A?IIEOeUeEEE AeA?AEAAIEE OAOI?*IEE OI?AA?NEOAO

IIE?I A?OAE?E AI?ENIAE*

OAeE 681.51+519.6+556.013

IAOAIAOE*IA IIAeAETHAAIIss I?IOeAN?A CAA?OAeIAIIss OA I*EUAIIss ??*EIAEO
AIAe

Niaoe?aeuei?noue 01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei?
iaoiaee

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

A?IIEOess — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o A?iieoeueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoao?
I?i?noa?noaa ina?oe Oe?a?ie.

Iaoeiaee ea??aiee eaiaeeaeao oaoi?/ieo iaoe, aeioeaio A?aaei Aieiaeeie?
A?oae?eiae/,

A?iieoeueeee aea?aeaaiee oaoi?/iee oi?aa?neoao, ia?oee i?i?aeoi? —
i?i?aeoi? c iaoeiai? ?iaioe, aeiiii?/ii? iie?oeee oa i?aeia?iaeieo
ca(yce?a

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

/eai-ei?aniiiaeaio AII Oe?a?ie Aa?eaiue Aiaoie?e Oaaei?iae/, ?inoeooo
i?iaeai iiaeaethaaiiy a aia?aaoeoe? IAI Oe?a?ie,

caa?aeoaa/ a?aeae?eii iiaeaethaaiiy

aeeiai?/ieo nenoai.

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

Ea?oiee ?iiai Iaoiiae/,

A?iieoeueeee aea?aeaaiee oaoi?/iee oi?aa?neoao, caa?aeoaa/ eaoaae?e
aaoiiaoeee oa ?ioi?iaoe?eii-aei??thaaeueii? oaoi?ee

I?ia?aeia onoaiiaa: Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie «EI?»,
o?ceei-oaoi?/iee oaeoeueoao, I?i?noa?noai ina?oe Oe?a?ie, i. Ee?a.

Caoeno a?aeaoaeaoueny » » 1999 ?. i
aiaeei? ia can?-aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae05.052.01 o
A?iieoeueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoao? ca aae?anith: 286021,
i. A?iieoey, Oiaeueieoeueea oina, 95.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? A?iieoeueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo.

Aaoi?aoa?ao ?ic?neaiee » » 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

Eeniai? A.I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Inoaii?i /anii c?inoa? caa?oaeiaiiy iaaeieeoiueiai
na?aaeiaeua. Cie?aia, iia??oo?oueny ye?noue ??/eiaeo aiae. Canoinoaaiiy
aoaeue-yeeo caoiae?a aeey caiia?aaiiy oeueiai iaiiaeeeaa aac
iiia?aaeiuei? ioe?iee aeieia?/iiai noaio ??/ie. Iaeiei ?c iaee?aueo
iaoiae?a ioe?ithaaiiy oa cae?eniaiiy i?iaiico ? iaoaiaoe/ia
iiaeaethaaiiy.

A Oe?a?i? oa ca ei?aeiiii aaea ?ic?iaeaii aaaaoi iaoaiaoe/ieo iiaeaeae,
ye? iienothoue ??/eia? i?ioeane oa ci?ie yeino? ??/eiaeo aiae. Iniiaieie
iaaeie?eaie neeaaeieo iiaeaeae ?, ii-ia?oa, oa, ui ?o canoinoaaiiy ia
i?aeoeoe? aeiaaa? aaeeei? e?eueeino? ??ciiiai?oieo aeaieo, aeey cai?o
yeeo iio??aia aeiaaeueia ia?aaea aaoiiaoe/ieo noaioe?e aeieia?/iiai
iii?oi?eiao, ui a Oe?a?i? a?aenooiy, a ii-ae?oaa, aiie ia i?enoiniaai?
aeey ?ica(ycaiiy caaea/ neioaco nenoai ea?oaaiiy iienoaaieie i?ioeanaie.
Iaaeie?eii ii??aiyii i?inoeo iiaeaeae a aaaaoueio aeiaaeeao ?
iacaaacia/aiiy aaeaeaaoiiai a?aeia?aaeaiiy ?aaeueieo ??/eiaeo i?ioean?a.
Ioaea, aeioe?eueiei ? ?ic?iaea oaei? iaoaiaoe/ii? iiaeae?, yea ia eeoa
aaeaeaaoii a?aeaeca?eaethaaea a ??/eia? i?ioeane, aea ? iiaea a aooe
aeei?enoaia a iiaeaeueoiio aeey neioaco caeiio ea?oaaiiy ye?noth aiaee.

?ic?iaea oa ai?iaaaeaeaiiy oaeeo iaoaiaoe/ieo iiaeaeae a Oe?a?i?
aeicaieeei a iie?aueoe ye?noue iii?oi?eiao aiaee a ??/eao oa iieaaoeoe
?? iiaeaeueoee eiio?ieue i?ae /an i?aeoe/iiai aiaeiei?enooaaiiy.

Ca(ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aea?aiee
iai?yiie aeine?aeaeaiue ni?aiaaea? c iai?yieii aeine?aeaeaiue ca
aea?aeathaeaeaoiith iaoeiai-aeine?aeiith ?iaioith ? 47–Ae–172

(? aea?ae. ?a?no?aoe?? 0197U012588) ia oaio “?ic?iaea iiaeaeae oa
?ino?oiaioaeueieo i?ia?aiieo cania?a aiae?co aeieia?/iiai noaio ??/ie a
iaaeao i?iieneiaiai oeaio?o”, caoaa?aeaeaiith I?i?noa?noaii ina?oe
Oe?a?ie ia 1997–1999 ?iee, yea aeeiio?oueny a A?iieoeueeiio aea?aeaaiiio
oaoi?/iiio oi?aa?neoao? i?ioyaii aeacaiiai ia??iaeo.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith aeine?aeaeaiiy ? ?ic?iaea
iaoaiaoe/iiai, iaoiaee/iiai, aeai?eoi?/iiai oa i?ia?aiiiai caaacia/aiiy
aeey iiaeaethaaiiy i?ioean?a caa?oaeiaiiy oa i/euaiiy ??/eiaeo aiae oa
?ica(ycaiiy eiie?aoieo i?aeoe/ieo caaea/ ia eiai iniia?. Aeey
aeinyaiaiiy oe??? iaoe iaiao?aeii ?ica(ycaoe ianooii? caaea/?:

I?iaanoe aiae?c a?aeiieo iiaeaeae oa iaoiaeee iiaeaethaaiiy ??/eiaeo
i?ioean?a, ui aieeaathoue ia ye?noue ??/eiaeo aiae.

?ic?iaeoe iia? i?aeoiaee aei iiaoaeiae iaoaiaoe/ieo iiaeaeae aeeiai?ee
yeino? ??/eiaeo aiae oa neioacoaaoe iia? iiaeae?.

?ic?iaeoe aeai?eoie ?ica(ycaiiy ??aiyiue cai?iiiiiaaieo iiaeaeae oa
aeiaanoe ca?aei?noue oeeo aeai?eoi?a.

?ic?iaeoe aeai?eoie ?aeaioeo?eaoe?? ia?aiao??a oa no?oeoo?e
cai?iiiiiaaieo iiaeaeae ca oiia iayaiino? an?o iaiao?aeieo aeaieo.

I?iaanoe aiae?c iaiiaiioe aeaieo, yea ia? i?noea ia i?aeoeoe?, oa
?ic?iaeoe aeai?eoie ?aeaioeo?eaoe?? iiaeaeae ca oeeo oiia.

?ic?iaeoe iaeao i?eeeaaeieo i?ia?ai aeey ?aae?caoe?? cai?iiiiiaaiiai
iaoaiaoe/iiai, iaoiaee/iiai oa aeai?eoi?/iiai caaacia/aiiy i?ioean?a
iiaeaethaaiiy ??/eiaeo aiae.

Canoinoaaoe ?ic?iaeai? iiaeae? oa aeai?eoie: aeey iiaeaethaaiiy
aeeiai?ee iieaciee?a yeino? aiaee ia eiie?aoi?e ae?eyioe? ?aaeueii?
??/ee a iaaeao aaeeeiai i?iieneiaiai i?noa; aeey a?aeiiaeaiiy aoiae?a
??/eiaiai ia(?eoa ? onoiaiiy iaiiaiioe ao?aeieo aeaieo; aeey
i?iaiicoaaiiy yeino? ??/eiaeo aiae; aeey aeyaeaiiy oa ?aeaioeo?eaoe??
oa?aeoa?enoee iaca?a?no?iaaieo aoiae?a.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. A ?iaio? io?eiaii ianooii?
iaoeia? ?acoeueoaoe:

Cai?iiiiiaaii iiaee i?aeo?ae aei ?icaeooy iniiaii? ae?eyiee ??/ee ia
ieceo aeaiaioa?ieo ae?eyiie c iaeiei aeaea?aeii caa?oaeiaiiy c
iiaeeea?noth a?aooaaiiy aeia?eueii? ?o e?eueeino?.

