Aea, iaea?eueo oe?iei aeei?enoiao?oueny
ocaaaeueithth/ee e?eoa??e E?iaeaea??, oa?aeoa?ecoth/ee oa?iino?ee?noue
?cio?iiieo iaoa??ae?a aaee/eiith ?oei?aiiai ia?aiaaeo oaiia?aoo?, a oiio
?ac?, eiee eiao?oe?aio oaieiiai?io aeinoaoiuei aaeeeee. O?oaei?noue
aeine?aeaeaiiy oa i?aaeeueii? ioe?iee oa?iino?eeino? ca aeiiiiiaith
ocaaaeueithth/iai e?eoa??th iieyaa? o oiio, ui oeae ia?aiao?
aecia/a?oueny o?eueee aeanoeainoyie ?cio?iiieo iaoa??ae?a, oaeeie ye
iiaeoeue THiaa, eiao?oe?aio Ioanniia, oaiia?aoo?iee eiao?oe?aio
e?i?eiiai ?acoe?thaaiiy, a?aieoey i?oeiino?. Iani?aaae?, oa?iino?ee?nue
nooo?ai caeaaeeoue a?ae nooiaiy aieeao oaiia?aoo?e oa ai?cio?ii?? ia
oaieio?ce/i? oa iaoai?/i? aeanoeaino? iaoa??ae?a, a?ae eiino?oeoe?eieo
oa aaiiao?e/ieo ia?aiao??a (oi?ie oa ?ici???a), a?ae oiia ciai?oiuei?
ae?? (oa?iioaea?, aei?ii?ithaaiiy, eiiaaeoe?eiee oaieiiai?i). Iaaeie?eii
e?eoa??th E?iaeaea?? a?yaey?oueny oa, ui o iueiio ia a?aoiaaii aieea
eiao?oe?aioa oaieiiai?io, aeeiai?/ieo aoaeo?a, e?ioeaai? oaeaeeino?
?iciianthaeaeaiiy oaiea, ui iniaeeai aaaeeeai aeey aeniei?ioaineaieo
i?ioean?a, a oaeiae aieeao eiioaeoiiai oa?i?/iiai iii?o ia no?ee?noue
iaoa??ae?a.

?icaeyaeo caaaeaieo ooo aeooaeueieo iaae??oaieo ieoaiue i?enay/aia
oaia??oiy ?iaioa.

Iaoith ?iaioe aeyaey?oueny:

— iaea?aeaoe i?inoi?iai-/aniaee ?iciiae?e oaiia?aoo?e oa oa?iii?oaeieo
iai?oaeaiue o e?enoaeao (oa aeaioa?iaeo nenoaiao) oeee?iae?e/ii? oa
i?yiieooii? oi?ie c o?aooaaiiyi noaiaiaai? caeaaeiino? eiao?oe?aioa
oaieii?ia?aeiino? a?ae oaiia?aoo?e, ?ia?oe?? oaieiaiai iioieo,
ai?cio?ii?? oa ?ici??ieo aoaeo?a;

— c’ynoaaoe ca’ycie i?ae iaeneiaeueieie cia/aiiyie a?aae??io?a
oaiia?aoo?e oa oa?iii?oaeieo iai?oaeaiue c oaieio?ce/ieie
oa?aeoa?enoeeaie oa oa?iino?ee?noth iaoa??ae?a;

— anoaiiaeoe e?eoa??e oa?iino?eeino?, yeee aecia/a? oiiae ?oeioaaiiy
iaoa??ae?a o caeaaeiino? a?ae ooiaeaiaioaeueieo, oaieiaeo oa
eiino?oeoe?eieo aeanoeainoae.

Iaoiae aeinyaiaiiy iinoaaeaiii? iaoe caniiao?oueny ia iine?aeiaiiio
ae??oaii? ??aiyiue oaieii?ia?aeiino? (ia?aaie?/iiai oa a?ia?aie?/iiai
oeio) oa oa?iii?oaeiino? (c o?aooaaiiyi aeeiai?/ieo aoaeo?a) i?e
caaeaaaieo e?aeiaeo oiiaao (i?e e?i?eiiio i?aeeii? oaiia?aoo?e
na?aaeiaeua a oiiaao eiiaaeoeaiiai oaieiiai?io c iiaa?oiath ii caeiio
Iuethoiia, i?e oa?iioaea??, i?e aei?ii?ithaaii?).

Iaoeiaa iiaecia aeena?oaoe?eii? ?iaioe iieyaa? o ianooiiiio:

— iaea?aeaii i?inoi?iai-/aniaee ?iciiae?e oaiia?aoo?e oa oa?iii?oaeieo
iai?oaeaiue o e?enoaeao oeee?iae?e/ii? oi?ie, iaa??aaeiieo c aieiai?
iiaa?oi? ii e?i?eiiio caeiio c noaeith oaeaee?noth c o?aooaaiiyi
noaiaiaai? caeaaeiino? eiao?oe?aioa oaieii?ia?aeiino? a?ae oaiia?aoo?e;

— cai?iiiiiaaii e?eoa??e oa?iino?eeino?, yeee aeicaiey? neeanoe oi/ia
oyaeaiiy i?i a?aeiiniee ii?? oaieiaiio oaea?o iioe/ieo e?enoae?/ieo
iaoa??ae?a.

— iaea?aeai? oi?ioee, iienoth/? oa?aeoa? ci?ithaaiiy oa?iii?oaeiiai
noaiiaeua aeaioa?iai? ieanoeie, yea aeieea? i?ae ae??th neeueieo
oaieiaeo iai?oaeaiue, a caeaaeiino? a?ae aaiiao?e/ieo ia?aiao??a oa
oa?iiiaoai?/ieo aeanoeainoae neeaaeath/eo ?? iaoa??ae?a;

— aecia/aii /an ?iciianthaeaeaiiy ?aae?aeueiiai oaieiaiai iioieo o
iaoa??aeao oeee?iae?e/ii? oi?ie oa anoaiiaeaia eiai caeaaei?noue a?ae
oaeaeeino? ?iciianthaeaeaiiy oaiea oa ?ioaineaiino? oaieiiai?io;

— iaea?aeaii ?iciiae?e oaiia?aoo?e o neeaaeaiiio iaiaaeaiiio
oeee?iae??, eiee ii an?i eiai iiaa?oiyi a?aeaoaa?oueny oaieiiai?i ca
caeiiii Iuethoiia, a oaiia?aoo?a na?aaeiaeua ci?ith?oueny ca /anii
e?i?eii.

I?aeoe/ia oe?ii?noue ?iaioe. Cai?iiiiiaaii:

— e?eoa??e oa?iino?eeino?, yeee oa?aeoa?eco? a?aeiioaiiy a?aieoe?
i?oeiino? aei aaee/eie iaeneiaeueieo oa?iii?oaeieo iai?oaeaiue, ye?
iiaeooue aooe aeei?enoai? aeey aeai?o noeeioeeyoe?eiiai e?enoaea i?e
aeaioiaeaii? aeaoaeoi??a ?ii?coth/eo aei?ii?ithaaiue;

— niin?a aecia/aiiy /ano ?iciianthaeaeaiiy ?aae?aeueiiai oaieiaiai
iioieo, aeicaieyth/ee iie?ioeoe oi/i?noue oa caaania/eoe aeinoia??i?noue
aei??thaaiiy eiao?oe?aio?a iiaeeiaiiy aei?ii?ithaaiiy o aaeeeiaaaa?eoieo
i?ici?eo e?enoaeao oeee?iae?e/ii? oi?ie;

— ?ic?aooiee oaieiaeo i?ioean?a o ai?cio?iiieo e?enoaeao, iaa??aaeiieo
?aae?aoe??th o iaaeeaeaii? oa?i?/iiai oa?o iaoiaeii ina?aaeiaiiy
ooieoe?iiaeueieo iii?aaie, caaania/o? aa?io oi/i?noue i?e ioe?ioe?
aieeao e?eoa??th Noa?ea oa ai?cio?ii?? iaoa??ae?a ia ??aaiue
oa?iii?oaeieo iai?oaeaiue;

— aiae?oe/i? ni?aa?aeiioaiiy, iienoth/? ?iciiae?e oaiia?aoo?e a
neeaaeaiiio iaiaaeaiiio oeee?iae??, ye? iiaeooue aooe aeei?enoai? aeey
aei??thaaiiy eiao?oe?aio?a oaiia?aoo?ii?ia?aeiino? e?enoae?a, c aenieith
oaieii?ia?aei?noth;

— ?ic?aooieia? ni?aa?aeiioaiiy aeey oa?iii?oaeieo iai?oaeaiue,
aeieeath/eo o aeaioa?ia?e nenoai?, ye? aeaaeooue iiaeeea?noue
ia?aaea?uaoe ci?iaiiy o?ce/ieo oa aaeaac?eieo aeanoeainoae eiioaeooth/eo
iaoa??ae?a.

