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

?INOEOOO I?IAEAI IAOEIIAOAeOAAIIss

?i. A.I. I?aeai?iiai

Oii?oea Ieaa Aieiaeeie?iae/

OAeE 518.5

IIAeAETHAAIIss O?CE*IEO IIE?A IAOIAeAIE

OAI??? R-OOIEOe?E OA IA*?OEI? EIA?EE

01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o a?aeae?e? i?eeeaaeii? iaoaiaoeee oa ia/enethaaeueieo

iaoiae?a ?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI
Oe?a?ie

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

i?ioani? Oaa/aiei Ieaenaiae? Ieeieaeiae/,

?inoeooo i?iaeai iaoeiiaoaeoaaiiy

?i. A.I. I?aeai?iiai IAI Oe?a?ie,

aieiaiee iaoeiaee ni?a?ia?oiee .

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

i?ioani? sseiae?a Na?a?e Anaaieiaeiae/,

Oi?aa?neoao aioo??oi?o ni?aa IAN Oe?a?ie,

ia/aeueiee oaeoeueoaoo oi?aae?iiy oa ?ioi?iaoeee

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

Eooeaiei Eaii?ae Ieeieaeiae/,

Oa?e?anueeee ?inoeooo iiaeaaeii? aaciaee IAN Oe?a?ie,

i?ioani? eaoaae?e iiaeaaeii? oaoi?ee

I?ia?aeia i?aai?caoe?y: ?inoeooo e?aa?iaoeee ?i. A.I. Aeooeiaa IAI
Oe?a?ie, a?aeae?e i?eeeaaeii? iaoaiaoeee, i. Ee?a

Caoeno a?aeaoaeaoueny « 24 » 06 1999 ?. i 14 aiaeei? a
aoaeeoi???

O? iiaa?oo ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.180.01 a
?inoeooo? i?iaeai iaoeiiaoaeoaaiiy ?i. A.I.I?aeai?iiai IAI Oe?a?ie
(310046, i.Oa?e?a, aoe.Aei.Iiaea?nueeiai, 2/10).

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? ?inoeoooo i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith: 310046,
i. Oa?e?a, aoe. Aei. Iiaea?nueeiai, 2/10

Aaoi?aoa?ao ?ic?neaiee « 20 » 05 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Caeoeaa A.I.

Caaaeueia oa?aeoa?enoeea ?iaioe

Aeooaeuei?noue oaie. I?e noai?aii? nenoai aeine?aeaeaiiy caaea/
?ic?aooieo o?ce/ieo iie?a aaaeeeai a?aoiaoaaoe oaoi?/i? oa oaoiieia?/i?
aeiionee ia aaiiao?e/io oa o?ce/io ?ioi?iaoe?th, iia??oiino? aei??o
o?ce/ieo aaee/ei oa iioeaee ie?oaeaiiy. O ca’yceo c oeei aeieea?
iaiao?aei?noue ?icaeoeo nenoai ?ic?aooieo iie?a c iaoith io?eiaiiy
aeiione?a ia ?ica’ycie oa iiaeaeueoiai aenia?oiiai aeniiaeo.

A aeaiee /an aaoiiaoecaoe?y i?ia?aioaaiiy a aaeoc? iaoaiaoe/ii? o?ceee
aeinyaea cia/iiai i?ia?ano. Aoaeoeai?noue i?iaeaiii-i???ioiaaieo iia oa
niaoe?ae?ciaaieo nenoai iieyaa? a nei?i/aii? /ano ae??oaiiy aaaaoueio
iaoeiai-oaoi?/ieo caaea/, a oaeiae noai?aii? aace aeey ia?aoiaeo aei
?iaeono??aeueieo iaoiae?a oa iiai? oaoiieia?? i?ia?aioaaiiy. Oae? iiae
oa nenoaie ? ?ino?oiaioaeueiith aacith aeey i?iaaaeaiiy ia/enethaaeueieo
aenia?eiaio?a, ui ca?eueiythoue iaoaiaoee?a oa ?iaeaia??a a?ae ?ooeiii?
?iaioe ii noai?aiith oa iaeaaiaeaeaiith a?ii?caeeeo i?ia?ai. Aeey
i?iaaaeaiiy ia/enethaaeueieo aenia?eiaio?a a aaeoc? iaoaiaoe/ii? o?ceee
a aaaaoueio aeiaaeeao iaiao?aeii na?eicia oa aeeaiea aea/aiiy i?ioeano
/e yaeua, ui iiaeaeth?oueny, i?ciaiiy caeii?a i?e?iaee oa ?o i?iya?a o
neeaaei?e aca?iiae??. Ie??i oiai, i?e ae??oaii? caaea/ iaoaiaoe/ii?
o?ceee iaiao?aeii a?aoiaoaaoe ieoaiiy ca?aeiino?, no?eeino?
ia/enethaaeueiiai i?ioeano, oi/iino? ia/eneaiue, aoaeoeaiino? iaoiae?a,
ui canoiniaothoueny ? o. ?i. Oe? ianoaaeie noai?ththoue aeiaeaoeia?
o?oaeiiu? i?e ?ic?iaoe? iaoaiaoe/iiai caaacia/aiiy aeey ae??oaiiy
e?aeiaeo caaea/. A?o/eciyieie oa caei?aeiiieie aeine?aeieeaie ?ic?iaeaii
aaeeeo e?euee?noue i?eeeaaeieo nenoai i?ia?aioaaiiy, iaeao?a i?eeeaaeieo
i?ia?ai, ui iathoue i?iaeaiii-i???ioiaai? iiae oa aeei?enoiaothoueny
aeey aeine?aeaeaiiy caaea/ c ??cieo i?eeeaaeieo iaeanoae.

