EE?ANUeEEE OI?AA?NEOAO ?IAI? OA?ANA OAA*AIEA

CAAA?AIE?I Ieoaeei TH??eiae/

OAeE 539.3

OI*IEE ?ICA’ssCIE A?AIE*IEO CAAeA*

AeEss I?OAEIIAI NA?AAeIAEUA

C AA?AOAIIIIAe?AIEI AEETH*AIIssI

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

Ee?a – 1999

5

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a Ee?anueeiio oi?aa?neoao? ?iai? Oa?ana Oaa/aiea

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

/eai-ei?aniiiaeaio IAI Oe?a?ie,

i?ioani?

Oe?oei Aiae??e Oaioaiiae/,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,

caa?aeoaa/ eaoaae?e

oai?aoe/ii? oa i?eeeaaeii? iaoai?ee

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe

Nai/aieia ?ai? Einoyioeiiae/,

?inoeooo iaoai?ee ?i. N. I. Oeiioaiea

IAI Oe?a?ie,

aieiaiee iaoe. ni?a?ia?oiee

aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

i?ioani?

Ia?oeiaiei Ieoaeei Aioiiiae/,

Oe?a?inueeee aea?aeaaiee oi?aa?neoao

oa?/iaeo oaoiieia?e,

caa?aeoaa/ eaoaae?e aeui? iaoaiaoeee,

I?ia?aeia onoaiiaa: Aea?aeaaiee oi?aa?neoao “Euea?anueea iie?oaoi?ea”

(290013, i. Euea?a — 13, aoe. N. Aaiaea?e, 12)

Caoeno a?aeaoaeaoueny “ 08 ” aa?aniy 1999 ?. i 16 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee E 26.001.21 i?e Ee?anueeiio
oi?aa?neoao? ?iai? Oa?ana Oaa/aiea (252127, i. Ee?a — 127, i?iniaeo
Aeooeiaa 2, ei?ion 7, iaoai?ei-iaoaiaoe/iee oaeoeueoao)

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeia?e a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea (252033, i. Ee?a — 33, aoe.
Aieiaeeie?nueea, 64).

Aaoi?aoa?ao ?ic?neaiee “ 20 ” eeiiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Eaie/ O. TH.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue ? nooi?iue aeine?aeaeaiiy oaiaoeee aeena?oaoe??.
Aeei?enoaiiy iaoaiaoe/ieo iiaeaeae i?oaeiiai na?aaeiaeua o iiaoaeia?
?ica’yce?a a?aie/ieo caaea/ oai??? i?oaeiino? caaaeaee iio?aao? oi/iiai
aecia/aiiy a?aieoeue ?o canoiniaiino? aei iieno ?aaeueieo i?ioean?a c
iaoith ei?aeoiiai aiae?co iaoai?/ieo aoaeo?a, ui aeieeathoue.
I?iaaaeaiiy iiaiiai iiae?aiiai aiae?co ? aeicaiey? anoaiiaeoe ye
iiaeeea? ni?iuaiiy a aeei?enoaii? aeaii? iaoaiaoe/ii? iiaeae?, oae ?
nooi?iue ?? ei?aeoiino? noiniaii iaoai?/ieo yaeu, ui iathoue aooe
iiyniai?.

A iaaeao i?inoi?iai? aaiiao?e/ii e?i?eii? oai??? i?oaeiino?, ui
aeei?enoiao? oaiiiaiieia?/iee caeii Aoea, iio?aaa a i?iaaaeaii? iiaiiai
ei?aeoiiai aiae?co iaoai?/ieo oa?aeoa?enoee i?oaeiiai na?aaeiaeua, yea
i?noeoue aei?noe? aeeth/aiiy o aeaeyae? oi?a, e?ice, aa?aoaiiiiae?aiiai
o?ea, i?eaiaeeoue aei iaiao?aeiino? ?icaeoeo iaoaiaoe/iiai aia?aoa aeey
iiaoaeiae ?ica’yce?a ??aiyiiy Eaia aeey o?e, ui a?aeianai? aei
oeeee?aeieo eii?aeeiao.