Iniaenoee aianie caeiaoaa/a. Caeiaoaa/ai a/aiiai nooiaiy eaiaeeaeaoa
oaoi?/ieo iaoe aoea i?iaaaeaia ?iaioa, yea iia’ycaia c iiooeii oa
aiae?cii iaoeiaeo ioae?eaoe?e, ui i?enay/ai? oai? aeaii? aeena?oaoe??.
Aeeiiaia no?oeoo?ecaoe?y oaie oa noi?iiaai? caaea/? aeine?aeaeaiiy.
Ae??oaiiy oeeo caaea/ ca aeiiiiiaith iaoaiaoe/iiai iiaeaethaaiiy iie?a
oaiia?aoo?e oa oa?iii?oaeiino? aeicaieeei caeiaoaa/o aeinoaoiuei iiaii
?ice?eoe oe?eue ?iaioe oa i?iaanoe ?ic?aooiee oa?iino?eeino? ? aecia/eoe
oaieio?ce/i? oa?aeoa?enoeee e?enoae?a neeaaeii? oi?ie. A oiae?
aeine?aeaeaiiy caeiaoaa/ai aoei aeyaeaii oe?eee ?yae iiaeo ?acoeueoao?a,
ye? aoee iioae?eiaai? o ainueie noaooyo [1-8]. Aaoi?ii aeena?oaoe?eii?
?iaioe aaciina?aaeiuei

— O ia?o?e noaoo? i?e aeine?aeaeaii? oaieiaeo i?ioean?a o e?enoaeao
oeee?iae?e/ii? oi?ie a iaieiioe?, eiee ii an?i eiai iiaa?oiyi
a?aeaoaa?oueny oaieiiai?i ca caeiiii Iuethoiia, a oaiia?aoo?a
iaaeieeoiueiai na?aaeiaeua ci?ith?oueny c /anii e?i?eii cai?iiiiiaaii
niin?a aei??thaaiiy oaieio?ce/ieo oa?aeoa?enoee iaoa??ae?a iaoiaeii
eaac?noaoe?iia?iiai ?aaeeio.

— O ae?oa?e noaoo? i?iaaaeai? ?ic?aooiee i?inoi?iai-/aniaiai ?iciiae?eo
oaiia?aoo?ieo iie?a oa oa?iii?oaeieo iai?oaeaiue, aeieeath/eo o aeeneao
ca oiiaaie e?i?eiiai i?aeeiio oaiia?aoo?e iaaeieeoiueiai na?aaeiaeua a
caeaaeiino? a?ae ?ioaineaiino? oaieiiai?io, oaeaeeino? iaa??ao,
oa?iiiaoai?/ieo oa?aeoa?enoee oa aaiiao?e/ieo eiino?oeoe?eieo
ia?aiao??a.

— O o?ao?e noaoo? ia iniia? e?i?eiiai iaoaiaoe/iiai iiaeaethaaiiy
cai?iiiiiaaii iaoiae ?ic?aooieo iie?a oa aeeiai?/ieo oa?iii?oaeieo
iai?oaeaiue, ye? aeieeathoue i?ae ae??th ??ceiai a?aae??ioo oaiia?aoo?e
o e?enoae? oeee?iae?e/ii? oi?ie c iaieiieith.

— O /aoaa?o?e noaoo? i?e aeine?aeaeaii? i?ioeano ia?aiino oaiea o
oeee?iae?e/iiio o?e? c noaeith oaeaee?noth aecia/aii /an
?iciianthaeaeaiiy ?aae?aeueiiai oaieiaiai iioieo oa eiai caeaaeiino?
a?ae ?ioaineaiino? oaieiiai?io iiaa?oi? oeee?iae?a c iaaeieeoi?i
na?aaeiaeuai oa oaeaeeino? iioe?aiiy oaiea.

— O i’yo?e noaoo? i?e aeine?aeaeaii? oa?iii?oaeiino? e?enoae?a
oeee?iae?e/ii? oi?ie i?e iaa??a? aieiai? iiaa?oi? ca caeiiii
Noaoaia-Aieueoeiaia cai?iiiiiaaii e?eoa??e oa?iino?eeino?, yeee a?aoiao?
ai?cio?iii? aeanoeaino? iaoa??ae?a.

— O oino?e noaoo? ?ic?aoiaaii ?iciiae?e oaiia?aoo?e oa aeeiai?/ieo
oa?iii?oaeieo iai?oaeaiue, ye? aeieeathoue o oiie?e ieanoeioe? i?ae
ae??th oaieiai? ?ia?oe??, aecia/aii /an iiyae no?eae?a iaeneiaeueieo
iai?oaeaiue, iaoiiaeaieo oi?oaith oa oaieiaith oaeeyie.

— O nueii?e noaoo? iaea?aeaii ??oaiiy caaea/ ianoaoe?iia?ii?
oaieii?ia?aeiino? oa oa?iii?oaeiino? aeey aeiaaiai oeee?iae?e/iiai o?ea,
iaa??aaeiiiai c iiaa?oi? e?i?eii c noaeith oaeaee?noth /enaeueiei
?ioaa?i-?ioa?iieyoe?iiei, iaoiaeii eiee eiao?oe?aio
oaiia?aoo?ii?ia?aeiino? ia ? noaeei, a a caeaaeiino? a?ae oaiia?aoo?e
ci?ith?oueny ii noaiaiaaiio caeiio.

— O ainuei?e noaoo? cai?iiiiiaaii niin?a ioe?iee oa?iino?eeino? o
aeaioa?iaeo eiiiiceoe?yo i?e oiia? ??cii? oaiia?aoo?ii? ae??.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
iiaeaaaeenue ia ianooiieo eiioa?aioe?yo:

— I?aeia?iaei?e eiioa?aioe?? “Noeeioeeeyoi?u — 93” (a. Oa?ueeia,
Oe?aeia, 1993);

— The First International Conference in Material Science of Chalegenide
and Diamont-Structure Semiconductors (Chirnivtsi, Ukraine, 1994);

— 5-e I?aeia?iaei?e eiioa?aioe?? “Eaca?iua oaoiieiaee-95” (a. Oaoo?a,
Iineianeie iae., ?inney, 1995);

— Iaoeiai-oaoi?/i?e eiioa?aioe?? “Oaoieea e oeceea yeaeo?iiiuo nenoai e
ono?ienoa” (a. Noiu, Oe?aeia, 1995).

Ioae?eaoe??. Ii iaoa??aeai aeena?oaoe?? iioae?eiaaii a?n?iue noaoae:
o?noue noaoae o aeo?iae? “O?ceea oa o?i?y ia?iaee iaoa??ae?a”
(?in?enueea Aeaaeai?y iaoe), oa aea? noaoo? o aeo?iae? “Ooieoe?iiaeuei?
iaoa??aee” (Iaoe?iiaeueia Aeaaeai?y iaoe Oe?a?ie). Aeieeaaei? iineeaiiy
ia oeacai? ?iaioe iaaaaeai? a e?ioe? aaoi?aoa?aoo.

