IAOeIIIAEUeIA AEAAeAIIss IAOE OE?A?IE
?INOEOOO I?EEEAAeIEO I?IAEAI IAOAI?EE ? IAOAIAOEEE
?i. ss. N. I?AeNO?EAA*A
Ia i?aaao ?oeiieno
OAeE 539.3:620.198
AAA?ENUe
Ieaenaiae? Iao?iae/
Aecia/aiiy oa?iiiai?oaeaiiai noaio iie?eoue
i?e aenieioaiia?aoo?iiio iaieeaii?
Niaoe?aeuei?noue 01.02.04. – iaoai?ea aeaoi?i?aiiai
oaa?aeiai o?ea
Aaoi?aoa?ao
aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy
eaiaeeaeaoa o?ceei–iaoaiaoe/ieo iaoe
EUeA?A–1998
Aeena?oaoe??th ? ?oeiien.
?iaioa aeeiiaia a ?inoeooo? i?eeeaaeieo i?iaeai iaoai?ee ?
iaoaiaoeee ?i. ss.N.I?aeno?eaa/a
Iaoe?i-
iaeueii? aeaaeai?? iaoe Oe?a?ie.
Iaoeiaee ea??aiee: eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe,
i?ia?aeiee iaoeiaee ni?a?ia?oiee
OAA*OE Iaaei ?iiaiiae/
Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
i?ioani?, caa. a?aeae?eii ?IIII
?i. ss.N.I?aeno?eaa/a IAI Oe?a?ie
AA*EAAE* Ieaenaiae? ?iiaiiae/
aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
i?ioani?, aieiaiee iaoeiaee
ni?a?ia?oiee ?inoeoooo iaoai?ee
?i. N.I.Oeiioaiea IAI Oe?a?ie
AANEEAIEI Aiaoie?e Oeoiiiae/
I?ia?aeia onoaiiaa: Aea?aeaaiee oi?aa?neoao “Euea?anueea
iie?oaoi?ea”, eaoaae?a oai?aoe/ii? iaoai?ee,
i.Euea?a
Caoeno a?aeaoaeaoueny “28” a?oaeiy 1998 ?. i 15
aiae.
ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.195.01
a ?inoeooo? i?eeeaaeieo i?iaeai iaoai?ee ? iaoaiaoeee ?i.
ss.N.I?aeno?eaa/a IAI Oe?a?ie (i.Euea?a, aoe.Iaoeiaa, 3″a”).
C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe?
?inoeoooo i?eeeaaeieo i?iaeai iaoai?ee ? iaoaiaoeee
?i.ss.N.I?aeno?eaa/a IAI Oe?a?ie.
A?aeceae ia aaoi?aoa?ao i?ineii iaaeneeaoe ca aae?anith:
290601, INI, i.Euea?a, aoe.Iaoeiaa, 3″a”, ?IIII, a/aiiio
nae?aoa?th niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.195.01.
Aaoi?aoa?ao ?ic?neaii ” 25 ” eenoiiaaea 1998 ?.
A/aiee nae?aoa? niaoe?ae?ciaaii? ?aaee, OAA*OE
eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe Iaaei
?iiaiiae/
– 1 –
CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE
Aeooaeuei?noue oaie. Iaei??th c aaaeeeaeo i?iaeai iaoai?ee,
oaoi?ee, ?ioeo noi?aeieo iaoe ? caaacia/aiiy iaiao?aeii?
aeiaaia?/iino? ? ?iai/i? caeaoiino? aeaiaio?a eiino?oeoe?e ?
iaoei, ye? i?aoeththoue a ?aaeueieo oiiaao aenieoaoaoe?? (aa?aneai?
na?aaeiaeua, i?aeaeuai? ??ai? oaiia?aoo? ? iaoai?/ieo iaaaioaaeaiue).
Aeooaeueiei oaeiae ? ieoaiiy iaaeaiiy oaeeo ooieoe?iiaeueieo
aeanoeainoae ye ei?ic?eia no?ee?noue, ciinino?ee?noue,
aea?ino?ee?noue, i?oei?noue oa ?io? oe?iei aeinooiiei eiino?oeoe?eiei
iaoa??aeai.
Aoaeoeaiei niiniaii iie?auaiiy aenieoaoaoe?eieo aeanoeainoae aeaiaio?a
eiino?oeoe?e, ca?eueoaiiy ?o ?iai/iai ?ano?no ? canoinoaaiiy
aaaaoiooieoe?iiaeueieo iie?eoue. Iaeiei ?c iioe?aieo iaoiae?a iaianaiiy
oaeeo iie?eoue ? aenieioaiia?aoo?ia (cie?aia ieaciiaa) iaieeaiiy
iie?eoue c ?ioeo iaoa??ae?a, ui a a?eueoino? aeiaaee?a ? iaea?eueo
aeioe?eueiei, a ?ieiee – ?aeeii iiaeeeaei niiniaii iaianaiiy iie?eoue.
Oai?aoe/iiio oa aenia?eiaioaeueiiio aeine?aeaeaii? i?ioean?a, ye?
iathoue i?noea i?e aenieioaiia?aoo?iiio iaieeaii?, i?enay/ai? ?iaioe
A.A.Eoae?iiaa, A.I.?aaiiaa, TH.N.Ai?eniaa, A.Oano?, I.Ii??aae?,
A.A.Aa?a?iea, ?.I.?aaiiaa, ?.E.Aaeea?a, I.A.Eoi??yiiaa, A.A.Ieioiaa,
A.A.Eyoaiea, A.?.Iioio?nueeiai, E.?.Oooeinueeiai, A.?.Eiieeiaa,
A.O.Oaoeinueeiai, ss.N.I?aeno?eaa/a, I.?.Oaa/oea, Ae.A.?aauoea oa ?ioeo
a?o/eciyieo ? caei?aeiiieo aaoi??a.
Na?aae aaaaoueio i?e/ei, ye? iiaeooue nooo?a aieeaaoe ia
cieaeaiiy i?oeiino? iie?eoue, ? oi?ioaaiiy a iaieethaaeueiiio oa??
cia/ieo caeeoeiaeo iai?oaeaiue. Aenia?eiaioaeueia aecia/aiiy caeeoeiaeo
iai?oaeaiue a nenoai? o?ei-iie?eooy iia’ycaia ?c nooo?aeie o?oaeiiuaie
/a?ac iaeo oiaueio iie?eooy, neeaaei?noue aei??thaaiue. Oiio aaaeeeaa
i?noea a ?ica’ycaii? oe??? i?iaeaie, e??i aenia?eiaioaeueieo,
a?aeaiaeeoueny iaoiaeai oai?aoe/iiai aeine?aeaeaiiy, ?ic?aooieo ?
i?iaiicoaaiiy ??aiy caeeoeiaeo iai?oaeaiue a nenoaiao o?ei-iie?eooy oa
ea?oaaiiy oeei ??aiai.
Iaeiae, ?ia?o c oai?aoe/iiai aeine?aeaeaiiy iai?oaeaiue ?
aeaoi?iaoe?e, ui oi?iothoueny a nenoai? o?ei-iie?eooy a caeaaeiino? a?ae
?aaeei?a iaianaiiy, iioae?eiaaii iaei. Oi?ioaaiiy iie?eooy
aenieioaiia?aoo?iei iaieeaiiyi a?aeaoaa?oueny i?e neeaaeieo,
??ciiiai?oieo, aca?iica’ycaieo ? iaaeinoaoiuei aea/aieo yaeuao, ye?
c?icoi?ei, ia iiaeia a?aooaaoe a ?aieao aoaeue-yei? iaoaiaoe/ii?
iiaeae?. Oiio aeooaeueiith ? iaiao?aei?noue iiaeaeueoiai ocaaaeueiaiiy
ia iniia? aea/aiiy aenia?eiaioaeueieo aeine?aeaeaiue ?nioth/eo
iaoaiaoe/ieo iiaeaeae oeyoii iiaeeaeaiiy aeine?aeaeaiue oa?iiiaoai?/ieo
?aaeei?a oaoiieia?/iiai eaioethaa aeaioiaeaiiy ae?ia?a c
iie?eooyie: i?aeaioiaea iniiae (iaa??aaiiy, ioieiaeaeaiiy
oiui) – aaciina?aaeiuei iaianaiiy iie?eooy – ianooiia oa?iiia?iaea;
aeaoaeueiee aiae?c iai?oaeaii-aeaoi?iiaaiiai noaio iniiae oa iie?eooy
ia eiaeiiio aoai? iaieeaiiy c a?aooaaiiyi ?aae?aoe?eii-eiiaaeoeaiiai
oaieiiai?io c iaoith aeai?o ?aoe?iiaeueiiai ni?aa?aeiioaiiy ia?aiao??a
nenoaie oa oaiia?aoo?ieo ?aaeei?a iaieeaiiy, caaacia/aiiy iaiao?aeiiai
??aiy caeeoeiaeo iai?oaeaiue o nenoai? oa yeino? iie?eoue.