Iaoa ? caaea/? aeena?oaoe?eiiai aeine?aeaeaiiy. Iniiaia iaoa
aeena?oaoe?eiiai aeine?aeaeaiiy iieyaaea a oiio, uia iiaoaeoaaoe oi/iee
?ica’ycie ??aiyiiy Eaia aeey iaeano?, ciai?oiuei? aei aa?aoaiiiiae?aiiai
o?ea, a naiiio caaaeueiiio aeiaaeeo a?aie/ieo oiia, ? aacoth/enue ia
io?eiaiiio ?ica’yceo, cae?enieoe e?euee?niee aiae?c iaoai?/ieo
oa?aeoa?enoee o aeiaaeeao inaneiao?e/iiai oa iainaneiao?e/iiai ci?uaiue
aei?noeiai aa?aoaiiiiae?aiiai o?ea a i?oaeiiio na?aaeiaeu? a caeaaeiino?
a?ae /enea Ioaniia m.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeaia
aeena?oaoe?eia ?iaioa iaeaaeeoue aei iai?yieo eiiieaenii? iaoeiai?
i?ia?aie Ee?anueeiai Oi?aa?neoaoo ia 19972000 ?. ca oaiith
“Aeine?aeaeaiiy caeiiii??iinoae aeaoi?ioaaiiy neeaaeieo iaoai?/ieo
no?oeoo? c o?aooaaiiyi yaeu ? aoaeo?a ca’yciino? iie?a ??cii? i?e?iaee ?
?ic?iaea iaoiae?a ?o e?euee?niiai iieno”.

Iaoeiaa iiaecia aeena?oaoe?eiiai aeine?aeaeaiiy oa?aeoa?eco?oueny
ianooiieie iniiaieie ?acoeueoaoaie:

1. Iaoiaeaie i?yiiai ?ioaa?oaaiiy ? e?aeiaeo caaea/ aia?oa iiaoaeiaaii
aiaeia oi?ioe Oaa?oea aeey ocaaaeueiaieo aiae?oe/ieo ooieoe?e a
a?iiey?i?e nenoai? eii?aeeiao. Ca aeiiiiiaith io?eiaieo oi?ioe aeaii
iiaiee e?euee?niee oa aneiioioe/iee aiae?c iaoai?/ieo oa?aeoa?enoee i?e
?on? aa?aoaiiiiae?aiiai o?ea o ??aeei? iiaeae? Noiena, ui a?aeiia?aea?
i?oaeiiio na?aaeiaeuo c /eneii Ioaniia wmetafile8? ??U????????????
???????????yyy????.????1?????? ???????
?a???&??yyyy?????Ayyyayyy ??`?? ???&? ?MathType??
????u?th??????2. Cai?iiiiiaaii aeei?enoiaoaaoe aeey ?ica’ycaiiy
a?aie/ieo caaea/ i?inoi?iai? oai??? i?oaeiino? i?aaenoaaeaiiy eiiiiiaio
aaeoi?a ia?ai?uaiue o aeaeyae? aeaaa?a?/ieo eiia?iaoe?e aa?iii?eieo
ooieoe?e, ye? iiaeii? caaeiaieueiyoe niaoe?aeueiei eeth/iaei ??aiyiiyi.
Aia?oa aaeaeiny caanoe ?ica’ycie ??aiyiiy Eaia aeey iaeano?, ciai?oiuei?
aei aa?aoaiiiiae?aiiai o?ea, i?e aeia?eueieo a?aie/ieo oiiaao aei
ooieoe?iiaeueiiai ??aiyiiy ia o?ueio ia?aeaeueieo eiioo?ao c ??aieie
eiao?oe??ioaie i?e cia/aiiyo iaa?aeiii? ooieoe?? ia e?aei?o eiioo?ao.

3. Iieacaii, ui io?eiaia ooieoe?iiaeueia ??aiyiiy ? /anoeiiei aeiaaeeii
aaeoi?ii? e?aeiai? caaea/? ??iaia c ?ic?eaiith iao?eoeath eiao?oe??io?a,
cai?iiiiiaaii iaeei ?c niinia?a ?aaoey?ecaoe?? oaei? iao?eoe?,
iiaoaeiaaii ?ica’ycie oe??? caaea/? o iaei?ino?oiio aeiaaeeo.

4. Aia?oa cae?eniaii e?euee?nia ia/eneaiiy iai?oaeaiue ia eiioo??
aa?aoaiiiiae?aiiai aeeth/aiiy oa neee iii?o i?e cnoa? ye a
inaneiao?e/iiio, oae ? a iainaneiao?e/iiio aeiaaeeao. I?iaaaeaii
aneiioioe/iee aiae?c aeacaieo iaoai?/ieo oa?aeoa?enoee a ieie? aa?oeie
aa?aoaiiiiae?aiiai aeeth/aiiy.