No?oeoo?a oa ia’?i ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny ?c
anooio, i’yoe ?icae?e?a, aeniiae?a, cae?i/aiiy oa nieneo oeeoo?ii?
e?oa?aoo?e. Caaaeueiee ia’?i aeena?oaoe?eii? ?iaioe neeaaea? 114
noi??iie, o oiio /ene? 6 oaaeeoeue, 22 ?enoiee oa a?ae?ia?ao?th c 102
iaeiaioaaiue.

INIIAIEE CI?NO ?IAIOE.

O anooi? ei?ioei iaiaiai?th?oueny ia’?eo aeine?aeaeaiiy,
iaa?oioiao?oueny aeooaeuei?noue aea?aii? oaie, aeacothoueny oe?e? ?
caaea/? i?iaaaeaieo aeine?aeaeaiue, a oaeiae oi?ioeththoueny iniiai?
?acoeueoaoe, ye? io?eiai? a aeena?oaoe??. Iaaiaeeoueny ia?ae?e
iioae?eiaaieo ca oaiith aeena?oaoe?? noaoae ? iaoeiaeo eiioa?aioe?e, ia
yeeo aoee aeieeaaeai? iniiai? ?acoeueoaoe aeaii? aeena?oaoe??.

Ia?oee ?icae?e i?noeoue iniiaiiieiaei? oai?aoe/i? ?iaioe ii
oaiia?aoo?iei iieyi oa oa?iii?oaeiei iai?oaeaiiyi o aeeneo, oeee?iae??
oa ieanoei?, ?acoeueoaoe yeeo aeei?enoiaothoueny caeiaoaa/ai aeae? ?
iaea?aeaee ?icaeoie o aeena?oaoe??.

?icaeyiooi ??oaiiy ianoaoe?iia?iiai ??aiyiiy oaieii?ia?aeiino? aeey
oiieiai aeeneo oa aeiaaiai oeee?iae?o, oaiia?aoo?a iiaa?oi? yeeo (aai
oaiia?aoo?a iaaeieeoiueiai na?aaeiaeua) ci?ith?oueny c /anii ii
e?i?eiiio caeiio c noaeith oaeaee?noth.

I?aee?aneaii, ui c aeinoaoi?i nooiaiai oi/iino? a aeiaaiio oeee?iae??
i?e wmetafile8? ?? ???????????
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a????&??yyyy?????Ayyy·yyy@??—?? ???&? ?MathType??°?
???u?????????»????-?????ued???ue ???u?th??????Iaaaaeaii
aea?ae oi?ioe aeey aecia/aiiy oa?iii?oaeieo iai?oaeaiue o aeeneo oa
oeee?iae?? i?e ieineiio inaneiao?e/iiio oaiia?aoo?iiio iie?. Ia
i?eeeaae? caaea/? i?i oa?ii?aae?aoe?eiee iaa??a aeiaaiai oeee?iae?a
iienaii (c aeei?enoaiiyi iiiyooy oa?i?/iiai oa?o) iaaeeaeaia aiae?oe/ia
??oaiiy ??aiyiiy oaieii?ia?aeiino? Oo?ue? iaoiaeii ina?aaeiaiiy
ooieoe?iiaeueieo iii?aaie. Iiaeaii a?ia?aie?/ia ??aiyiiy
oaieii?ia?aeiino?, yea (ia a?aei?io a?ae ??aiyiiy Oo?ue?)
canoiniao?oueny aeey ?ic?aooie?a aeniei?ioaineaieo oaieiaeo i?ioean?a,
yeui oaieioa iioe?th?oueny oi/ ? c aeoaea aaeeeith, aea ne?i/aiiith
oaeaee?noth. Noenei aeeeaaea?oueny aea?ae ni?aa?aeiioaiue, iaiao?aeieo
aeey iiaeaeueoiai ia/eneaiiy (a oaia??oi?e ?iaio?) aeeiai?/ieo
oa?iii?oaeieo iai?oaeaiue a iane?i/aiii aeiaaiio oeee?iae?? oa oiie?e
ieanoeioe?. I?eaaaeaii ??oaiiy ??aiyiiy ianoaoe?iia?ii?
oaieii?ia?aeiino? Oo?ue? aeey aeaioa?iai? oaa?aeine??ieaii? ieanoeie i?e
a?aie/ieo oiiaao ia?oiai ?iaeo.

O ae?oaiio ?icae?e? iaa?oioiaaia iaiao?aei?noue ??oaiiy caaea/?
iae?i?eii? ianoaoe?iia?ii? oaieii?ia?aeiino? oa oa?iii?oaeiino? aeey
aeiaaiai oeee?iae?a, iiaa?oiy yeiai iaa??aa?oueny c /anii t e?i?eii c
noaeith oaeaee?noth wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
?a???&??yyyy?????AyyyAyyy ??A?? ???&?
?MathType??P????u?th??????Ca aeiiiiiaith ?ioaa?aeueiiai iaoiaeo
oaieiaiai aaeaino, (yeee aeicaiey? caanoe ianoaoe?iia?ia iae?i?eia
??aiyiiy oaieii?ia?aeiino? o /anoeiieo iio?aeieo i?e etha?e caeaaeiino?
eiao?oe??ioa oaieii?ia?aeiino? a?ae oaiia?aoo?e aei cae/aeiiai ??aiyiiy
? ae??oeoe eiai i?e a?aie/ieo oiiaao o?aoueiai ?iaeo) ciaeaeai? ?
cai?iiiiiaai? c?o/i? aeey ?iaeaia?ieo ?ic?aooie?a oi?ioee, ye?
iienothoue ?iciiae?e oaiia?aoo?e oa oa?iii?oaeieo iai?oaeaiue ia
eaac?noaoe?iia?i?e noaae?? iaa??ao.

A oeueiio ?icae?e? ?icaeyiooa oaeiae caaea/a i?i oa?iii?oaei?
iai?oaeaiiy o aeeneao, i?aeaeaoeo ae?? oaiia?aoo?e, ci?ithaaii? ii
e?i?eiiio caeiio c /anii a oiiaao eiiaaeoeaiiai oaieiiai?io c
iaaeieeoi?i na?aaeiaeuai. Aeyaeaii, ui iiaeeco oi?oe?a ci?ith?oueny
ea?oeia ?iciiae?eo ?aae?aeueieo oa oaiaaioe?aeueieo iai?oaeaiue.
Aeyaeaii, ui iai?oaeaiiy aeinyaiooue iaeneioio ia eaac?noaoe?iia?i?e
noaae?? iaa??ao. Iieacaii, ui ?aae?aeueia eiiiiiaioa oa?iii?oaeieo
iai?oaeaiue aeinyaa? iaea?eueoeo cia/aiue o oeaio?aeuei?e /anoei?
aeeneo; oaiaaioe?aeueia eiiiiiaioa — a eooia?e oi/oe?; inueiaa
eiiiiiaioa — o oeaio?aeuei?e /anoei? aieiai? iiaa?oi?, a cnoaia
eiiiiiaioa iiaeeco eooiai? oi/ee aeeneo.

Oae ye oaiaaioe?aeueia eiiiiiaioa oa?iii?oaeieo iai?oaeaiue ii iaeneioio
ia?aaeuo? on? ?io? eiiiiiaioe, oi ?? cia/aiiy iae?aeiny i?e ioe?ioe?
oa?iino?eeino? iaoa??aeo.

