I?I?NOA?NOAI INA?OE OE?A?IE

OA?E?ANUeEEE AeA?AEAAIEE OAOI?*IEE

OI?AA?NEOAO ?AAe?IAEAEO?II?EE

OA?AIEIANUeEEE ?AAI AeIEO?IAE*

OAeE 681.5.015:519.6

AAAAOIE?IEIA? AEAI?EOIE I?IAIICOAAIIss ? IOe?ITHAAIIss IANOAOe?IIA?IEO
IA?AIAO??A

05.13.03 – Nenoaie ? i?ioeane ea?oaaiiy

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Oa?e?a–1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Oa?e?anueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoao?
?aae?iaeaeo?ii?ee I?i?noa?noaa ina?oe Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?

?oaeaiei Ieaa A?eai?iae/,

Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?aae?iaeaeo?ii?ee, caa.
eaoaae?ith AII.

Io?oe?ei? iiiiaioe: aeieoi? oaoi?/ieo iaoe, i?ioani?

Aiaeyinueeee ?aaai Aieiaeeie?iae/,

Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?aae?iaeaeo?ii?ee,
i?ioani? eaoaae?e oaoi?/ii? e?aa?iaoeee;

Eao?aao Aea?aeaaii? i?ai?? Oe?a?ie

aeieoi? oaoi?/ieo iaoe, i?ioani?

Etha/ee Eaii?ae Ieoaeeiae/,

Oa?e?anueeee aea?aeaaiee iie?oaoi?/iee oi?aa?neoao, i?ioani? eaoaae?e
nenoaiiiai aiae?co oa oi?aae?iiy

I?ia?aeia onoaiiaa: Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie

“EI?” I?iina?oe Oe?a?ie, i.Ee?a.

Caoeno a?aeaoaeaoueny 29 ethoiai 2000  ?. i 13 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.052.02 a Oa?e?anueeiio aea?aeaaiiio
oaoi?/iiio oi?aa?neoao? ?aae?iaeaeo?ii?ee ca aae?anith: 61166,
i. Oa?e?a, i?. Eai?ia, 14, fax (0572) 40-91-13.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? Oa?e?anueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo ?aae?iaeaeo?ii?ee ca aae?anith:
61166, i. Oa?e?a, i?. Eai?ia, 14.

Aaoi?aoa?ao ?ic?neaiee 28 n?/iy 2000  ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Aacei?iaaeiee A.A.

Iaae?oeiaaii a o/aiai-ae?iaie/iio aeaeaaie/a-iie?a?ao?/iiio oeaio??
OOO?A. 61166, i. Oa?e?a, i?. Eai?ia, 14.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeinyaiaiiy iaoeiai-oaoi?/iiai i?ia?ano iaoiiaeee
ao?iee ?icaeoie iiaeo ?ioi?iaoe?eieo oaoiieia?e ?, ye iane?aeie oeueiai,
aeieeiaiiy neeaaeieo oaoi?/ieo eiiieaen?a ea?oaaiiy ia’?eoaie ??cieo
oei?a. Iaiao?aei?noue ae??oaiiy caaea/ ea?oaaiiy a ?aaeueiiio ianooaa?
/ano i?aae’yaey? iaai? aeiiae ye aei aeai?eoi?a ea?oaaiiy, oae ? aei
iaoaiaoe/ieo iiaeaeae aeine?aeaeoaaieo ia’?eo?a.

Ne?ae a?aecia/eoe, ui iaoaiaoe/i? iiaeae?, ye? noai?ththoueny,
aeei?enoiaothoueny ia o?eueee c iaoith aaciina?aaeiueiai ea?oaaiiy, a e
c iaoith i?iaiicoaaiiy iaeaooiuei? iiaaae?iee ia’?eoo. Oea aeicaiey?
i?aeaeueoe aoaeoeai?noue ea?oaaiiy oeyoii caa/anii? ei?aeoe?? ea?oth/eo
neaiae?a. E??i oiai, caaea/a i?iaiicoaaiiy ? aeineoue aaaeeeaith ? naia
yaey? niaith aacoiiaiee ?ioa?an. Oaeei /eiii, aea?? oa iaa?oiooaaiiy
iaoaiaoe/ii? iiaeae? ? oeaio?aeueieie ieoaiiyie iaoaiaoe/iiai
i?iaiicoaaiiy.

O ca’yceo c oei, ui a ?aaeueieo i?ioeanao ? aeaiaio aeiaaeeiaino?, i?e
ae??oaii? caaea/ i?iaiicoaaiiy oa ?aeaioeo?eaoe?? aeei?enoiaothoue
aeai?eoie, a iniia? yeeo, ye i?aaeei, eaaeaoue oai??y iaeiaioeo
eaaae?ao?a (?aa?an?eiee aiae?c), oai??y ia?e?anueeeo i?ioean?a, oai??y
oiiaieo aaon?anueeeo i?ioean?a ? ye? iio?aaothoue ??ciiai ia’?io ciaiue
a??ia?aeiinieo oa?aeoa?enoee aeine?aeaeoaaiiai ia’?eoo. A oiiaao
a?aenooiino? aai iaiiaiioe ai??i?ii? ?ioi?iaoe?? iaea?eueo aoaeoeaiei ?
aeei?enoaiiy oai??? iaeiaioeo eaaae?ao?a. Ne?ae a?aecia/eoe, ui iaoiae
iaeiaioeo eaaae?ao?a (IIE) oa eiai ?aeo?aioiee aiaeia – ?aeo?aioiee IIE
(?IIE) ia oeae /an aeinoaoiuei aeia?a aea/aii oa ai?iaiaaii ia
i?aeoeoe?.

Iaeiae yeui ia?aiao?e aeine?aeaeoaaieo ia’?eo?a ci?iththoueny, oi
canoiniaothoue aeaye? iiaeeo?eaoe?? ?IIE. Cie?aia aa?ieo ?acoeueoao?a
iiaeia aeinyaoe, yeui iaea?aeaoe ?aeo?aioi? aeai?eoie iaoiaea iioi/iiai
?aa?an?eiiai aiae?co (I?A), a yeiio aeei?enoiao?oueny e?ioeaaa
e?euee?noue aei??thaaiue. A e?oa?aoo?? oae? aeai?eoie iaceaathoue
aaaaoie?ieiaeie.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
?iaioa aeeiiaia a?aeiia?aeii aei eii?aeeiaoe?eiiai ieaio
iaoeiai-aeine?aeieo ?ia?o Oa?e?anueeiai aea?aeaaiiai oaoi?/iiai
oi?aa?neoaoo ?aae?iaeaeo?ii?ee a ?aieao ainiaeiaia??ii? ?iaioe ?94-33-1
“?ic?iaea i?eioeei?a iiaoaeiae, iaoiae?a oa aeai?eoi?a iaoaiaoe/iiai
iiaeaethaaiiy neeaaeieo aeeiai?/ieo ia’?eo?a” oa a ?aieao
aea?aeathaeaeaoii? oaie “?ic?iaeoe iia? i?eioeeie ?aeaioeo?eaoe??
aaaaoiaei??ieo oaoiieia?/ieo eiiieaen?a a oiiaao ae?? eieuei?iaeo
caaaae”.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoa ?iaioe iieyaa? a ?ic?iaoe? oa
aeine?aeaeaii? aaaaoie?ieiaeo aeai?eoi?a i?iaiicoaaiiy oa ioe?ithaaiiy
ianoaoe?iia?ieo ia?aiao??a a oiiaao ai??i?ii? iaaecia/aiino? oa
noai?aiiy iaiao?aeiiai i?ia?aiiiai caaacia/aiiy.