– 2 –
Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa aeeiiaia
a ?inoeooo? i?eeeaaeieo i?iaeai iaoai?ee ? iaoaiaoeee
?i.ss.N.I?aeno?eaa/a IAI Oe?a?ie a ?aieao iaoeiai-aeine?aeieo oai:
“?ic?iaea aiae?oe/ieo iaoiae?a ?ic?aooieo oa
i?iaiicoaaiiy aeiaaia?/iino? iie?eoue a o?i?/ii aeoeaieo na?aaeiaeuao
caeaaeii a?ae ?aaeei?a ?o iaianaiiy oa aenieoaoaoe??” (?
aea?aeaaii? ?a?no?aoe?? 01.88.0022727); “Iiaoaeiaa iaoaiaoe/ieo iiaeaeae
oa aeine?aeaeaiiy iae?i?eieo aoaeo?a iaoaiiaeeooc?? ? oa?iiiaoai?ee
o?e c iie?eooyie, i?ioean?a ei?ic?eiiai ?oeioaaiiy eaoiaeieo ?
aiiaeieo iie?eoue” (? aea?aeaaii? ?a?no?aoe?? 0193U009585); oaie
AeEIOI Oe?a?ie 04.05.00/002-95 “?ic?iaeoe iaoiaeeee i?enei?aiiai
aei?iaoaaiiy oa i?iaiicoaaiiy aeiaaia?/iino? eaeioa?aiaeo oa
iaoae?/ieo iie?eoue a ii?nuee?e aiae?, a aoiinoa?ieo aa?aneaieo
na?aaeiaeuao”.
Iaoith ?iaioe ? iiaoaeiaa ocaaaeueiaii? iiaeae? i?ioean?a i?e
aenieioaiia?aoo?iiio iaianaii? caoenieo iie?eoue ( c a?aooaaiiyi aia?a??
aei?ii?ithaaiiy, oaieiaeo aoaeo?a iioieo ieaciioa??iiai aaco,
?aae?aoe?eii-eiiaaeoeaiiai oaieiiai?io nenoaie o?ei – iie?eooy c
iaaeieeoi?i na?aaeiaeuai, ??cieo oei?a iaoai?/ieo oiia cae??ieaiiy
iniiae) aeey aeai?o ?aoe?iiaeueieo ?aaeei?a iaianaiiy, oai?aoe/iiai
i?iaiicoaaiiy caeeoeiaiai iai?oaeaiiai noaio, aeey iiaoaeiae e?eoa???a
i?oeiino? oa aeiaaia?/iino? ae?ia?a c iie?eooyie.
Iaoeiaa iiaecia ?iaioe iieyaa? a ianooiiiio:
– iiaoaeiaaii ocaaaeueiaio iaoaiaoe/io iiaeaeue iieno oa?iiiaoai?/ieo
i?ioean?a i?e aenieioaiia?aoo?iiio iaieeaii? caoenieo iie?eoue;
– io?eiaii ocaaaeueiai? iae?i?ei? a?aie/i? oiiae oaieiiai?io o?e c
na?aaeiaeuai /a?ac iie?eooy c a?aooaaiiyi aei?ii?ithaaiiy;
– ?ic?iaeaii /enaeueii-aiae?oe/io iaoiaeeeo aeine?aeaeaiiy ?
?ic?aooieo oaiia?aoo?ieo iie?a oa caeeoeiaiai iai?oaeaiiai noaio
ieineeo ? oeee?iae?e/ieo o?e i?e iaieeaii? iaeii- oa aeainoi?iiiueiai
iie?eooy;
– ae?iaeaii ?aeiiaiaeaoe?? c aeai?o oa?i?/ieo oiia iaieeaiiy,
ni?aa?aeiioaiue aaiiao?e/ieo, oaieio?ce/ieo oa o?ceei-iaoai?/ieo
ia?aiao??a nenoaie o?ei-iie?eooy c iaoith ea?oaaiiy caeeoeiaeie
iai?oaeaiiyie oa ?ioeie aenieoaoaoe?eieie aeanoeainoyie iie?eoue, ye?
nooo?ai caeaaeaoue a?ae ??aiy caeeoeiaeo iai?oaeaiue.
A??ia?aei?noue iniiaieo iieiaeaiue ? io?eiaieo ?acoeueoao?a
caaacia/o?oueny o?ce/iith iaa?oioiaai?noth iinoaiiaie iae?i?eieo
caaea/ oaieii?ia?aeiino? oa oa?iii?oaeiino? c o?aooaaiiyi oaieiiai?io
aei?ii?ithaaiiyi, no?ia?noth iaoaiaoe/ieo iaoiae?a ?o ?ica’ycaiiy,
ocaiaeaeai?noth ie?aieo /anoeiaeo aeiaaee?a c a?aeiieie a
e?oa?aoo?? oai?aoe/ieie ?acoeueoaoaie, ia?aa??eith iiaoaeiaaiiai
eiiieaeno i?eeeaaeieo i?ia?ai ia oanoiaeo caaea/ao, io?eiaiiyi
o?ce/ii ianoia?a/eeaeo ?acoeueoao?a.
– 3 –
I?aeoe/ia cia/ei?noue. ?acoeueoaoe aeine?aeaeaiue iathoue ye
oai?aoe/ia, oae ? i?aeoe/ia cia/aiiy. Aiie iiaeooue aooe
aeei?enoai? a iaoeiiaoaeoaaii?, i?eeaaeiaoaeoaaii?, o?i?/i?e
i?iieneiaino? oa ?i., aea canoiniaothoueny aenieioaiia?aoo?i? iie?eooy
aeey i?aeaeuaiiy aenieoaoaoe?eieo oa?aeoa?enoee aeaoaeae, ?ic?iaeythoue
? aaeineiiaeththoue oaoiieia?? ?o iaianaiiy. ?ic?iaeaia ocaaaeueiaia
iaoaiaoe/ia iiaeaeue i?noeoue ieceo ia?aiao??a nenoaie ? iiaoaeiaaia ia
?? aac? /enaeueii-aiae?oe/ia iaoiaeeea aeicaiey? a eiiieaen?
a?aoiaoaaoe aieea aecia/aeueieo oaieiaeo oa iaoai?/ieo oaeoi??a
ia oa?aeoa?ieo oaoiieia?/ieo aoaiao aeaioiaeaiiy ae?iao c iie?eooy ?
ia i?aenoaa? ?acoeueoao?a ?ic?aooie?a iioei?coaaoe oaiia?aoo?i? ?aaeeie
? caeeoeiaee iai?oaeaiee noai nenoaie o?ei-iie?eooy, aeei?enoiaoaaoe
oae? ?acoeueoaoe i?e oai?aoe/iiio i?iaiicoaaii? ?o ?iai/iai ?ano?no.
Iniaenoee aianie caeiaoaa/a. ?acoeueoaoe aeine?aeaeaiue, iaaaaeai? a
aeena?oaoe??, io?eiai? aaoi?ii naiino?eii. Iaoeiaee ea??aiee a?aa
o/anoue o iiaoaeia? ocaaaeueiaii? iiaeae?, oi?ioethaaii? caaea/ oa
iaaiai?aii? iaea?aeaieo ?acoeueoao?a. A ni?eueieo ioae?eaoe?yo
ni?aaaoi?ai iaeaaeeoue: ?iaioe [1, 2] – aeo?aei? iiaeaeuei?
ni?aa?aeiioaiiy; [3, 4] – ?aeay ocaaaeueiaiiy aeo?aeii? iaoaiaoe/ii?
iiaeae? ia aanue oaoiieia?/iee eaioetha aeaioiaeaiiy ae?iao c
iie?eooyi; ?iaioe [5, 11] – ni?euei? ioae?eaoe??, a yeeo eiaeai ?c
ni?aanoi??a i?aaenoaaeya na?e iai?yiie aeine?aeaeaiue; a ?aoo? ni?eueieo
ioae?eaoe?e ni?aaaoi?e a?aee o/anoue a iaaiai?aii? io?eiaieo
?acoeueoao?a oa iiaeeeainoae ?o i?aeoe/iiai canoinoaaiiy.
Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeiiia?aeaeenue ia ia?aae?
“Aeina?ae canoinoaaiiy eiiiiceoieo iaoa??ae?a a
n?euenueeiainiiaea?nueeiio iaoeiiaoaeoaaii?” (*a?i?a?a, 1985 ?.), o?ao?e
i?aeaaeocaa?e iaoeiai-i?aeoe/i?e eiioa?aioe?? “Caoeno noaeai a?ae
ei?ic?? oa ia?inoaiiy” (Eae?i?ia?aae, 1986 ?.), VII-e E?aniiaea?nuee?e
e?aeia?e eiioa?aioe?? “No/ani? i?iaeaie i?e?iaeiciaanoaa. I?eeeaaei?
ieoaiiy oaieiianiiai?io” (E?aniiaea?, 1986 ?.), III-e Ananithci?e
eiioa?aioe?? “Iaoai?ea iaiaeii??aeieo no?oeoo?” (Euea?a, 1991 ?.),
i?aeia?iaei?e eiioa?aioe?? “Oai??y iaaeeaeaiue oa caaea/?
ia/enethaaeueii? iaoaiaoeee” (Aei?i?iiao?ianuee, 1993 ?.) ,
i?aeia?iaei?e eiioa?aioe??-aenoaaoe? “Ei?ic?y-94” (Euea?a,
1994 ?.), ae?oaiio i?aeia?iaeiiio neiiic?oi? oe?a?inueeeo
?iaeaia??a-iaoai?e?a (Euea?a, 1995 ?.), i?aeia?iaeiiio oaoiieia?/iiio
oi?oi? ESSENTIA-96 (I?aaa, 1996 ?.), XXXI-e iieuenuee?e eiioa?aioe?? c
iaoai?ee aeaoi?i?aiiai oaa?aeiai o?ea Sol.Mec. (I??e?,
Ieueooei, 1996 ?.), 5-e ?a?iiaenuee?e eiioa?aioe?? c iiaeo i?ioean?a,
iaoa??ae?a oa ?o canoinoaaiiy EUROMAT 97 (Iaano??oo, I?aea?eaiaee, 1997
?.).