Cai?iiiiiaaii iiaee i?aeo?ae aei iiaoaeiae iaoaiaoe/ieo iiaeaeae
??/eiaeo i?ioean?a ia iniia? oii?yaeeoaaiiy oeeo i?ioean?a ca
i?e/eiii-iane?aeeiaith iciaeith.

?ic?iaeaii niaoe?aeueiee eean aeeoa?aioe?eieo ??aiyiue aeey
iaoaiaoe/iiai iieno ??/eiaeo i?ioean?a.

Iaea?aeaii iaoaiaoe/i? iiaeae? aeeiai?ee iieaciee?a yeino? ??/eiaeo
aiae, ye? a?aoiaothoue ia eeoa an? iniiai? ??/eia? i?ioeane, ui
aieeaathoue ia ye?noue oeeo aiae, a ? ?o ianoaoe?iia?iee oa?aeoa?.

Iieacaii, ui ?ic?iaeai? iiaeae? aeiaaathoue iaioa ao?aeieo aeaieo,
ii??aiyii c a?aeiieie iiaeaeyie, ca oiiae oaei? ae oi/iino?.

Iaea?aeai? iaoaiaoe/i? iiaeae? o?ainoi?iiaaii a i?ino?? noaio
iieaciee?a yeino? ??/eiai? aiaee, ui aeicaieeoue canoiniaoaaoe ?o a
iiaeaeueoiio aeey ?ica(ycaiiy ??cieo caaea/ ea?oaaiiy oe??th ye?noth.

Iiaoaeiaaii aeai?eoie ?ica(ycaiiy ??aiyiue cai?iiiiiaaieo iiaeaeae oa
aeaaaeaii ? aeiaaaeaii oiiae ?o ca?aeiino? oa ei?aeoiino?.

?ic?iaeaii aeai?eoie ?aeaioeo?eaoe?? iiaeaeae, iioeiaeueieo ca
e?eoa???i i?i?ioio noie eaaae?ao?a iioeaie ye ca oiia iiaiioe ao?aeieo
aeaieo, oae ? ca oiia a?aenooiino? aeayeeo c ieo.

Oaeineiiaeaii aeai?eoie a?aeiiaeaiiy oa?aeoa?enoee iniiaieo aoiae?a
??/eiai? nenoaie ca aeaieie, c?a?aieie a nai?e ??/oe?.

Cai?iiiiiaaii aeai?eoie ?aeaioeo?eaoe?? io?oe?eii iaca?a?no?i-aaieo
aoiae?a ??/ee.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Io?eiai? iaoaiaoe/i?
iiaeae? oa aeai?eoie iiaeia aeei?enoiaoaaoe ia i?aeoeoe? aeey
?ica(ycaiiy ??cieo caaea/ iiaeaethaaiiy aeeiai?ee aaaaoueio iieaciee?a
yeino? aiaee na?aaei?o ? iaeeo ??aieiieo ??/ie c aeia?eueiith
e?euee?noth i?inoi?iai-cina?aaeaeaieo aeaea?ae i?e?iaeieo noie?a oa
aio?iiiaaiieo no?/ieo aiae.

?ic?iaeaiee aaoi?ii aeena?oaoe?? iaeao i?ia?ai IIAeE?I?I, a yeiio
aeei?enoai? ?acoeueoaoe aeena?oaoe??, ? ai?iaaaeaeaiei oa
aeei?enoiao?oueny aeey iiaeaethaaiiy yeino? aiaee ??/ee I?aaeaiiee Aoa a
iaaeao i?noa A?iieoe? a Aea?aeoi?aae?ii? aeiaaciaee o A?iieoeuee?e
iaeano? oa a I?aaeaiii-Aocueeiio aanaeiiaiio aiaeiainiiaea?nueeiio
ia(?aeiaii?. Ia?aa??ea i?aoeacaeaoiino? oa iiaeeeainoae iaeaoo i?ia?ai
i?iaaaeaia oaeiae a AAO «A?iieoeyaiaei?iaeo». Ie?ai? oai?aoe/i?
?acoeueoaoe aeena?oaoe?eii? ?iaioe oa aaoi?nueeee iaeao i?ia?ai
IIAeE?I?I ai?iaaaeaeaii a o/aiaee i?ioean. Ai?iaaaeaeaiiy
i?aeoaa?aeaeothoueny a?aeiia?aeieie aeoaie.

?ic?iaeaiee aaoi?nueeee iaeao i?ia?ai IIAeE?I?I iiaea aooe canoiniaaiee
? aeey ?ioeo ??/ie, iiae?aieo aei ??/ee I?aaeaiiee Aoa. Oaeiae, a?i
eaaei iiaeeo?eo?oueny aeey aiae?co i?ioean?a a ??/eao, a?aei?iieo ca
oa?aeoa?enoeeaie a?ae ??/ee I?aaeaiiee Aoa.

Iniaenoee aianie caeiaoaa/a. Na?aae i?eaaaeaieo ieae/a a nieneo
iioae?eiaaieo i?aoeue ca oaiith aeena?oaoe?? a ni?aaaoi?noa? caeiaoaa/ai
iioae?eiaaii eeoa iaeio ?iaioo, yea i?eaaaeaia i?ae iiia?ii 8. Iniaenoee
aianie caeiaoaa/a a oe?e ?iaio? iieyaa? a ianooiiiio: c?iaeaii e?eoe/iee
aiae?c a?aeiieo iaea?eueo iioe?aieo i?aeoiae?a aei iiaoaeiae iiaeaeae
??/eiaeo i?ioean?a oa cai?iiiiiaaii iiaee i?aeo?ae oa iiaoaiio iiaoaeiao
iiaeae? aeeiai?ee cia/aiue iieaciee?a yeino? aiaee aeayei? ae?eyiee
??/ee.

An? ?io? ioae?eaoe?? aeeiiai? iaeiiin?aii ? i?noyoue a nia? aeeeth/ii
?acoeueoaoe, io?eiai? aaoi?ii aeena?oaoe?? naiino?eii.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. ?acoeueoaoe aeine?aeaeaiue,
aeeeaaeai? a aeena?oaoe?ei?e ?iaio?, i?ieoee ai?iaaoe?th ia 12-oe
iaoeiaeo eiioa?aioe?yo oa neiiic?oiao, na?aae yeeo: I?aeia?iaeia iaoeiaa
eiioa?aioe?y “Oeceei-oaoie/aneea e oaoiieiae/aneea i?eeiaeaiey
iaoaiaoe/aneiai iiaeaee?iaaiey” (i. Oa?nii, 1998 ?.), 20-e I?aeia?iaeiee
iaoeiaee neiiic?oi nooaeaio?a oa iieiaeeo iaoeiaeo i?aoe?aiee?a (20TH
ISS) (Zielona Gora, Poland, 1998 ?.), 3-oy oa 4-oa I?aeia?iaei?
iaoeiai-oaoii/i? eiioa?aioe?? «Eiio?ieue ? oi?aae?iiy a oaoi?/ieo
nenoaiao» (EOON) (i. A?iieoey, 1995, 1997?.), 5-oa I?aeia?iaeia
iaoeiai-oaoii/ia eiioa?aioe?y «Eiio?ieue ? oi?aae?iiy a neeaaeieo
nenoaiao» (EONN) (i. A?iieoey, 1999 ?.),

5-oa Oe?a?inueea eiioa?aioe?y c aaoiiaoe/iiai oi?aae?iiy (Aaoiiaoeea —
98) (i. Ee?a, 1998 ?.), Anaoe?a?inueeee nai?ia? «No/ani? i?iaeaie
aiaeiiinoa/aiiy oa ciaca?aaeaiiy no?/ieo aiae» (i. O?oneaaaoeue, 1998
?.), XXIII—XXVII iaoeiai-oaoi?/i? eiioa?aioe??
i?ioani?nueei-aeeeaaeaoeueeiai neeaaeo, ni?a?ia?oiee?a oa nooaeaio?a
AAeOO c o/anoth ?iaeaia?ii-oaoi?/ieo i?aoe?aiee?a i?aei?e?inoa i?noa
A?iieoe? ? iaeano? (i. A?iieoey, 1994, 1995, 1996, 1997, 1998 ?.).

Ioae?eaoe??. ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a 5 noaooyo a
iaoeiaeo aeo?iaeao, a 6 ca??eao aeiiia?aeae aai oac aeiiia?aeae,
c?iaeaieo ia iaoeiai-oaoi?/ieo eiioa?aioe?yo aai nai?ia?ao;

2 ?iaioe caaeaiiiiaaii.