Iinoaaeaia iaoa iaa?oiooaaea oae? caaea/? aeine?aeaeaiiy:

— aea/aiiy oa aiae?c ?nioth/eo i?aeoiae?a aei i?iaiicoaaiiy oa
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a ia’?eo?a ea?oaaiiy;

— ?ic?iaea oa aeine?aeaeaiiy aaaaoie?ieiaeo aeai?eoi?a i?iaiicoaaiiy oa
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a ia’?eo?a, ui ooieoe?iiothoue a
oiiaao nooo?ai? ai??i?ii? iaaecia/aiino?;

— ?ic?iaea ?aeiiaiaeaoe?e uiaei aeai?o ia?aiao??a aaaaoie?ieiaeo
aeai?eoi?a i?iaiicoaaiiy oa ioe?ithaaiiy;

— i?ia?aiia ?aae?caoe?y ?ic?iaeaieo aeai?eoi?a oa i?iaaaeaiiy iaoeiiiai
aenia?eiaioo c iaoith aeiaaaeaiiy ?o aoaeoeaiino?;

— canoinoaaiiy ?ic?iaeaieo aeai?eoi?a i?e ae??oaii? eiie?aoieo
i?aeoe/ieo caaea/.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a iieyaa? a oiio, ui

— ?ic?iaeaii aaaaoie?ieia? aaeaioeai? aeai?eoie i?iaiicoaaiiy oa
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a, ye? ii?aeiothoue a nia?
aeanoeaino? aeai?eoi?a I?A oa IIE c aeniiiaioe?eiei caaaeoaaiiyi
?ioi?iaoe??;

— i?iaaaeaii aeine?aeaeaiiy ieoaiue ca?aeiino? cai?iiiiiaaieo
aeai?eoi?a;

— aeine?aeaeaii ieoaiiy ia/enethaaeueii? no?eeino? aaaaoie?ieiaeo
aeai?eoi?a i?iaiicoaaiiy oa ioe?ithaaiiy, ?ic?iaeaii ?aaoey?eciaai?
aaaaoie?ieia? aeai?eoie, aeine?aeaeaii ?o ca?aei?noue oa cai?iiiiiaaii
?aeiiaiaeaoe?? uiaei aeai?o ?o ia?aiao??a;

— cai?iiiiiaaii aeai?eoi d-e?ieiaiai i?iaiicoaaiiy, yeee ia? ciio
ia/oeeaino?, oa aeine?aeaeaii eiai ca?aei?noue;

— ?ic?iaeaii nenoaio ?i?oaoe?eiiai iiaeaethaaiiy ?aeo?aioieo aeai?eoi?a
i?iaiicoaaiiy oa ioe?ithaaiiy, yea aeicaiey? i?iaiaeeoe anaa?/i?
aeine?aeaeaiiy oa ii??aiyeueiee aiae?c aeai?eoi?a.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a ?iaioe iieyaa? a oiio, ui
?ic?iaeai? aaaaoie?ieia? aaeaioeai? aeai?eoie aeicaieythoue oni?oii
ae??ooaaoe oe?ieee eean caaea/ i?iaiicoaaiiy, ioe?ithaaiiy oa ea?oaaiiy
ca oiia ai??i?ii? iaaecia/aiino? ? i?e oeueiio ? ?iaa??aioieie aei
eiie?aoiiai oeio aeine?aeaeoaaiiai ia’?eoo.

Io?eiai? a oiae? aeeiiaiiy aeena?oaoe?eii? ?iaioe ?acoeueoaoe ciaeoee
canoinoaaiiy a Aea?aeaaiiio iaoeiai-aeine?aeiiio oa i?iaeoiiio ?inoeooo?
iniiaii? o?i?? “I?io?i” i. Oa?e?a i?e ?ic?iaoe? ANO oaoiieia?/ieie
i?ioeanaie ae?iaieoeoaa eaeueoeeiiaaii? niaee ia Eoia?aaenueeiio
niaeiaiio caaiae?, a oaeiae a iaa/aeueiiio i?ioean? ia eaoaae?? AII
Oa?e?anueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo ?aae?iaeaeo?ii?ee.

Iniaenoee aianie caeiaoaa/a. An? iniiai? ?acoeueoaoe iaea?aeaii iniaenoi
caeiaoaa/ai. A ?iaioao [1, 2, 7, 8] aaoi?o iaeaaeaoue iiaeeo?eaoe??
aaaaoie?ieiaeo aeai?eoi?a, a ?iaio? [3] – i?ioeaaeo?a ei?aeoe?? ciie
ia/ooeeaino?; a ?iaio? [4] – aeiaaaeaiiy ca?aeiino? aeai?eoio; a ?iaioao
[5, 6] – aeai?eoie ioe?ithaaiiy; a ?iaioao [9, 12] – ?i?oaoe?eia
iiaeaethaaiiy; a ?iaioao [10, 13] – ?ic?iaea iaoiaeeee iiaeaethaaiiy.

Ai?iaaoe?y ?acoeueoao?a ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?eii?
?iaioe aeiiia?aeaeenue oa iaaiai?thaaeenue ia Oe?a?inueeeo eiioa?aioe?yo
ii aaoiiaoe/iiio ea?oaaiith “Aaoiiaoeea 96” (Naaanoiiieue, 1996),
“Aaoiiaoeea 99” (Oa?e?a, 1999), 1-e – 5-e I?aeia?iaeieo eiioa?aioe?yo
“Oai??y ? oaoi?ea ia?aaea/?, i?eeiio oa ia?iaee ?ioi?iaoe??” (Oa?e?a,
Ooaina (?O), 1995 – 1999), 1-io I?aeia?iaeiiio iieiae?aeiiio oi?oi?
“Aeaeo?ii?ea ? iieiaeue a OOI noi??//?” (Oa?e?a, 1997), 42-io
I?aeia?iaeiiio iaoeiaiio eieiea?oi? (?eueiaiao, I?ia//eia, 1997).

Ioae?eaoe??. Ca ?acoeueoaoaie aeine?aeaeaiue iioae?eiaaii 13 ae?oeiaaieo
i?aoeue, c ieo 6 o iaoeiaeo oaoiaeo aeaeaiiyo, 7 aeiiia?aeae oa oac.

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny c anooio,
/ioe?ueio ?icae?e?a, aeniiaeo ? aeiaeaoe?a ? ia? caaaeueiee ianya —-
noi??iie. I?noeoue —- iaethie?a, —- oaaeeoeue, nienie aeei?enoaieo
e?oa?aoo?ieo aeaea?ae c —- iaeiaioaaiue.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe??, ?? iaoeiao oa
i?aeoe/io oe?ii?noue, noi?ioeueiaaii iaoo ?iaioe, iiaeaii ?? caaaeueio
oa?aeoa?enoeeo.

Ia?oee ?icae?e aeena?oaoe?? i?enay/aii iaeyaeo noaio i?iaeaie oa
iinoaiiaoe? caaea/? aeine?aeaeaiiy.