Noai?aiiy i?iaeaiii-i???ioiaaieo iia oa niaoe?ae?ciaaieo nenoai
iiaeeeai a oiio aeiaaeeo, yeui aeey eiie?aoii? i?eeeaaeii? iaeano?
?ic?iaeaiee oi?aa?naeueiee iaoaiaoe/iee aia?ao, yeee aeicaiey?
aeinoaoiuei aoaeoeaii iienoaaoe aeai?eoi?/i? i?ioeane c o?aooaaiiyi
an??? ?ioi?iaoe?? i?i caaea/o, ui ?ica’yco?oueny. Oaeei iaoaiaoe/iei
aia?aoii aeey ae??oaiiy e?aeiaeo caaea/ iaoaiaoe/ii? o?ceee ? oai??y
R-ooieoe?e (i?aeia?iaeia aa?aa?aoo?a RFM — R-functions
method), iaoiaee oa caniae yei? ?icoe?ththoue iiaeeeaino? aa??aoe?eieo
oa i?iaeoe?eieo iaoiae?a ii ?ica’yceo e?aeiaeo caaea/ a iaeanoyo
neeaaeii? oi?ie.

?acoeueoaoe, ui io?eiai? a aaeoc? aeiaeaoe?a oe??? oai???, aeicaieeee
noai?eoe eiiieaen i?ia?aiieo oa iiaieo cania?a aeey aaoiiaoecaoe??
iaoeiaeo aeine?aeaeaiue a iaoaiaoe/i?e o?ceoe?. Oea niaoe?ae?ciaai?
nenoaie na??? «Iiea», ui noai?ai? aeey ae??oaiiy e?aeiaeo caaea/, ye?
noi?ioeueiaai? aeey ??aiyiue c /anoeiieie iio?aeieie i?e aeia?eueieo
e?aeiaeo oiiaao oa neeaaeii? aaiiao??? iaeano?, ui aeine?aeaeo?oueny.
Nenoaie na??? «Iiea» ? a?aee?eoeie nenoaiaie, ye? iino?eii
aeiiiaiththoueny iiaeie i?ia?aiieie iiaeoeyie ??ciiai i?ecia/aiiy. Oe?
nenoaie ciaoiaeyoueny o iino?eiiio ?icaeoeo.

No/ani? oaiaeaioe?? ?icaeoeo i?eeeaaeieo i?ia?aiieo nenoai iia’ycai? c
i?aeaeuaiiyi ??aiy ?o ?ioaa?iaaiino?, ?ioaeaeooaeueiino? oa aeinooiiino?
aeey ei?enooaa/?a, ye? ? niaoe?ae?noaie a i?iaeaiieo iaeanoyo ae??oaiiy
oeo /e ?ioeo eean?a caaea/. I?iaeaia noai?aiiy oaeeo nenoai ? aaaeeeaith
iaoeiaith i?iaeaiith, a aeine?aeaeaiiy a oe?e aaeoc? — aeooaeueieie oa
ia?niaeoeaieie.

Aaaiiee aianie a ?icaeoie oeueiai iai?yieo aeine?aeaeaiue a aaeoc?
iaoaiaoe/ii? o?ceee aianee a?o/eciyi? a/ai? — A.I. Aeooeia, A.I. ?e’?i,
A.ss. Ea?iia, A.N. Ieoaeaae/, A.N. Iini?eia, A.E. ?aa/ia, A.A.
Naia?nueeee, E.A. Na?a??iei, A.A. Neiiaoeueeee, TH.A. Noiyi, E.E.
THuaiei, I.I. ssiaiei, ?.I. Iie/aiia, A.I. Iaiueei, E.A. Eo?ia, O.?.
Oaeei,I.I. Oaa/aiei, I.N. Nei?eii oa ?io?. Iaeiei c aaaeeeaeo aniaeo?a
oeeo aeine?aeaeaiue ? aaoiiaoecaoe?y ae??oaiiy e?aeiaeo caaea/, ye?
iia’ycai? c ?ic?aooieii aca?iiae?th/eo o?ceei-iaoai?/ieo iie?a ??cii?
i?e?iaee.