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoao?a aeena?oaoe?eii? ?iaioe iieyaa?
a ianooiiiio. Iiaoaeiaaiee aoaeoeaiee iaoaiaoe/iee aia?ao aeey
?ica’ycaiiy a?aie/ieo caaea/ aeey i?oaeiiai na?aaeiaeua c
aa?aoaiiiiae?aiei aeeth/aiiyi iiaea neoaeeoe iniiaith aeey
aeine?aeaeaiiy i?iaeai i?inoi?iai? aaiiao?e/ii oa o?ce/ii e?i?eii?
oai??? i?oaeiino? aeey o?e, a?aeianaieo aei oeeee?aeieo nenoai
eii?aeeiao. Aeey io?eiaiiy ye?nii? ea?oeie iiaaae?iee iaoai?/ieo
oa?aeoa?enoee caaea/? a ia?ai?uaiiyo aeinoaoiuei ?icaeyaeaoe aeey
aeiaaee?a /enae Ioaniia wmetafile8? ??U????????????
???????????yyy????.????1?????? ???????
?????&??yyyy?????AyyyayyyA??`?? ???&? ?MathType??
????u?th??????Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. ??ci? aniaeoe
aeaii? aeena?oaoe?eii? ?iaioe aoei i?aaenoaaeaii ia iaoeiaeo nai?ia?ao
“I?iaeaie iaoai?ee” eaoaae?e oai?aoe/ii? oa i?eeeaaeii? iaoai?ee
Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea i?ae ea??aieoeoaii
/eaia-ei?aniiiaeaioa IAI Oe?a?ie A. O. Oe?oea, aeiiia?aeaeeny ia
I?aeia?iaei?e iaoeia?e eiioa?aioe?? “No/ani? i?iaeaie iaoai?ee ?
iaoaiaoeee” (Oe?a?ia, i. Euea?a, 1998), ia iaoeia?e eiioa?aioe?? Annual
GAMM conference at the University of Metz /GAMM-99/ (O?aioe?y, i. Iaooe,
1999), ia 4-io I?aeia?iaeiiio neiiic?oi? oe?a?inueeeo
?iaeaia??a-iaoai?e?a o Eueaia? (Oe?a?ia, i. Euea?a, 1999) c
iioae?eoaaiiyi oac aeiiia?aeae. Iniiai? ?acoeueoaoe aeine?aeieoeueei?
?iaioe ciaeoee a?aeia?aaeaiiy a o?ueio ioae?eaoe?yo o oaoiaeo iaoeiaeo
aeaeaiiyo.

No?oeoo?a oa ia’?i aeena?oaoe??. A?aoiaoth/e iinoaaeaia ia?aae
aeena?oaoe?eiei aeine?aeaeaiiyi caaaeaiiy, aeena?oaoe?y no?oeoo?ii
neeaaea?oueny c anooio, oanoe ?icae?e?a (12 i?ae?icae?e?a), aeniiae?a,
nieneo aeei?enoaii? e?oa?aoo?e oa /ioe?ueio aeiaeaoe?a. Caaaeueiee ianya
neeaaea? 154 noi??iee, nienie aeei?enoaieo aeaea?ae caeia? 5 noi??iie
(80 iaeiaioaaiue), aeiaeaoee neeaaeathoue 21 noi??ieo.

CI?NO ?IAIOE

O anooi? iaa?oioiao?oueny aeooaeuei?noue i?iaaaeaiiy aeena?oaoe?eiiai
aeine?aeaeaiiy, aecia/a?oueny eiai iaoa oa caaaeaiiy, anoaiiaeth?oueny
ca’ycie ?c iaoeiaeie i?ia?aiaie i?aai?caoe??, aea aeeiioaaeanue ?iaioa.
Oi?ioeththoueny iaoeiaa iiaecia oa i?aeoe/ia cia/aiiy io?eiaieo
?acoeueoao?a, ui aeiinyoueny ia caoeno. Iiaea?oueny ia?ae?e iaoeiaeo
eiioa?aioe?e, nai?ia??a oa ioae?eaoe?e, a yeeo a?aeia?aaeai? ??cie
aniaeoe i?iaaaeaiiai aeine?aeaeaiiy.