Iiai?noth aeena?oaoe?eia ?iaioa aeiiia?aeaeanue ? iaaiai?thaaeanue ia
nai?ia?? a?aeae?eo iaoai?ee aeaoi?i?aiiai oaa?aeiai o?ea oeueiai ae
?inoeoooo (Euea?a, 1998 ?.) oa niaoe?ae?ciaaiiio eaae?o?eaoe?eiiio
nai?ia?? “Iaoai?ea aeaoi?i?aiiai oaa?aeiai o?ea” ?inoeoooo i?eeeaaeieo
i?iaeai iaoai?ee ? iaoaiaoeee ?i.ss.N.I?aeno?eaa/a IAI Oe?a?ie
(Euea?a, 1998 ?.).
Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?eii? ?iaioe iioae?eiaaii
13 iaoeiaeo i?aoeue.
– 4 –
No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny c anooio,
o?ueio ?icae?e?a iniiaiiai iaoa??aeo, aeniiae?a oa nieneo aeei?enoaieo
aeaea?ae ?c 80 iaeiaioaaiue. Caaaeueiee ianya ?iaioe 165 noi??iie, a
oiio /ene? 49 ?enoie?a.
INIIAIEE CIINO ?IAIOE
O anooi? iaa?oioiao?oueny aeooaeuei?noue aeaii? i?iaeaie,
noi?ioeueiaaia iaoa ?iaioe, iaaaaeaii iniiai? ?acoeueoaoe, io?eiai? a
?iaio?, oa iniiai? iieiaeaiiy , ui aeiinyoueny ia caoeno.
O ia?oiio ?icae?e? ia iniia? iioae?eiaaieo c aeine?aeaeoaaii?
i?iaeaie ?ia?o i?iaiae?ciaaii iniaeeaino? oa caeiiii??iino?
oi?ioaaiiy iie?eoue aenieioaiia?aoo?iei iaieeaiiyi, no/aniee noai
i?iaeaie. C a?aooaaiiyi oeueiai, a cai?iiiiiaai?e ocaaaeueiai?e iiaeae?
aanue oaoiieia?/iee i?ioean iaianaiiy iie?eooy ?icae?eaii ca /anii ia
o?e ?ioa?aaee: iiia?aaei? iaa??aaiiy iiaa?oi? iniiae, iaianaiiy
iie?eooy, ianooiia oa?iiia?iaea. Ca aecia/aeuei? aea?aii oae? oaeoi?e:
oaieiaa aei?ii?ithaaiiy c??co niiea ieaciio?iio c o?aooaaiiyi /anoeiaiai
iiaeeiaiiy aia?a?? ?iai/ei na?aaeiaeuai ? iiaa?oiath ae?iao;
aei?ii?ithaaiiy (iiaeeiaiiy) ia’?iii ieaciioa??iiai aaco; aeania
aei?ii?ithaaiiy iiaa?oi? ae?iao; aei?ii?ithaaiiy (iiaeeiaiiy) ioi/oth/ei
na?aaeiaeuai; eiiaaeoeaia iaa??aaiiy iiaa?oi? nenoaie
i?aeeeaaeea-iie?eooy iioieii ieaciioa??iiai aaco; ianooiia
?aae?aoe?eii-eiiaaeoeaia ioieiaeaeaiiy iniiae c iie?eooyi (i?ney
aeeeth/aiiy ieaciio?iio).
O a?aeiieo c e?oa?aoo?ewmetafile8? ???????????????
???????????yyy????.????1????????????? @???&?
?MathType??????:????u?th?????? Cai?iiiiiaaia a ia?oiio
?icae?e? aeena?oaoe?? iae?i?eia iaoaiaoe/ia iiaeaeue aeicaiey? a?eueo
iiaii iienaoe i?ioeane i?e aenieioaiia?aoo?iiio iaianaii? iie?eoue,
?icoe?eoe aeine?aeaeaiiy oa?iiiaoai?/ieo ?aaeei?a oaoiieia?/iiai
eaioethaa aeaioiaeaiiy ae?iao c iie?eooyi, ?ic?aoiaoaaoe oa
aiae?coaaoe caeeoeiaee iai?oaeaii-aeaoi?iiaaiee noai iniiae oa iie?eooy
ia eiaeiiio c aeae?eaieo aoai?a iaieeaiiy c a?aooaaiiyi
?aae?aoe?eii-eiiaaeoeaiiai oaieiiai?io. Oea aeicaieeei aeae?aoe
?aoe?iiaeuei? ni?aa?aeiioaiiy ia?aiao??a nenoaie oa oaiia?aoo?ieo
?aaeei?a iaieeaiiy aeey caaacia/aiiy iaiao?aeiiai ??aiy caeeoeiaeo
iai?oaeaiue oa yeino? iie?eoue.
I?e ?icaeoo? i?ioeano iaieeaiiy iie?eooy a /an? ia o?e ?ioa?aaee,
ii/aoie a?aee?eo wmetafile8? ???????????????
???????????yyy????.????1????????????? ????&?
?MathType?? ????` ????u@th??????
______________________________________________________________
wmetafile8? ???????????????
???????????yyy????.????1????????????? @???&?
?MathType??????:????u?th??????
– 5 –
Caaa?oaiith i?ioeano iaieeaiiy a?aeiia?aea? iiiaio
/anowmetafile8? ??E????????????
???????????yyy????.????1????????????? @???&?
?MathType??P????? ????u@th?????? I?e iiaoaeia? iaoaiaoe/ii?
iiaeae? oaieiaiai ?aaeeio iaieeaiiy aaaaea?ii, ui iaoa??ae iie?eooy –
i?oio?iiiee, oaieio?ce/i? oa o?ceei-iaoai?/i? aeanoeaino? eiai a?aei?ii?
a?ae oaeeo aeanoeainoae iaoa??aeo iniiae. I?e oeueiio iaieethaaia
nooe?eueia iie?eooy oiaueiith wmetafile8? ??AE????????????
???????????yyy????.????1????????????? `???&?
?MathType??P?????????u@th?????? I?e ye?ni?e iiia?aaei?e ia?iaoe?
iiaa?oi? iniiae iiaeia aaaaeaoe, ui ia a?aieoe? eiioaeoo i?aeeeaaeee c
iie?eooyi ia? ia? i?noea ?aeaaeueiee oaieiaee eiioaeo
wmetafile8? ?? ???????????
???????????yyy????.????1????????????? ???&?
?MathType??P?????????u@th??????aea wmetafile8?
??a???????????? ???????????yyy????.????1??????
??????? `???&??MathType??P?????????u@th??????
wmetafile8? ??s???????????
???????????yyy????.????1???????????????.???&?
?MathType????
???u?????????”????-?????,!???,¦??? ????u@th??????wm
etafile8? ??s???????????
???????????yyy????.????1??????????????a-???&?
?MathType????
???u?????????”????-?????,???,[??? ????u@th??????wm
etafile8? ??u???????????
???????????yyy????.????1??????????????a”???&?
?MathType????
???u?????????”????-?????,???,[??? ????u@th??????
Ooo aaaaeaii oae? iicia/aiiy:
wmetafile8? ??TH????????????
???????????yyy????.????1????????????? ???&?
?MathType??P?????????u@th??????wmetafile8? ??y????????????
???????????yyy????.????1????????????? `???&?
?MathType??P?????????u@th??????wmetafile8? ??›????????????
???????????yyy????.????1????????????? ????&?
?MathType??P?????????u@th??????wmetafile8? ??&???????????
???????????yyy????.????1????????????? ???&?
?MathType??P?????????u@th??????
– 6 –
wmetafile8? ??y????????????
???????????yyy????.????1????????????? A???&?
?MathType??P?????????u@th??????wmetafile8? ??›????????????
???????????yyy????.????1????????????? ???&?
?MathType??P?????????u@th??????wmetafile8? ??c????????????
???????????yyy????.????1????????????? A???&?
?MathType??P?????????u@th??????wmetafile8? ?? ???????????
???????????yyy????.????1????????????? A???&?
?MathType??P?????????u@th??????wmetafile8? ??y????????????
???????????yyy????.????1????????????? `???&?
?MathType??P?????????u@th??????wmetafile8? ??c????????????
???????????yyy????.????1????????????? ???&?
?MathType??P????????u@th?????? Ii/aoeiaee ?iciiae?e oaiia?aoo?e
wmetafile8? ??c????????????
???????????yyy????.????1????????????? ???&?
?MathType??P?????????u@th?????? I?e iiaoaeia? ocaaaeueiaii?
a?aie/ii? oiiae oaieiiai?io o?e /a?ac oiie? iie?eooy aeey ?ioa?aae?a
/ano iaieeaiiy wmetafile8? ??*????????????
???????????yyy????.????1????????????? A???&?
?MathType??P????? ????u@th?????? wmetafile8? ??n???????????