Aeooaeueiei ? noai?aiiy iiaeo oaoiieia?e, ye? iiaeooue iai?ioethaaoe
neeaaeieie, aaaaoioaeoi?ieie oa noioanoe/ieie ia’?eoaie, i?aeo?eioaaoe
neeaaei? aca?iica’ycee i?ae aeaieie, aeeiioaaoe ei?aeooth/? ae?? a
oiiaao iaaecia/aiino? oa ?iaeoe aeniiaee i?e iaaeinoa/? ?ioi?iaoe??.
?ioeie neiaaie, iaiao?aei? ?ioi?iaoe?ei? oaoiieia?? c aeaiaioaie
ooo/iiai ?ioaeaeoo. Ia/enethaaiiy a nenoaiao ?ic?aooieo iie?a, ye
i?aaeei, iathoue aeaoa?i?iiaaiee oa?aeoa?, a oei /anii ?aaeuei? i?ioeane
o iaai?e i??? ? noioanoe/ieie, i?noyoue a nia? aeayeo ia/?oe?noue. Aeey
oiai, uia a?aooaaoe oeth ia/?oe?noue, aeioe?eueii oae ia?aoai?eoe
?nioth/o noaio aeine?aeaeaiiy o?ce/ieo iie?a, uia a ?acoeueoao?
aaaaoiaa??aioiiai ia/eneaiiy io?eiaoe a?eueo oi/iee «ia/?oeee»
?ica’ycie, yeee aoaea aeeae/a aei ?aaeueiino?. Iio??aii aaanoe a noaio
ae??oaiiy o?aooaaiiy aeiione?a, oiaoi aeaea?ae ia/?oeino?, ui iaea?eueo
neeueii aieeaathoue ia ?acoeueooth/ee ?ica’ycie. I?aeoeea na?ae/eoue, ui
oaeeo aeaea?ae, ye i?aaeei, o?e: aeiionee iiaeae? (ia aaiiao?e/i? oa
o?ce/i? oa?aeoa?enoeee), iiieeee iaoiaeo (c??caiiy ?yaeo, iiieeee
e?iaa??caoe??) oa iiieeee ie?oaeaiiy. Iaiao?aeii anoaiiaeoe aieea ia
??oaiiy aa??thaaiiy oeeo aaee/ei a iaaeao aeiione?a oa aeine?aeeoe
iiaeeeaino? iiaoaeiae aeiione?a ia ?ica’ycie. O ca’yceo c oeei cia/iee
?ioa?an i?aaenoaaey? ?ic?iaea nenoai aeine?aeaeaiiy o?ceei-iaoai?/ieo
iie?a, ui i???ioiaai? ia aaaaoiaa??aioia ae??oaiiy e?aeiaeo caaea/ c
iaoith a?aooaaiiy aa??thaaiiy aaee/ei, ui ?icaeyaeathoueny, a iaaeao
caaeaieo aeiione?a.

Aeine?aeaeaiith oaeeo i?iaeai iaoiaeaie ?ioa?aaeueii? iaoaiaoeee a
aaeoc? aaiiao?e/iiai i?iaeooaaiiy i?enay/ai? oai??y ?ioa?aaeueii?
aaiiao??? TH.A. Noiyia oa iaoeia? ?ic?iaee eiai o/i?a I.I. ?ioey, O.?.
?iiaiiai? oa ?ioeo.

A aeai?e aeena?oaoe?ei?e ?iaio? i?iiiiothoueny eiino?oeoeai? iaoiaee oa
aeai?eoie iiaeaethaaiiy o?ce/ieo iie?a iaoiaeaie oai??? R-ooieoe?e oa
ia/?oei? eia?ee c a?aooaaiiyi aeiione?a ia aaiiao?e/io oa o?ce/io
?ioi?iaoe?th, a oaeiae iiieeie ie?oaeaiiy.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie a?oioo?oueny ia
oiio, ui aeena?oaoe?ei? aeine?aeaeaiiy aaoi? aeeiioaaa o 1994-1999 ??.
o a?aeae?e? i?eeeaaeii? iaoaiaoeee oa ia/enethaaeueieo iaoiae?a
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy IAI Oe?a?ie a?aeiia?aeii aei

— aea?aeathaeaeaoii? oaie ?185 A.?.?0194E0353430 IAI Oe?a?ie
«Aeniei?ioaeaeooaeuei? nenoaie i?ia?aioaaiiy, i???ioiaai? ia
aeei?enoaiiy aeaaa?a?ciaaieo no?oeoo?ieo oi?ioe ?ica’ycaiiy e?aeiaeo
caaea/» (1994-1997 ??.);

— aea?aeathoaeaoii? oaie ? 1 A.?. ?0198E0054125 IAI Oe?a?ie
«?icaeoie oai??? R-ooieoe?e /RFM/, iioe?aiiy ?? i?aaeiaoii? iaeano?,
oaeineiiaeaiiy eiino?oeoeaieo oa i?ia?aiieo cania?a» (1998-2001 ??.);

— a?aioo 1.4/162 I?i?noa?noaa o ni?aaao iaoee oa oaoiieia?e «?ic?iaea
iiaeo iaoiae?a iaoaiaoe/iiai iiaeaethaaiiy caaea/ iaoai?ee nooe?eueieo
na?aaeiaeu ia iniia? oai??? R-ooieoe?e oa iaa?o?iaaeiaeo /eneaiue»
(1998-2001 ??.).

Iaoith ?iaioe ? noai?aiiy ia iniia? ooiaeaiaioaeueieo ?acoeueoao?a
oai??? R-ooieoe?e oa ia/?oei? eia?ee iaoiae?a iiaeaethaaiiy ?aaeueieo
o?ceei-iaoai?/ieo iie?a, ui a?aoiaothoue aeiionee oa iioeaee aei???a, a
oaeiae aoaeoeaieo ia/enethaaeueieo aeai?eoi?a aeey ?o ?aae?caoe?? oa
aeine?aeaeaiiy ?icia?aeaethaaiiy ia/enethaaeueiiai i?ioeano.

Aeey aeinyaiaiiy iaoe aeena?oaoe?? aoei iinoaaeaii caaea/?: aeine?aeeoe
ca’ycie oai??? R-ooieoe?e oa ia/?oei? eia?ee; ?ic?iaeoe iaoiaee
aiae?oe/iiai iiaeaethaaiiy ia/?oeeo aaiiao?e/ieo ia’?eo?a o
aeaiaei??iiio i?inoi??; aeine?aeeoe aeaea?aea ia/?oeino? a ?aaeueieo
caaea/ao iiaeaethaaiiy iie?a oa ?o noioanoe/i? oa?aeoa?enoeee; noai?eoe
no?oeoo?i? iiaeae? o?ce/ieo iie?a c o?aooaaiiyi ia/?oeino? aaiiao?e/ieo
oa o?ce/ieo aeaieo oa aeai?eoie ?aae?caoe??; aeine?aeeoe oa
?aoe?iiaeueii aeei?enoaoe aeaiaioe ?ioa?aaeueiiai aiae?co aeey
o?aooaaiiy iiieeie ie?oaeaiiy.