Iienaii oaoiieia?/io noaio ae?iaieoeoaa eaeueoeeiiaaii? niaee (AEN) oa
?icaeyiooi ieoaiiy iioei?caoe?? i?ioean?a AEN. O?oaeiiu? ae??oaiiy
caaea/? iioei?caoe?? iaoiiaeai? neeaaei?noth o?ceei-o?i?/ieo i?ioean?a
ia?a?iaee ne?iaeie, a?aenooi?noth aeinoaoiuei iiaieo iaoaiaoe/ieo
iiaeaeae oeeo i?ioean?a, ianoaoe?iia?i?noth ?o oa?aeoa?enoee, nooo?aei
aieeaii cao?aiue oaoiieia?/ieo ?aaeei?a, ye? aeieeathoue aiane?aeie
ci?ie ia?aiao??a iioie?a aac?a oa oaieiaeo ?aaeei?a oieiaeeeueiee?a ?
o.ae. O ca’yceo c oei, ui iaea?eueoei oeeeeii AEN ? ai?a/iee, a
aoaeoeai?noue ?iaioe a?aeae?eaiiy oeueiai oeeeeo nooo?ai aieeaa? ye ia
aoaeoeai?noue ?iaioe noi?aeieo a?aeae?eaiue, oae ? ia ye?noue aioiaiai
i?iaeoeoo, ?icaeyiooi i?iaeaio noai?aiiy aaeaioeaii? nenoaie ea?oaaiiy
oeei oeeeeii. Iieacaii, ui oaea nenoaia iiaeiia i?noeoe a eiioo??
cai?ioiiai ca’yceo ?aeaioeo?eaoi?, yeee ia o?eueee ioe?ith? oa ooi/ith?
ia?aiao?e iaoaiaoe/ii? iiaeae? c iaoith ei?aaoaaiiy o ?aaeueiiio /an?
ea?oth/eo neaiae?a, a e i?iaiico? cia/aiiy aeo?aeieo ci?iieo. ?icaeyiooi
?nioth/? aeai?eoie iaeiie?ieiaiai oa iniaeeaino? d-e?ieiaiai
i?iaiicoaaiiy ca aeiiiiiaith a?aeiia?aeieo iiaeeo?eaoe?e ?IIE.

Noi?ioeueiaaii caaea/o i?iaiicoaaiiy ye caaea/o neioaco iaoaiaoe/ii?
iiaeae?, ae??oaiiy yei? aeeth/a? aea?? no?oeoo?e iiaeae? (no?oeoo?ia
?aeaioeo?eaoe?y) oa ioe?ithaaiiy ?? ia?aiao??a (ia?aiao?e/ia
?aeaioeo?eaoe?y). ?icaeyiooi ?nioth/? iaoiaee no?oeoo?ii?
?aeaioeo?eaoe?? oa aeaee iaoaiaoe/ieo iiaeaeae, ui aeei?enoiaothoueny c
iaoith i?iaiicoaaiiy. Iieacaii, ui oe? iiaeae? iiaeia caanoe aei
??aiyiiy inaaaeie?i?eii? ?aa?an?? ?c ci?iieie eiao?oe??ioaie

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iiaoaeia? ?aeo?aioieo aeai?eoi?a ioe?ithaaiiy, ui iio?aaothoue iaiaaeaio
e?euee?noue ?ioi?iaoe??, oa aea/aiith ?o aeanoeainoae.

Ae?oaee ?icae?e aeena?oaoe?? i?enay/aii ?ic?iaoe? ?aeo?aioieo aeai?eoi?a
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a, ui aacothoueny ia iaoiae? I?A.

sse a?aeiii, iaeiie/aiiy ?ioi?iaoe?? aeicaiey? o?eueo?oaaoe caaaaeo, ui
iaiiaeeeai i?e aeei?enoaii? iaiaaeaii? e?eueeino? aei??thaaiue. Oiio c
iaoith iaaeaiiy aeai?eoio aeiaeaoeiaeo o?eueo?oth/eo aeanoeainoae i?e
eiai iiaoaeia? aeei?enoiao?oueny ?aeay aeniiiaioe?eiiai caaaeoaaiiy
?ioi?iaoe??. A?aeiia?aeia ioe?iea ia? aeaeyae:

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?MathType??0????u th??????iaeiie/aiiy ?ioi?iaoe??:

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???u?????????»????-????????????????a????A???u t
h??????neeaeaiiy ?ioi?iaoe??:

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?a???&??yyyy?????Ayyy?yyy ????? ???&? ?MathType??
???u?????????»????-??????????sse aeaeii ?c ni?aa?aeiioaiue
(3)–(6), aeey ei?aeoe?? ioe?iee nn|L i?e iaaeoiaeaeaii? iiai?
?ioi?iaoe?? ia/eneththoueny aeiiii?aeia ioe?iea cn+1|L+1 oa aeiiii?aeia
eiaa??aoe?eia iao?eoey Pn+1|L+1. A ?iaio? iaea?aeaii oaeiae oi?ioee
ia?a?aooaaiiy ioe?iee cn+1|L aaciina?aaeiuei c ioe?iee nn|L, ye? ia
aeei?enoiaothoue oe? aeiiii?aei? ia/eneaiiy (oe? oi?ioee aeinoaoiuei
a?ii?caee? ? oiio ia iaaiaeyoueny). A?aeiia?aei? ?aeo?aioi?
ni?aa?aeiioaiiy iaea?aeaii ? aeey ioe?iee, yea ei?aao?oueny ca i?aaeeii
“ceeaeaiiy-iaeiie/aiiy”.

Aeey aeine?aeaeaiiy ieoaiue ca?aeiino? cai?iiiiiaaieo aeai?eoi?a
aaiaeeoueny ooieoe?y Eyioiiaa

wmetafile8? ??c???????????
???????????yyy????.????1?????? ???????
Aa???&??yyyy?????Ayyy?yyy ??h?? ???&?
?MathType???????u?y??????aea wmetafile8? ??‡???????????
???????????yyy????.????1?????? ???????
A@???&??yyyy?????Ayyy?yyy???h?? ???&?
?MathType???????u?y??????Aeiaaaeaii, ui i?enooiy a (7) iao?eoey
wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????Ayyy!yyy ??A?? ???&?
?MathType??p????u?y?????? wmetafile8? ??W???????????
???????????yyy????.????1?????? ???????  
???&??yyyy?????Ayyy!yyya??A?? ???&?
?MathType??p????u?y??????? aeiaeaoii aecia/aiith, yeui ii/aoeiaa
iao?eoey P0|L aea?aia iaa?ae’?iii aecia/aiith (iai?eeeaae, ye a ?IIE).
Anoaiiaeaii oiiae, ye? iiaeii? aeeiioaaoenue, uia ooieoe?y Eyioiiaa aoea
iaa?ae’?iiith oa iaiaaeaiith. Aeiaaaeaii, ui a ?ac?, eiee oe? oiiae
aeeiiothoueny, iioeaea ioe?ithaaiiy c /anii ciaioo?oueny.

Aiae?c onoaeaiiai ?aaeeio iieacaa, ui o aeiaaeeo wmetafile8?
????????????? ???????????yyy????.????1??????
??????? ` ???&??yyyy?????Ayyy!yyy`???? ???&?
?MathType??P????u th??????Cai?iiiiiaai? aeai?eoie aeei?enoiaothoue
iaiaaeaio e?euee?noue aei??thaaiue (ci?iia a?eii) L oa eiao?oe??io
caaaeoaaiiy ?ioi?iaoe?? wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
 @???&??yyyy?????AyyyIyyy???m?? ???&?
?MathType??0????u th??????Iieacaii, ui c oi/ee ci?o ai?ioueae c
caaaaeaie ia?aiao? L ne?ae aeae?aoe yeiiiaa a?eueoei (a ?IIE L =n, oiaoi
aeei?enoiaothoueny an? aei??thaaiiy), a c oi/ee ci?o e?aueo aeeiai?/ieo
aeanoeainoae — ia aeoaea aaeeeei. Oae a ?ac? e?i?eiiai ae?aeoo
ia?aiao??awmetafile8? ??i???????????
???????????yyy????.????1?????? ???????
`????&??yyyy?????Ayyy!yyyA ???? ???&?
?MathType??P????u th?????? wmetafile8? ??u???????????
???????????yyy????.????1?????? ???????  a
???&??yyyy?????Ayyy¬yyy  ??L?? ???&?
?MathType??°????uAyE?????a na?aaeiueieaaae?aoe/ia a?aeoeeaiiy –