???????????yyy????.????1?????????????@ ???&?
?MathType??
???u?????????"????-?????¬???¬???¬O???¬%???
????u@th??????i?e caaeiaieaii? a?aie/ieo oiia (1) oa (3).
Ooo wmetafile8? ??¬???????????
???????????yyy????.????1??????????????a???&?
?MathType??p???? ????u@th??????wmetafile8? ??t???????????
???????????yyy????.????1????????????? `???&?
?MathType??A?
???u?????????"????-?????,a???,???? J????u@th??????wme
tafile8? ??®????????????
???????????yyy????.????1?????????????a@???&?
?MathType??@????`J????u@th??????wmetafile8? ?????????????
???????????yyy????.????1??????????????@???&?
?MathType??p???? ????u@th??????wmetafile8? ??p????????????
???????????yyy????.????1?????????????@`???&?
?MathType?? ?????????u@th?????? Iia?aoi?iei iaoiaeii
?ica'ycie ??aiyiiy oaieii?ia?aeiino? io?eiaii a ianooiiiio aeaeyae?:
wmetafile8? ??N???????????
???????????yyy????.????1????????????? A)???&?
?MathType??p ???u?????????"????-?????L“???L0
???u??????????"????-????ue???????????-????O-?I???Oe
AeI???a-AeI???O•&?5&???O•&Aey&???a•&Ae5&???A
????u@th?????? wmetafile8? ??O???????????
???????????yyy????.????1?????????????a ???&?
?MathType???
???u??????????"????-?????ue???????????-????orO???o/
ae????rae???oUOz???oUae3/4????Uaez???
a ????u@th??????
- 7 -
aea wmetafile8? ??$???????????
???????????yyy????.????1??????????????a???&?
?MathType??p???? ????u@th?????? wmetafile8? ??®????????????
???????????yyy????.????1?????????????a@???&?
?MathType??@????`????u@th?????? wmetafile8? ??e???????????
???????????yyy????.????1?????????????@ ???&?
?MathType??P
???u?????????"????-?????,???,o???,???,???,R
???,*??? ????u@th?????? wmetafile8? ??e???????????
???????????yyy????.????1?????????????@@ ???&?
?MathType??P
???u?????????"????-?????,>???,???,???,U???,a
ea wmetafile8? ?????????????
???????????yyy????.????1?????????????`a???&?
?MathType??p ???u?????????”????-?????,???
E????.????u@th??????
I?aenoaaeyth/e a ae?ac (3) cai?noue wmetafile8? ??c????????????
???????????yyy????.????1????????????? `???&?
?MathType??P?????????u@th?????? Ca aeiiiiiaith iaeeie/ieo
ooieoe?e Oaa?naeaea nenoaio ocaaaeueiaieo iae?i?eieo a?aie/ieo oiia
aeey o?ueio aeae?eaieo ?ioa?aae?a /ano i?aaenoaaeii iaeiei
ni?aa?aeiioaiiyi ianooiiei /eiii:
wmetafile8? ??t???????????
???????????yyy????.????1?????????????` ,???&?
?MathType??`?
???u??????????”????-?????ue???????????-????6Cae???6?
”?ae???>?C”?ae???6P????6P”?4???>?P”??
???6p???6-”????>?p”????6Ae???6A”?©?
??>?A”?e??? ????u@th??????aea wmetafile8?
??—??????????? ???????????yyy????.????1??????
????????a1???&??MathType????
???u?????????”????-?????,wmetafile8? ??™???????????
???????????yyy????.????1????????????? A5???&?
?MathType??
???u?????????”????-??????????I????e????n????
????u@th?????? wmetafile8? ??!???????????
???????????yyy????.????1????????????? ????&?
?MathType??? ???u?????????”????-?????¬±???¬????¬,
???¨??? ????u@th??????wmetafile8? ??t???????????
???????????yyy????.????1????????????? a4???&?
?MathType??
???u?????????”????-??????????I????e????n????
????u@th??????
– 8 –
O ae?ac? (7) aaaaeaii ianooii? iicia/aiiy:
wmetafile8? ?????????????
???????????yyy????.????1????????????? `???&?
?MathType??????????u@th??????
wmetafile8? ??n???????????
???????????yyy????.????1?????????????@` ???&?
?MathType??`???? ????u@th??????wmetafile8? ??«???????????
???????????yyy????.????1?????????????@` ???&?
?MathType??`????????u@th??????wmetafile8? ??!???????????
???????????yyy????.????1?????????????a@???&?
?MathType??p????um????u@th??????wmetafile8? ??t???????????
???????????yyy????.????1??????????????A???&?
?MathType??? ???u?????????”????-?????*???
’????????u@th?????? A oeueiio ae ?icae?e? iaaaaeaii nenoaio
ocaaaeueiaieo a?aie/ieo oiia iaoai?/ii? aca?iiae?? iniiae /a?ac oiiea
iie?eooy oa io?eiaii ni?aa?aeiioaiiy aeey ?ic?aooieo ona?aaeiaieo
oa?aeoa?enoee oaiia?aoo?e a iie?eoo?.
O ae?oaiio ?icae?e? aeine?aeaeaii oa?iii?oaeiee noai nenoaie o?ei –
iie?eooy c ieineeie iiaa?oiyie i?e aenieioaiia?aoo?iiio iaieeaii?.
?icaeyaea?oueny i?ioean aenieioaiia?aoo?iiai aeainoi?iiiueiai iaieeaiiy
iie?eoue ??cii? oiaueie (wmetafile8? ??AE????????????
???????????yyy????.????1????????????? `???&?
?MathType??P?????????u@th???????iciiae?e oaiia?aoo?e ii oiauei?
iniiae iieno?oueny ?ica’yceii ??aiyiiy oaieii?ia?aeiino?
wmetafile8? ??????????????
???????????yyy????.????1?????????????aA ???&?
?MathType??a?
???u?????????”????-?????¬i???¬%???¬???¬† ???
????u@th??????
– 9 –
yeee caaeia?eueiy? ii/aoeia?e oiia?
wmetafile8? ??w???????????
???????????yyy????.????1????????????? ????&?
?MathType??P?????????u@th??????oa ocaaaeueiai?e a?aie/i?e oiia?
(8).
Ooo wmetafile8? ??I???????????
???????????yyy????.????1??????????????a???&?
?MathType??? ???u?????????”????-?????????
®????????u@th?????? wmetafile8? ?????????????
???????????yyy????.????1??????????????????&?
?MathType??p???? ????u@th??????A ?icaeyaeoaaiiio aeiaaeeo
a?aie/i? oiiae (7) iaoeiooue ianooiiee aeaeyae:
wmetafile8? ?????????????
???????????yyy????.????1???????????????/???&?
?MathType??p?
???u??????????”????-?????ue???????????-????¶g????¶$
c????3/4?gc????¶t????¶tc?X???3/4?tc????¶
??!???¶=c?!???3/4??c?!???¶O!?u!???¶O!c??!???3/
4?O!c?u!??? ????u@th?????? wmetafile8? ??/???????????
???????????yyy????.????1?????????????? 0???&?
?MathType??p?
???u??????????”????-?????ue???????????-????¶??@???¶c?
@???3/4??c?@???¶¬?L???¶¬c? Ioaea, iath/e
noi?ioeueiaaio iae?i?eio e?aeiao caaea/o oaieii?ia?aeiino? (9)-(11)
iiaeia i?iaanoe ?ic?aooiie ?iciiae?eo oaiia?aoo?e ii oiauei? iniiae
(aeeth/ath/e oaiia?aoo?o a cii? eiioaeoo oa?o c iie?eooyi) aeey
aeia?eueiiai iiiaioo /ano: a?ae ii/aoeo iaa??aaiiy iiaa?oi?
iniiae iioieii ieaciioa??iiai aaco aei iiiaioo caaa?oaiiy iaianaiiy
iie?eooy ? iiaiiai inoeaaiiy aioiaiai ae?iao. Oaea iinoaiiaea caaea/?
aea? ciiao a caeaaeiino? a?ae eiie?aoieo aeiia, ui noaaeyoueny aei
oi?ioaaiiy iaoai?/ii? nenoaie oa? – aeainoi?iii? iie?eooy, oeyoii
i?aeai?o a?aeiia?aeieo aaiiao?e/ieo , oaieio?ce/ieo oa iecee ?ioeo
aecia/aeueieo oaeoi??a ua aei i?aeoe/ii? ?aae?caoe?? io?eiaieo
?acoeueoao?a iioei?coaaoe oaiia?aoo?i? ?aaeeie iaianaiiy.
?iciiae?e oaiia?aoo?e ii oiauei? oa?o iaoiiaeth? a iueiio
oaieia? iai?oaeaiiy, ye? aecia/athoueny ca a?aeiieie ni?aa?aeiioaiiyie
wmetafile8? ??I???????????
???????????yyy????.????1??????????????????&?
?MathType??? ???u?????????”????-?????L???
/????????u@th??????wmetafile8? ??V???????????
???????????yyy????.????1?????????????`????&?
?MathType??p?????????u@th??????aea wmetafile8?
??c???????????? ???????????yyy????.????1??????
??????? ???&??MathType??P?????????u@th?????? Iaa?aeii?
eiinoaioe wmetafile8? ??p????????????
???????????yyy????.????1?????????????@`???&?