A ia?oiio ?icae?e? iiaeaii iaeyae e?oa?aoo?e, a yeiio oeyoii e?eoe/iiai
aiae?co ?icaeyiooi ?icaeoie i?inoi?iai? oai??? i?oaeiino? a iai?yieo
iiaoaeiae ?ica’yce?a a?aie/ieo caaea/ a ia?ai?uaiiyo aeey o?e,
a?aeianaieo aei oeeee?aeieo eii?aeeiao. A ia?oo /a?ao oaaao i?eae?eaii
caaea/ai noieniai? oa/??, iaoaiaoe/ia iiaeaeue yei? ni?aiaaea? c
??aiyiiyi Eaia ?c /eneii Ioaniia wmetafile8? ??U????????????
???????????yyy????.????1?????? ???????
?a???&??yyyy?????Ayyyayyy ??`?? ???&? ?MathType??
????u?th??????A ae?oaiio ?icae?e? “Oai??y iioaioe?aeo ? ??aiyiiy Eaia
a a?iiey?i?e nenoai? eii?aeeiao” cina?aaeaeaii aacia? oi?ie
i?aaenoaaeaiiy ?ica’yce?a aa?iii?eiiai ? a?aa?iii?eiiai ??aiyiue.

Ne?ae cacia/eoe, ui o aeiaaeeo aa?aoaiiiiae?aiiai o?ea, yea ?
iaeiica’yciei o?eii, o?aaa iieeanoe wmetafile8? ??ss????????????
???????????yyy????.????1?????? ???????
?????&??yyyy?????AyyyayyyA??`?? ???&? ?MathType??
????u?th??????Aeey aecia/aiiy ooieoe?e wmetafile8?
??A???????????? ???????????yyy????.????1??????
??????? a ???&??yyyy?????Ayyyayyy`??A?? ???&?
?MathType??P????u?th?????? wmetafile8? ??K???????????
???????????yyy????.????1?????? ???????  
`0???&??yyyy?????Ayyy?yyy 0??S ?? ???&? ?MathType??0
???u?????????»????-?????)1/4???i ???u??
???????»????-????i???“4???-?????“<??????? ???????? @??? E ???¦L???????-????’???Ae???-?????I???? *????*???????Qo???Q_ ???u?????????"????-????Ve ???Vq???-?????Q????Q????Q„???Q+???-????l —???l???-?????Q  ???QU$???-????E'???E'???u?th??????aea aeey aecia/ieea oe??? nenoaie aaaaeaii iicia/aiiy: wmetafile8? ??8??????????? ???????????yyy????.????1?????? ??????? a?%???&??yyyy?????Ayyy?yyy@%????? ???&? ?MathType??? ???u?????????"????-?????l????l.???T???U???( O ???(X ???u?????????"????-????????@???u?yA?????Aacoth/enue ia io?eiaiiio ?ica’yceo (16), iiaoaeiaaii e?i?? oieo i?e iao?eaii? aei?noeiai aa?aoaiiiiae?aiiai o?ea a’yceith ianoeneeaith ??aeeiith aeey cia/aiue aaiiao?e/iiai ia?aiao?a wmetafile8? ??Q??????????? ???????????yyy????.????1?????? ??????? @a???&??yyyy?????Ayyy°yyy ????? ???&? ?MathType??P? ???u?????????"????-????? F??? U??? I??? n???u?th??????A ae?oaiio i?ae?icae?e? “Aiae?c iniiaieo oa?aeoa?enoee iioieo a’ycei? ??aeeie i?e ?on? aa?aoaiiiiae?aiiai o?ea” iaaaaeaii cia/aiiy aeo?iai? ooieoe?? a iaeano?, ciai?oi?e aei aa?aoaiiiiae?aiiai o?ea. sse aaaeeeaee aeiaaeie, iiaeaii cia/aiiy aeo?iai? ooieoe?? ia eiioo?? wmetafile8? ??U???????????? ???????????yyy????.????1?????? ??????? ? ???&??yyyy?????AyyyAyyya??A?? ???&? ?MathType??P????u?th?????? wmetafile8? ?????????????? ???????????yyy????.????1?????? ???????  A*???&??yyyy?????Ayyy®yyy?*??I?? ???&? ?MathType?? ???u?????????"????-??????i???Uei???Ea???? ???u?????????"????-????®????C????-?????C????AeG ???AeG ???AeB ????; ????q???u?yA?????aeey yeiai ia iniia? oai??? eeoe?a ?c canoinoaaiiyi aeaieo aeey ia?oiai ei?aiy aeaoa?i?iaioa (17) anoaiiaeaii, ui a eieaeueieo eii?aeeiaoao wmetafile8? ??I???????????? ???????????yyy????.????1?????? ??????? aa???&??yyyy?????Ayyyayyy ??A?? ???&? ?MathType??P????u?th??????Oeyoii i?yiiai ?ioaa?oaaiiy ooiaeaiaioaeueiiai ni?aa?aeiioaiiy aaeoi?iiai iiey wmetafile8? ????????????? ???????????yyy????.????1?????? ???????  A ???&??yyyy?????Ayyy?yyy? ??O?? ???&? ?MathType??P????u?th?????? wmetafile8? ?? ??????????? ???????????yyy????.????1?????? ??????? ??4???&??yyyy??[email protected]??-?? ???&? ?MathType??P ???u?? ???????"????-?????af???f ???u?????????"????-????±W???±> ???‹ ???e1/4
???u?? ???????»????-????o1/4 ???™???-????™
???»i???»i???»???±u???±U
???u?????????»????-????E(???Eaeey yeiai anoaiiaeaii, ui, ye
? aeey aeo?iai? ooieoe?? wmetafile8? ??_???????????
???????????yyy????.????1?????? ???????
 ????&??yyyy?????Ayyy¦yyyA??F?? ???&? ?MathType??Aacoth/enue
ia caeii? Aoea, ui ca’yco? eiiiiiaioe oaici??a iai?oaeaiue oa
oaeaeeinoae aeaoi?iaoe?e, o aeiaaeeo wmetafile8? ??U????????????
???????????yyy????.????1?????? ???????
?a???&??yyyy?????Ayyyayyy ??`?? ???&? ?MathType??
????u?th?????? wmetafile8? ??S???????????
???????????yyy????.????1?????? ???????
?A(???&??yyyy?????Ayyy?yyy?(????? ???&? ?MathType??aea
wmetafile8? ??Ia iniia? io?eiaieo cia/aiue aeey eiiiiiaio oaici?a
iai?oaeaiue (18) iiaeaia oi?ioea neee iii?o i?e ?on? aa?aoaiiiiae?aiiai
o?ea:

wmetafile8? ??¤???????????
???????????yyy????.????1?????? ??????? 
????&??yyyy?????Ayyy¬yyy@??I?? ???&? ?MathType??
???u?????????»????-??????@????????Y????‰)
???u?????????»????-?????)??????-???????? O
e??? Oe??? N?????????@???u?yA?????ui ni?aiaaea?
c? cia/aiiyi neee iii?o, yea ?ic?aoiao?oueny /a?ac a?aieoeth ooieoe??
oieo ia iane?i/aiino?. Iiaoaeiaaii a?ao?e neee iii?o a caeaaeiino? a?ae
aaiiao?e/iiai ia?aiao?a wmetafile8? ??±????????????
???????????yyy????.????1?????? ???????
?A???&??yyyy?????AyyyAyyy???A?? ???&?
?MathType??P????u?th??????I?iaaaeaiee aneiioioe/iee aiae?c iniiaieo
iaoai?/ieo oa?aeoa?enoee iioieo a’ycei? ianoeneeai? ??aeeie i?e ?on?
aei?noeiai aa?aoaiiiiae?aiiai o?ea anoaiiaea ?nioaaiiy e?eoe/iiai
cia/aiiy aaiiao?e/iiai ia?aiao?a ??aiiai

O caeeth/i?e /anoei? aeena?oaoe?? noi?ioeueiaaii iniiai? aeniiaee
aeine?aeaeaiiy iinoaaeaieo i?iaeai.

Neiino?oeiaaii iaoaiaoe/iee aia?ao aeey iiaoaeiae ?ica’yce?a aeia?eueieo
a?aie/ieo caaea/ oai??? i?oaeiino? a ia?ai?uaiiyo aeey iaeano?,
ciai?oiuei? aei aa?aoaiiiiae?aiiai o?ea, neioac oi?i, ui
i?aaenoaaeythoue eiiiiiaioe aaeoi?a ia?ai?uaiue o aeaeyae? e?i?eieo
aeaaa?a?/ieo eiia?iaoe?e aa?iii?eieo ooieoe?e, ? iaoiae?a iiaoaeiae
?ica’yce?a a?aeiia?aeieo eeth/iaeo ??aiyiue, yeei iiaeii? caaeiaieueiyoe
aeai? aa?iii?ei? ooieoe??. Iiaoaeiaaii aiaeia oi?ioe Oaa?oea aeey x-
aiae?oe/ii? ooieoe?? a a?iiey?i?e nenoai? eii?aeeiao iacaeaaeii iaeei
a?ae iaeiiai iaoiaeaie i?yiiai ?ioaa?oaaiiy ? e?aeiaeo caaea/.