Iaoiaee aeine?aeaeaiiy. Iaoiaeieia?/iith iniiaith ? oai??y R-ooieoe?e,
yea i???ioiaaia ia ?icoe?aiiy iiaeeeainoae aa??aoe?eieo oa ?ioeo
iaoiae?a ae??oaiiy e?aeiaeo caaea/ iaoaiaoe/ii? o?ceee; ia/?oea eia?ea,
yea aea? iiaeeea?noue ia?aeoe a?ae ?aeaae?ciaaiiai aeaoa?i?iiaaiiai
iiaeaethaaiiy aei a?eueo ?aaeueiiai noioanoe/iiai iiaeaethaaiiy o?ce/ieo
iie?a; ?ioa?aaeueiee aiae?c, ui aeicaiey? a?aoiaoaaoe iiieeee
ie?oaeaiiy; aeaaa?a aeeoa?aioe?eieo ei?oaae?a, yea eaaeeoue a iniia?
oi?iae?caoe?? ia/enethaaeueieo i?ioean?a ?ica’ycaiiy e?aeiaeo caaea/;
oai??y ia?aeaeueieo nenoai; no/ani? ?aea? oa oaoiieia?? i?ia?aioaaiiy.

Iaoeiaa iiaecia ?acoeueoao?a aeena?oaoe??, ye? aeianai? ia caoeno,
iieyaa? a ?ic?iaoe? ia iniia? oai??? R-ooieoe?e oa ia/?oei? eia?ee
iaoiae?a oa aeai?eoi?a iiaeaethaaiiy o?ceei-iaoai?/ieo iie?a, ye?
a?aoiaothoue oaoi?/i? aeiionee, iioeaee aei???a oa iiieeee ie?oaeaiiy,
oa ia iniia? ?o aiae?co aeicaiey? c?iaeoe aenia?oiee aeniiaie i?i
i?eeiyoi?noue ciaeaeaiiai ??oaiiy.

Cie?aia, iiaeciith oa?aeoa?ecothoueny oae? ?ic?iaee:

Aeine?aeaeaii ca’ycie oai??? R-ooieoe?e oa ia/?oei? eia?ee. Aeiaaaeaii,
ui i?e

oa iiiaeeia oiiaieo R-ooieoe?e ? ooieoe?iiaeueii caieiaiith. A
caieiai?e iiiaeei? oiiaieo R[0,1]-ooieoe?e aeine?aeaeai? ieoaiiy
ooieoe?iiaeueii? iiaiioe, iiaoaeiae ae?ac?a oa ?o oioiaeieo
ia?aoai?aiue.

Ia iniia? ?acoeueoao?a aeine?aeaeaiue a oai??? R-ooieoe?e oa ia/?oe?e
eia?oe? ?ic?iaeai? iaoiaee oa aeai?eoie iiaeaethaaiiy ia/?oeeo iaeanoae
neeaaeii? oi?ie.

3. ?ic?iaeai? ia/?oe? iiaeae? iiey oa no?oeoo?e ia/?oeeo
(?ioa?aaeueieo) ?ica’yce?a, cai?iiiiiaaia iaoiaeeea ?o ?aae?caoe??.
Iieacaii, ui ?aae?caoe?y no?oeoo?e ia/?oeiai ?ica’yceo aeey iiaeae?
iiey c ia/?oeeie e?aeiaeie oiiaaie caiaeeoueny aei nenoaie e?i?eieo
??aiyiue c k i?aaeie /anoeiaie , a aeey iiaeae? iiey c ia/?oeith
iaeanoth ?iciaaea?oueny ia k ??cieo nenoai e?i?eieo ??aiyiue.

4. Aeey i?aeaeuaiiy oi/iino? oa ocaiaeaeaiino? iaeiie/aii? oa
iaoiaee/ii? iia??oiino? c iaoith caa??aaiiy ii?iaeueiiai caeiio
?iciiae?eo aeey ia/?oeiai ?ica’yceo cai?iiiiiaaii aeei?enoiaoaaoe
caniae ?ioa?aaeueiiai aiae?co. Eiino?oeoeaii canoiniaaia iaoiaeeea
ioe?iee iioeaie ie?oaeaiiy c aaoiiaoe/iei aeeoa?aioe?thaaiiyi a
?ioa?aaeueieo iaoiaeao. ?ic?iaeaii ?ioa?aaeuei? ia/enethaa/? aeey
iia?aoe?e aeaaa?e aeeoa?aioe?eieo ei?oaae?a.

5. Aeine?aeaeaii caaea/? ?icia?aeaethaaiiy noaie ?aae?caoe??
cai?iiiiiaaii? iaoiaeeee iiaeaethaaiiy.

I?aeoe/ia oe?ii?noue oa ?aae?caoe?y ?acoeueoao?a ?iaioe iieyaa? a
?ic?iaoe? oa i?aeoe/iiio aeine?aeaeaii? iaoiae?a oa aeai?eoi?a
iiaeaethaaiiy o?ce/ieo iie?a, ui eiino?oeoeaii a?aoiaothoue aeiionee ia
o?ce/io oa aaiiao?e/io ?ioi?iaoe?th ? iiaeooue aeei?enoiaoaaoenue aeey
oe?ieiai eeano aeine?aeieoeueeeo oa i?iaeoieo caaea/. ?acoeueoaoe
iiaeooue aooe canoiniaai? a aenia?oieo nenoaiao, nenoaiao aaoiiaoecaoe??
iaoeiaeo aeine?aeaeaiue i?e ?ica’yceo caaea/ a oiiaao ai??i?ii?
iaaecia/aiino?, aaoiiaoecaoe?? i?iaeooaaiiy.