wmetafile8? ??E???????????
???????????yyy????.????1?????? ??????? 
 #???&??yyyy?????Ayyy?yyy`#??U?? ???&? ?MathType?? 
???u?????????»????-?????„—????—???„d????d???„
???????„a????a????§
????????e???????uqyE?????aea wmetafile8?
??i???????????? ???????????yyy????.????1??????
??????? ?@???&??yyyy?????Ayyyyyy????? ???&?
?MathType??P????u*thE????? wmetafile8? ??‰???????????
???????????yyy????.????1?????? ???????
?@???&??yyyy?????Ayyy¬yyy???¬?? ???&? ?MathType??a?
???u?????????»????-?????eU???eo ???u th??????wmetafile8?
??’??????????? ???????????yyy????.????1??????
???????   ???&??yyyy?????Ayyy!yyya??A?? ???&?
?MathType??p????u?y??????C (9) aeaeii, ui ?c c?inoaiiyi L ci?uaiiy
ioe?iie oaeiae c?inoa?. C ae?oaiai aieo, ?c ca?eueoaiiyi L ciaioo?oueny
/anoeia na?aaeiueieaaae?aoe/iiai a?aeoeeaiiy, yea iaoiiaeaia iayai?noth
caaaaee (ae?oaee aeiaeaiie o i?aa?e /anoei? (10)). Oaeei /eiii,
iioeiaeueia cia/aiiy L caeaaeeoue a?ae oaeaeeino? ae?aeoo ia?aiao??a, ui
ioe?iththoueny, oa noaoenoe/ieo aeanoeainoae ei?enieo neaiae?a oa
caaaae. A oae ye oey ?ioi?iaoe?y iae/ano?oa ? iaa?aeiiith, oi
aeei?enoaoe ia i?aeoeoe? oea iioeiaeueia cia/aiiy L aeaey?oueny
iaiiaeeeaei.

sse?niee aiae?c iaea?aeaieo ni?aa?aeiioaiue aeicaieea c?iaeoe aeniiaie
i?i oa, ui i?e ioe?ioe? ianoaoe?iia?ieo ia?aiao??a i?e iaeiio ??ai?
caaaae ne?ae a?aoe wmetafile8? ??u????????????
???????????yyy????.????1?????? ???????
A ???&??yyyy?????AyyyYyyy`??e?? ???&? ?MathType????
???u?????????»????-?????[?u???zx???u th???????icaeyiooi
iaoiaee aeai?o eiao?oe??ioa wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
 @???&??yyyy?????AyyyIyyy???m?? ???&?
?MathType??0????u th??????Aeai?eoie oeio (3)–(6) neoaeaoue aeey
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a oa iaeiie?ieiaiai i?iaiicoaaiiy.
A ?iaio? ?icaeyiooa caaea/a d-e?ieiaiai i?iaiicoaaiiy ca aeiiiiiaith
iiaeeo?eiaaieo ?aeo?aioieo aeai?eoi?a I?A c aeniiiaioe?eiei caaaeoaaiiyi
?ioi?iaoe??.

O o?aoueiio ?icae?e? ?icaeyaeathoueny ieoaiiy i?aeaeuaiiy
ia/enethaaeueii? no?eeino? i?ioean?a i?iaiicoaaiiy oa ioe?ithaaiiy.

Aeey iaa?iaiiy iao?eoe? wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????Ayyy!yyy ??A?? ???&?
?MathType??p????u?y?????? wmetafile8? ??d???????????
???????????yyy????.????1?????? ???????  
???&??yyyy?????Ayyyyyya??M?? ???&? ?MathType??`?
???u?????????»????-???????????]??????H????]H??????U
???]U?????»???]»???u?y?????? wmetafile8?
??R??????????? ???????????yyy????.????1??????
???????  ????&??yyyy?????Ayyy?yyy@??O?? ???&?
?MathType??a????uqyE?????Ia?oa oiiaa iaeeaaea? iaiaaeai?noue ia
aeiaaeeio aaeoi?a, a ae?oaa – ia iai?yiie i?ae wmetafile8?
??????????????? ???????????yyy????.????1??????
??????? ?A???&??yyyy?????Ayyyyyy????? ???&?
?MathType??P????u?y??????Ii aiaeia?? c ?aaoey?eciaaiei IIE a ?iaio?
i?iiiio?oueny ?aaoey?eciaaiee I?A, ioe?iea yeiai ia? aeaeyae

wmetafile8? ??l???????????
???????????yyy????.????1?????? ???????
 ????&??yyyy?????Ayyy!yyyA??A?? ???&?
?MathType??p????u?y??????aea wmetafile8? ??I????????????
???????????yyy????.????1?????? ???????
a`???&??yyyy?????AyyyIyyy ???? ???&?
?MathType??P????u th??????Aaaaeaiiy e?eoa??th wmetafile8?
??U??????????? ???????????yyy????.????1??????
??????? `  ???&??yyyy?????Ayyy!yyy` ???? ???&?
?MathType??sseui ioe?ieo caienaoe o aeaeyae?

wmetafile8? ??t???????????
???????????yyy????.????1?????? ???????  
???&??yyyy?????Ayyy!yyya??A?? ???&?
?MathType??p????u?y??????aea

wmetafile8? ??„???????????
???????????yyy????.????1?????? ??????? 
 ???&??yyyy?????Ayyy1/2yyy`??Y?? ???&? ?MathType??
???u th??????oi ??aiyiiy (12) iieno? aaaaoiaei??iee o?eueo? ?c
aeiaaeeiaeie ia?aiao?aie, ao?aeieie neaiaeaie yeiai ? wmetafile8?
??????????????? ???????????yyy????.????1??????
???????   ???&??yyyy?????Ayyy!yyy`??A?? ???&?
?MathType??0????u?y??????Cai?iiiiiaaii ?aaoey?eciaaiee aeai?eoi I?A c
aeniiiaioe?eiei caaaeoaaiiyi ?ioi?iaoe?? ? iaea?aeaii eiai ?aeo?aioi?
oi?ie, ye? ?aae?cothoue i?aaeea “iaeiie/aiiy-neeaeaiiy” oa
“neeaeaiiy-iaeiie/aiiy”. Oae aeey i?aoethth/iai ca i?aaeeii
“iaeiie/aiiy-neeiaiiy” ?aaoey?eciaaiiai aeai?eoio O?A ni?aa?aeiioaiiy
(3), (4) iaaoaathoue aeaeyaeo

wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
aa???&??yyyy?????Ayyyµyyy ??•?? ???&? ?MathType??
???u?????????»????-?????h? ???h????uqyE????? wmetafile8?
??%??????????? ???????????yyy????.????1??????
???????  ????&??yyyy?????Ayyyµyyy@??O?? ???&? ?MathType??