Ianya ? no?oeoo?a aeena?oaoe??. Aeena?oaoe?eia ?iaioa i?noeoue anooi,
i(youe ?icae?e?a, aeniiaee, nienie aeei?enoaieo aeaea?ae oa
o?noiaaeoeyoue aeiaeaoe?a. Caaaeueiee ianya aeena?oaoe?? 275 noi??iie, c
yeeo iniiaiee ci?no, aeeeaaeaiee ia 140 noi??ieao ae?oeiaaiiai oaenoo,
i?noeoue 6 ?enoie?a. Nienie aeei?enoaieo aeaea?ae neeaaea?oueny c 157
iaeiaioaaiue. Aeiaeaoee i?noyoue i?ii?aei? iaoaiaoe/i? aeiaaaeaiiy,
oi?ioee oa ?ic?aooiee, aeiaeaoeia? aiae?oe/i? oa iiynithaaeuei?
iaoa??aee, i?ia?aie ?ica(ycaiiy caaea/ ia AII, aeai?eoie ?iaioe oeeo
i?ia?ai, ?acoeueoaoe ?ic?aooie?a oa aeoe ai?iaaaeaeaiiy ?acoeueoao?a
?iaioe.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue i?iaeaie aeine?aeaeaiue, cacia/aii
ca(ycie ?iaioe c iaoeiaeie i?ia?aiaie, oaiaie. Aeacaii iaoo oa caaea/?
aeine?aeaeaiue. I?eaaaeaii oa?aeoa?enoeeo iaoeiai? iiaecie oa
i?aeoe/iiai cia/aiiy iaea?aeaieo ?acoeueoao?a, a oaeiae iienaii ?o
ai?iaaoe?th, ioae?eaoe?? oa ai?iaaaeaeaiiy.

A ia?oiio ?icae?e? i?iaaaeaii iaeyae oa aiae?c iniiaieo ??/eiaeo
i?ioean?a oa iieaciee?a yeino? ??/eiaeo aiae, a oaeiae aiae?c a?aeiieo
iaea?eueo iioe?aieo iaoaiaoe/ieo iiaeaeae ?o aeeiai?ee.

??/eia? i?ioeane ?icaeyaeathoueny, aieiaiei /eiii, c oi/ee ci?o ?o
aieeao ia ye?noue ??/eiaeo aiae, e?euee?niith oa?aeoa?enoeeith yei? ?
iieacieee yeino? aiaee (IssA). Aieiaieie iieacieeaie yeino? ??/eiaeo
aiae ? o?i?/i? (eiioeaio?aoe?y a aiae? ??cieo o?i?/ieo ?a/iaei,
iai?eeeaae, acioo, oinoi?o, iaooii?iaeoeo?a, oaiie?a, oei?eae?a,
caaeneeo ?a/iaei, oiui) oa aaeoa??ieia?/i? (ai?no o aiae? nai?io?o?a,
eeoeiaeo iaee/ie, naeueiiiae, oiui). ? ua ?ioaa?aeuei? iieacieee yeino?,
iai?eeeaae: ieenethaai?noue, aaee/eia o?i?/iiai /e a?io?i?/iiai
niiaeeaaiiy eenith, aei?noe?noue, oiui.

Na?aae ??/ie acyo? aei ?icaeyaeo na?aaei? oa iae? ??aieii? ??/ee, ye? ?
iaea?eueo iioe?aieie a Oe?a?i?. A oeeo ??/eao iiaeaethaaiiy iiaeia
cae?enithaaoe eeoa ii iaei?e i?inoi?ia?e eii?aeeiao? — z, a?nue yei?
ni?yiiaaia acaeiaae iniiaii? oa/?? ??/ee.

Aiae?c iieacaa, ui aieiaieie iaaeie?eaie iaea?eueo iioe?aieo iiaeaeae
aeeiai?ee yeino? ??/eiaeo aiae ? iaa?aeiia?aei?noue iaoaiaoe/iiai iieno
aeeiai?oe? iieaciee?a yeino? ?aaeueieo ??/eiaeo aiae /a?ac iaa?aooaaiiy
ianoaoe?iia?iino? ??/eiaeo i?ioean?a; iaiao?aei?noue cai?o aaeeei?
e?eueeino? ao?aeieo aeaieo, ye? ia i?aeoeoe? iiaeooue aooe a?aenooi?ie;
iaiiaeeea?noue ?o aeei?enoaiiy aeey ?ica(ycaiiy, a iiaeaeueoiio, caaea/
ea?oaaiiy ye?noth ??/eiaeo aiae.

I?iaaaeaiee aiae?c a?aeiieo iiaeaeae ci?ie yeino? ??/eiaeo aiae
aeicaieea aecia/eoe iaoo ? caaea/? aeine?aeaeaiiy.

A ae?oaiio ?icae?e? cai?iiiiiaaii iiaee i?aeo?ae aei iiaoaeiae
iaoaiaoe/ii? iiaeae? aeeiai?ee iieaciee?a yeino? ??/eiaeo aiae oa ca
oeei i?aeoiaeii iiaoaeiaaii a?aeiia?aei? iaoaiaoe/i? iiaeae?.

Ae?eyieo ??/ee, i?ioeane yei? iiaeaeththoueny («ae?eyieo iiaeaethaaiiy»
— «AeI»), i?iiiio?oueny ?icaeyaeaoe ye aaaaoiaei??io e?aa?iaoe/io
nenoaio, ia aoiaee yei? iaaeoiaeyoue ??ci? aieeae: no?/i? aiaee (c
ye?noth u), aiaee i?eoie oa i?aecaiieo aeaea?ae (rI), aoiinoa?i? iiaaee
/e noiee a?ae aiaeiiai o?ainii?oo oa iaeii??iiai oeioo (rII), i?e?iaei?
iiaa?oiaa? noiee (rII?), oiui, ye? aieeaathoue ia ye?noue x aiaee a
??/oe?. Aeo?aeiith oa?aeoa?enoeeith nenoaie ? ye?noue aiaee y a i?noeyo
aiaeiei?enooaaiiy oa aiaeiniiaeeaaiiy. A yeino? ao?aeieo U, R, aeo?aeieo
ci?iieo Y oa ci?iieo noaio X o?ao?othoue cia/aiiy iieaciee?a yeino?
a?aeiia?aeieo aiae oa iio?aei? a /an? a?ae ieo.

Ae?eyieo iiaeaethaaiiy i?iiiio?oueny ?icaeaaoe ia NAe a?eueo ae??aieo
aeaiaioa?ieo ae?eyiie (AAe) oaeei /eiii, uia ia eiaei?e c ieo aoei ia
a?eueoa iaeiiai aoiaeo oa aoee a iaci?iieie iniiai? a?ae?aae?/i?
oa?aeoa?enoeee ??/ee (aeea. ?en. 1).

v1 v2 vNae

y1 u2 y2 rI(3)
uNae yNae

x1(0)=x0 x1(t1) x2(t2)
xNae(tNae) xNae(T)

1 2 …
Nae

0 L1 L2
LNae-1 LNae = L

z

ti = [0, Ti], Ti = (Li – Li-1)/vi, L0 = 0, i = 1, 2, …, Nae, T =
L/vn?.

?en. 1. Noaia ae?eyiee ??/ee c ?icaeooyi ?? ia aeaiaioa?i?
ae?eyiee.

Aeey eiaeii? c oeeo aeaiaioa?ieo ae?eyiie aoaeo?oueny ie?aia iiaeaeue.
? oie oaeo, ui a oe?e iiaeae? eiaeai ao?ae a?aoiao?oueny ie?aii,
aeicaiey? a iiaeaeueoiio aeei?enoiaoaaoe iiaoaeiaaio iiaeaeue aeey
?ica(ycaiiy caaea/ ea?oaaiiy ye?noth aiaee.

Ocaaaeueiaio iaoaiaoe/io iiaeaeue aeeiai?ee aeayeiai iieacieea yeino?
??/eiai? aiaee an??? AeI i?iiiio?oueny caienoaaoe a aeaeyae?:

(1)

aea W — iao?eoe? iia?aoi??a iaae iaaieie ao?aeieie, aeo?aeieie ci?iieie
/e ci?iieie noaio; t — /an; v — oaeaee?noue oa/?? ??/ee; L — caaaeueia
aeiaaeeia AeI; Li — aeiaaeeia ?-i? AAe; T — caaaeueiee /an, ca yeee
aiaee ??/ee i?ioiaeyoue AeI; ny(i) —e?euee?noue aeoiae?a ia ?-?e AAe; X0
— ii/aoeia? oiiae — ye?noue aiae ??/ee, ui iaaeoiaeyoue aei ia?oi? AAe c
iniiaiith aiaeioieith ??/ee.

Cia/aiiy iieacieea yeino? aiaee ia aoaeue-ye?e aeaiaioa?i?e ae?eyioe?
??/ee iiaeii? caaeiaieueiyoe ?yaeo aeiia: 1) cia/aiiy x ia iiaeii? aooe
a?ae(?iieie; 2) a?eueo? cia/aiiy x icia/athoue a?eueoa caa?oaeiaiiy,
iaio? — iaioa; 3) cia/aiiy x ia iiaeii? ca?eueooaaoeny c? ca?eueoaiiyi t
/e z; 4) onoaeaia cia/aiiy (t /e z ( () x iiaeiii aei??aithaaoe ioeth.
Oe? aeiiae aeeiiothoueny aai iiaeooue aooe aeeiiai? aeey ia?aaaaeii?
a?eueoino? o?i?/ieo oa aaeoa??ieia?/ieo iieaciee?a yeino? aiaee. A ?ac?
?o iaaeeiiaiiy iiaeia canoinoaaoe a?aeiia?aei? caoiaee: 1) iiaeaethaaoe
cia/aiiy (x — xmin); 2) iiaeaethaaoe cia/aiiy (xmax — x); 3) ?icaeoe AAe
ua ia aeae?eueea, ia eiaei?e c yeeo cia/aiiy x o?eueee ca?eueoothoueny
/e o?eueee ciaioothoueny — aeey ae?eyiie c? ca?eueoaiiyi canoinoaaoe
ae?oaee cao?ae; 4) iiaeaethaaoe cia/aiiy (x — xono).