?ic?iaee neeaaeathoue iniiao aeey ?icaeoeo nenoai na??? «Iiea» c
i?aaeiaoiith

iaeanoth, ui aeeth/a? noioanoe/ia iiaeaethaaiiy. ?acoeueoaoe ?iaioe
ai?iaaaeaeai? o a?aeae?e? i?eeeaaeii? iaoaiaoeee oa ia/enethaaeueieo
iaoiae?a ?IIao ?i. A.I. I?aeai?iiai IAI Oe?a?ie i?e aeeiiaii?
aea?aeathoaeaoii? oaie «Aeniei?ioaeaeooaeuei? nenoaie i?ia?aioaaiiy,
i???ioiaai? ia aeei?enoaiiy aeaaa?a?ciaaieo no?oeoo?ieo oi?ioe
?ica’ycaiiy e?aeiaeo caaea/».

Ioae?eaoe??. Ca oaiith aeena?oaoe?? iioae?eiaai? 19 ae?oeiaaieo i?aoeue:
6 noaoae

(c ieo 3 — o ca??ieeao iaoeiaeo i?aoeue, 3 — aeaiiiiaai? o A?I?O?), 5
oac aeiiia?aeae a i?aoeyo i?aeia?iaeieo iaoeiaeo eiioa?aioe?e oa 8
?ioi?iaoe?eieo eenoe?a OI?IIOA? i?e I?i?noa?noa? Oe?a?ie o ni?aaao iaoee
oa oaoiieia?e.

Iniaenoee aianie caeiaoaa/a a ?iaioe, iioae?eiaai? o ni?aaaoi?noa?. A
on?o cacia/aieo ioae?eaoe?yo aaoi? i?eeiaa o/anoue o ?ic?iaoe?
oai?aoe/ieo iieiaeaiue, aeai?eoi?a oa ?o ?aae?caoe?? ia IAII. E??i oiai,
aaoi?o iaeaaeaoue: a ?iaioao [1,4,9,10,13] — iaoiaee oa aeai?eoie
iiaeaethaaiiy ?aaeueieo o?ce/ieo iie?a, ui a?aoiaothoue noioanoe/iee
oa?aeoa? oaoiieia?/ieo aeiione?a aeey aaiiao?e/ii? oa o?ce/ii?
?ioi?iaoe??, a [2] — iaoiaee iiaeaethaaiiy aaiiao?e/ieo ia’?eo?a ?c
aeei?enoaiiyi oai??? R-ooieoe?e oa ia/?oei? eia?ee; a [7] — ?ic?iaea
?ioa?aaeueieo ia/enethaa/?a a na?aaeiaeu? «Iiea»; o ?iaioao [3, 6, 17] —
aeine?aeaeaiiy oeyo?a oaeineiiaeaiiy niaoe?ae?ciaaieo nenoai aiae?co
o?ceei-iaoai?/ieo iie?a.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?? aeiiia?aeaeenue oa
iaaiai?thaaeenue ia Anaoe?a?inuee?e i?aeia?iaei?e eiioa?aioe?? «?ic?iaea
oa canoinoaaiiy iaoaiaoe/ieo iaoiae?a a iaoeiai-i?aeoe/ieo
aeine?aeaeaiiyo», i?enay/ai?e 70-??//th a?ae aeiy ia?iaeaeaiiy i?ioani?a
I.N. Eacei??nueeiai (i. Euea?a, 1995?.); I?aeia?iaei?e eiioa?aioe??
«Oai??y ? oaoi?ea ia?aaea/?, i?eeiaiiy oa ia?iaee ?ioi?iaoe??» (i.
Ooaina, 1995,1996??.); I?aeia?iaei?e eiioa?aioe?? «Parallel simulation
of complex systems and large-scale application» (i. Aeaeoo,
I?aea?eaiaee, 1996?.); I?aeia?iaei?e eiioa?aioe?? «Iaoaiaoe/i? iiaeae?
oa /enaeuei? iaoiaee iaoai?ee nooe?eueieo na?aaeiaeu» (i. Iiainea??nuee,
1996?.) oa ia XIV I?aeia?iaei?e eiioa?aioe?? c ?ioa?aaeueii? iaoaiaoeee
(i. Iiainea??nuee, 1998?.).

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny c anooio,
/ioe?ueio aeaa, aeniiae?a, nieneo aeei?enoaieo aeaea?ae ?c 121
iaeiaioaaiiy, 22 iaethie?a, 4 oaaeeoeue, 123 noi??iie ae?oeiaaiiai
oaenoo. Onueiai 131 noi??iea.

Ci?no ?iaioe

O ANOOI? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe??, noi?ioeueiaaii
iaoo ? caaea/? ?iaioe, ?? iaoeiao iiaecio oa i?aeoe/io oe?ii?noue, ?
iiaeaia ?? caaaeueia oa?aeoa?enoeea.

IA?OA AEAAA i?enay/aia iaa?oiooaaiith ?ic?iaee iaoiae?a iiaeaethaaiiy
o?ceei-iaoai?/ieo iie?a c a?aooaaiiyi oaoiieia?/ieo aeiione?a, iioeaie
aei???a oa iiieeie ie?oaeaiiy. Iienai? iniiai? iai?yiee ?ic?iaee
iaoiae?a oa aeai?eoi?a iiaeaethaaiiy. A iniiao ?ic?iaee iieeaaeai? ?aea?
oai??? R-ooieoe?e, yea aeicaiey? ae??ooaaoe e?aeia? caaea/? iaoaiaoe/ii?
o?ceee a iaeanoyo neeaaeii? eiio?ao?aoe??, ia/?oei? eia?ee, ui aeicaiey?
iiaeaethaaoe ia/?oe? ?ica’ycee.