?MathType?? ?????????u@th?????? wmetafile8? ??i???????????
???????????yyy????.????1?????????????` ???&?
?MathType??p????????u@th??????
– 10 –
Ca?aeii c aea?aiith iiaeaeeth iieno oaieiaeo i?ioean?a i?e
aenieioaiia?aoo?iiio iaieeaii? iai?oaeaiiy a iie?eoo? aeieeathoue i?ney
iiiaioo e?enoae?caoe?? iie?eoue a /an wmetafile8? ??oe????????????
???????????yyy????.????1?????????????` ???&?
?MathType??p????? ????u@th?????? A ?ioa?aae? /ano wmetafile8?
??oe???????????? ???????????yyy????.????1??????
???????` ???&??MathType??p????? ????u@th??????
wmetafile8? ??V???????????
???????????yyy????.????1?????????????`????&?
?MathType??p???????u@th?????? wmetafile8? ??‡???????????
???????????yyy????.????1?????????????`????&?
?MathType??p???????u@th?????? Coneeey wmetafile8?
??c???????????? ???????????yyy????.????1??????
??????? ????&??MathType??P????????u@th??????
wmetafile8? ??A???????????
???????????yyy????.????1????????????? a???&?
?MathType??? ???u?????????"????-?????,O???,Ue
???u??????????"????-????ue???????????-????A?¦$???A@
–?$??????–?$???A±¦Q???A±–?•?????±–?Q??? ?
??u@th?????? wmetafile8? ??A???????????
???????????yyy????.????1????????????? @???&?
?MathType??? ???u?????????"????-?????,???,„
???u??????????"????-????ue???????????-????A+
¦I???Ae–?I?????+
–?I???A¦!???A–?a?????–?!??? ???u@th??????
aea wmetafile8? ?????????????
???????????yyy????.????1??????????????????&?
?MathType??p???? .????u@th??????wmetafile8? ??/???????????
???????????yyy????.????1?????????????@`???&?
?MathType??P????8????u@th??????wmetafile8? ??k???????????
???????????yyy????.????1??????????????????&?
?MathType??p???? ????u@th?????? Cia/aiiy wmetafile8?
??k??????????? ???????????yyy????.????1??????
????????????&??MathType??p???? ????u@th??????
wmetafile8? ??q???????????
???????????yyy????.????1?????????????AA???&?
?MathType??`?????????u@th?????? wmetafile8? ??I?e oeueiio
wmetafile8? ??O???????????
???????????yyy????.????1?????????????? ???&?
?MathType??p???? ????u@th??????
- 11 -
wmetafile8? ??¤???????????
???????????yyy????.????1????????????? ???&?
?MathType??
???u?????????"????-??????O????Ue????a????y
???????u@th??????wmetafile8? ??????????????
???????????yyy????.????1?????????????` $???&?
?MathType??a?
???u?????????"????-?????,V???,O???,0???,????
????u@th??????
aea wmetafile8? ??k???????????
???????????yyy????.????1?????????????a?"???&?
?MathType???
???u?????????"????-?????lo???lA???l???lae???
a.????u@th?????? wmetafile8? ??????????????
???????????yyy????.????1?????????????a`"???&?
?MathType???
???u?????????"????-?????lo???lA???l???lae???
a.????u@th?????? Io?eiai? a oeueiio ?icae?e? ni?aa?aeiioaiiy iiaeaii
a iaea?eueo caaaeueiiio aeaeyae?. Iieeaaeath/e a ieo iaaiei /eiii
cia/aiiy aaiiao?e/ieo, oaieio?ce/ieo oa o?ceei-iaoai?/ieo oa?aeoa?enoee
nenoaie, iiaeia io?eiaoe ni?aa?aeiioaiiy aeey aeine?aeaeaiiy ?
?ic?aooieo caeeoeiaiai oa?iiiai?oaeaiiai noaio i?aeoe/ii aaaeeeaeo
/anoeiaeo aeiaaee?a.
A ?iaio? aeey ?ica'ycaiiy ianoaoe?iia?ii? iaeiii??ii? caaea/?
oa?iii?oaeaino? c iae?i?eieie a?aie/ieie oiiaaie (11) ?ic?iaeaia
/enaeueii-aiae?oe/ia iaoiaeeea ?ic?aooieo oa?iii?oaeiiai noaio nenoaie
oa? - aeainoi?iii? iie?eooy, ui aaco?oueny ia iniia? ?ic?iaeaii?
iaoaiaoe/ii? iiaeae? oa c aeei?enoaiiyi iayaii? noaie
e?ioeaai-??cieoeaaiai iaoiaeo.
A aeena?oaoe?? ca aeaieie c e?oa?aoo?e i?iaiae?ciaaii niiniae aeai?o
ia?aiao??a iiae?aieo caaea/.
C iaoith aeine?aeaeaiiy aieeao ci?ie ?aaeei?a iaianaiiy iie?eoue ia
caeeoeiaee oa?iiiai?oaeaiee noai nenoaie iniiaa-iie?eooy ?icaeyiooi
i?ioean iaieeaiiy ia ieineo iniiao ?c noae? 20 aeainoi?iiiueiai
caoeniiai i?o?iiiaiai iie?eooy iaeiaeiai? oiaueie wmetafile8?
????????????? ???????????yyy????.????1??????
??????? @???&??MathType??P?????????u@th?????? Aiae?c
io?eiaieo /eneiaeo ?acoeueoao?a, cie?aia, iieacaa, ui i?e iaaieo
ni?aa?aeiioaiiyo oiauei iniiae oa iie?eoue a inoaii?o iiaeooue
aeieeaoe ye noeneath/?, oae ? ?icoyaoth/? caeeoeia? coneeey, I?e
iaianaii? iie?eooy ia iniiao 0,01i coneeey a iie?eoo? ? noeneath/eie, ui
? aaaeaiei oaeoii i?e aeaioiaeaii? ae?ia?a c ieaciiiaieeaieie
iie?eooyie, a i?e iaianaii? iie?eooy o??? ae oiaueie ia iniiao
0,05i - iaaacia/ieie (a caeaaeiino? a?ae eiie?aoieo oiia aenieoaoaoe??)
?icoyaoth/eie. I?e/iio oe? ?icoyaoth/? caeeoeia? coneeey aeinyaathoue
naiai iaeneioio ua ia aoai? iaiiaiiai inoeaaiiy i?aeeeaaeee c iie?eooyi,
ui iiaea i?ecaanoe aei eiai ?ico??neoaaiiy.
Aeey aecia/aiiy aieeao ci?ie oiaueie naiiai iie?eooy ia
caeeoeia? coneeey aoei i?iaaaeaii aenia?eiaio, a yeiio oiaueia iie?eooy
ca?eueooaaeanue a 10 oa 20 ?ac ii??aiyii c ii/aoeiaith. O aeiaaeeo
ca?eueoaiiy oiaueie iie?eooy ia iniia? oiaueiith 0,01i niinoa??aaeinue
cia/ia c?inoaiiy noeneath/eo coneeue a iie?eoo?. I?e ca?eueoaii? oiaueie
iie?eooy, ui iaiineeinue ia iniiao oiaueiith 0,05i - c?inoaiiy
?icoyaoth/eo coneeue, i?e/iio c?inoaiiy ? aeinyaiaiiy aeno?aiaeueiiai
cia/aiiy oaeeie coneeeyie a?aeaoaaeenue aeineoue oaeaeei (10-15n), ui
iiaea ni?e/eieoe ?oeioaaiiy iie?eooy ia ?aii?e noaae?? ioieiaeaeaiiy.
Ne?ae oieeaoe oaeiae ? cia/iiai c?inoaiiy noeneath/eo caeeoeiaeo
coneeue, ine?eueee oea iiaea i?ecaanoe aei a?aeoa?oaaiiy iie?eooy.
- 12 -
Ioaea, i?aeae?ath/e iaaiei /eiii ni?aa?aeiioaiiy oa?aeoa?ieo ?ici???a
iie?eooy, iniiae oa /an ?? iiia?aaeiueiai i?ae?a??ao, iiaeia aeinyaoe
a?aeiia?aeiiai ??aiy (ca ciaeii oa aaniethoiith aaee/eiith) caeeoeiaeo
coneeue a iie?eoo?. Oaiia?aoo?i? ?aaeeie iaianaiiy iie?eooy o an?o
aeiaaeeao i?aeae?aeenue oaeei /eiii, uia a cii? eiioaeoo aeinyaaeanue
oaiia?aoo?a, ia ieae/a ca oaiia?aoo?o ieaaeaiiy (e?enoae?caoe??)
iaoa??aeo iie?eooy, ui caaacia/o? iaae?eia c/aieaiiy iie?eooy c
iniiaith.
O o?aoueiio ?icae?e? aeine?aeaeaii caeeoeiaee oaiiiai?oaeaiee noai
oeee?iae?e/ieo o?e i?e aenieioaiia?aoo?iiio iaianaii? ia ?o ciai?oith
iiaa?oith caoenieo iie?eoue. O ia?oiio ia?aa?ao? noi?ioeueiaaii
iae?i?eio e?aeiao caaea/o oaieii?ia?aeiino? aeey aeiaaiai ii?iaeienoiai
e?oaiaiai oeee?iae?a c iaeiinoi?iii?i ciai?oi?i iie?eooyi, Oaieio?ce/i?,
o?ceei-iaoai?/i? oa ?aae?aoe?ei? oa?aeoa?enoeee iaoa??ae?a iniiae ?
iie?eooy a?aei?ii? i?ae niaith. sse ? a iiia?aaeiueiio ?icae?e?,
i?eionea?oueny, ui i?ae iniiaith ? iie?eooyi oaieiaee ? iaoai?/iee
eiioaeo ? ?aeaaeueiei. A ia?oiio ?ioa?aae? /ano wmetafile8?