Iiaoaeiaa iaoaiaoe/ii? iiaeae? aeeiai?ee cia/aiue aeayeiai iieacieea
yeino? aiaee, yea ? aeaiaioii ocaaaeueiaii? iiaeae?, cae?enithaaeanue a
aeae?eueea aoai?a. Nii/aoeo aoea ?ic?iaeaia iaoaiaoe/ia iiaeaeue, yea
iieno? aeeiai?eo iieacieea yeino? a o?eniaai?e eii?aeeiao? i?inoi?o. Oey
iiaeaeue aoaeoaaeanue ia iniia? ianooiieo i??eoaaiue. An? ??/eia?
i?ioeane naiii/euaiiy, eio?? aieeaathoue ia ye?noue ??/eiaeo aiae,
iiaeia ca?oioaaoe ca iine?aeiaii-iane?aeeiaith aca?iiae??th. A
aeae?eaieo a?oiao eiaeai i?ioean, ie??i i?ioean?a ia?oi? oa inoaiiuei?
a?oi, ia?aoai?th? i?iaeoeoe ae?? i?ioean?a iiia?aaei?o a?oi, ? eeoa
i?ioeane inoaiiuei? a?oie i?ecaiaeyoue aei aaciina?aaeiuei? ci?ie
cia/aiue iieaciee?a yeino? aiaee. I?ioeane ae ia?oi? a?oie aieeaathoue
ia oie noai oa neeaae ?a/iaeie /e i?e?ii?aai?ci?a, ui iaae?eoia aei
??/ee. Aiae?c an?o i?ioean?a a ??/eao aeicaieea anoaiiaeoe, ui a
a?eueoino? aeiaaee?a iiaeia iaiaaeeoenue o?ueiia a?oiaie, a ?iiae? e
aeaiia /e iaei??th. Iai?eeeaae, aei a?oi c ia?oi? aei ia?aaeinoaiiuei?
iiaeooue iaeaaeaoe i?ioeane o?i?/iiai ia?aoai?aiiy, a?io?i?/ii?
o?ainoi?iaoe??, oiui, a aei inoaiiuei? a?oie — i?ioeane inaaeaeaiiy,
iiaeeiaiiy a?ae?ia?iioaie, aeia?iaoaaiiy, oiui. I?ioeane ??cieo a?oi
i?io?eathoue c ??cieie oaeaeeinoyie ? /a?ac oea, ?o aca?iiae?th o?aaa
?icaeyaeaoe ye iine?aeiaii-iaeii/ania i?io?eaiiy. Iine?aeiaii — oiio, ui
ianooiiee ii/eia?oueny eeoa oiae?, eiee aaea ii/aany iiia?aaei?e ?
c(yaeeenue ye?nue ?acoeueoaoe eiai ae??, a iaeii/anii — oiio, ui
ianooiiee ii/eia?oueny oiae?, eiee iiia?aaei?e, ye i?aaeei, ua ia
cae?i/eany.

A yeino? iaoaiaoe/iiai iieno a?oi iine?aeiaii-iaeii/anieo i?ioean?a
i?iiiio?oueny oaeee eean aeeoa?aioe?eieo ??aiyiue:

(2)

(3)

aea Gl (t) — ooieoe?y, yea a?aoiao? aieea l-? (l = 1, 2 /e 3) e?eueeino?
a?oi iine?aeiaii-iaeii/anieo i?ioean?a ia ci?io cia/aiiy iieacieea
yeino? ??/eiai? aiaee x; k1, k2, k3— eiao?oe??ioe i?iii?oe?eiino? i?ae
oaeaeeinoyie i?io?eaiiy a?aeiia?aeii i?ioean?a ia?oi?, ae?oai? oa
o?aouei? a?oi, ca oiia ?o ?cieueiaaiiai i?io?eaiiy, oa cia/aiiyi
iieacieea x, ia yeee aiie ae?thoue.

Aieiaieie o?ce/ieie iieiaeaiiyie, ye? a?aoiaothoueny a (2), (3) ?,
ii-ia?oa, oa, ui ia?oa a?oia i?ioean?a aieeaa? ia cia/aiiy x, ye oea
caaaeueiii?eeiyoi, ca cae/aeiei aeniiiaioe?eiei caeiiii. Oaeaee?noue aea
i?io?eaiiy i?ioean?a ae?oai? oa o?aouei? a?oi, caeaaeeoue a?ae
oaeaeeino? i?io?eaiiy i?ioean?a iiia?aaei?o a?oi. Iaoaiaoe/iee ae?ac
oaeaeeino? i?io?eaiiy i?ioean?a l-i? a?oie a?aoiao? ?ica(ycie iiaeae?
(2) aeey i?ioean?a (l-1)-i? a?oie. Ii-ae?oaa, a ?ac? ci?ie /ano t a?ae 0
aei ( aeey l = 2 /e 3 cia/aiiy ooieoe?? Gl(t) iiaeii? ci?ithaaoenue a?ae
0 aei –kl. Oiaoi, eiee ciaioaiiy x a?aeaoaa?oueny o?eueee ia 2-?e /e
3-?e noaae??, a ii/aoeiaee iiiaio /ano (aei iiyae ?acoeueoao?a ae??
i?ioean?a i?ii?aeieo a?oi) ciaioaiiy ua ia a?aeaoaa?oueny. A
iane?i/aiiino? ae, eiee i?ioeane i?ii?aeieo a?oi aaea iaeaea
caaa?oeeeny, oaeaee?noue i?ioean?a inoaiiuei? l-i? a?oie aaea ia
caeaaeeoue a?ae oaeaeeino? i?ioean?a a?oi i?ii?aeieo.

A?aooaaiiy i?ioean?a ?icaaaeaiiy oa ia?ai?ooaaiiy ia a yeino? i?ioean?a
yei?nue c a?oi, a a yaiiio aeaeyae? c aeei?enoaiiyi iiaeae? (2), (3)
aeey iieno ?ioeo o?ceei-o?i?/ieo, a?ieia?/ieo oa a?io?i?/ieo i?ioean?a,
i?ecaaei aei io?eiaiiy i?inoi?iai-?iciiae?eaii? iiaeae?, yea iieno?
ci?io iieacieea yeino? aiaee ye a /an?, oae ? a i?inoi??:

(4)

x(0, z) = x0(z), x(t, 0) = a(t), x(t, L) = b(t). (5)

aea v*, (* — a?aeiia?aeii oi?iaeuei? oaeaee?niee oa
oo?aoeaioii-aeeoociee eiao?oe??ioe; x0(z) (ii/aoeia? oiiae), a(t), b(t)
(a?aie/i? oiiae) — aeaye? ooieoe??.

Caien oe??? iiaeae? aeey aeayeiai ia(?io ??/eiaiai iioieo, yeee
ia?anoaa?oueny ?c oaeaee?noth oa/?? ??/ee ? aeey yeiai eii?aeeiaoe /ano
t ? i?inoi?o z ? iia(ycaieie: z = v(t, aeicaiey? i?eaanoe ?? aei
i?inoi?iai-cina?aaeaeaii? aeeiai?/ii? iiaeae?, yea iicaaaeaia a?eueoino?
iaaeie?e?a a?aeiieo iaea?eueo iioe?aieo iiaeaeae:

(6)

(7)

Io?eiaio iiaeaeue o?ainoi?iiaaii aei noaiaea?oeciaaii? oi?ie — a
i?ino?? noaio iieaciee?a yeino? ??/eiaeo aiae

(8)

(9)

yeee aeicaiey? aeei?enoiaoaaoe ?? a yeino? aeaiaioo ocaaaeueiaii?
iaoaiaoe/ii? iiaeae?, yea a oaeiio ?ac?, iaaoaa? aeaeyaeo:

(10)

(11)

aea C — iao?eoey niinoa?aaeaiue; (?, (? — eiao?oe??ioe, eio??
a?aoiaothoue oa, yea /anoeia aiae, ui iaae?eoee c a?aeiia?aeiiai aoiaeo,
ae?noaeany oa?aaoa?o ??/ee aei ii/aoeiaiai noai?o ?-i? AAe ??/ee.