Iaaaaeai? iaiao?aei? aeey oai?aoe/ieo ?ic?iaie a?aeiiino? c oai???
R-ooieoe?e oa no?oeoo?ieo iaoiae?a, eio?? noinothoueny iiaeaethaaiiy
aaiiao?e/ieo ia’?eo?a oa iiaoaeoaaiiy iaaeeaeaieo ??oaiue (no?oeoo?
??oaiue) e?aeiaeo caaea/. ?icaeyiooi aa??aoe?ei? iaoiaee, ui
aeei?enoiaothoueny. Aeeiiaii aiae?c no/anieo cania?a ia/?oei? eia?ee
a?aeiia?aeii aei iinoaaeaieo caaea/.

Aeine?aeaeai? iniiai? iai?yiee ?aae?caoe?? i?aeoiae?a, ui
aeine?aeaeothoueny, ca aeiiiiiaith eiino?oeoeaieo iaoiae?a
?ioa?aaeueiiai aiae?co oa ia?aeaeueieo ia/eneaiue.

A Ae?OA?E AEAA? iaaiaeeoueny iien iaoiae?a a?aooaaiiy aeiione?a i?e
iiaeaethaaii? o?ce/ieo iie?a, iaoiaeeee iiaeaethaaiiy iaoiaeaie oai???
R-ooieoe?e oa ia/?oei? eia?ee oa aeai?eoi?a ia/enethaaiiy ooieoe??
iaeaaeiino?. Cai?iiiiiaai? i?aeoiaee aei iieno ia’?eo?a a eean? ooieoe?e
ia/?oei? eia?ee oa R-ooieoe?e, iiaoaeoaaiiy ia/?oeiai ?ica’yceo caaea/?,
ia/enethaaiiy ooieoe?? iaeaaeiino? iioi/iiai ??oaiiy, oa io?eiaiiy ia ??
iniia? aenia?oiiai aeniiaeo i?i i?eeiyoi?noue ciaeaeaiiai ??oaiiy.

Aeey ?ethno?aoe?? ia/?oeino? ?aaeueii? caaea/? iiaeaethaaiiy ?icaeyiaii
caaea/o Ae???oea aeey aeeoa?aioe?aeueiiai ??aiyiiy caaaeueiiai aeaeyaeo.
I?eionoeii, caaeaia iaeanoue D oa e?aeia? oiiae c a?aooaaiiyi aeiione?a:

Ci?ithth/e aeiionee ia aaiiao??th oa e?aeia? oiiae a caaeaieo iaaeao,
io?eio?ii aeiionee ia ?ica’ycie U, yeei iiaeiai caaeia?eueiyoe
?ica’ycie ?aaeueii? e?aeiai? caaea/?.

Iaoiaeeea iiaeaethaaiiy, ui cai?iiiiiaaia, aeey caaea/? aiae?co
neeaaea?oueny c oaeeo aoai?a:

iiaoaeoaaiiy iiaeae?, ui a?aoiao? ?icieo?noue;

iiaoaeoaaiiy ia/?oeiai aiae?oe/iiai iieno iaeano? D ca aeiiiiiaith
iaoiae?a oai??? R-ooieoe?e oa ia/?oei? eia?ee;

aaia?oaaiiy aea??ee iioi/ieo ia’?eo?a ca aeiiiiiaith aa??aoe?? o?ce/ieo
aaee/ei a iaaeao aeiione?a ia e?aeia? oiiae;

?ica’ycie e?aeiai? caaea/? aeey eiaeiiai aeaiaioa aea??ee;

oi?ioaaiiy ?ioa?aae?a c iiaeeeaeo ?ica’yce?a e?aeiai? caaea/?
(oi?ioaaiiy aeiione?a ia ?ica’ycie);

iiaoaeoaaiiy iiaeae? iioi/ii? e?aeiai? caaea/?;

ia/eneaiiy ooieoe?? iaeaaeiino? aeey iioi/ii? iaeano? a?aeiinii
aoaeiiii?;

?ica’ycaiiy iioi/ii? caaea/? oa aenia?oiee aeniiaie i?i i?eeiyoi?noue
ciaeaeaiiai ?ica’yceo.

. Aeiiiaieii nenoaio oioiaeiinoae ia/?oei? eia?ee ocaaaeueiaieie
caeiiaie aeeeth/aiiy o?aoueiai oa noia?a/iino?

? oeaio? iiiaeeie [0,1].

Oiae? aoaeooue iaoe i?noea oaa?aeaeaiiy.

Oaa?aeaeaiiy 1. Ooieoe?? ia/?oei? eia?ee ? oiiaieie R-ooieoe?yie ia
a?ae??ceo [0,1], ui aecia/athoueny iiae?eaiiyi:

a o?ueiocia/iiio oa aeaicia/iiio aeiaaeeao a?aeiia?aeii.

Oaaaeaeaiiy 2. Ooieoe?? aeaaa?e eia?ee ? noi?ia?aeieie aeey oiiaieo
R[0,1] -ooieoe?e.

Aeiaaaeaii oai?aie.

Oai?aia 1.Iiiaeeia {R[0,1]} oiiaieo R-ooieoe?e ? ooieoe?iiaeueii
caieiaiith.