I?iaaaeaiee e?euee?niee aiae?c caaea/ i?i ci?uaiiy aei?noeiai
aa?aoaiiiiae?aiiai o?ea o i?oaeiiio na?aaeiaeu? ye a inaneiao?e/iiio,
oae ? a iainaneiao?e/iiio aeiaaeeao iieacaa, ui ci?ia /enea Ioaniia
wmetafile8? ??A aeiaeaoeo A ?icaeyiooi io?eiaiiy iaeiiai
?ioaa?aeueiiai ni?aa?aeiioaiiy niaoe?aeueiiai aeaeyaeo, ui
aeei?enoiao?oueny a iaoiae? i?yiiai ?ioaa?oaaiiy.

A aeiaeaoeo A iiaoaeiaaii ?ica’ycie aaeoi?ii? e?aeiai? caaea/? ??iaia
aeey eoneiai- aiae?oe/iiai aaeoi?a c ?ic?eaiith iao?eoeath eiao?oe??io?a
o iaei?ino?oiio aeiaaeeo.

A aeiaeaoeo A iaaaaeaii oaaeeoe? /enaeueieo cia/aiue ia?oeo ei?ai?a
ooieoe?e Eaaeaiae?a aa?oiueiai ?iaeaeno 0, 1, 2, 3 oa aeaoa?i?iaioo, ui
aeieea? a inaneiao?e/ieo a?aie/ieo caaea/ao.

A aeiaeaoeo A i?aaenoaaeaii caaaeuei? oi?ioee aieiaiiai aaeoi?a oa
aieiaiiai iiiaioo ae?? i?oaeiiai na?aaeiaeua ia aeia?eueia aei?noea
aeeth/aiiy inaneiao?e/ii? oi?ie.

Iniiai? iieiaeaiiy aeena?oaoe?eiiai aeine?aeaeaiiy ciaeoee nai?
a?aeia?aaeaiiy a ianooiieo ioae?eaoe?yo o oaoiaeo iaoeiaeo aeaeaiiyo:

1. Caaa?aieei I. TH. Aaeeiue iiaeoiae e ?aoaieth iaiau?iiie nenoaiu
o?aaiaiee oeia Eioe-?eiaia // Aeiiia?ae? IAI Oe?a?ie. – 1999. – ? 5. –
N. 30-33.

2. Caaa?aie?i I. TH. Eeane/iee i?aeo?ae aei ?ica’ycaiiy ??aiyiiy Eaia a
inaneiao?e/iiio aeiaaeeo aeey aa?aoaiiiiae?aiiai o?ea // A?niee
Ee?anueeiai oi?aa?neoaoo, Na?.: o?c.-iao. iaoee. – 1999. – Aei.1. – N.
14-18.

3. Caaa?aie?i I. TH. Eeane/iee i?aeo?ae aei ?ica’ycaiiy ??aiyiiy Eaia
aeey aa?aoaiiiiae?aiiai o?ea // Iaoeiiciaanoai. – 1999. – ? 3. – N.
23-31.

Caaa?aie?i I. TH. Oi/iee ?ica’ycie a?aie/ieo caaea/ aeey i?oaeiiai
na?aaeiaeua c aa?aoaiiiiae?aiei aeeth/aiiyi. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.02.04 – iaoai?ea
oaa?aeiai aeaoi?i?aiiai o?ea. – Ee?anueeee oi?aa?neoao ?iai? Oa?ana
Oaa/aiea, Ee?a, 1999.