A?aecia/aii, ui ?acoeueoaoe i?e ?ic?aooieao oa?iino?eeino? aoaeooue oei
iaae?ei?o?, /ei a?eueoa ?ioaineai?noue oaieiiai?io. Oiio ui ca?eueoaiiy
?ioaineaiino? oaieiiai?io ca?eueoo? iaeneioi iai?oaeaiue ? oei naiei
cieaeo? a?aie/ii aeiiouai? oaeaeeino? iaa??ao hOI. Aeo?ae ia oe?
oaeaeeino? icia/a?, ui e?eoe/i? iai?oaeaiiy o iaoa??ae? aeinyaee
a?aieoe? i?oeiino?. A?aie/ii aeiiouai? oaeaeeino? iaa??ao
?ic?aoiaoaaeeny, a oaeiae aei??thaaeeny o aenia?eiaio? aeey aeene?a
ae?aiao?aie 410-2 i, 610-2 i oa 810-2 i. ?acoeueoaoe iiaeai? o
c??aiyeuei?e oaaeeoe? aeey eoaiia?acieo aeene?a (inueiaee ia?a??c ?
eaaae?aoii).

Oaaeeoey. A?aie/ii aeiiouai? oaeaeeino? iaa??ao hOI eoaiia?acieo aeene?a
c naeai?aeo oeeieo ??cieo ae?aiao??a d i?e ?ioaineaiiio oaieiiai?i?
iiaa?oi?a c iaaeieeoi?i na?aaeiaeuai.

d, ii40506080100120hOIp, oC/iei97.362.143.624.515.711.4HOI
oC/iei100-4526—

Aeyaeaii, ui ?ic?aooieia? e?eoa??? oa?iino?eeino? iiaiaeaeothoueny c
aenia?eiaioaeueieie. Iaaaeeea ?ica?aei?noue iaoiiaeaia oei, ui i?e
?ic?aooieao ?ioaineai?noue oaieiiai?io i?eioneaeany iane?i/aiii
aaeeeith, ui ye caaaeaee ?iaeoueny, yeui cia/aiiy /enea A?i iaa?aeiii. A
?acoeueoao? a?eueo aei?noe? oiiae i?aae’yaeythoueny aei aaee/eie
a?aie/ii aeiiouaieo oaeaeeinoae iaa??ao. Ia naiiio ae?e?, a aenia?eiaio?
/enei A?i, ?iia??ii, i?eeia? e?ioeaaa cia/aiiy.

O o?aoueiio ?icae?e? ?icaeyiooi ieoaiiy i?i oa?iino?ee?noue
ai?cio?iiieo o?e oeee?iae?e/ii? oi?ie, i?aeaeaoeo ?aae?aoe?eiiio iaa??ao
c aieiai? iiaa?oi? ca caeiiii Noaoaia-Aieueoeiaia.

Caaea/a i?i ?iciiae?e oa?iii?oaeieo iai?oaeaiue o aeiaaiio oeee?iae??
?ica’yco?oueny c aeei?enoaiiyi iiiyooy oa?i?/iiai oa?o (i?ioean
oaieii?ia?aeiino? ?iciiae?eaii ia aeaa aoaie — ?ia?oe?eiee, eiee oaieiaa
cao?aiiy ua ia aeinyaei oeaio?o oeee?iae?a, oa ?aaoey?iee, yeee
oa?aeoa?eco?oueny o/anoth onueiai o?ea a i?ioean? iaa??ao) iaoiaeii
ona?aaeiaiiy ooieoe?iiaeueieo iii?aaie (aeeiio?oueny ?aaoey?ecaoe?y
iaa??ao ii aeeaa?aaioe?? a?aae??ioa oaiia?aoo?e ii a?aeiioaiith aei
caaea/ ianoaoe?iia?ii? oaieii?ia?aeiino?; ia ?ia?oe?eiiio noai? iaa??ao
ona?aaeiaiiy aeeiio?oueny ca oiiae, ui oaieiaa caoaeaeaiiy aacia?a?aii
iioe?th?oueny c noaeith e?ioeaaith oaeaee?noth; ia ?aaoey?iiio
(aii?yaeeiaaiiio) noai? iaa??ao ona?aaeiaiiy aeeiio?oueny ii anueiio
o?eo; ca’ycie i?ae iaa?aeiieie ooieoe?yie /ano anoaiiaeth?oueny o
eiaeiiio ie?aiiio aeiaaeeo i?e oiia? ia?ic?eaiino? oaiia?aoo?ieo iie?a
i?ia??oi? ia iai?ia??oi? cii o?ea ia a?aieoe? ?iciiae?eo.

Aoaeoeai?noue canoinoaaiiy iaaeeaeaiiai iaoiaeo ia?aa??aia oa
iaa?oioiaaia oi?ioith caiaeith c ?acoeueoaoaie oaeeo /enaeueieo
?ic?aooie?a.

Iieacaii, ui ?aae?aeuei?, oaiaaioe?aeuei? ? inueia? eiiiiiaioe
iai?oaeaiue aeinyaathoue iaeneioio o iiiaio /ano, eiee caaa?oo?oueny
?ia?oe?eiee aoai iaa??ao. Aea inueia? iai?oaeaiiy (??ai? ia in? oa ia
iiaa?oi? oeee?iae?a) iaea?eueo iaaacia/i? aeey iaoa??ae?a. ?o e?eoe/i?
cia/aiiy aoaeooue iaiaaeoaaoe ?ioaineo?eaoe?th i?ioean?a oa?iiia?iaee.
Aaee/eio oa?iii?oaeieo iai?oaeaiue iiaeia ?aaoethaaoe c aeiiiiiaith
oa?ii?aae?aoe?eiiai e?eoa??th Noa?ea, wmetafile8? ??G???????????
???????????yyy????.????1?????? ???????
?????&??yyyy?????Ayyy¶yyy@??6?? ???&? ?MathType????
???u?????????»????-?????@j???@6???u y??????Ciaiueooth/e
Sk ie aoaeaii cieaeoaaoe aaee/eio e?eoe/ieo iai?oaeaiue. Ioe?iee aeey
naio??iaeo caaioiaie iieacaee, ui oa?iino?ee?noue caa?aaeaoueny, yeui
e?eoa??e Noa?ea aoaea ci?ithaaoeny o a?aieoeyo a?ae ioey aei iaeeieoe?.

A oaia??oiueiio ?icae?e? aeine?aeaeo?oueny oaeiae i?ioean oaieiia?aiino
o oeee?iae?e/iiio o?e?, i?aeaeaoiio ae?? ??ceiai a?aae??ioo iaonoaeaii?
oaiia?aoo?e.

Aeey e?ioeaai? oaeaeeino? iioe?aiiy oaiea iaoiaeii ona?aaeiaiiy
ooieoe?iiaeueieo iii?aaie ia ?ia?oe?eiiio oa ?aaoey?iiio aoaiao iaa??ao
?ica’ycaii a?ia?aie?/ia ??aiyiiy oaieii?ia?aeiino? i?e oiia?, ui
oaiia?aoo?a na?aaeiaeua, iieaath/iai oeee?iae? o ia/aeueiee iiiaio /ano
i?aeaeuo?oueny a?ae On aei cia/aiiy O0, a ia iiaa?oi? a?aeaoaa?oueny
eiiaaeoeaiee oaieiiai?i ca caeiiii Iuethoiia:

wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
?????&??yyyy?????Ayyyyyy@??-?? ???&? ?MathType????
???u?????????»????-?????@@????@????@???@i???@
7???@Y???@ ???@???@???@@???u?th??????

wmetafile8? ??F??? ????????
?????????????yyy????.??????1?????? ??????? 
a???&??yyyy?????Ayyy¦yyy ??AE?? ???&? ?MathType??P?
???uthY?????

wmetafile8? ??a???????????
???????????yyy????.????1?????? ???????
? +???&??yyyy?????Ayyy©yyy`+??©?? ???&?
?MathType???????uYya?????