Oai?aia 2. Nenoaia R-ooieoe?e

oiiaieo R-ooieoe?e.

, oi ciaeaeaii ooieoe?th iaeaaeiino? neeaaeii? ia/?oei? iiiaeeie.

Ooieoe?? iaeaaeiino? /ano?oa anueiai caaeathoueny ia/enethaaeueieie
ooieoe?yie, oiaoi aeai?eoiaie ia/eneaiue. Aeine?aeaeaiiy, ui aoee
i?iaaaeai?, iieacaee, ui aeey iiaoaeoaaiiy ooieoe?? iaeaaeiino? ?
?aoe?iiaeueieie ianooii? aeai?eoie: eean oa?aeoa?enoee ii aeene?aoi?e
iiiaeei? oa?aeoa?ieo oi/ie oa eean ?ioaa?aeueieo oa?aeoa?enoee. A
ia?oiio aeiaaeeo aoaeo?ii iien iaeano? ?icieooy a?aieoe? oa ciaoiaeeii
a?aeiioaiiy e?eueeino? oa?aeoa?ieo oi/ie a?aieoe?, a yeeo ooieoe?y
?icieooy a?eueoa ioey aei caaaeueii? e?eueeino? oa?aeoa?ieo oi/ie. O
ae?oaiio eean? aeai?eoi?a ooieoe?y iaeaaeiino? ciaoiaeeoueny ye
a?aeiioaiiy ?ioaa?ae?a ii eiioo?o oa ieiu? ia?aoeio iioi/ii? iaeano? c
ia/?oeith iaeanoth aei a?aeiia?aeieo ?ioaa?ae?a iioi/ii? iaeano?.

?icaeyiaii iiaeaeue o?ce/iiai iiey, iai?eeeaae, caaea/o Ae???oea. *?oeo
iiaeaeue iiey aoaeaii iicia/aoe /a?ac o:

.

?? ?ica’ycie no?oeoo?iei iaoiaeii aoaeo?oueny o aeaeyae?:

— aiaeeoe/iee iien iaeano? D;

— iaaecia/ai? eiao?oe??ioe;

— ooieoe?y, ui i?iaeiaaeo? e?aeia? oiiae ana?aaeeio iaeano?.

A?aeiia?aeii aei iaaaaeaieo aeua aeaea?ae ia/?oeino? iiaoaeo?ii ia/?oeo
iiaeaeue iiey:

iio??aii io?eiaoe ia/?oeee ?ica’ycie:

— iiaeaeue, ui a?aoiao? aa??thaaiiy aaiiao?e/ieo oa?aeoa?enoee.

aoaea iaoe aeaeyae:

, io?eia?ii k ??cieo nenoai ??aiyiue. A oeueiio aeiaaeeo aeey
i?aeaeuaiiy oaeaeeiae?? i?ioeano ?o ae??oaiiy aeioe?eueii
aeei?enoiaoaaoe ?icia?aeaethaaiiy ia/enethaaeueiiai i?ioeano ii
caaea/ao.

— iine?aeiaiino? aeey aaiiao???. A ?acoeueoao? ?aae?caoe?? aea??ee
io?eio?ii ?ica’ycee.

. ?ioa?aaeuei? ?ica’ycee ? iniiaith aeey iiaoaeoaaiiy aenia?oieo
nenoai.

A aeaieo iaoiaeao aaaeeeai, uia aeey ?ioa?aaeueiiai ?ica’yceo
caa??aaany oie aea caeii ?iciiae?eo, ui ? aeey ii/aoeiaeo aeaieo.
Ca?aeii c oeaio?aeueiith a?aie/iith oai?aiith Eyioiiaa, oeueiai iiaeia
aeinyaiooe, yeui iaeiie/aia iia??oi?noue ia aoaea aeii?ioaaoe iaae
iaoiaee/iith. Oiio aeioe?eueii ?icaeyiooe i?iaeaio a?aooaaiiy iioeaie
ie?oaeaiiy, ye? aeieeathoue a i?ioean? ?ica’ycaiiy e?aeiaeo caaea/.

O?AOss AEAAA i?enay/aia ieoaiiyi ?aae?caoe?? cai?iiiiiaaieo i?aeoiae?a
iiaeaethaaiiy a ia/enethaaeueiiio na?aaeiaeu? «Iiea», ?ic?iaoe? iiaeaeae
ia/enethaaeueiiai i?ioeano ia iniia? ?ioa?aaeueiiai aiae?co oa
?icia?aeaethaaiiy aeai?eoi?a iiaeaethaaiiy o?ce/ieo iie?a.