Aeey nei?i/aiiy caieno, iiaeae? ia iniia? aeeoa?aioe?eiiai ??aiyiiy
ia?oiai oa ae?oaiai ii?yaee?a iacaaii, a?aeiia?aeii: iiaeaeyie ia?oiai
ii?yaeeo (III) oa iiaeaeyie ae?oaiai ii?yaeeo (IAeI).

A o?aoueiio ?icae?e? aeeiiaii ?ica(ycaiiy ??aiyiue iaoaiaoe/ieo
iiaeaeae oa ?ic?iaeaii aeai?eoie ? iaoiaeeee ?o canoinoaaiiy.

?ica(ycee ??aiyiue iiaeae? ia?oiai ii?yaeeo:

(12)

Aeey ?ica(ycaiiy ??aiyiue iiaeae? ae?oaiai ii?yaeeo, ye? ? cae/aeieie
iaeii??aeieie aei?noeeie aeeoa?aioe?eieie ??aiyiiyie ae?oaiai ii?yaeeo
c? ci?iieie a /an? eiao?oe??ioaie, iiaoaeiaaii niaoe?aeueiee
ia/enethaaeueiee aeai?eoi c aeei?enoaiiyi ci?iiiai e?ieo ?ioaa?oaaiiy hn
oa iayaieo e?ioeaaeo ??cieoeue ((h = const):

(13)

(14)

(15)

(16)

(17)

(18)

(0) = 0), ye? noi?ioeueiaaii ? aeiaaaeaii a aeaeyae? aeaio oai?ai:

(0) = 0, aoa ca?aeiei, iaiao?aeii ? aeinoaoiuei, uia aeey iueiai
aeeiioaaeany oiiaa:

(19)

(20)

Oai?aia 2. sseui aeey ?yaeo cia/aiue x[n] (n = 1, 2, …, N), yeee
ii?iaeaeo?oueny aeai?eoiii (13)—(18) ca ii/aoeiaeo oiia

(0) = 0, aeeiio?oueny oiiaa

(21)

oiae?: 1) oeae ?yae ? ca?aeiei ? a ?ac? n ( ( cia/aiiy x[n] ( 0;

2) aeey an?o cia/aiue x[n] aeeiio?oueny ni?aa?aeiioaiiy:

(22)

A /aoaa?oiio ?icae?e? ?ic?iaeaii aeai?eoie oa iaoiaeeee ?aeaioeo?eaoe??
iiaeaeae aeeiai?ee iieaciee?a yeino? ??/eiaeo i?ioean?a. Ocaaaeueiaiee
aeai?eoi ?aeaioeo?eaoe?? iiaeaeae neeaaea?oueny c oaeeo aoai?a: 1) ca??
ao?aeieo aeaieo, ?o ianooaaoaaiiy, iiaoaeiaa noaie «Ao?ae—aeo?ae» oa
aecia/aiiy ii/aoeiaeo oiia; 2) ?aeaioeo?eaoe?y ia?aiao??a iiaeaeae; 3)
?aeaioeo?eaoe?y no?oeoo?e iioeiaeueii? iiaeae?.

. Iiaeaeeth c iioeiaeueiith no?oeoo?ith ? oa iiaeaeue c iioeiaeueieie
cia/aiiyie ia?aiao??a, eio?a caaacia/o? iaeiaioee eaaae?ao iioeaee aeey
anueiai ae?aiaciio aeaieo aei??thaaiue (0, 1, …, Ni).

Oaeee aeai?eoi ?aeaioeo?eaoe?? iioeiaeueii? iiaeae? caaacia/o?
aeae?eaiiy o?aiaea i?ioeano ci?ie cia/aiiy iieacieea yeino? aiaee, yeee
? noioanoe/iei /a?ac noioanoe/i?noue aoiae?a ??/eiaiai ia(?eoa.
Aeei?enoaiiy iaoiaeo iaeiaioeo eaaae?ao?a aeicaiey? a?aeo?eueo?oaaoe
iaoi/iino? oa aeiaaeeia? iiieeee aecia/aiiy ao?aeieo aeaieo.

i(j)(k) (i = 1, 2, …, Nae; j = 0, 1, …, Ni; k = 1, 2, …, Nk; Nk
—caaaeueia e?euee?noue IssA, ye? iiaeaeththoueny) a ieo, i?e/iio aeey
eiaeiiai iieacieea iiaeiii aeeiioaaoenue ni?aa?aeiioaiiy:

(23)

aai oi/a a

(24)

aea Nmin — i?i?iaeueii aeiionoeia aeey i?iaaaeaiiy ?aeaioeo?eaoe??
e?euee?noue aeaieo aei??thaaiue (aeey III — 4, aeey IAeI — 6).

Aei aeiaeaoeiaeo ao?aeieo aeaieo iaeaaeaoue ianooii?: aeai? i?i aoiaee
??/ee (aeo?aoe aiae q oa cia/aiiy iieaciee?a u, rI, rII, rIII ?o
yeino?); iniiai? a?ae?aae?/i? ia?aiao?e aiaeioiee ??/ee. Aac
aeiaeaoeiaeo aeaieo iiaeia ia?eoenue aai aecia/eoe ?o iaoaiaoe/ii ca
iaeiei c oaeeo niinia?a (ca ciaioaiiyi ?ioi?iaoe??, yea iaiao?aeia aeey
?ic?aooie?a):

1) aeei?enoaiiy aeai??aiaaiai i?eioeeio iiaeaethaaiiy: cae?e-niaiiy
iiaeaethaaiiy ? aeey i?eoie ca cai?iiiiiaaieie iiaeaeyie;

0 a?aeiia eeoa a ona?aaeiai?e oi/oe? — aeai?eoi

A.A. O?ieiaa — ?.Ae. ?iaeceeea?a; a) iaia? i?yeeo oi/ieo aeaieo, a
oa?aeoa? oa/?? i?eoiee caaacia/o? aeineoue oaeaeea ia?ai?ooaaiiy ?? aiae
c? no?/ieie — aeai?eoi aeiaeaaaiiy ianiiioie?a (aeiaooe?a aeo?ao aiae ia
cia/aiiy iieaciee?a ?o yeino?);

3) iaeii/ania ?aeaioeo?eaoe?y ia?aiao??a oa no?oeoo?e iaoaiaoe/ii?
iiaeae? ?acii ?c noaiii oa aoiaeaie iniiaii? ??/ee — i?aeo?ae iniiaaiee
ia i?eiouaii?, ui aeeiai?ea cia/aiue iieaciee?a yeino? ??/eiaeo aiae oa
aiae, ui iaaeoiaeyoue c? aoiae?a — iaeiaeiaa.

Iniaeea?noth iaoaiaoe/iiai iiaeaethaaiiy ??/eiaeo i?ioean?a ? ua e oa,
ui ia caaaeaee iayai? aeai? i?i an? aeaea?aea no?/ieo aiae. Iiaeooue
aooe io?oe?eii iaca?a?no?iaai? aoiaee. Aeyaeoe oae? aoiaee, aecia/eoe ?o
i?noeaciaoiaeaeaiiy oa ye?noue aiae, ui iaaeoiaeyoue c ieo, iiaeia,
aeiaeaaoe oe? ?o ia?aiao?e aei aaeoi?o ia?aiao??a iiaeaeae, eio??
iiaeii? aooe ?aeaioeo?eiaai?.

A i(yoiio ?icae?e? ?ic?iaeaia iaoaiaoe/ia, iaoiaee/ia oa aeai?eoi?/ia
caaacia/aiiy canoiniaaii aei iiaeaethaaiiy aeeiai?ee cia/aiue iieaciee?a
yeino? aiaee ??/ee I?aaeaiiee Aoa a iaaeao i?noa A?iieoe? ca aeaieie
aei??thaaiue 1996 oa 1997 ?ie?a, iaaeaieo oaeeie onoaiiaaie:
Aea?aeoi?aae?iiy aeiaaciaee o A?iieoeuee?e iaeano?, A?iieoeueea iaeania
naiai?aeainoaioe?y, I?aaeaiii-Aocueea aanaeiiaa aiaeiainiiaea?nueea
ia(?aeiaiiy, AAO «A?iieoeyaiaei?iaeo».