aea wmetafile8? ??wmetafile8? ??t??? ????????
?????????????yyy????.??????1?????? ???????
`????&??yyyy?????AyyyYyyy@???? ???&?
?MathType???????u????????????-????? 9??? /
???u?th??????wmetafile8? ?????????????
???????????yyy????.????1?????? ??????? ? 
???&??yyyy?????Ayyy°yyy` ??0?? ???&? ?MathType??`?
???u?????????»????-?????›I???y ???u??
???????»????-????‡y???&F???-?????&N???X?¬???X
?¬???X?[ ???u?th??????G — iiaeoeue i?oaeiino? i?e cnoa?,
wmetafile8? ??‰????????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????Ayyy ??? ??A?? ???&?
?MathType??P????u?th??????Onoiooi i?ioe??//y, yea iaoiiaeaii
canoinoaaiiyi ??aiyiiy oaieii?ia?aeiino? Oo?ue? (aeaaaeaiiai a
i?eiouaii? iane?i/aiii? oaeaeeino? iioe?aiiy oaiea) aeey iieno i?ioean?a
ia?aiino oaiea c e?ioeaaith oaeaee?noth. Aecia/aii /an iioe?aiiy
?aae?aeueiiai oaieiaiai iioieo.

wmetafile8? ??T?????????????
???????????yyy????.????1?????? ??????? ?
???&??yyyy?????AyyyAyyya???A?? ???&?
?MathType??P????&??yyyy???????????????yyy?yyywmetafile8?
??®??????????? ???????????yyy????.????1??????
??????? `A???&??yyyy?????Ayyy¶yyy????? ???&?
?MathType???? ???u?????????»????-?????5???af ???u??
???????»????-????if??? ???-?????
µ???4???4???4M???ue???uem???u?th??????Ano
aiiaeaii, ui oeae /an ianoa? i?ci?oa i?e ciaioaii? oaieiiai?io iiaa?oi?
oeee?iae?a c iaaeieeoi?i na?aaeiaeuai oa oaeaeeino? iioe?aiiy oaiea (a
ii??aiyii? c oaeaee?noth i?oaeieo oaeeue). Iaaaaeai? ioe?iee aeey
aethi?i?th. I?e a?aeiia?aeieo oiiaao oaieiiai?io /an iioe?aiiy
?aae?aeueiiai oaieiaiai iioieo o aaeeeiaaaa?eoieo c?aceao iiaea aooe
ca?a?no?iaaiee iaei?ia?oe?eiei aeao/eeii oaiia?aoo?e.

?icae?e /aoaa?oee i?enay/aiee ??oaiith aeeiai?/ieo caaea/
oa?iii?oaeiino? aeey oeee?iae?a a iaieiioe? (a yeino? iiaeaeueiiai
iaoa??aeo iae?a?oueny ?iaeeo iao??th a eaa?oeaa?e iaieiioe?) i?e oiiaao,
ui oaiia?aoo?a iaaeieeoiueiai na?aaeiaeua ?aioii i?aeaeuo?oueny aei
aeayeiai cia/aiiy ? aeey oiiei? ieanoeiee (aethi?i?e), i?aeaeaoi?
oaieiaiio oaea?o i?e e?ioeaa?e oaeaeeino? iioe?aiiy oaiea.

Iieacaii, ui i?e cia/iino? aoaeoo (no?eaie aeeiai?/ieo iai?oaeaiue
ia?aaeuo? nai? eaac?aeeiai?/ia cia/aiiy a aeaa ?ace) aeiaaio?eaae?noue
ae?? aeoaea iaea (510-3 n aeey NaJ ? 310-12 n aeey aethi?i?th).