Aeena?oaoe?eia ?iaioa i?enay/aia noai?aiith aoaeoeaiiai iaoaiaoe/iiai
aia?aoo aeey iiaoaeiae oi/iiai ?ica’yceo a?aie/ieo caaea/ i?inoi?iai?
oai??? i?oaeiino? a ia?ai?uaiiyo aeey iaeano?, ciai?oiuei? aei
aa?aoaiiiiae?aiiai o?ea. ?ica’ycie ??aiyiiy Eaia aeey aeia?eueieo
a?aie/ieo oiia caaaeaii aei e?aeiai? caaea/?, ui ca’yco? cia/aiiy
ooeaii? aiae?oe/ii? ooieoe?? ia o?ueio ia?aeaeueieo eiioo?ao. Iieacaii,
ui oeyoii ia?aoai?aiiy aeaii? e?aeiai? caaea/? aei caaea/? c ??aieie
eiao?oe??ioaie i?e cia/aiiyo ia e?aei?o eiioo?ao iiaeeeai cae?enieoe
/enaeueio ?aae?caoe?th ?? ?ica’yceo ia iniia? ?ioaa?aeueiiai ??aiyiiy
O?aaeaieueia ae?oaiai ?iaeo c iaeaea ??cieoeaaei yae?ii. Iiaoaeiaaii
aiaeia oi?ioe Oaa?oea aeey x-aiae?oe/ii? ooieoe?? a a?iiey?i?e nenoai?
eii?aeeiao.

Eeth/ia? neiaa: aa?aoaiiiiae?aia o?ei, oeeee?aei? eii?aeeiaoe, ??aiyiiy
Eaia, iiaeaeue Noiena, oi/iee ?ica’ycie, nenoaia ??aiyiue oeio
Eio?-??iaia, oi?ioee Oaa?oea, e?aeiaa caaea/a aeey aiae?oe/ii? ooieoe??.

Caaa?aieei I. TH. Oi/iia ?aoaiea a?aie/iuo caaea/ aeey oi?oaie n?aaeu n
aa?aoaiiia?aciui aeeth/aieai. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.02.04 – iaoaieea
oaa?aeiai aeaoi?ie?oaiiai oaea. – Eeaaneee oieaa?neoao eiaie Oa?ana
Oaa/aiei, Eeaa, 1999.

Aeenna?oaoeeiiiay ?aaioa iinayuaia nicaeaieth yooaeoeaiiai
iaoaiaoe/aneiai aiia?aoa aeey iino?iaiey oi/iiai ?aoaiey a?aie/iuo
caaea/ i?ino?ainoaaiiie oai?ee oi?oainoe a ia?aiauaieyo aeey iaeanoe,
aiaoiae ii ioiioaieth e aa?aoaiiia?aciiio oaeo. ?aoaiea o?aaiaiey Eaia
aeey i?iecaieueiuo a?aie/iuo oneiaee i?eaaaeaii e e?aaaie caaea/a,
eioi?ay naycuaaao cia/aiey eneiiie aiaeeoe/aneie ooieoeee ia o??o
ia?aeeaeueiuo eiioo?ao. Iieacaii, /oi ioo?i i?aia?aciaaiey aeaiiie
e?aaaie caaea/e e caaea/a n ?aaiuie eiyooeoeeaioaie i?e cia/aieyo ia
e?aeieo eiioo?ao aiciiaeii inouanoaeoue /eneaiioth ?aaeecaoeeth a?
?aoaiey ia iniiaa eioaa?aeueiiai o?aaiaiey O?aaeaieueia aoi?iai ?iaea n
ii/oe ?aciinoiui yae?ii. Iino?iai aiaeia oi?ioe Oaa?oea aeey
x-aiaeeoe/aneie ooieoeee a aeiiey?iie nenoaia eii?aeeiao.

Eeth/aaua neiaa: aa?aoaiiia?aciia oaei, oeeeeeaeiua eii?aeeiaou,
o?aaiaiea Eaia, iiaeaeue Noiena, oi/iia ?aoaiea, nenoaia o?aaiaiee oeia
Eioe-?eiaia, oi?ioeu Oaa?oea, e?aaaay caaea/a aeey aiaeeoe/aneie
ooieoeee.

Zabarankin M. Yu. The Exact Solution of Boundary-Value Problems for
Elastic Medium with a Spindle-shaped Inclusion. – Manuscript.

Dissertation for the Candidate Degree in Physics and Mathematics by
speciality 01.02.04 – Mechanics of Solids. – Kyiv Taras Shevchenko
University, Kyiv, 1999.

The dissertation is devoted to the construction of exact solution of the
boundary-value problems for elastic medium with a spindle-shaped
inclusion.

The structure of the dissertation is the following: introduction, six
chapters (the first one is the bibliography review), conclusion, the
bibliography and four appendixes.