Aeey i?iaaaeaiiy iiaeaethaaiiy aaoi?ii aeena?oaoe?? iaienaii iaeao
i?eeeaaeieo i?ia?ai (III) «IIAeE?I?I» — «IIaeaethaaiiy AeEiai?ee
??/eiaeo I?Ioean?a», a yeiio aeei?enoai? an? ?ic?iaeai? a aeena?oaoe??
aeai?eoie oa iiaeae?. Canoinoaaiiy oeueiai iaeaoo i?ia?ai aeey
iiaeaethaaiiy iaeaaaeeea?oeo o?i?/ieo oa aaeoa??ieia?/ieo iieaciee?a
yeino? aiaee aeey ae?eyiee ??/ee I?aaeaiiee Aoa, ?icoaoiaaii? a iaaeao
i?noa A?iieoe?, aeaei oni?oi? ?acoeueoaoe. Ia ?en. 2 i?eaaaeaii a?ao?ee
caeaaeiino? cia/aiue iieaciee?a «Aaee/eia iiaiiai a?io?i?/iiai
niiaeeaaiiy eenith» (?en. 2a; iioeaea i?ae cia/aiiyie, ia/eneaieie ca
iiaeaeeth, oa aenia?eiaioaeueieie aeaieie noaiiaeoue 3,8 %),
«Eiioeaio?aoe?y caaeneeo ?a/iaei» (?en. 2a; 0,7 %) oa «Ai?no nai?io?o?a,
aei??yiee i?e oaiia?aoo?? 22 0N» (?en. 2a, a, ae; 2,4%) a?ae eii?aeeiaoe
z.

a) a) ae)

?en. 2. I?eeeaaee iiaeaethaaiiy iieaciee?a yeino? aiaee

(o?anoeeaie iicia/ai? aei??yi? cia/aiiy IssA; nooe?eueieie e?i?yie —
cia/aiiy IssA, ia/eneai? ca iiaeaeeth; ai?eciioaeueieie ioieoe?ieie
e?i?yie — a?aie/ii aeiionoei? cia/aiiy iieaciee?a; aa?oeeaeueieie —
i?noey ?icoaooaaiiy aoiae?a;

neiaie «(«aeaco? cia/aiiy IssA, aei??yia a eiio?ieueiiio noai?? AeI).

Aeey oeeo IssA ?ica(ycaii ianooii? caaea/?: ia/eneaii cia/aiiy
iieaciee?a yeino? aiaee a i?noeyo ?icoaooaaiiy i?nueeeo ieyae?a (?en.
2a, a, a); i?iaaaeaii ia?aa??eo aaeaeaaoiino? iiaeae? a eiio?ieueiiio
noai?? (?en. 2a, a, a); i?iaaaeaii a?aeiiaeaiiy aeaieo i?i ye?noue aiae
a ae?eao i?eoie ??/ee (?en. 2a, a, a); aeyaeaii io?oe?eii
iaca?a?no?iaai? aoiaee oa aecia/aii ye?noue aiae, ui iaaeoiaeyoue c ieo
(?en. 2a); cae?eniaii i?iaiicoaaiiy yeino? aiaee ca oiia ?ioeo aeaieo
i?i aoiaee (?en. 2ae). Ia?aa??ea ?acoeueoao?a iiaeaethaaiiy a
eiio?ieueiiio noai?? aeiaaea, ui iiaoaeiaai? iiaeae? ? aeinoaoiuei
aaeaeaaoieie ??/eiaei i?ioeanai, ui iienothoueny (iioeaea noaiiaeoue
iaeeieoe? a?aenioe?a).

Ca oeie ae aenia?eiaioaeueieie aeaieie i?iaaaeaii ii??aiyeueia
iiaeaethaaiiy ca iaoiaeeeaie A.A. Ea?aooaaa oa A.A. O?ieiaa — ?.Ae.
?iaeceeea?a. Ia ?en. 3 oa 4 i?eaaaeaii a?ao?ee cia/aiue iieacieea
«Eiioeaio?aoe?y caaeneeo ?a/iaei» ca oeeie iaoiaeeeaie.

?acoeueoaoe ii??aiyeueiiai iiaeaethaaiiy iieacaee, ui oe? iaea?eueo
iioe?ai? iaoiaeeee aeathoue nooo?ai a?eueoo iiieeeo (aeanyoee, a ?iiae?
e nioi?, a?aenioe?a), i?ae cai?iiiiiaai? aaoi?ii.

?en. 3. Iaoiaeeea A.A. Ea?aooaaa

(E = 11,2 %). ?en. 4. Iaoiaeeea A.A. O?ieiaa —

?.Ae. ?iaeceeea?a (E = 112,1 %).

Aeae?eaii iniiai? neeaaeia? na?aaeiueieaaae?aoe/iiai a?aeoeeaiiy (NEA)
?acoeueoao?a iiaeaethaaiiy a?ae ?o o?aiaeo, ye? iaoiiaeai? iaoi/iinoyie
a cai?? ao?aeieo aeaieo oa ?o ia?iaoe?. Aeey aeayeeo c oeeo neeaaeiaeo
anoaiiaeaii /enaeuei? cia/aiiy, aeey ?ioeo — ?ic?iaeaii ni?aa?aeiioaiiy
oa aeai?eoie ?o ioe?ithaaiiy. Ia/eneaiiy NEA aeey III IIAeE?I?I
iieacaei, ui aiii noaiiaeoue 8,9%, oiaoi ? aeineoue iaeei. A oea
icia/a?, ui oeae iaeao i?ia?ai caaacia/o? aeineoue oi/i? ?acoeueoaoe ? ?
aeioe?eueiei aei aeei?enoaiiy ia i?aeoeoe?.

Aeniiaee

Noeoii?noue iaaaaeaieo o ?iaio? ?acoeueoao?a aeicaiey? aoaeoaaoe
aaeaeaaoi? iaoaiaoe/i? iiaeae? oa i?iaiaeeoe ca ?o aeiiiiiaith
iiaeaethaaiiy aeeiai?ee yeino? ??/eiaeo aiae, ia yeo aieeaathoue ??ci?
i?ioeane caa?oaeiaiiy oa i/euaiiy. Iiaeaeue o?ainoi?iiaaii aei aeaeyaeo,
yeee aeicaiey? aeei?enoiaoaaoe ?? aeey ?ica(ycaiiy a iiaeaeueoiio caaea/
ea?oaaiiy ye?noth ??/eiai? aiaee. Aeey ?aeaioeo?eaoe?? iiaeae? iio??aii
iaioa aeaieo, i?ae aeey a?aeiieo iiaeaeae oaei? ae oi/iino?. ?ic?iaeai?
aeai?eoie aeicaieythoue onoaaoe iaiiaiioo ao?aeieo aeaieo,
a?aeiiaethth/e aeai? i?i aoiaee oa aeyaeyth/e ? ?aeaioeo?eoth/e ?ai?oa
io?oe?eii iaca?a?no?iaai? aoiaee-aeaea?aea no?/ieo aiae. ?ic?iaeaiee
aaoi?ii iaeao i?eeeaaeieo i?ia?ai aeicaiey? aeeiioaaoe iiaeaethaaiiy
yeino? aiaee ia ae?eyioe? ??/ee I?aaeaiiee Aoa, ?icoaoiaai?e a iaaeao
i?noa A?iieoe?, a i?ney iaaieo iiaeeo?eaoe?e — ? aeey aoaeue-yei? ?ioi?
iaei? /e na?aaeiuei? ??aieiii? ??/ee Oe?a?ie.

A aeena?oaoe?ei?e ?iaioe iaea?aeaii oae? iniiai? iaoeia? oa i?aeoe/i?
?acoeueoaoe:

Cai?iiiiiaaii iiaee i?aeo?ae aei ?icaeooy iniiaii? ae?eyiee
iiaeaethaaiiy ia ieceo aeaiaioa?ieo ae?eyiie c ia a?eueo, i?ae c iaeiei
aeaea?aeii caa?oaeiaiiy aeey a?aooaaiiy aeia?eueii? e?eueeino? aeaea?ae
caa?oaeiaiue. Iiaoaeiaaii ocaaaeueiaio iaoaiaoe/io iiaeaeue aeeiai?ee
cia/aiue iieaciee?a yeino? ??/eiai? aiaee c aeei?enoaiiyi oeueiai
i?aeoiaeo.

Iiaoaeiaaii iaoaiaoe/i? iiaeae? ??/eiaeo i?ioean?a ia iniia?
oii?yaeeoaaiiy oeeo i?ioean?a ca i?e/eiii-iane?aeeiaith iciaeith, aeey
/iai ?ic?iaeaii niaoe?aeueiee eean aeeoa?aioe?eieo ??aiyiue. ?ic?iaeai?
iiaeae? aeiaaathoue iaioa ao?aeieo aeaieo, ii??aiyii c a?aeiieie
iiaeaeyie, ye? caaacia/othoue oaeo ae naio oi/i?noue. Iaea?aeai?
iaoaiaoe/i? iiaeae? o?ainoi?iiaaii a i?ino?? noaio iieaciee?a yeino?
??/eiai? aiaee, ui aeicaieeoue canoiniaoaaoe ?o a iiaeaeueoiio aeey
?ica(ycaiiy ??cieo caaea/ ea?oaaiiy oe??th ye?noth.

Iiaoaeiaaii aeai?eoie ?ica(ycaiiy ??aiyiue cai?iiiiiaaieo iiaeaeae oa
aeaaaeaii ? aeiaaaeaii oiiae ?o ca?aeiino? oa ei?aeoiino?. ?ic?iaeaii
aeai?eoie ?aeaioeo?eaoe?? iiaeaeae, iioeiaeueieo ca no?oeoo?ith oa
ia?aiao?aie ca e?eoa???i i?i?ioio noie eaaae?ao?a iioeaie i?ae
aenia?eiaioaeueieie aeaieie oa cia/aiiyie, ia/eneaieie ca iiaeaeeth.