???u?????????»????-????????????????i????—???u t
h??????wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
@ ???&??yyyy?????Ayyyyyy`??i?? ???&?
?MathType??p????u th??????Aeine?aeaeaii ieoaiiy ca?aeiino?
?aaoey?eciaaieo aeai?eoi?a ? aeiaaaeaii, ui i?e aeeiiaii? oiia
ca?aeiino? aeey ia?aaoey?eciaaieo aeai?eoi?a I?A aoaeooue aeeiioaaoeny ?
oiiae ca?aeiino? aeey ?aaoey?eciaaieo i?e aeai?? wmetafile8?
??I???????????? ???????????yyy????.????1??????
??????? a ???&??yyyy?????AyyyIyyya???? ???&?
?MathType??P????u th??????Aiae?c io?eiaieo ?acoeueoao?a na?ae/eoue i?i
oa, ui aeey iaea?eueo aoaeoeaii? ?iaioe aeai?eoi?a ia?aiao?
?aaoey?ecaoe?? iiaeiai aooe ci?iiei. Iieacaii, ui aea?? iioeiaeueiiai
cia/aiiy wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????Ayyy??? ???? ???&?
?MathType??P????u th??????sseui a?aeiinii caaaaee wmetafile8?
??o???????????? ???????????yyy????.????1??????
??????? ? ???&??yyyy?????Ayyyyyy`???? ???&?
?MathType??P????u?y?????? wmetafile8? ??;???????????
???????????yyy????.????1?????? ???????
@`???&??yyyy?????Ayyyyyy ??i?? ???&? ?MathType??`?
???u?????????»????-?????S?H????yH????S?I???yI???u 
th??????oi cia/iiai ni?iuoaaiiy i?ioean?a ioe?ithaaiiy oa i?iaiicoaaiiy,
a ?acii c oei ? i?aeaeuaiiy ?o no?eeino? iiaeia aeinyaoe, yeui
aeei?enoaoe a aeai?eoiao ciio ia/ooeeaino?. Aaaaeaiiy ciie ia/ooeeaino?
iieyaa? a canoinoaaii? a aeai?eoiao cai?noue a?aeoeeaiiy wmetafile8?
??w??????????? ???????????yyy????.????1??????
??????? `@ ???&??yyyy?????Ayyy!yyy? ???? ???&?
?MathType??P????u?y?????? wmetafile8? ??M???????????
???????????yyy????.????1?????? ???????
`????&??yyyy?????Ayyy1/2yyyA???? ???&?
?MathType??p???u th??????aea wmetafile8? ??I????????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????AyyyIyyy ??m?? ???&?
?MathType??0????u th??????Oea ? aeioe?eueiei ua e oiio, ui iaa?oue
eiee ia?aiao?e iiaeae? (1) aecia/aii oi/ii, cia/aiiy aeo?aeieo neaiae?a
ia’?eoa oa iiaeae? aoaeooue a?ae??ciyoeny ia aaee/eio caaaaee (15).
Oaeee i?aeo?ae aeei?enoaii i?e ae??oaii? caaea/? d-e?ieiaiai
i?iaiicoaaiiy ianoaoe?iia?iiai i?ioeano ca aeiiiiiaith ?aaoey?eciaaiiai
aeai?eoio oeia Ea/iaaea, yeee ia? aeaeyae

wmetafile8? ??“???????????
???????????yyy????.????1?????? ???????
?????&??yyyy?????Ayyy±yyy@??1?? ???&? ?MathType?? 
???u?????????»????-?????x,???»,???xu ???»u ???x

???»

???xe???»e???ej???e®???u?y??????aea wmetafile8?
??t??????????? ???????????yyy????.????1??????
??????? ?a???&??yyyy?????Ayyyyyy ???? ???&?
?MathType??P????u th?????? wmetafile8? ??u???????????
???????????yyy????.????1?????? ???????
 a???&??yyyy?????Ayyyyyy ??M?? ???&? ?MathType??`?
???u?????????»????-???????1???]1?????th???]th???
??# ???]# ?????? ???]? ???u th??????aea wmetafile8?
??O??????????? ???????????yyy????.????1??????
??????? ?? ???&??yyyy?????Ayyyyyy@ ???? ???&?
?MathType??P????u th??????Aeine?aeaeaiiy ieoaiue ca?aeiino? aeai?eoio
(17) iieacaei, ui aeey oiai, uia ooieoe?y Eyioiiaa wmetafile8?
?????????????? ???????????yyy????.????1??????
???????  A???&??yyyy?????Ayyyyyy???M?? ???&? ?MathType??`?
???u?????????»????-???????(???](?????o???]o????
?TH???]TH?????«???]«???u?y??????wmetafile8?
??Y??????????? ???????????yyy????.????1??????
??????? @a???&??yyyy?????Ayyyyyy ??i?? ???&? ?MathType??`?
???u?????????»????-?????S?H????yH????S?w???yw???u 
th??????wmetafile8? ??*???????????
???????????yyy????.????1?????? ???????
  (???&??yyyy?????Ayyy?yyy`(??S?? ???&? ?MathType???
???u?????????»????-?????HJ???H+???uqyE????? wmetafile8?
??·??????????? ???????????yyy????.????1??????
??????? AA???&??yyyy?????Ayyy!yyy???a?? ???&?
?MathType??A????uqyE?????aea wmetafile8? ??!???????????
???????????yyy????.????1?????? ???????
 ????&??yyyy?????Ayyyyyy@??M?? ???&? ?MathType??`?
???u?????????»????-???????????]?????????]?????¤
???]¤?????q???]q???u?y?????? wmetafile8?
??·??????????? ???????????yyy????.????1??????
??????? ` ???&??yyyy?????Ayyy!yyya ???? ???&?
?MathType??P????uqyE????? wmetafile8? ??A???????????
???????????yyy????.????1?????? ???????  ?
???&??yyyy?????Ayyyyyy@ ??M?? ???&? ?MathType??`?
???u?????????»????-???????u???]u?????B???]B????
? ???] ?????L ???]L ???u?y??????sse aeieeaa? c (19),
?ici?? ciie ia/oeiino? caeaaeeoue a?ae /ano, ia?aiao??a aeai?eoio p ?
wmetafile8? ??o????????????
???????????yyy????.????1?????? ???????
?a???&??yyyy?????Ayyyyyy ???? ???&?
?MathType??P????u?y?????? wmetafile8? ??C???????????
???????????yyy????.????1?????? ??????? `
@#???&??yyyy?????Ayyy?yyy?#?? ?? ???&? ?MathType??°
???u?????????»????-?????=U???cU???=a???ca???
a???9 ????ae????F ???Oo ???o
???O??????uaeyE?????*aoaa?oee ?icae?e i?enay/aii
aenia?eiaioaeueiei aeine?aeaeaiiyi neioaciaaieo aeai?eoi?a oa ?o
i?aeoe/iiio canoinoaaiith.

C iaoith i?iaaaeaiiy anaa?/iiai aiae?co aeai?eoi?a oa ia?aa??ee
iaea?aeaieo oai?aoe/ieo ?acoeueoao?a aoei ?ic?iaeaii iiaeaethth/ee
eiiieaen iiaoaeiaaiee ca iiaeoeueiei i?eioeeiii, yeee aeicaiey?
ia’?aeioaaoe i?ia?aii? eiaee, ui caaie?iaaii eiii?eyoi?aie ??cieo iia.
Iienaii aieiai? aeiee eiiieaeno, ca aeiiiiiaith yeeo iiaeia i?iaanoe
iiaeaethaaiiy aoaeue yeiai ?aeo?aioiiai aeai?eoio ioe?ithaaiiy oa
i?iaiicoaaiiy. A aeena?oaoe?? i?eaaaeaii no?oeoo?o i?ia?aie, ?ioa?oaen
ei?enooaa/a, ina?oeaii iniiai? i?eioeeie iiaeaethaaiiy oa iaaaaeaii
?acoeueoaoe noaoenoe/ieo aeine?aeaeaiue.

?enoiie. A?eii a?ao?/iiai aeieo

Iiaeaethaaiiy aeicaieeei i?iaanoe ii??aiyeueiee aiae?c aeai?eoi?a ?
?ic?iaeoe ?aeiiaiaeaoe?? uiaei ?o i?aeoe/iiai aeei?enoaiiy.

?acoeueoaoe i?iaaaeaieo aeine?aeaeaiue aoee aeei?enoai? a Aea?aeaaiiio
iaoeiai-aeine?aeiiio oa i?iaeoiiio ?inoeooo? iniiaii? o?i?? “I?io?i”,
i. Oa?e?a i?e noai?aii? aaoiiaoeciaaii? nenoaie ea?oaaiiy oaoiieia?/ieie
i?ioeanaie AEN ia Eoa?aaenueeiio niaeiaiio caaiae? (Ocaae?noai).