In the introduction to the dissertation the author stresses out the
reasons of choosing the theme for dissertation, the innovations
delivered, the approbation of the researcher’s results (conferences,
publications etc.).

The components of the displacement vector in general case are presented
as algebraic combinations of the four harmonic functions. Using
technique O. Tedone each harmonic function is expressed by its own
boundary value in a region, which is exterior to the spindle-shaped
inclusion. Because the number of unknown harmonic functions in the
presentation of the displacement vector exceeds the number of the
boundary conditions for their determination the clue relations, which
have the form of linear partial differential equations connecting given
functions, have been constructed. The advantage of such solution forms
for the problems, which are set up in cyclide coordinates, consists in
the absence of the differential dependencies in the boundary conditions.
This enables one using the boundary conditions to express the sought
harmonic functions in a simple manner by the boundary value of one of
them, which is named carrier-function. The carrier-function is
determined from the corresponding clue relation. The Lame equation
solution is considered to be known if the boundary values of all sought
harmonic functions have been determined. In the Second Chapter the
solution forms based on vorticity and dilatation functions are
considered in detail.

In view of complicated structure of vectorial clue relations the
attention is solely paid to the development of the construction methods
of scalar clue relation solutions. These ones include the method of
direct integration and the method of boundary-value problems for
analytical functions, which are considered in the Third Chapter. The
method of the clue relation reduction to a boundary-value problem is
general, unlike the method of direct integration, which is effective in
an axisymmetrical case of the boundary conditions only. However, the way
of the boundary-value problem producing is not always simple. Schwarz
formulas for x-analytical functions are independently constructed by the
methods of direct integration and reduction to the boundary-value
problem for the analytical function.

Solving of the wide class problems of elasticity is reduced to the
functional equation that binds the values of the sought analytical
function on three parallel contours. In case when the coefficients at
the exterior contours are equal it turns out that this equation is
possible to reduce to the Riemann vectorial boundary-value problem for
the analytical function with the discontinued coefficient matrix. The
reduction manner is suggested. The regularization manner of such
discontinued coefficient matrix is offered. In a simple case the
analytical solution for this vectorial problem is obtained. Numerical
realization of the functional equation on three parallel contours could
be rationally performed using complex Fourier transformation by the
reduction manner to Fredholm integral equation.

The motion of the rigid spindle with constant velocity in the Stokers
fluid is considered in Chapter Four. The exact solution of this motion
problem is presented by the biharmonic classic stream function. The
stream lines of the Stokes flow about spindle are constructed. Based on
the obtained Schwarz formulas for x-analytical function the pressure
function is introduced in the analytical form. Numerical calculations of
the vorticity and pressure function values are performed on the contour
of spindle. Also the vorticity and pressure function values are
asymptotically evaluated near the apex on the spindle surface. The
resistance force exerted on the spindle is calculated depending on the
geometrical parameter. The formulas for stress tensor components are
obtained on the spindle surface.

The exact solution of the second fundamental boundary-value problem of
elasticity in axisymmetrical case for the elastic medium containing the
spindle-shaped inclusion is suggested in Chapter Five. The displacements
vector is presented as algebraic combination of the vortex function and
the arbitrary harmonic vector. The Fourier transform of the
boundary-value vorticity function is determined from the Fredholm
integral equation of the second kind with quasi-difference kernel. The
displacement problem of the rigid spindle along axis of symmetry is
considered as an example. The vorticity and pressure function formulas
are presented on the spindle inclusion surface. The force exerted on the
inclusion is calculated depending on the geometrical parameter and the
different values of Poisson number.

In general case of the boundary conditions the Lame equation solution
for the region exterior to the spindle-shaped inclusion is offered in
Chapter Six. This solution is initially presented by the algebraic
combination of the dilatation function and an arbitrary harmonic vector.
Being an analytical function, the Fourier transform of the dilatation
boundary-value k-harmonic is determined from the conjugation problem at
three parallel contours in the complex plane. Obtained problem is
reduced to Fredholm integral equation with a quasi-difference kernel. In
order to illustrate the general theory the force exerted on any
spindle-shaped inclusion is calculated depending on the geometrical
parameter and different values of Poisson number m for the case of the
displacement rigid inclusion along transverse axis on the constant
magnitude.

Key words: spindle, cyclide coordinates, Lame equation, Stokes model,
exact solution, equations system of Cauchy-Riemann type, Schwarz
formulas, boundary-value problem for analytical function.

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