O?aooaaiiy e?ioeaai? oaeaeeino? ci?ithaaiiy oaiia?aoo?e o oaa?aeeo o?eao
a?ae??ciy?oueny iayai?noth ia iaeiiai, a aeaio no?eae?a iai?oaeaiiy.
Ia?oee no?eaie iaoiiaeaiee iioe?aiiyi o iaoa??ae? a?ae iiaa?oi? aei
oeaio?o ca /an wmetafile8? ??<??? ???????? ?????????????yyy????.??????1?????? ??????? ? ???&??yyyy?????AyyyYyyy`??Y?? ???&? ?MathType??A????u????????????-????? P??? H ???u y?????? O ?icae?e? i’yoiio iaaaaeai? eiioaeoi? nenoaie ieinei? oa oeee?iae?e/ii? oi?ie. Ae??oo?oueny caaea/a i?i oa?iii?oaei? iai?oaeaiiy, aeieeath/? o aeiaa?e aeaioa?ia?e ieanoei?, i?aeaeao?e ?aioiaiio ci?iaiith oaiia?aoo?e ia ?? iiaa?oiyo. Iaaeai? oi?ioee i?inoi?iai-/aniaiai ?iciiae?eo iai?oaeaiue, ye? aeicaieythoue aeinoaoiuei oi/ii aecia/aoe iaeneiaeueio aaee/eio oa?iii?oaeieo iai?oaeaiue, a oaeiae ioe?ithaaoe aieea oa?iiiaoai?/ieo oa ?ici??ieo oaeoi??a. Aeyaeaii, ui iaeneiaeuei? iai?oaeaiiy eiioeaio?othoueny a cii? eiioaeoo ieanoeie oa iie?eooy. Iiaeai? ?ic?aooiee ia oa?iino?ee?noue ieanoei c naeai?aeo oeeieo, iie?eoeo aeiaciith ie?aeith. Ciaeaeaii, ui oa?iino?ee?noue aeaoaeoi?a c naeai?aeo oeeieo (oiaueiith a?ae 210-3 i aei 210-2 i) c aeiaciei iie?eooyi caa?aaeaoueny, yeui ?? oiaueia aoaea ia iaio 10-7 i. ?acoeueoaoe i?aeoaa?aeaeothoueny aenia?eiaioii. A oeueiio ?icae?e? iaaaaeaii ??oaiiy caaea/? oaieii?ia?aeiino? aeey iaiaaeaiiai oeee?iae?a a iaieiioe?, eiee oaieiiai?i cae?enith?oueny ca caeiiii Iuethoiia, a oaiia?aoo?a na?aaeiaeua aeyaey?oueny e?i?eiith ooieoe??th /ano. Iaea?aeai? oi?ioee aeey ?iciiae?eo oaiia?aoo?e a ethaee iiiaio /ano. Aeyaeaii, ui ??cieoey oaiia?aoo?e i?ae iiaa?oiath ? oeaio?ii oeee?iae?a wmetafile8? ??????????????? ???????????yyy????.????1?????? ??????? ?A???&??yyyy?????AyyyAyyy???A?? ???&? ?MathType??P????u?th??????I?aee?aneaii i?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Ii-ia?oa, ii c??aiyiith aenia?eiaioaeueii? caeaaeiino? wmetafile8? ??????????????? ???????????yyy????.????1?????? ??????? ?A???&??yyyy?????AyyyAyyy???A?? ???&? ?MathType??P????u?th??????Ia cae?i/aiiy iaaeai? ioe?iee aieeao ai?cio?ii?? iaoa??aeo ia ?acoeueoaoe i?e ia/eneaii? iaeneiaeueieo oa?iii?oaeieo iai?oaeaiue. A?aooaaiiy ai?cio?ii?? iiaea nooo?ai aieeiooe ia ?acoeueoaoe e?euee?nieo ?ic?aooie?a. Iieacaii, ye ia eaac?noaoe?iia?i?e noaae?? iaa??ao, aei??ea ??cieoeth oaiia?aoo?e iiaa?oi? oa iaaeieeoiueiai na?aaeiaeua, ia/eneeoe /enei A?i oa i?e a?aeiiiio cia/aii? eiao?oe??ioa oaieii?ia?aeiino?, eiao?oe??io oaieiiai?io. INIIAI? ?ACOEUeOAOE OA AENIIAEE. 1. Iaea?aeaii i?inoi?iai-/ania? ?iciiae?ee oaiia?aoo?e oa oa?iii?oaeieo iai?oaeaiue o aeiaaiio oeee?iae??, oaiia?aoo?a aieiai? iiaa?oi? yeiai ci?ith?oueny e?i?eii c /anii c noaeith oaeaee?noth, a eiao?oe??io oaieiiia?aeiino? c?inoa? o caeaaeiino? a?ae oaiia?aoo?e ii noaiaiaaiio caeiio. Iieacaii, ui ??cieoey oaiia?aoo?e i?ae iiaa?oiath oa oeaio?ii oeee?iae?a oa oaiiii?oaei? iai?oaeaiiy, aeinyaath/e iaea?eueoeo cia/aiue iaeii/aniai o iiiaio aeoiaeo ia eaac?noaoe?iia?io noaae?th iaa??ao, iane/othoueny i?e noae?e oaieii?ia?aeiino? oa, iaaiaee, a iiaeaeueoiio oaeaeei ciaioothoueny i?e noaiaiaa?e caeaaeiino? oaieii?ia?aeiino? a?ae oaiia?aoo?e. Iieacaii, ui /ei neeuei?oa eiao?oe??io oaieii?ia?aeiino? caeaaeeoue a?ae oaiia?aoo?e, oei ?ai?oa ianooia? eaac?noaoe?iia?ia noaae?y iaa??ao, oei iai?oaeaiiy iaioa, a i?noea, aea oaiaaioe?aeueia eiiiiiaioa ci?ith? ciae, cnoaa?oueny aeeae/a aei iiaa?oi?. Iieacaii, ui ia eaac?noaoe?iia?i?e noaae?? iaa??ao oaieiaee i?ioean iiaeia iienaoe ca aeiiiiiaith i?inoeo aiae?oe/ieo oi?ioe. 2. Aeine?aeaeai? oa?iii?oaei? iai?oaeaiiy o aeeneo i?e e?i?eiiio i?aeeii? oaiia?aoo?e iaaeieeoiueiai na?aaeiaeua. Aeyaeaii, ui on? eiiiiiaioe i?oaeiino? iaeneiaeuei? ia eaac?noaoe?iia?i?e noaae?? iaa??ao, aea naieie a?eueoeie c ieo aeyaeythoueny oaiaaioe?aeuei? iai?oaeaiiy ia iiaa?oi? aeeneo (aeey eoaiia?acieo aeene?a aiie i?eaeecii o /ioe?e ?ace a?eueoa i?ae aeey oiieeo). Iieacaii, ui i?e iiai?e ?ioi?iaoe?? i?i iaoai?/i? oa oaieio?ce/i? aeanoeaino? iaoa??ae?a oa?iino?ee?noue aeene?a c aeinoaoiueith oi/i?noth iiaeia ioe?ithaaoe ?ic?aooieiaei oeyoii aac i?iaaaeaiiy aei?iaoaaiue. 3. ?icaeyiooi ieoaiiy i?i no?ee?noue ai?cio?iiieo e?enoae?a oeee?iae?e/ii? oi?ie i?e ?aae?aoe?eiiio iaa??a? aieiai? iiaa?oi? ca caeiiii Noaoaia-Aieueoeiaia. Iieacaii, ui i?eaeeciee iaoiae ona?aaeiaiiy ooieoe?iiaeueieo iii?aaie aea? i?aaeeueio aaee/eio oa?iii?oaeieo iai?oaeaiue. Iieacaii, ui ?ioaineo?eaoe?y i?ioean?a oa?iiia?iaee aei?ii?ithaaiiyi iaiaaeaia e?eoe/ieie cia/aiiyie inueiaeo iai?oaeaiue i?eeiath/eo ??ai? ? nai? iaea?eueo? ii aaee/ei? cia/aiiy ia in? oa iiaa?oi? oeee?iae?a, o iiiaio cae?i/aiiy ?ia?oe?eiiai aoaio iaa??ao. 4. Oeyoii ??oaiiy a?ia?aie?/iiai ??aiyiiy oaieii?ia?aeiino? iaea?aeaii ?iciiae?e oaiia?aoo?e o aeiaaiio oeee?iae?? ia ?ia?oe?eiiio oa ?aaoey?iiio aoaiao iaa??ao. Aecia/aii /an iioe?aiiy ?aae?aeueiiai oaieiaiai iioieo. Iieacaii, ui oeae /an ianooia? i?ci?oa i?e ciaioaii? oaieiiai?io iiaa?oi? oeee?iae?a c iaaeieeoi?i na?aaeiaeuai, oa oaeaeeino? iioe?aiiy oaiea (ii ??aiyiith c oaeaee?noth iioe?aiiy i?oaeieo oaeeue). Iieacaii, ui i?e a?aeiia?aeieo oiiaao oaieiiai?io, /an iioe?aiiy ?aae?aeueiiai oaieiaiai iioieo o aaeeeiaaaa?eoieo c?aceao iiaeooue aooe ca?a?no?iaai? iaei?ia?oe?eiei aeao/eeii oaiia?aoo?. 5. ?ica’ycai? aeeiai?/i? caaea/? oa?iii?oaeiino? aeey oeee?iae?a o iaieiioe? i?e oiia?, ui oaiia?aoo?a iaaeieeoiueiai na?aaeiaeua ?aioiai i?aeaeuo?oueny aei aeayeiai cia/aiiy oa aeey oiiei? ieanoeiee, i?aeaeaoi? oaieiaiio oaea?o i?e e?ioeaa?e oaeaeeino? iioe?aiiy oaiea. Iieacaii, ui i?e cia/iino? aoaeoo (no?eaie aeeiai?