?ic?iaeaii aeai?eoie onoiaiiy iaiiaiioe ao?aeieo aeaieo oa aeai?eoie
?aeaioeo?eaoe?? cai?iiiiiaaieo iiaeaeae ca oeeo oiia. Oaeineiiaeaii
aeai?eoie a?aeiiaeaiiy oa?aeoa?enoee iniiaieo aoiae?a ??/eiai? nenoaie
ca aeaieie, c?a?aieie a nai?e ??/oe?. Cai?iiiiiaaii aeai?eoie
?aeaioeo?eaoe?? io?oe?eii iaca?a?no?iaaieo aoiae?a ??/ee.

Iaienaii iaeao i?eeeaaeieo i?ia?ai aeey i?iaaaeaiiy iiaeaethaaiiy
yeino? ??/eiai? aiaee, aaeaioiaaiee aei ae?eyiee ??/ee I?aaeaiiee Aoa,
?icoaoiaaii? a iaaeao i?noa A?iieoe?. I?ney iaaieo iiaeeo?eaoe?e
?ic?iaeaiee III iiaea aooe aaeaioiaaiee ? aei aoaeue-yei? ?ioi? iaei? /e
na?aaeiuei? ??aieiii? ??/ee Oe?a?ie.

I?iaaaeaii iiaeaethaaiiy aeeiai?ee cia/aiue iieaciee?a yeino? aiaee
ae?eyiee ??/ee I?aaeaiiee Aoa, ?icoaoiaaii? a iaaeao i?noa A?iieoe?:
aeeiiaii a?aeiiaeaiiy aeaieo i?i ye?noue aiae a ae?eao i?eoie ??/ee,
ia/eneaii cia/aiiy iieaciee?a yeino? aiaee a i?noeyo ?icoaooaaiiy
i?nueeeo ieyae?a, i?iaaaeaii ia?aa??eo aaeaeaaoiino? iiaeae? a
eiio?ieueiiio noai??, aeyaeaii io?oe?eii iaca?a?no?iaai? aoiaee oa
aecia/aii ye?noue aiae, ui iaaeoiaeyoue c ieo, cae?eniaii i?iaiicoaaiiy
yeino? aiaee aeey ?ioeo aeaieo i?i aoiaee.

Nienie iioae?eiaaieo i?aoeue ca oaiith aeena?oaoe??.

Iie?i A.A. Ocaaaeueiaia iaoaiaoe/ia iiaeaeue ??/ee a iaaeao aaeeeiai
i?iieneiaiai oeaio?o // A?niee AI?.— 1995.— ? 1.— N. 26—31.

Iie?i A.A. Neioac iiaeae? ??/ee ia iniia? oii?yaeeoaaiiy iniiaieo
i?ioean?a// A?niee AI?.—1997. — ? 2. — N.: 43—48.

Iie?i A.A. Neioac i?inoi?iai-?iciiae?eaii? iiaeae? ??/ee ia iniia?
iiaeae? oii?yaeeoaaiiy iniiaieo i?ioean?a // A?niee AI?.— 1997.— ? 3. —
N.: 52—56.

Iie?i A.A. Iiaoaeiaa aeai?eoio ?ica(ycaiiy ??aiyiue, ye? iiaeaeththoue
aeeiai?eo ci?ie o?i?/ieo oa aaeoa??ieia?/ieo iieaciee?a yeino? ??/eiaeo
aiae // A?niee AI?. —1998.— ? 2.— N. 41—47.

Iie?i A.A. Aei ieoaiiy i?i ca?aei?noue aeai?eoio ?ica’ycaiiy ??aiyiue,
ye? iiaeaeththoue aeeiai?eo o?i?/ieo oa aaeoa??ieia?/ieo iieaciee?a
yeino? ??/eiaeo aiae // A?niee AI?. —1998.— ? 3.— N. 28—35.

Iie?i A.A. Iiaeaeue ??/ee ye ia’?eoa ea?oaaiiy // Ca. oac 3-i?
Iiaeia?iaeii? eiio. «Eiio?ieue ? oi?aaeiiiy a oaoii/ieo nenoaiao»
(EOON-95). — *. 1. — A?iieoey: Oeiia?. OAN. — 1995.— N. 47.

Iie?i A.A. Neioac iaoaiaoe/ii? iiaeaei o i?inoi?i noaio iieacieeia
yeinoi ?i/eiai? aiaee // I?aoe? 4-i? Iiaeia?iaeii? eiio. «Eiio?ieue ?
oi?aaeiiiy a oaoii/ieo nenoaiao» (EOON-97).—O.1.—Aiiieoey:
OIIAA?NOI-Aiiieoey, 1997.—N.168—173.

Iie?i A.?., Iie?i A.A. Iiaee i?aeo?ae aei iiaeaethaaiiy i?ioean?a a
??/eiaeo nenoaiao / O?oaeu Iaaeaeoia?. eiio. “Oeceei-oaoie/aneea e
oaoiieiae/aneea i?eeiaeaiey iaoaiaoe/aneiai iiaeaee?iaaiey”.— E.: CAI
“THaeiieea?aona?aen”, 1998.— N. 172—175.

Mokin V.B. New Models of Processes in a River // 20TH International
Scientific Symposium of Students and Young Research Workers.— Zielona
Gora, Poland, 1998. — Vol.V, Part II: Management.— P. 67—71.

Iie?i A.A. Iiaee i?aeo?ae aei eiii(thoa?iiai iiaeaethaaiiy aeeiai?ee
??/eiaeo i?ioean?a / Ca. oac nai?ia?o «No/ani? i?iaeaie aiaeiiinoa/aiiy
oa ciaca?aaeaiiy no?/ieo aiae». — E.: Ciaiiy, 1998.— N. 15.

AIIOAOe??

Iie?i A.A. Iaoaiaoe/ia iiaeaethaaiiy i?ioean?a caa?oaeiaiiy oa i/euaiiy
??/eiaeo aiae. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa
ia/enethaaeuei? iaoiaee. — A?iieoeueeee aea?aeaaiee oaoi?/iee
oi?aa?neoao, A?iieoey, 1999.

Aeena?oaoe?y i?ena(y/aia ?ic?iaoe? iaoaiaoe/ieo iiaeaeae oa
i?iaaaeaiith ca ?o aeiiiiiaith iiaeaethaaiiy aeeiai?ee yeino? ??/eiaeo
aiae, ia yeo aieeaathoue ??ci? i?ioeane caa?oaeiaiiy oa i/euaiiy.
?ic?iaeaii niaoe?aeueiee eean iiaeaeae, ye? iienothoue i?ioeane a ??/oe?
c oi/ee ci?o ?o aieeao ia ci?io yeino? ??/eiaeo aiae. ?ic?iaeaii
aeai?eoie ?aeaioeo?eaoe?? iioeiaeueii? no?oeoo?e oa ia?aiao??a iiaeaeae
ca oiia iiaiioe oa iaiiaiioe ao?aeieo aeaieo. Cai?iiiiiaaii iaoiaeeee oa
aeai?eoie a?aeiiaeaiiy aoiae?a ??/eiaiai ia(?eoa ye a?aeiieo
cacaeaeaa?aeue, oae ? io?oe?eii iaca?a?no?iaaieo. ?ic?iaeai? iiaeae?
neioaciaaii a i?inoi?? ci?iieo noaio yeino? aiaee, ui aea? ciiao
aeei?enoaoe ?o a iiaeaeueoiio aeey ?ica(ycaiiy caaea/ ea?oaaiiy ye?noth
aiaee. Canoinoaaiiy ia i?aeoeoe? ?ic?iaeaiiai aaoi?ii aeena?oaoe??
iaeaoo i?eeeaaeieo i?ia?ai, a yeiio ao?eai? ?ic?iaeai? aeai?eoie oa
iiaeae?, aeey ?ica(ycaiiy caaea/ ioe?ithaaiiy yeino? aiaee a ??/oe?
I?aaeaiiee Aoa a i?no? A?iieoey aeaei oni?oi? ?acoeueoaoe oa aeiaaei
aeioe?euei?noue eiai aeei?enoaiiy.

Eeth/ia? neiaa: iaoaiaoe/ia iiaeaeue, ??/eia? i?ioeane, iieacieee
yeino? aiaee, iiaeae? aeey i?iaiico ? ea?oaaiiy, ?aeaioeo?eaoe?y
iaca?a?no?iaaieo aoiae?a.

Mokin V.B. Mathematical modelling of processes of pollution and
clearing of river waters. — Manuscript.

Thesis for a candidate’s degree by speciality 01.05.02 — mathematical
modelling and computer methods. — Vinnitsa State Technical University,
Vinnitsa, 1999.