??e???????????? ???????????yyy????.????1??????
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oaiia?aoo?e acaeiaae ?aae?ona oeee?iae?a wmetafile8?
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wmetafile8? ??o???????????
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l5???l ???l???lA???—???u@th??????yeee
caaeia?eueiy? ii/aoeiao oiiao
wmetafile8? ??i???????????
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?MathType??P?????????u@th??????oa ocaaaeueiai? a?aie/i? oiiae
oeio (8) i?e wmetafile8? ??O????????????
???????????yyy????.????1????????????? `???&?
?MathType??P?????????u@th?????? wmetafile8? ??c???????????
???????????yyy????.????1?????????????a????&?
?MathType???? ???u?????????"????-?????
- 13 -
Ooo aaaaeaii oae? iicia/aiiy:
wmetafile8? ??P???????????
???????????yyy????.????1?????????????`a???&?
?MathType???
???u?????????"????-?????i????i®???`????u@th??????wm
etafile8? ??4???????????
???????????yyy????.????1????????????? a???&?
?MathType??P?????????u@th??????Aeey ia?oiai ?ioa?aaeo /ano a
aeiaaiio e?oaiaiio ii?iaeienoiio oeee?iae?? i?e ieineiio inaneiao?e/iiio
oaiia?aoo?iiio iie? wmetafile8? ?????????????
???????????yyy????.????1????????????? ????&?
?MathType??P?????????u@th?????? wmetafile8? ??+???????????
???????????yyy????.????1?????????????`a???&?
?MathType??p ???u?????????"????-?????I???E ????
???/????????u@th?????? wmetafile8? ??C???????????
???????????yyy????.????1?????????????``#???&?
?MathType??p ???u?????????"????-?????TH???U ???
???s????????u@th??????Ooo wmetafile8?
??!??????????? ???????????yyy????.????1??????
??????? ????&?
?MathType??P?????????u@th??????wmetafile8? ??h???????????
???????????yyy????.????1????????????? ????&?
?MathType??@
???u?????????"????-?????,®???,I???©l???u@th??????wm
etafile8? ??????????????
???????????yyy????.????1?????????????? ???&?
?MathType??p???? .????u@th??????wmetafile8? ?????????????
???????????yyy????.????1????????????? A???&?
?MathType??P?????????u@th?????? Cia/aiiy eiinoaio wmetafile8?
??a???????????? ???????????yyy????.????1??????
??????? ????&??MathType??P?????????u@th??????
wmetafile8? ??-???????????
???????????yyy????.????1??????????????`???&?
?MathType??p???? ????u@th?????? sseui oi?oeaa? iiaa?oi?
oeee?iae?a ? a?eueieie a?ae ciai?oi?o iaaaioaaeaiue, eiiiiiaioa
aaeoi?a ia?ai?uaiue wmetafile8? ??c????????????
???????????yyy????.????1????????????? ???&?
?MathType??P?????????u@th?????? wmetafile8? ??
??????????? ???????????yyy????.????1?????????????
????&??MathType??P?????????u@th??????? ia caeaaeeoue a?ae
?aae?ona wmetafile8? ??c????????????
???????????yyy????.????1??????????????`???&?
?MathType??@?????????u@th?????? Oiae? ?c caeiio Aoea aeey
eiiiiiaioe oaici?a iai?oaeaiue wmetafile8? ??TH????????????
???????????yyy????.????1??????????????A???&?
?MathType??p???? ????u@th??????
- 14 -
wmetafile8? ?????????????
???????????yyy????.????1????????????? ???&?
?MathType???? ???u?????????"????-?????1/2???
±????????u@th??????a cia/aiiy eiinoaioe wmetafile8?
??c???????????? ???????????yyy????.????1??????
??????? a???&??MathType??P?????????u@th??????
wmetafile8? ?? Ioaea, iath/e cia/aiiy an?o eiinoaio, io?eia?ii
ae?ace aeey aecia/aiiy a?aei?iieo a?ae ioey eiiiiiaio oaici?a
iai?oaeaiue wmetafile8? ??Ae???????????
???????????yyy????.????1?????????????? ???&?
?MathType??p???? ????u@th??????aecia/aiiy iai?oaeaiue,
aeaoi?iaoe?e oa ia?ai?uaiue io?eia?ii c (21)-(24), iieeaaeath/e a
ieo wmetafile8? ?? ???????????
???????????yyy????.????1????????????? a???&?
?MathType??P?????????u@th?????? Aiaeia?/ia neooaoe?y ia? i?noea ?
a ?ioa?aae? /ano wmetafile8? ??!???????????
???????????yyy????.????1?????????????` ???&?
?MathType??p????? ????u@th?????? A o?aoueiio ?ioa?aae? /ano
aiane?aeie e?enoae?caoe?? ia iiaa?oi? iniiae iie?eooy ? a neeo inueiai?
neiao??? a iueiio aeieeathoue eeoa ii/aoeia? coneeey wmetafile8?
??c???????????? ???????????yyy????.????1??????
??????? ????&??MathType??P????????u@th??????
wmetafile8? ??
??????????? ???????????yyy????.????1?????????????
?a???&??MathType??@
???u?????????"????-??????O????o????n????O????
???u@th??????
wmetafile8? ??
??????????? ???????????yyy????.????1?????????????
?????&??MathType??@ ???u?????????"????-??????
????+????)???????????u@th??????aea wmetafile8?
??TH???????????? ???????????yyy????.????1??????
??????? A???&?
?MathType??P?????????u@th??????wmetafile8? ??????????????
???????????yyy????.????1??????????????????&?
?MathType??p???? .????u@th??????wmetafile8? ?????????????
???????????yyy????.????1??????????????a???&?
?MathType??p?????????u@th?????? Iaa?aeii? eiinoaioe, ui i?noyoueny
a (26), o ae?acao aeey aecia/aiiy eiiiiiaio oaici?a iai?oaeaiue (21) ?
(24) ciaeaeaii c ianooiieo a?aie/ieo oiia:
wmetafile8? ??o???????????
???????????yyy????.????1????????????? A ???&?
?MathType??? ???u?????????"????-?????,D???,”
??? ????u@th?????? Oaeei /eiii, io?eiaii oi?ioee aeey aecia/aiiy
caeeoeiaiai oa?iiiai?oaeaiiai noaio aenieioaiia?aoo?iiai iie?eooy o
aeiaaeeo a?eueieo oa cauaieaieo oi?oeaaeo iiaa?oiiue oeee?iae?a.
- 15 -
Aeey oai?aoe/ii? ioe?iee ni?aa?aeiioaiiy ia?aiao??a nenoaie oa ?aaeeio
iaieeaiiy ia caeeoeia? coneeey a iie?eoo? aoei cae?eniaii ieceo
/eneiaeo aenia?eiaio?a aeey iaai?o ni?aa?aeiioaiue aaiiao?e/ieo
?ici???a iniiae oa iie?eooy, o?eaaeinoae iiia?aaeiueiai iaa??aaiiy
iiaa?oi? iniiae iioieii ieaciioa??iiai aaco, ii/aoeiaeo oaiia?aoo?
iniiae, ni?aa?aeiioaiue iiaeoe?a i?oaeiino? oa eiao?oe??io?a e?i?eiiai
oaiia?aoo?iiai ?icoe?aiiy iaoa??ae?a iniiae oa iie?eooy i?e
a?eueieo oa cauaieaieo a?ae inueiaiai ia?ai?uaiiy oi?oeaaeo iiaa?oiyo.
sse iieacaee aeine?aeaeaiiy, a caeaaeiino? a?ae eiie?aoieo oa?i?/ieo
oiia iaieeaiiy ? iaaieo ni?aa?aeiioaiue aecia/aeueieo ia?aiao??a a
iie?eoo? aeieeathoue ?icoyaoth/? ? noeneath/? caeeoeia? coneeey, a ?o
e?eoe/i? cia/aiiy aeinyaathoueny ia ii/aoeia?e aai e?ioeaa?e noaae??
ioieiaeaeaiiy aioiaiai ae?iao c iie?eooyi, ui iiaea aooe i?e/eiith
?oeioaaiiy iie?eoue (ye ?ico??neoaaiiy, oae ? a?aeoa?oaaiiy).
Aiae?c io?eiaieo ?acoeueoao?a aeicaiey? ua ia noaae?? i?iaeooaaiiy
?aaeei?a iaieeaiiy iie?eoue i?ae?a?aoe ?aoe?iiaeuei? ?aaeeie iaianaiiy,
oai?aoe/ii i?iaiicoaaoe ?o i?oei?noue oa aeiaaia?/i?noue.
O aeniiaeao ei?ioei noi?ioeueiaaii iniiai? ?acoeueoaoe ?iaioe.