O aeniiaeao noenei noi?ioeueiaaii iniiai? iaoeia? oa i?aeoe/i?
?acoeueoaoe aeena?oaoe?eii? ?iaioe.

INIIAI? ?ACOEUeOAOE OA AENIIAEE

1. I?iaaaeaii aiae?c no/aniiai noaio i?iaeaie i?iaiicoaaiiy oa
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a a oiiaao ai??i?ii?
iaaecia/aiino?. ?icaeyiooi caaea/o i?iaiicoaaiiy ye caaea/o neioaco
iaoaiaoe/ii? iiaeae? ? aena?oeaii iniiai? aoaie ?? ae??oaiiy.
I?iaiae?ciaaii ?nioth/? iiaeae? oa aeai?eoie ioe?ithaaiiy
ianoaoe?iia?ieo ia?aiao??a i?e a?aenooiino? ?ioi?iaoe?? i?i oa?aeoa? ?o
ae?aeoa. Iaa?oioiaaii aeei?enoaiiy aaaaoie?ieiaeo ?aeo?aioieo
aeai?eoi?a, ye? ii?aeiothoue a nia? aeanoeaino? aeai?eoi?a I?A oa ?IIE c
aeniiiaioe?eiei caaaeoaaiiyi ?ioi?iaoe??.

2. Cai?iiiiiaaii iiaeeo?eiaaio ioe?ieo I?A oa iaea?aeaii e?eueea ??
?aeo?aioieo oi?i, ye? a?ae??ciythoueny i?ae niaith iine?aeiai?noth
aeei?enoaiiy ?ioi?iaoe??, ui iaaeoiaeeoue, ? ?aae?cothoue i?aaeea
“iaeiie/aiiy-neeaeaiiy” oa “neeaeaiiy-iaeiie/aiiy”. Aeine?aeaeaia
ca?aei?noue aeai?eoi?a ? anoaiiaeaii oiiae iaa?ae’?iiino? oa
iaiaaeaiino? aaaaeaieo ooieoe?e Eyioiiaa. Aeiaaaeaii, ui a ?ac?
aeeiiaiiy oeeo oiia iioeaea ioe?ithaaiiy c /anii ciaioo?oueny. Aiae?c
onoaeaiiai ?aaeeio ioe?ithaaiiy noaoe?iia?ieo ia?aiao??a iieacaa, ui a
oeueiio aeiaaeeo cai?iiiiiaai? ?aeo?aioi? ioe?iee ? iaci?uaieie.
?ic?iaeai? ?aeo?aioi? ni?aa?aeiioaiiy iiaeeo?eiaaii c iaoith
aeei?enoaiiy ?o aeey ae??oaiiy caaea/? d-e?ieiaiai i?iaiicoaaiiy.

3. ?icaeyiooi ieoaiiy uiaei aeai?o ia?aiao??a aaaaoie?ieiaeo aeai?eoi?a:
e?eueeino? aei??thaaiue L, ye? aeei?enoiaothoueny a aeai?eoiao, oa
eiao?oe??ioa caaaeoaaiiy ?ioi?iaoe?? wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
 @???&??yyyy?????AyyyIyyy???m?? ???&?
?MathType??0????u th??????4. I?iaiae?ciaaii iaoiaee i?aeaeuaiiy
ia/enethaaeueii? no?eeino? aaaaoie?ieiaeo aeai?eoi?a i?iaiicoaaiiy oa
ioe?ithaaiiy. Iieacaii, ui iaeiei c iaea?eueo aoaeoeaieo iaoiae?a ?
iiia?aaeiy o?eueo?aoe?y ao?aeieo neaiae?a, canoinoaaiiy yei? iac?o/ii,
iaeiae, a ?aaeueiiio /an?. Aeei?enoaiiy ?aea? ?aaoey?ecaoe?? aeicaieeei
iaea?aeaoe no?ee? iiaeeo?eaoe?? I?A – ?aaoey?eciaai? ioe?iee I?A.
Aea/aii aieea ia?aiao?a ?aaoey?ecaoe?? ia aeanoeaino? aeai?eoio I?A,
yeee yaey? niaith aaaaoiaei??iee o?eueo?. Aeiaaaeaii, ui oeae o?eueo? ?
aaniethoii aneiioioe/ii no?eeei. Aeine?aeaeaii ieoaiiy ca?aeiino?
?aaoey?eciaaieo aaaaoie?ieiaeo aeai?eoi?a oa aoaeoeaiiai aeai?o
ia?aiao?a ?aaoey?ecaoe??.

5. ?icaeyiooi i?aeoe/i? ia?aaeoiiae aeei?enoaiiy ni?iuaieo aeai?eoi?a
i?iaiicoaaiiy oa ioe?ithaaiiy. Iieacaii, ui i?e iayaiino? ?ioi?iaoe??
o?eueee i?i iaiaaeai?noue caaaae aeioe?eueii aeei?enoiaoaaoe a
aeai?eoiao ciio ia/ooeeaino?. Neioaciaaii aeai?eoi d-e?ieiaiai
i?iaiicoaaiiy oa aeine?aeaeaia eiai ca?aei?noue. Cai?iiiiiaaii i?aaeei
aaeaioeaii? ei?aeoe?? ciie ia/ooeeaino?.

6. Ca ?acoeueoaoaie oai?aoe/ieo aeine?aeaeaiue ?ic?iaeaii eiiieaen
i?ia?ai iiaeaethaaiiy, ui ?aae?cothoue neioaciaai? aeai?eoie. I?iaaaeaii
?i?oaoe?ei? aenia?eiaioe, ye? i?aeoaa?aeeee i?aoeacaeaoi?noue
?ic?iaeaieo i?ioeaaeo?. Aeaii ii??aiyeueio oa?aeoa?enoeeo ?ic?iaeaieo
aeai?eoi?a c a?aeiieie oa ?ic?iaeaii ?aeiiaiaeaoe?? uiaei ?o i?aeoe/iiai
canoinoaaiiy.

7. Ca aeiiiiiaith neioaciaaieo aeai?eoi?a iiaoaeiaaii iaoaiaoe/i?
iiaeae? oaoiieia?/ieo i?ioean?a ai?a/iiai oeeeeo ae?iaieoeoaa
eaeueoeeiiaaii? niaee, ye? aoee aeei?enoai? a Aea?aeaaiiio
iaoeiai-aeine?aeiiio oa i?iaeoiiio ?inoeooo? iniiaii? o?i?? “I?io?i”
i. Oa?e?a i?e noai?aii? ANO OI ia Eoia?aaenueeiio niaeiaiio caaiae?.

NIENIE IIOAE?EIAAIEO I?AOeUe CA OAIITH AeENA?OAOe??

1. ?oaeaiei I.A., Aaaaeaeaiia N.A., Oa?aieianeee E.Ae. Iiaeeoeeaoeey
aeai?eoiia ?aeo??aioiiai IIE aeey eaeaioeoeeaoeee ianoaoeeiia?iuo
ia?aiao?ia i?e iaee/ee ia?aie/aiiuo iiiao // ANO e i?eai?u aaoiiaoeee:
Na.iao/.o?oaeia. –Aui.105. –Oa?ueeia: OOO?Y. –1997. –N.16-21.

2. Aaaaeaeaiia N.A., Iaianaiei TH.A., Oa?aieianeee E.Ae. Ia iaeiie
iiaeeoeeaoeee iiiaioaaiaiai aeai?eoia eaeaioeoeeaoeee // ANO e i?eai?u
aaoiiaoeee: Na.iao/.o?oaeia. –Aui.106. –Oa?ueeia: OOO?Y. –1997.
–N.30-33.