The dissertation is devoted to the elaboration of mathematical models
and conducting with their help of modelling of dynamics of river waters
quality, on which the various processes of pollution and clearing of
waters influence. The special class of models describing the river
processes from point of view of their influence to river waters quality
has been worked up. The algorithms of identification of models optimal
structure and parameters are worked out for a completeness and
incompleteness of entered data. It is offered techniques and algorithms
of restoring of river inputs as known beforehand, and officially
nonregistered. The developed models are synthesized in space of
condition variables of the water quality. It is giving a possibility of
their further use for solving of management problem of the river water
quality. Use in practice developed by the author the package of applied
programs, in which the developed algorithms and models are introduced,
for solving of estimation problems of water quality in the river
Southern Boog in Vinnitsa has given successful outcomes and has proved
expediency of its use.

Key words: mathematical model, river processes, water quality indices,
models for prediction and management, identification of nonregistered
inputs.

Iieei A.A. Iaoaiaoe/aneia iiaeaee?iaaiea i?ioeannia caa?yciaiey e
i/enoee ?a/iuo aiae. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 01.05.02 — iaoaiaoe/aneia iiaeaee?iaaiea e
au/eneeoaeueiua iaoiaeu. — Aeiieoeeee ainoaea?noaaiiue oaoie/aneee
oieaa?neoao, Aeiieoea, 1999.

Aeenna?oaoeey iinayuaia ?ac?aaioea iaoaiaoe/aneeo iiaeaeae e
i?iaaaeaieth n eo iiiiuueth iiaeaee?iaaiey aeeiaieee ea/anoaa ?a/iuo
aiae, ia eioi?ia aeeytho ?acee/iua i?ioeannu caa?yciaiey e i/enoee.

Aeey yoiai i?aaeeiaeaii o/anoie ?aee, i?ioeannu eioi?iai
iiaeaee?othony, ?anniao?eaaoue eae iiiaiia?ioth eeaa?iaoe/aneoth
nenoaio, iniiaiie oa?aeoa?enoeeie ninoiyiey eioi?ie yaeyaony ea/anoai
aiaeu a ?aea, ia aa aoiaeu iinooiatho aiciouaiey a aeaea ?acee/iuo
aio?iiiaaiiuo noi/iuo aiae e i?e?iaeiuo noieia, aeeythuea ia ea/anoai
?a/iie aiaeu, a auoiaeaie nenoaiu yaeythony ianoa aiaeiiieueciaaiey e
aiaeiiio?aaeaiey, ?aniieiaeaiiua ia yoii o/anoea ?aee.

I?aaeeiaeai iiaue iiaeoiae e ?acaeaieth iniiaiiai o/anoea
iiaeaee?iaaiey ia ?yae yeaiaioa?iuo o/anoeia n ia aieaa, /ai iaeiei
enoi/ieeii caa?yciaiey aeey o/aoa i?iecaieueiiai eo eiee/anoaa.
Iino?iaia iaiauaiiay iaoaiaoe/aneay iiaeaeue aeeiaieee cia/aiee
iieacaoaeae ea/anoaa ?a/iie aiaeu n eniieueciaaieai yoiai iiaeoiaea.

Iino?iaiu iaoaiaoe/aneea iiaeaee ?a/iuo i?ioeannia ia iniiaaiee
oii?yaei/aiey yoeo i?ioeannia ii i?e/eiii-neaaenoaaiiiio i?eciaeo, aeey
/aai ?ac?aaioai niaoeeaeueiue eeann aeeooa?aioee-aeueiuo o?aaiaiee.
O?ainoi?iaoeey iiaeaeae n o/aoii iniaaiiinoae aeeiaieee ?a/iiai iioiea
iicaieeea oiaiueoeoue iauai o?aaoaiuo aoiaeiuo aeaiiuo, ii n?aaiaieth n
ecaanoiuie iiaeaeyie, eioi?ua iaania/eaatho oaeoth aea oi/iinoue.
Iieo/aiiua iaoaiaoe/aneea iiaeaee i?aia?aciaaiu a i?ino?ainoai ninoiyiee
iieacaoaeae ea/anoaa ?a/iie aiaeu, iicaieythuaa eniieueciaaoue eo a
aeaeueiaeoai aeey ?aoaiey ?acee/iuo caaea/ oi?aaeaiey yoei ea/anoaii.

Iino?iaiu aeai?eoiu ?aoaiey o?aaiaiee i?aaeeiaeaiiuo iiaeaeae.
Auaaaeaiu e aeieacaiu oneiaey eo noiaeeiinoe e ei??aeoiinoe. ?ac?aaioaiu
aeai?eoiu eaeaioeoeeaoeee iiaeaeae n iioeiaeueiie no?oeoo?ie e
ia?aiao?aie ii e?eoa?eth ieieioia noiiu eaaae?aoia ioeaie iaaeaeo
yenia?eiaioaeueiuie aeaiiuie e cia/aieyie, au/eneaiiuie ii iiaeaee.

I?iaiaeece?iaaia aiciiaeiay iaiieiioa aoiaeiuo aeaiiuo, iaiaoiaeeiuo
aeey eaeaioeoeeaoeee iiaeaeae, eioi?ay iiaeao eiaoue ianoi ia i?aeoeea.
N?aaee aoiaeiuo aeaiiuo auaeaeaiu iniiaiua aeaiiua, aac eioi?uo
eaeaioeoeeaoeey iiaeaeae iaaiciiaeia a i?eioeeia, e aeiiieieoaeueiua
aeaiiua, aac eioi?uo eaeaioeoeeaoeey iiaeaeae aiciiaeia, oioy e n
iaiueoae oi/iinoueth. ?ac?aaioaiu aeai?eoiu ono?aiaiey iaiieiiou
aoiaeiuo aeaiiuo ca n/ao aeiiieieoaeueiie eioi?iaoeee. Aeey neo/ay
iaono?aieiie iaiieiiou aoiaeiuo aeaiiuo ?ac?aaioaiu niaoeeaeueiua
aeai?eoiu eaeaioeoeeaoeee i?aaeeiaeaiiuo iiaeaeae ii aeaiiui eiathueiny.
Iino?iaiu aeai?eoiu ainnoaiiaeaiey oa?aeoa?enoee iniiaiuo aoiaeia ?a/iie
nenoaiu ii aeaiiui, nia?aiiui a naiie ?a/ea.

I?aaeeiaeaiu aeai?eoiu eaeaioeoeeaoeee ioeoeeaeueii
iaca?aaeno?e?iaaiiuo aoiaeia ?aee, iicaieythuea eeai ii i?aaeiieaaaaiui
i?ino?ainoaaiiui eii?aeeiaoai e ?anoiaeo aiaeu, iinooiathuae ni aoiaeia,
ii?aaeaeyoue ea/anoai yoie aiaeu, eeai ii?aaeaeyoue iaeiia?aiaiii e
i?ino?ainoaaiiua eii?aeeiaou aoiaeia, e ea/anoai aiae ii
i?aaeiieaaaaiiio ?anoiaeo eee ?anoiae aiae ii i?aaeiieaaaaiiio ea/anoao.

?ac?aaioaiiue aaoi?ii aeenna?oaoeee iaeao i?eeeaaeiuo i?ia?aii
iicaieyao iiaeaee?iaaoue ea/anoai aiaeu ia o/anoea ?aee THaeiue Aoa,
?aniieiaeaiiii a i?aaeaeao ai?iaea Aeiieoeu, a iinea aaeaioaoeee — e
aeey ethaie ae?oaie iaeie eee n?aaeiae ?aaieiiie ?aee Oe?aeiu. Iaeao
i?ia?ai iicaieyao ?aoaoue oaeea caaea/e: au/eneaiea cia/aiee iieacaoaeae
ea/anoaa aiaeu eae a noai?ao aiaeiiieueciaaiey e aiaeiiio?aaeaiey, oae e
a ethauo ae?oaeo noai?ao a i?aaeaeao o/anoea ?aee, i?ioeannu eioi?iai
iiaeaee?othony; ainnoaiiaeaiea aeaiiuo i ea/anoaa aiae, iinooiathuae ni
aoiaeia ?a/iie nenoaiu; auyaeaiea ioeoeeaeueii iaca?aaeno?e?iaaiiuo
aoiaeia e ii?aaeaeaiea ia?aiao?ia aiae, iinooiathueo ec ieo;
i?iaiice?iaaiea ea/anoaa aiaeu a ?aea.

N?aaiaiea iieo/aiiuo ?acoeueoaoia n ?acoeueoaoaie iiaeaee?iaaiey
ea/anoaa aiaeu ia o/anoea ?aee THaeiue Aoa, ?aniieiaeaiiii a i?aaeaeao
ai?iaea Aeiieoeu, i?e iiiiue ecaanoiuo iiaeaeae e aeai?eoiia iieacaei,
/oi ?ac?aaioaiiua a aeenna?oaoeee iiaeaee e aeai?eoiu aeatho nouanoaaiii
eo/oea ?acoeueoaou, /ai nouanoaothuea.

Eeth/aaua neiaa: iaoaiaoe/aneay iiaeaeue, ?a/iua i?ioeannu, iieacaoaee
ea/anoaa aiaeu, iiaeaee aeey i?iaiica e oi?aaeaiey, eaeaioeoeeaoeey
iaca?aaeno?e?iaaiiuo aoiaeia.

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