INIIAI? ?ACOEUeOAOE ?IAIOE OA EI?IOE? AENIIAEE
1. A ?iaio? iiaoaeiaaii ocaaaeueiaio iaoaiaoe/io iiaeaeue
oa?iiiaoai?/ieo i?ioean?a i?e aenieioaiia?aoo?iiio iaieeaii? iie?eoue c
o?aooaaiiyi aia?a?? aei?ii?ithaaiiy, oaieiaiai aieeao iioieo
ieaciioa??iiai aaco, ?aae?aoe?eii-eiiaaeoeaiiai oaieiiai?io nenoaie
iniiaa - iie?eooy c iaaeieeoi?i na?aaeiaeuai, niinia?a cae??ieaiiy
c?acea aeey aeai?o ?aoe?iiaeueieo ?aaeei?a iaianaiiy iie?eoue.
2. Iia?aoi?iei iaoiaeii io?eiaii ocaaaeueiai? iae?i?ei? a?aie/i?
oiiae ?aae?aoe?eii-eiiaaeoeaiiai oaieiiai?io o?e c iie?eooyie oa
iaaaaeaii nenoaio ocaaaeueiaieo a?aie/ieo oiia oa?iiiaoai?/ii?
aca?iiae?? i?aeeeaaeee /a?ac oiie? iie?eooy ia oa?aeoa?ieo
aeae?eaieo ?ioa?aaeao ca /anii.
3. Ia iniia? iiaoaeiaaieo aeo?aeieo ni?aa?aeiioaiue noi?ioeueiaaii
a?aeiia?aei? iae?i?ei? e?aeia? caaea/? oa?iii?oaeiino?, ?ic?iaeaii
/enaeueii-aiae?oe/io iaoiaeeeo ?ic?aooieo oaiia?aoo?ieo ?aaeei?a ?
caeeoeiaiai oa?iiiai?oaeaiiai noaio nenoaie i?aeeeaaeea-iie?eooy aeey
ieineeo oa oeee?iae?e/ieo c?ace?a i?e iaeii- oa aeainoi?iiiueiio
iaieeaii? ia ?o iiaa?oi? caoenieo iie?eoue.
4. I?iaiae?ciaaii aieea eiaeiiai c aeae?eaieo aecia/aeueieo
oaeoi??a (iiia?aaeiueiai i?ae?a??ao iniiae, iaa??aaiiy iniiae iioieii
ieaciioa??iiai aaco, ci?ie oiaueie iie?eooy oa iniiae, ni?aa?aeiioaiiy
eiao?oe??io?a oaiia?aoo?iiai ?icoe?aiiy, iaoai?/ieo oa?aeoa?enoee
iaoa??ae?a i?aeeeaaeee ? iie?eooy, aieeao ?aae?aoe?eii? neeaaeiai?
oaieiaiai iioieo) ia caeeoeiaee oa?iiiai?oaeaiee noai iaoai?/ii?
nenoaie o?ei-iie?eooy.
- 16 -
Aiae?c io?eiaieo ?acoeueoao?a ?ic?aooie?a iieacaa, ui a caeaaeiino?
a?ae ni?aa?aeiioaiiy aaiiao?e/ieo ?ici???a iniiae oa iie?eooy a
inoaiiueiio ia iaaieo aoaiao ioieiaeaeaiiy nenoaie iiaeooue aeieeaoe ye
noeneath/?, oae ? ?icoyaoth/? caeeoeia? coneeey, aeinyaaoe iaeneioio ua
ia ii/aoeia?e noaae?? ioieiaeaeaiiy ? ni?e/eiyoe ?oeioaaiiy iie?eooy.
Ia i?aenoaa? aiae?co caeeoeiaiai oaiia?aoo?iiai noaio ii?iaeienoiai
oeee?iae?a c iaeiinoi?iaa?i ciai?oi?i iie?eooyi aeyaeaii, ui cauaieaiiy
a?ae inueiaiai ia?ai?uaiiy oeee?iae?a i?ecaiaeeoue aei aeieeiaiiy
a iie?eoo? (i?ney oieiaeaeaiiy) aeayeeo e?eoe/ieo ?icoyaoth/eo
caeeoeiaeo coneeue, ye? iiaeooue iaoiiaeoe ?ico??neoaaiiy iie?eooy.
Iaaacia/iei iiaea aeyaeoenue c?inoaiiy aei iaaieo aeno?aiaeueieo
(iaeneiaeueieo) ?icoyaoth/eo cia/aiue caeeoeiaeo coneeue ia ii/aoeiaiio
aoai? ioieiaeaeaiiy iie?eooy. Iiaeaeue aeicaiey? c iaoith ea?oaaiiy
aaee/eiith caeeoeiaeo coneeue aeae?aoe ?aoe?iiaeuei? ?aaeeie
iaianaiiy iie?eoue.
wmetafile8? ??T?????????????
???????????yyy????.????1?????????????
`@???&??yyyy?????Ayyy·yyy????????&?
?MathType??`????&??yyyy??????????wmetafile8? ??T?????????????
???????????yyy????.????1?????????????
`@???&??yyyy?????Ayyy·yyy????????&?
?MathType??`????&??yyyy??????????
?IAIOE, A ssEEO IIOAEIEIAAII INIIAII IIEIAEAIIss AeENA?OAOe??
1. Aaa?enue A.I., Eaauoe Ae.A., Oaa/oe I.?.
Oaiia?aoo?iua ?aaeeiu a nenoaia iiaeeiaeea-iie?uoea i?e
aunieioaiia?aoo?iii iaiueaiee // Eiaeaia?ii-oece/aneee aeo?iae. - 1988.
- ?6. - N.1033. ?oe. aeai. a AEIEOE 25.01.1988, ?aa. ?664-A88.
2. Aaa?enue A.I., Eaauoe Ae.A., Oaa/oe I.?.
Ii?aaeaeaiea inoaoi/iuo iai?yaeaiee a nenoaia neie-iie?uoea
i?e aeaonoi?iiiai aunieioaiia?aoo?iii iaiueaiee // Iao. iaoiaeu e
oec.-iao. iiey. - 1989. - Aui. 29. - N.8-12.
3. Oaa/oe I.?., Aaa?enue A.I. Aeeyiea eo/enoiai
iaa?aaa ia oaiia?aoo?iua ?aaeeiu e inoaoi/iua iai?yaeaiey
i?e aunieioaiia?aoo?iii iaiueaiee // Iao. iaoiaeu e oec.-iao. iiey.
- Aui. 30. - N.69-73.
4. Aaa?enue A.I., Oaa/oe I.?. Iaoaiaoe/aneia
iiaeaee?iaaiea i?ioeannia i?e aunieioaiia?aoo?iii iaiueaiee iie?uoee
// Iao. iaoiaeu e oec.-iao. iiey. - 1991. - Aui. 33. - N. 13-18.
5. Oaa/oe I.?., Nai/eia A.E., Aaa?enue A.I. Iaoiaeu
?an/aoa ?aoeeiiaeueiuo ?aaeeiia iaianaiey ieaciaiiuo e
aeeoooceiiiuo iie?uoee // Iiuo i?eiaiaiey eiiiiceoiuo iaoa?eaeia a
naeueneioicyenoaaiiii iaoeiino?iaiee: Oacenu aeieeaaeia niaauaiey / a.
*a?ieaia, ethiue 1985 a./ - *a?ieaia, Aineiinaeueoicoaoieea ONN?,
1985. - N.136.
6. Aaa?enue A.I. Oaieiaua ?aaeeiu e inoaoi/iua
iai?yaeaiey i?e aeaonoi?iiiai ieaciaiiii iaiueaiee iie?uoee n o/aoii
aeeyiey oaiia?aoo?u ieaciaiiie no?oe // Caueoa noaeia io ei??icee
e ia?anoaiey: Oacenu aeieeaaeia 3-e iaaeio?aneaaie iao/ii-oaoie/aneie
eiioa?aioeee / a.Eaeeieia?aae, naioya?ue 1985/ - Eaeeieia?aae, OeIEE
ON III "?eoi", 1985, - N. 115-116.
- 17 -
7. Aaa?enue A.I. Oaieiiaiai i?e aunieioaiia?aoo?iii iaiueaiee
iie?uoee. // Nia?aiaiiua aii?inu anoanoaiciaiey. I?eeeaaeiua aii?inu
oaieiianniiaiaia: Oacenu aeieeaaeia 7-e E?aniiaea?neie e?aaaie
eiioa?aioeee / a. E?aniiaea?, naioya?ue 1986a./ - E?aniiaea?,
E?aniiaea?neee iieeoaoie/aneee einoeooo, 1986. - N.40-43.
8. Aaa?enue A.I., Eaauoe Ae.A. Oa?iiiai?yaeaiiia ninoiyiea
neiy n aeaonoi?iiiei ieaciaiiui iie?uoeai // Iaoaieea iaiaeii?iaeiuo
no?oeoo?: Oacenu aeieeaaeia 3-e ananithciie eiioa?aioeee. / a. Eueaia,
ethiue 1991 a./ - Eueaia, Ei-o i?eee. i?iaeai iaoaieee e iaoaiaoeee AI
ONN?, 1991. - N.63.