3. Aaaaeaeaiia N.A., ?iaiaaiei A.A., Oa?aieianeee E.Ae., Oeiioaaa A.A.
Aeai?eoiu eaeaioeoeeaoeee n aaeaioeaii iano?aeaaaiie ciiie
ia/oanoaeoaeueiinoe // ANO e i?eai?u aaoiiaoeee: Na.iao/.o?oaeia.
–Aui.107. –Oa?ueeia: OOO?Y. –1998. –N.86-95.

4. ?oaeaiei I.A., Oa?aieianeee E.Ae., Ooaoai A., Iaea A.A.
Iiaeeoeoee?iaaiiue aeai?eoi oaeouaai ?aa?anneiiiiai aiaeeca a caaea/ao
eaeaioeoeeaoeee e i?iaiice?iaaiey // ?aaeeiyeaeo?iieea e eioi?iaoeea.
–1998. –?4. –N.58-61.

5. Aenae I.A., Aaaaeaeaiia N.A., Oa?aieianeee E.Ae. Ia iaeiii
?aaoey?eciaaiiii aeai?eoia eaeaioeoeeaoeee // ?aaeeiyeaeo?iieea e
eioi?iaoeea. –1999. –?1. –N29-31.

6. Aenae I.A., ?oaeaiei I.A., Oa?aieianeee E.Ae. Aaeaioeaiia ioeaieaaiea
iaeeiaeiie iiaeaee Aaiia?ooaeia // Aanoiee OAIO. Nenoaiiue aiaeec,
oi?aaeaiea e eioi?iaoeeiiiua oaoiieiaee. –Oa?ueeia. –1999. –Aui.70.
–N.104-107.

7. Iiaeeoeoee?iaaiiua aeai?eoiu IIE a caaea/a eaeaioeoeeaoeee eeiaeiiai
ianoaoeeiia?iiai iauaeoa / Aaaaeaeaiia N.A., ?oaeaiei I.A.,
Oa?aieianeee E.Ae.; OOO?Y. –Oa?ueeia, 1996. –6n. –Aeaeeia?.: 8 iaca.
–?on. Aeai. A AIOA Oe?aeiu 29.04.96, ?1092-Oe96.

8. Aaaaeaeaiia N.A., Iaianaiei TH.A., Oa?aieianeee E.Ae. Eaeaioeoeeaoeey
ianoaoeeiia?iuo ia?aiao?ia n iiiiuueth iiaeeoeoee?iaaiiuo aeai?eoiia IIE
// I?aoe? 3-? oe?. eiio. c aaoiiaoe/iiai ea?oaaiiy “Aaoiiaoeea-96”. –Oii
1. –Naaanoiiieue: NaaAOO. –1996. –N.130.

9. Aaaaeaeaiia N.A., ?oaeaiei I.A., Oa?aieianeee E.Ae. Ia iaeiii
iiaeoiaea e caaea/a ioeaieaaiey ianoaoeeiia?iuo ia?aiao?ia i?e iaee/ee
ia?aie/aiiuo iiiao // O?oaeu 2-e Iaaeaeoia?. eiio. “Oai?ey e oaoieea
ia?aaea/e, i?e?ia e ia?aaioee eioi?iaoeee”. –Oa?ueeia–Ooaina. –1997.
–N.268.

10. Aecae H.A., Iaianaiei TH.A., Oa?aieianeee E.Ae. I /eneaiiii
iino?iaiee iiaeeoeoee?iaaiiuo aeai?eoiia ni neieuecyuei ieiii i?e
iaee/ee ei??aee?iaaiiuo iiiao // 3-y Iaaeaeoia?iaeiay eiioa?aioeey
“Oai?ey e oaoieea ia?aaea/e, i?eaia e ia?aaioee eioi?iaoeee”. Oac.aeiee.
–Ooaina, –1997. –N.156.

11. Oa?aieianeee E.Ae. Aeeyiea ioeaie ai?ei?iuo noaoenoe/aneeo
oa?aeoa?enoee ia oi/iinoue ioeaiie // 1-e Iaaeaeoia?iaeiue iieiaeaaeiue
oi?oi “Yeaeo?iieea e iieiaeaaeue a XXI aaea”. Oac.aeiee. /OOO?A.
–Oa?ueeia: OOO?Y, –1997. –N.265

12. Aenae I.A., Aaaaeaeaiia N.A., Oa?aieianeee E.Ae. Eniieueciaaiea
yenia?oiuo ioeaiie i?e enneaaeiaaiee aeai?eoiia ia?aiao?e/aneiai
ioeaieaaiey // 4-y Iaaeae. eiio. “Oai?ey e oaoieea ia?aaea/e, i?eaia e
ia?aaioee eioi?iaoeee”. –Iao/iua o?oaeu. OOO?Y, –Oa?ueeia, –1998.
–N.198.

13. Aecae H.A., Oa?aieianeee E.Ae. *eneaiiia enneaaeiaaiea ia?aiao?ia
iaeeiaeiie ianoaoeeiia?iie iiaeaee Aaiia?ooaeia // 5-y Iaaeaeoia?iaeiay
eiioa?aioeey “Oai?ey e oaoieea ia?aaea/e, i?eaia e ia?aaioee
eioi?iaoeee”. Iao/iua o?oaeu. OOO?Y, –Oa?ueeia, –1999. –N.406-408.

AIIOAOe?ss

Oa?aieianueeee ?.Ae. Aaaaoie?ieia? aeai?eoie i?iaiicoaaiiy oa
ioe?ithaaiiy ianoaoe?iia?ieo ia?aiao??a. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 05.13.03 – nenoaie oa i?ioeane ea?oaaiiy. –
Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?aae?iaeaeo?ii?ee,
Oa?e?a, 1999.

Aeena?oaoe?eia ?iaioa i?enay/aia ?ic?iaoe? oa aeine?aeaeaiith
aaaaoie?ieiaeo ?aeo?aioieo aeai?eoi?a i?iaiicoaaiiy oa ioe?ithaaiiy
ianoaoe?iia?ieo ia?aiao??a ca oiia ai??i?ii? iaaecia/aiino? i?i ae?aeo
ia?aiao??a oa caaaaee. ?ic?iaeaii aaeaioeai? aeai?eoie, ui
aeei?enoiaothoue aeey ei?aeoe?? ioe?iie iaiaaeaio e?euee?noue
aei??thaaiue. Aeine?aeaeai? ieoaiiy ca?aeiino? aeai?eoi?a oa
cai?iiiiiaai? ?aeiiaiaeaoe?? uiaei aeai?o ?o ia?aiao??a: e?eueeino?
aeei?enoo?ieo aei??thaaiue oa eiao?oe??ioa caaaeoaaiiy ?ioi?iaoe??.
I?iaiae?ciaaii ia/enethaaeueio no?ee?noue ?ic?iaeaieo aeai?eoi?a oa
cai?iiiiiaaii iaoiaee ?? i?aeaeuaiiy. I?ia?aiia ?aae?caoe?y ?ic?iaeaieo
aeai?eoi?a, ?i?oaoe?eia iiaeaethaaiiy oa ?o aeei?enoaiiy aeey iiaoaeiae
iaoaiaoe/ieo iiaeaeae oa i?iaiicoaaiiy oiaeo oaoiieia?/ieo i?ioean?a
ae?iaieoeoaa eaeueoeeiiaaii? niaee i?aeoaa?aeeee ?o i?aoeacaeaoi?noue oa
aoaeoeai?noue.

Eeth/ia? neiaa: i?iaiicoaaiiy, ?aeaioeo?eaoe?y, ianoaoe?iia?i?noue,
iaaecia/ai?noue, ?aeo?aioiee aeai?eoi, ia/enethaaeueia no?ee?noue.