/ieo iai?oaeaiue iaeneiaeueiee ia iiaa?oi? ? ia?aaeuo? nai? eaac?aeeiai?/ia cia/aiiy a aeaa ?ace) aeiaaio?eaae?noue ae?? iaaeoi iaea. Iieacaii, ui o?aooaaiiy e?ioeaai? oaeaeeino? ci?iaiiy oaiia?aoo?e a oaa?aeeo o?eao a?aecia/aii iayai?noth ia iaeiiai, a aeaio no?eae?a iai?oaeaiue. Ia?oee iaoiiaeaiee i?oaeiith oaeeath ?icoe?aiiy, a ae?oaee, cai?ci?eee ca /anii, iaoiiaeaiee oaieiaith oaeeath. Aeyaeaii, ui i?e e?ioeaa?e oaeaeeino? iioe?aiiy oaiea iaeneioi aeeiai?/ieo iai?oaeaiue cieaeo?oueny ia 50%. 6. ?ica’ycaia caaea/a i?i oa?iii?oaei? iai?oaeaiiy, aeieeath/? a aeaioa?ia?e ieanoeioe? i?e no?eaeiia?aci?e ci?i? oaiia?aoo?e ?? iiaa?oi?a. Iieacaii, ui iaea?eueo? iai?oaeaiiy eiioeaio?othoueny a cii? eiioaeoo ieanoeie c iie?eooyi i?aeoe/ii ieoo?ai (ca 10-12 n). Iieacaii, ui ?ic?aooieia? caeaaeiino? e?eoe/ieo iai?oaeaiue a?ae oiaueie ieanoeie oa iie?eooy aeia?a iiaiaeaeothoueny c aenia?eiaioii. 7. ?ica’ycaii ??aiyiiy oaieii?ia?aeiino? aeey oeee?iae?a o iaieiioe?, eiee ii an?o ?? iiaa?oiyo a?aeaoaa?oueny oaieiiai?i ca caeiiii Iuethoiia, a oaiia?aoo?a na?aaeiaeua ci?ith?oueny e?i?eii c /anii. Aeyaeaii, ui ??cieoey oaiia?aoo?e i?ae iiaa?oiath oa oeaio?ii oeee?iae?a iaeneiaeueia o iiiaio aeoiaeo ia eaac?noaoe?iia?io noaae?th iaa??ao. Iieacaii, ui /an aeoiaeo ia oeth noaae?th nei?i/o?oueny c ciaioaiiyi /enea A?i ? ia caeaaeeoue a?ae ?ici???a oeee?iae?a, yeui a?aeiioaiiy eiai aeiaaeeie aei ?aae?ono ia ia?aaeuo? iaeeieoeth. Cai?iiiiiaaii aoaeoeaiee niin?a (ii aiae?oe/iei caeaaeiinoyi ??cieoe? oaiia?aoo?e i?ae iiaa?oiath oa oeaio?ii oeee?iae?a o iaieiioe? a?ae /ano iaa??ao i?e ?ioaineaiiio oaieiiai?i?) aei??thaaiiy eiao?oe??ioa oaiia?aoo?ii?ia?aeiino? o iaoa??aeao c aeia?ith oaieii?ia?aei?noth iaoiaeii eaac?noaoe?iia?iiai ?aaeeio. NIENIE IOAE?EAOe?E AAOI?A CA OAIITH AeENA?OAOe?? 1. A?ei?a A.A., Nie?iia I.I., Oanaiei A.I., Noaoieeiaa I.A. Oaieiaia iiea oeeeeiae?a a iaiei/ea i?e eeiaeiie caaeneiinoe oaiia?aoo?u ie?oaeathuae n?aaeu io a?aiaie. || Ooieoeeiiaeueiua iaoa?eaeu. - 1994. - o.1, ?2. - n.85 - 89. 2. Oanaiei A.I., Caai?oeei TH.A., Oaaei?aiei I.A., Eiia?ue A.E., Noaoieeiaa I.A. I oa?iii?i/iinoe aeeneia ec e?enoaeee/aneiai naeaieaea oeeiea i?e eeiaeiii eciaiaiee oaiia?aoo?u ie?oaeathuae n?aaeu. || Ooieoeeiiaeueiua iaoa?eaeu. - 1994. - o.1, ?2. - n.90 - 94. 3. Oanaiei A.I., Noaoieeiaa I.A. Aeeiaie/aneea iai?yaeaiey a e?enoaeeao, au?aueaaaiuo ii iaoiaeo Noieaa?aa?a. || Oeceea e oeiey ia?aaioee iaoa?eaeia. - 1994. - ?4-5. - n.206-209. 4. Oanaiei A.I., Noaoieeiaa I.A. I oaieii?iaiaeiinoe oeeeeiae?a i?e aicaeaenoaee ?aceiai a?aaeeaioa iaonoaiiaeaoaeny oaiia?aoo?u. || Oeceea e oeiey ia?aaioee iaoa?eaeia. - 1994. - ?6. - n.32-37. 5. A?ei?a A.A., Oanaiei A.I., Noaoieeiaa I.A. Oa?iinoieeinoue oae oeeeeiae?e/aneie oi?iu i?e ?aaeeaoeeiiiii iaa?aaa. || Oeceea e oeiey ia?aaioee iaoa?eaeia. - 1996. - ?2. - n.37-41. 6. A?ei?a A.A., Oanaiei A.I., Noaoieeiaa I.A. Aeeiaie/aneea iai?yaeaiey, aicieeathuea i?e oa?iioaea?a ia iiaa?oiinoe i?yiioaieueiie ieanoeiee. || Oeceea e oeiey ia?aaioee iaoa?eaeia. - 1996. - ?5. - n.18-21. 7. A?ei?a A.A., Oanaiei A.I., Noaoieeiaa I.A. Ii?aaeaeaiea oa?iioi?oaeo iai?yaeaiee a oeeeeiae?a ia eaacenoaoeeiia?iie noaaeee iaa?aaa n o/?oii caaeneiinoe eiyooeoeeaioa oaieii?iaiaeiinoe io oaiia?aoo?u. || Oeceea e oeiey ia?aaioee iaoa?eaeia. - 1997. - ?2. - n.109-112. 8. A?ei?a A.A., Oanaiei A.I., Noaoieeiaa I.A. Noieeinoue aeaooneieiie ieanoeiu i?e oa?iioaea?a. || Oeceea e oeiey ia?aaioee iaoa?eaeia. - 1998. - ?1. - n.22-26. AIIOAOe?ss Noaoi?eiaa I.A. “Iiaeaethaaiiy i?ioean?a oaieii?ia?aeiino? i?e ?ic?aooieao oa?iino?eeino? oa aecia/aii? oaieio?ce/ieo oa?aeoa?enoee e?enoae?a neeaaeii? oi?ie” - ?oeiien. Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe ca niaoe?aeuei?noth 05.02.01 - iaoa??aeiciaanoai. - ?inoeooo iiiie?enoae?a IAI Oe?a?ie, i. Oa?e?a, 1999 ?. Ia iniia? ae??oaiiy ??aiyiue oaieii?ia?aeiino? (ia?aaie?/iiai oa a?ia?aie?/iiai oeio) oa oa?iii?oaeiino? (c o?aooaaiiyi aeeiai?/ieo aoaeo?a) i?e caaeaaaieo e?aeiaeo oiiaao (e?i?eiiio i?aeeii? oaiia?aoo?e na?aaeiaeua a oiiaao eiiaaeoeaiiai oaieiiai?io c iiaa?oiath ca caeiiii Iuethoiia, oa?iioaea??, aei?ii?ithaaii?) iaea?aeaii ?iciiae?e oaiia?aoo?e oa iai?oaeaiue o caaio?aeao (oa aeaioa?iaeo nenoaiao) oeee?iae?e/ii? oa i?yiieooii? oi?ie. Aeyaeaii, ui ia a?aei?io a?ae noaei? oaieii?ia?aeiino? noaiaiaaa caeaaei?noue oaiia?aoo?ii?ia?aeiino? a?ae oaiia?aoo?e ye?nii ci?ith? ?iciiae?e oaiia?aoo?e oa iai?oaeaiue. Iieacaii, ui i?e iiai?e ?ioi?iaoe?? i?i iaoai?/i? oa oaieio?ce/i? aeanoeaino? iaoa??ae?a oa?iino?ee?noue aeene?a aeinoaoiuei oi/ii iiaeia ioe?ithaaoe ?ic?aooieiaei oeyoii. Iaoiae ina?aaeiaiiy ooieoe?iiaeueieo iii?aaie aea? a??io aaee/eio iai?oaeaiue o e?enoaeao, i?aeaeaoeo ?aae?aoe?eiiio iaa??ao. Oa?iioaea? aeeeeea? o oaa?aeeo o?eao aeeiai?