9. Oaa/oe I.?., Aaa?enue I.I. *enaeueii-aiae?oe/ia
aeine?aeaeaiiy oa?iii?oaeiiai noaio o?e i?e aenieioaiia?aoo?iiio
iaieeaii? c a?aooaaiiyi oaieiiai?io aei?ii?iaiiyi // Oai??y
iaaeeaeaiiy ? caaea/? ia/enethaaeueii? iaoaiaoeee: Oace
aeiiia?aeae i?aeia?iaeii? eiioa?aioe?? / i.Aei?i?iiao?ianuee, o?aaaiue,
1993 ?./ - Aei?i?iiao?ianuee, Aei?i?iiao?ianueeee aea?aeaaiee
oi?aa?neoao, 1993. - N. 213.
10. Oaa/oe I.?., Aaa?enue I.I. Iaoaiaoe/ia
iiaeaethaaiiy oa /enaeueii-aiae?oe/ia aeine?aeaeaiiy
oa?iiiai?oaeaiiai noaio oeee?iae?e/ieo o?e c iie?eooyie i?e
aenieioaiia?aoo?iiio iaieeaii? c a?aooaaiiyi oaieiiai?io
aei?ii?iaiiyi // I?iaeaie ei?ic?? oa i?ioeei?ic?eiiai caoenoo
eiino?oeoe?eieo iaoa??ae?a. Ei?ic?y-94: Iaoa??aee i?aeia?iaeii?
eiioa?aioe??-aenoaaee / i.Euea?a, aeiaoaiue 1994 ?./ - Euea?a,
O?ceei-iaoi?/iee ?inoeooo IAI Oe?a?ie, 1994. - N. 240.
11. Oaa/oe I.?., Aaa?enue I.I., Oaa/oe A.A.
Iaoaiaoe/ia iiaeaethaaiiy oa ?ic?aooiie ?aoe?iiaeueieo ?aaeei?a
iaianaiiy, i?iaiicoaaiiy i?oeiino? oa aeiaaia?/iino? iie?eoue a
aa?aneaieo na?aaeiaeuao // 2-e i?aeia?iaeiee neiiic?oi oe?a?inueeeo
?iaeaia??a-iaoai?e?a IN?IE-2: Oace aeiiia?aeae / i.Euea?a, ea?oaiue
1995/ - Euea?a, Aea?aeaaiee oi?aa?neoao "Euea?anueea iie?oaoi?ea",
1985. - N. 123.
12. Gavrys' Olexander, Shevchuk Pavlo. Calculation and
Study of the Residual Stress State of Bodies with High Temperature
Sprayed Coatings // XXXI Polish Solid Mechanics Conference Sol'Mec:
Book of Abstracts - Mierki n. Olsztynek, 1996. - P.103-104.
13. Shevchuk P., Gavrys' O. Mathematical Modelling and
Methods of Calculation Elements Surface Strengthening by Plasma
Sprayings // 5th European Conference on Advanced Materials, Processes
and Applications EUROMAT-97: Proceedings of the Conference. -
Maastricht, 1997. - Vol. 3. - P.253-256.
- 18 -
AIIOAOe?ss. Aaa?enue I.I. Aecia/aiiy oa?iiiai?oaeaiiai noaio iie?eoue
i?e aenieioaiia?aoo?iiio iaieeaii?. - ?oeiien.
Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.02.04 - iaoai?ea
aeaoi?i?aiiai oaa?aeiai o?ea.- ?inoeooo i?eeeaaeieo i?iaeai
iaoai?ee ? iaoaiaoeee ?i.ss.N.I?aeno?eaa/a IAI Oe?a?ie,
Euea?a, 1998.
A ?iaio? iiaoaeiaaii iaoaiaoe/io iiaeaeue oa?iiiaoai?/ieo i?ioean?a i?e
aenieioaiia?aoo?iiio iaianaii? iie?eoue c o?aooaaiiyi aia?a??
aei?ii?ithaaiiy, oaieiaiai iioieo ieaciioa??iiai aaco,
?aae?aoe?eii-eiiaaeoeaiiai oaieiiai?io nenoaie iniiaa - iie?eooy c
?iai/ei na?aaeiaeuai, ??ciiiai?oieo niinia?a cae??ieaiiy c?acea.
Io?eiaii ocaaaeueiai? iae?i?ei? a?aie/i? oiiae
?aae?aoe?eii-eiiaaeoeaiiai oaieiiai?io o?e c iie?eooyi oa nenoaio
ocaaaeueiaieo a?aie/ieo oiia oa?iiiaoai?/ii? aca?iiae?? iniiae /a?ac
oiie? iie?eooy. ?ic?iaeaii /enaeueii-aiae?oe/io iaoiaeeeo ?ica'ycoaaiiy
a?aeiia?aeieo iae?i?eieo e?aeiaeo caaea/ oa?iii?oaeiino?. Aeyaeaii ?yae
oa?aeoa?ieo iniaeeainoae oi?ioaaiiy oa iiaaae?iee caeeoeiaeo iai?oaeaiue
o iie?eooyo. Noi?ioeueiaaii a?aeiia?aei? ?aeiiaiaeaoe?? aeey ea?oaaiiy
oaeeie caeeoeiaeie iai?oaeaiiyie c iaoith ?aoe?iiae?caoe??
oaiia?aoo?ieo ?aaeei?a iaianaiiy iie?eoue.
Eeth/ia? neiaa: iaoaiaoe/ia iiaeaeue, aenieioaiia?aoo?ia iaieeaiiy,
?aae?aoe?eii-eiiaaeoeaiee oaieiiai?i, caoeni? iie?eooy, oaiia?aoo?ia
iiea, caeeoeia? iai?oaeaiiy.
AIIIOAOeEss. Aaa?enue A.I. Ii?aaeaeaiea oa?iiiai?yaeaiiiai ninoiyiey
iie?uoee i?e aunieioaiia?aoo?iii iaiueaiee.- ?oeiienue.
Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oeceei-iaoaiaoe-
/aneeo iaoe ii niaoeeaeueiinoe 01.02.04 - iaoaieea
aeaoi?ie?oaiiai oaa?aeiai oaea.- Einoeooo i?eeeaaeiuo i?iaeai
iaoaieee e iaoaiaoeee ei.ss.N.Iiaeno?eaa/a IAI Oe?aeiu, Eueaia,
1998.
A ?aaioa iino?iaii iaoaiaoe/aneoth iiaeaeue oa?iiiaoaie/aneeo i?ioeannia
i?e aunieioaiia?aoo?iii iaianaiee iie?uoee n o/aoii yia?aee eceo/aiey,
oaieiaiai iioiea ieaciiia?acothuaai aaca, ?aaeeaoeeiiii-eiiaaeoeaiiai
oaieiiaiaia nenoaiu iniiaa - iie?uoea n ?aai/ae n?aaeie, ?acee/iuo
niiniaia cae?aieaiey ia?acoea. Iieo/aii iaiauaiiua iaeeiaeiua a?aie/iua
oneiaey ?aaeeaoeeiiii-eiiaaeoeaiiai oaieiiaiaia oae n iie?uoeyie e
nenoaio iaiauaiiuo a?aie/iuo oneiaee oa?iiiaoaie/aneiai acaeiiaeaenoaey
iniiau /a?ac oiieea iie?uoey. ?ac?aaioaii /eneaiii-aiaeeoe/aneoth
iaoiaeeeo ?aoaiey niioaaonoaothueo iaeeiaeiuo e?aaauo caaea/
oa?iioi?oainoe. Auyaeaii ?yae oa?aeoa?iuo iniaaiiinoae oi?ie?iaaiey e
iiaaaeaiey inoaoi/iuo iai?yaeaiee a iie?uoeyo. Noi?ioee?iaaii
niioaaonoaothuea ?aeiiaiaeaoeee aeey oi?aaeaiey oaeeie inoaoi/iuie
iai?yaeaieyie n oeaeueth ?aoeeiiaeecaoeee oaiia?aoo?iuo ?aaeeiia
iaianaiey iie?uoee.
Eeth/aaua neiaa: iaoaiaoe/aneay iiaeaeue, aunieioaiia?aoo?iia iaiueaiea,
?aaeeaoeeiiii-eiiaaeoeaiue oaieiiaiai, caueoiua iie?uoey, oaiia?aoo?iia
iiea, inoaoi/iua iai?yaeaiey.
- 19 -
ABSTRACT. Gavrys' O.P. The Determination of Thermal-Stress State of
Coatings During High-Temperature Spraying.- Manuscript.
Thesis presented for a candidate's degree in
physics and mathematics by speciality 01.02.04 - Mechanics
of Deformable Bodies.-Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics, National Academy of
Sciences of Ukraine, Lviv, 1998.
The mathematical model of thermomechanical processes during
high-temperature spraying of coatings, while taking into account:
radiation energy; heat flow plasma forming gas; radiative-convectional
heat exchange of the system: base - coating with working media;
different methods of sample fixing, is constructed. The generalized
nonlinear boundary conditions of radiative-convectional of heat exchange
of bodies with coatings and system of generalized boundary conditions of
thermomechanical interaction of base through thin coatings are
obtained. Numeric-analytical method of solving of corresponding
nonlinear boundary problems of thermoelasticity is developed. The
number of characteristic peculiarities of forming and behaviour of
residual stresses in coatings has been discovered. Corresponding
recommendations for control of such residual stresses for
rationalization of temperature regimes of coating spraying have been
formulated.
Key words: mathematical model, high-temperature spraying,
radiative-convectional heat exchange, protective coatings, temperature
field, residual stresses.
Caeiaoaa/ I.I.Aaa?enue
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