AIIIOAOeEss

Oa?aieianeee E.Ae. Iiiaioaaiaua aeai?eoiu i?iaiice?iaaiey e ioeaieaaiey
ianoaoeeiia?iuo ia?aiao?ia. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.13.03 – nenoaiu e i?ioeannu oi?aaeaiey,
Oa?ueeianeee ainoaea?noaaiiue oaoie/aneee oieaa?neoao ?aaeeiyeaeo?iieee,
Oa?ueeia, 1999.

Aeenna?oaoeeiiiay ?aaioa iinayuaia ?ac?aaioea e enneaaeiaaieth
iiiaioaaiauo ?aeo??aioiuo aeai?eoiia i?iaiice?iaaiey e ioeaieaaiey
ianoaoeeiia?iuo ia?aiao?ia a oneiaeyo ai?ei?iie iaii?aaeaeaiiinoe i
ae?aeoa ia?aiao?ia e i?enoonoaothueo iiiaoao.

?ac?aaioaiu aeai?eoiu ioeaieaaiey e i?iaiice?iaaiey, eniieuecothuea aeey
iioaeoiaie ei??aeoeee ioeaiee ia?aie/aiiia /enei iaaethaeaiee e
yeniiiaioeeaeueiia acaaoeaaiea eioi?iaoeee e ni/aoathuaa oai naiui
naienoaa iaoiaea oaeouaai ?aa?anneiiiiai aiaeeca (O?A) e ?IIE n
yeniiiaioeeaeueiui acaaoeaaieai. Iieo/ai ?yae ?aeo??aioiuo oi?i
ioeaieaaiey, ioee/athueony ii?yaeeii eniieueciaaiey eiathuaeny
eioi?iaoeee e ?aaeecothueo i?aaeea “iaeiieaiea iiaie eioi?iaoeee” –
“na?in onoa?aaoae” e iaiai?io. Enneaaeiaaiu aii?inu noiaeeiinoe
aeai?eoiia e ii?aaeaeaiu oneiaey iaio?eoeaoaeueiinoe e ia?aie/aiiinoe
aaaaeaiiuo ooieoeee Eyioiiaa. Aeieacaii, /oi i?e auiieiaiee yoeo oneiaee
ioeaea ioeaieaaiey n oa/aieai a?aiaie oiaiueoaaony. Aiaeec
onoaiiaeaoaainy ?aaeeia i?e ioeaieaaiee noaoeeiia?iuo ia?aiao?ia
iieacae, /oi iieo/aaiua ioeaiee yaeythony ianiauaiiuie. ?ac?aaioaiu
niioaaonoaothuea iiaeeoeeaoeee aeai?eoiia aeey d-oaaiaiai
i?iaiice?iaaiey.

Eco/ai aii?in auai?a ia?aiao?ia aeai?eoiia: eiee/anoaa eniieuecoaiuo
iaaethaeaiee e eiyooeoeeaioa acaaoeaaiey eioi?iaoeee. Iieacaii, /oi
iioeiaeueiua cia/aiey yoeo ia?aiao?ia caaenyo io noaiaie
ianoaoeeiia?iinoe ioeaieaaaiuo ia?aiao?ia e noaoenoe/aneeo naienoa
iieaciuo neaiaeia e iiiao. I?aaeeiaeaiu ?aeiiaiaeaoeee ii auai?o yoeo
ia?aiao?ia i?e i?aeoe/aneii eniieueciaaiee ?ac?aaioaiiuo aeai?eoiia.

I?iaaaeai aiaeec au/eneeoaeueiie onoie/eainoe ?ac?aaioaiiuo aeai?eoiia e
?anniio?aiu iaoiaeu aa iiauoaiey. Iieacaii, /oi iaeiei ec iaeaieaa
yooaeoeaiuo iaoiaeia yaeyaony i?aaeaa?eoaeueiay oeeueo?aoeey aoiaeiuo
neaiaeia, eioi?ay, iaeiaei, ia oaeiaia i?e ioeaieaaiee a ?aaeueiii
a?aiaie. Eniieueciaaiea eaeae ?aaoey?ecaoeee iicaieeei iieo/eoue
onoie/eaua iiaeeoeeaoeee ioeaiie O?A-?aaoey?eciaaiiua ioeaiee O?A.
Enneaaeiaaii aeeyiea ia?aiao?a ?aaoey?ecaoeee ia naienoaa aeai?eoia,
iienuaathuaai iiiaiia?iue oeeueo?. Iieacaii, /oi aeaiiue oeeueo?
yaeyaony aaniethoii aneiioioe/anee onoie/eaui. Enneaaeiaaiu aii?inu
noiaeeiinoe ?aaoey?eciaaiiuo aeai?eoiia e iaeaieaa yooaeoeaiiai auai?a
ia?aiao?a ?aaoey?ecaoeee.

?anniio?aiu aiciiaeiinoe oi?iuaiey aeai?eoiia ioeaieaaiey e
i?iaiice?iaaiey. Iieacaii, /oi i?e iaee/ee eeoue eioi?iaoeee ia
ia?aie/aiiinoe iiiao, oeaeaniia?acii eniieueciaaoue a aeai?eoiao ciio
ia/oanoaeoaeueiinoe. ?ac?aaioai aeai?eoi d-oaaiaiai i?iaiice?iaaiey e
enneaaeiaaia aai noiaeeiinoue. I?aaeeiaeaii i?aaeei aaeaioeaiie
ei??aeoeee ciiu /oanoaeoaeueiinoe.

I?ia?aiiiay ?aaeecaoeey ?ac?aaioaiiuo aeai?eoiia e i?iaaaeaiiue
eieoaoeeiiiue yenia?eiaio iiaeoaa?aeeee eo ?aaioiniiniaiinoue e
yooaeoeaiinoue. I?aaeeiaeaiiua aeai?eoiu iicaieytho ?aoaoue oe?ieee
eeann caaea/ i?iaiice?iaaiey e ioeaieaaiey ianoaoeeiia?iuo ia?aiao?ia a
oneiaeyo ai?ei?iie iaii?aaeaeaiiinoe e i?e yoii eiaa?eaioiu e
eiie?aoiiio oeio enneaaeoaiiai iauaeoa.

?anniio?aii i?eiaiaiea ?ac?aaioaiiuo aeai?eoiia aeey ioeaieaaiey
ia?aiao?ia iaoaiaoe/aneeo iiaeaeae oaoiieiae/aneeo i?ioeannia
i?iecaiaenoaa eaeueoeeie?iaaiiie niaeu.

Eeth/aaua neiaa: i?iaiice?iaaiea, eaeaioeoeeaoeey, ianoaoeeiia?iinoue,
iaii?aaeaeaiiinoue, ?aeo??aioiue aeai?eoi, au/eneeoaeueiay
onoie/eainoue.

ABSTRACT

Terenkovsky I.D. “Multistep prediction algorithm and nonstationary
parameter estimation.” –Manuscript.

Thesis for a candidate’s degree by speciality 05.13.03 – control system
and processes. –Kharkov State Technical University of Radioelectronics,
Kharkov, 1999.

Dissertation is devoted to development and studying of multistep
recursive prediction algorithms and estimation of nonstationary
parameters in the presence of disturbancies and nucertainties in the
parameter drift. Adaptive algorithms using limited member of measurement
for error correction were developed. Convergence properties of the
algorithms were studied and recommendation for the algorithm parameters
(used number of measurements and data weighting coefficient) were
proposed. Numerical stability of the proposed algorithms was studied and
methods to improve it were proposed. Programming realization, simulation
and application of the algorithms to the sodium carbonate production
confirmed their effectiveness.

Key words: prediction, identification, nonstationarity, nucertainty,
recursive algorithm, numeric stability.

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