/i? iai?oaeaiiy ei?ioei/aniai? ae??. I?e e?ioeaa?e oaeaeeino? ?iciianthaeaeaiiy oaiea aoaeoe nooo?ai ciaioothoueny. Aeyaeaii, ui o aeaioa?iaeo nenoaiao, i?aeaeaoeo ??ce?e oaieia?e ae??, eiioeaio?aoi?ii iaeneiaeueieo iai?oaeaiue aeyaey?oueny a?aieoey ?icae?eo oa??a. Eeth/ia? neiaa: oaieii?ia?aei?noue, oaiia?aoo?ii?ia?aei?noue, oaieiiai?i, oa?iii?oaei?noue, oa?iino?ee?noue. AIIIOAOeEss Noaoieeiaa I.A. “Iiaeaee?iaaiea i?ioeannia oaieii?iaiaeiinoe i?e ?an/?oa oa?iinoieeinoe e ii?aaeaeaiee oaieioece/aneeo oa?aeoa?enoee e?enoaeeia neiaeiie oi?iu.” - ?oeiienue. Aeenna?oaoeey ia nieneaiea o/?iie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe ii niaoeeaeueiinoe 05.02.01. - iaoa?eaeiaaaeaiea, einoeooo iiiie?enoaeeia IAI Oe?aeiu, a. Oa?ueeia, 1999 a. Ia iniiaa iineaaeiaaoaeueiiai ?aoaiey o?aaiaiee oaieii?iaiaeiinoe (ia?aaiee/aneiai e aeia?aiee/aneiai oeia) e oa?iioi?oainoe (n o/?oii aeeiaie/aneeo yooaeoia) i?e caaeaiiuo e?aaauo oneiaeyo (eeiaeiii iiaeu?ia oaiia?aoo?u n?aaeu a oneiaeyo eiiaaeoeaiiai oaieiiaiaia n iiaa?oiinoueth ii caeiio Iuethoiia, oa?iioae?a, eceo/aiee), iieo/aii ?ani?aaeaeaiea oaiia?aoo?u e iai?yaeaiee a caaioiaeao (e aeaooneieiuo nenoaiao) oeeeeiae?e/aneie e i?yiioaieueiie oi?iu. Aeenna?oaoeeiiiay ?aaioa ninoieo ec aaaaeaiey, iyoe ?acaeaeia, auaiaeia, caeeth/aiey e nienea oeeoe?oaiie eeoa?aoo?u. A aaaaeaiee iainiiaaia aeooaeueiinoue oaiu aeenna?oaoeee, ii?aaeaeaiu oeaeue, iao/iay iiaecia e i?aoe/aneay oeaiiinoue ?aaiou, i?eaaaeaia eioi?iaoeey i ai?iaaoeee, no?oeoo?a, iau?ia ?aaiou e ee/iii aeeaaea aaoi?a, eceiaeaii e?aoeia niaea?aeaiea ?aaiou. Ia?aue ?acaeae niaea?aeeo iaci? iniiaiiieaaathueo oai?aoe/aneeo ?aaio ii oaiia?aoo?iui iieyi e oa?iioi?oaei iai?yaeaieyi a oeeeeiae?a, aeenea e ieanoeia, ?acoeueoaou eioi?uo eniieuecothony aaoi?ii a aeaeueiaeoai e iieo/eee ?acaeoea a aeenna?oaoeee. Ai aoi?ii ?acaeaea onoaiiaeaii, /oi a ioee/ea io iinoiyiiie oaieii?iaiaeiinoe noaiaiiay caaeneiinoue oaieii?iaiaeiinoe io oaiia?aoo?u a aeeeiiii oeeeeiae?e/aneii oaea, iaa?aaaaiii n iiaa?oiinoe ii eeiaeiiio caeiio ea/anoaaiii e eiee/anoaaiii eciaiyao oa?aeoa? i?ino?ainoaaiii-a?aiaiiiai ?ani?aaeaeaiey oaiia?aoo?u e oa?iioi?oaeo iai?yaeaiee. I?aaeeiaeaiu oaeiaiua aeey eiaeaia?iuo ?an/?oia oi?ioeu, iienuaathuea ?ani?aaeaeaiea oaiia?aoo?u e oa?iioi?oaeo iai?yaeaiee ia eaacenoaoeeiia?iie noaaeee iaa?aaa. Iieacaii, /oi i?e iieiie ieoi?iaoeee i iaoaie/aneeo e oaieioece/aneeo naienoaao iaoa?eaeia oa?iinoieeinoue aeeneia n aeinoaoi/iie noaiaiueth oi/iinoe iiaeii ioeaieaaoue ?an/?oiui ioo?i aac i?iaaaeaiey eniuoaiee. A o?aoueai ?acaeaea, ?anniio?ai aii?in i noieeinoe aiecio?iiiuo oae oeeeeiae?e/aneie oi?iu i?e ?aaeeaoeeiiiii iaa?aaa aieiaie iiaa?oiinoe ii caeiio Noaoaia-Aieueoeiaia. I?eaeeae?iiue iaoiae in?aaeiaiey ooieoeeiiaeueiuo iii?aaie aea?o i?aaeeueioth aaee/eio oa?iioi?oaeo iai?yaeaiee. Eioaineoeeaoeey i?ioeannia oa?iiia?aaioee eceo/aieai ia?aie/aia e?eoe/aneeie cia/aieyie inaauo iai?yaeaiee. Ii?aaeaeaii a?aiy ?ani?ino?aiaiey ?aaeeaeueiiai oaieiaiai iioiea a aeeeiiii oeeeeiae?a. Onoaiiaeaii, /oi aai aaee/eia aic?anoaao n oiaiueoaieai nei?inoe ?ani?ino?aiaiey oaiea e eioaineaiinoe oaieiiaiaia. A /aoa??oii ?acaeaea iieacaii, /oi oa?iioaea? aucuaaao a oa??aeuo oaeao aeeiaie/aneea iai?yaeaiey e?aoeia?aiaiiiai aeaenoaey. I?e eiia/iie nei?inoe ?ani?ino?aiaiey oaiea aeeiaie/aneea yoaeou nouanoaaiii oiaiueoathony. O/?o eiia/iie nei?inoe eciaiaiey oaiia?aoo?u a oa??aeuo oaeao ioee/aaony iaee/eai ia iaeiiai, a aeaoo nea/eia iai?yaeaiee. A ?acaeaea iyoii ?anniao?eaathony eiioaeoiua nenoaiu ieineie e oeeeeiae?e/aneie oi?iu. ?aoaaony caaea/a i oa?iioi?oaeo iai?yaeaieyo a aeaooneieiie ieanoeia, iiaeaa?aeaiiie aiacaiiiio eciaiaieth oaiia?aoo?u ia a? iiaa?oiinoyo. Onoaiiaeaii, /oi a ae?noeine?aie?iuo aeaooneieiuo nenoaiao eiioeaio?aoi?ii iaeneiaeueiuo iai?yaeaiee yaeyaony a?aieoea ?acaeaea nei?a. Iieo/aiu oi?ioeu i?ino?ainoaaiii-a?aiaiiiai ?ani?aaeaeaiey oaiia?aoo?u a ia?aie/aiiii oeeeeiae?a, ne?aie?iiii n iaiei/eie. Onoaiiaeaii, /oi ?aciinoue oaiia?aoo?u iaaeaeo iiaa?oiinoueth e oeaio?ii oeeeeiae?a iaeneiaeueia ia eaacenoaoeeiia?iie noaaeee iaa?aaa. Iieacaii, /oi a?aiy auoiaea ia yoo noaaeeth ia caaeneo io ?acia?ia oeeeeiae?a, anee ioiioaiea aai aeeeiu e ?aaeeono i?aauoaao aaeeieoeo. I?aaeeaaaaony yooaeoeaiue niinia ii aiaeeoe/aneei caaeneiinoyi ?aciinoe oaiia?aoo?u iaaeaeo iiaa?oiinoueth e oeaio?ii oeeeeiae?a a iaiei/ea io a?aiaie iaa?aaa i?e eioaineaiii oaieiiaiaia ecia?youe eiyooeoeeaio oaiia?aoo?ii?iaiaeiinoe iaoiaeii eaacenoaoeeiia?iiai ?aaeeia. Eeth/aaua neiaa: oaieii?iaiaeiinoue, oaiia?aoo?ii?iaiaeiinoue, oaieiiaiai, oa?iioi?oainoue, oa?iinoieeinoue. ABSTRACT M.V. Stashnikova “Simulation of heat conductivity processes in thermal stability calculations and determination of thermophysical characteristics of complicately shaped crystals”. - Manuscript. Master’s Thesis (Engineering), speciality 05.02.01 - Materials Science, Institute for Single Crystals, National Academy of Sciences of Ukraine, Kharkiv, 1999. Basing on solution of heat conductivity (of parabolic and hyperbolic type) and thermoelasticity equations (under account for dynamic effects) at specified edge conditions (linear temperature increase in a medium under convective heat exchange with a surface according to Newton law, thermal shock, radiation), the temperature and stress distribution has been determined for ingots and bilayer systems of culindrical and rectangular shape. It has been established that, unlike the case of constant heat conductivity, the power temperature dependence of heat conductivity results in qualitative changes of the temperature and stress distribution. The thermal stability of a disk can be estimated with a sufficient accuracy by way of calculation, providing the data on the material properties are full enough. The method of functional corrections averaging provides a correct stress value for crystals subjected to radiation heting. A thermal shock causes short-time dynamic stresses in solids. These effects are reduced substantially at finite heat transfer rave values. In bilayer systems subjected to severe thermal actions, it is just the layer interface that has been established to act as a concentrator of maximum stress. Keywords: heat conductivity, temperature conductivity, heat exchange, thermal elasticity, thermal stability.

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