Aeine?aeaeai? iiaeeeaino? ae??oaiiy i?iaeai a?aooaaiiy iiieeie
ie?oaeaiiy, ui aeieeathoue a i?ioean? ae??oaiiy e?aeiaeo caaea/
iaoaiaoe/ii? o?ceee. Aeey oeueiai i?iiiio?oueny aeei?enoiaoaaoe
eiino?oeoeai? caniae ?ioa?aaeueiiai aiae?co (iaoiaeeeo i?io. Kubota,
Oie?i), ye? aeicaieythoue cae?enieoe ioe?ieo iiieeie ie?oaeaiiy ca
aeiiiiiaith iaoiae?a aaoiiaoe/iiai aeeoa?aioe?thaaiiy. Iiaia
oi?iae?caoe?y ia/enethaaeueiiai i?ioeano ca aeiiiiiaith ei?oaaeii?
aeaaa?e aeicaieeea aaoiiaoecoaaoe i?ioeane ae??oaiiy e?aeiaeo caaea/ a
nenoai? «Iiea». I?e ?ic?iaoe? ooieoe?iiaeueiiai iaiiaiaiiy nenoaie aoea
i?eeiyoa no?aoaa?y /enaeueii-aiae?oe/iiai aeeoa?aioe?thaaiiy c
aeei?enoaiiyi iiiyooy aeeoa?aioe?aeueiiai ei?oaaeo. Nooue aeai?eoio
aeeoa?aioe?thaaiiy iieyaa? a ianooiiiio. Ia/eneaiiy iio?aeieo aenieiai
ii?yaeeo a?ae iniiaieo ooieoe?e (aeiaeaaaiiy, iiiaeaiiy, aeaiaioa?i?
ooieoe?? oa ?i.) iiaea aooe cae?eniaii ii oi/iei aeai?eoiai ia AII.Oae?
ia/eneaiiy io?eiaee iacao ei?oaaeieo iia?aoe?e. A ?acoeueoao? ?o
aeeiiaiiy ia/eneththoueny aeeoa?aioe?aeuei? ei?oaae? (cia/aiiy ooieoe??
oa ?o /anoeiieo iio?aeieo aei caaeaiiiai ii?yaeeo, ye? ?acii c
ei?oaaeieie iia?aoe?yie i?aeeyaathoue caeiiai ei?oaaeii? aeaaa?e).

, j=1,…,r.

— iiieeea ie?oaeaiiy ia j-io ia/enethaaeueiiio e?ioe?. Oiae?
ia/enethaaeueiee i?ioean aeey ooieoe?? c i ci?iieie iiaeia iiaeaoe
ianooiiei /eiii:

— i?ii?aei? ci?ii? ?c ne?i/aiiith oi/i?noth;

— iniiai? iia?aoe??;

;

— iiieeee ie?oaeaiiy.

):

.

aeyaeeiny aoaeoeaiei canoinoaaoe oi?ioee aeey aeeoa?aioe?thaaiiy
a?eoiaoe/ieo iia?aoe?e, ui canoiniao?oueny a aeaaa?? aeeoa?aioe?eieo
ei?oaae?a. Aeine?aeaeaii ieoaiiy aeei?enoaiiy aaciaeo oi?ioe
aaoiiaoe/iiai aeeoa?aioe?thaaiiy aeaaa?e aeeoa?aioe?eieo ei?oaae?a a
iaoiaeeoe? i?io. Kubota.

Oaeei /eiii, iniiao aeaaa?e aeeoa?aioe?eieo ei?oaae?a ? ioe?iee iiieeie
ie?oaeaiiy neeaaea? iaeei ? oie aea aacen — oi?ioea
/enaeueii-aiae?oe/iiai aeeoa?aioe?thaaiiy. Oea aeicaiey? ia iaeieo ? oeo
aea ia/eneaiiyo iio?aeieo aeeiioaaoe ?iaioo ii ?ica’yceo e?aeiaeo caaea/
? iaeii/anii a?aoiaoaaoe iiieeee ie?oaeaiiy, ui aea? iiaeeea?noue
iioei?coaaoe ia/enethaaeueiee i?ioean.

Aeine?aeaeai? iiaeeeaino? canoinoaaiiy iaoiaeeee ioe?iee iiieeie
ie?oaeaiiy aeey i?aeaeuaiiy oi/iino? aeeiiaiiy iia?aoe?e aeaaa?e
aeeoa?aioe?aeueieo ei?oaae?a. Iiaoaeiaai? ?ioa?aaeuei? ia/enethaa/? aeey
a?eoiaoe/ieo iia?aoe?e c? ne?i/aiiith oi/i?noth, oiaoi c a?aooaaiiyi
iiieeie ie?oaeaiiy, ye? i?aeaeuothoue aoaeoeai?noue ?aae?caoe??
ei?oaaeieo iia?aoe?e.

Iaaaaeaii i?eeeaae iiaoaeoaaiiy oi?ioee aeey ia/eneaiiy iiieeie
ie?oaeaiiy aeey iia?aoe?? iiiaeaiiy aeaio ei?oaae?a.

.

Aaaaeaii ianooii? iicia/aiiy aeey i?ii?aeieo ci?iieo:

.

Ca?aeii c cai?iiiiiaaiith a aeena?oaoe?? iaoiaeeeith aeei?enoaiiy
oi?ioee aaoiiaoe/iiai aeeoa?aioe?thaaiiy ae?ac aeey aa?oiuei? iaae?
aaniethoiiai cia/aiiy iiieeee ie?oaeaiiy io?eio?ii o aeaeyae?:

Aiaeia?/ii io?eio?ii ae?ace aa?oiuei? a?aieoe? iiieeee ie?oaeaiiy aeey
?ioeo iia?aoe?e ei?oaaeii? aeaaa?e.

Aeei?enoaiiy ?ioa?aaeueieo ia/enethaa/?a i?eaiaeeoue aei ca?eueoaiiy
ia’?io ?ia?o, oiio aeooaeueieie ? ieoaiiy ia?aeaeueieo ?aae?caoe?e.
?icaeyiooi ?icia?aeaethaaiiy aeey aeaaa?e aeeoa?aioe?eieo ei?oaae?a oa
?ioa?aaeueieo ia/enethaa/?a, yea caniiaaia ia y?onii-ia?aeaeueieo
oi?iao. Iiaoaeiaai? ia?aeaeuei? iia?aoi?i? noaie aeey ia/eneaiiy
aeeoa?aioe?aeueiiai ei?oaaeo ooieoe??, ei?oaaeieo iia?aoe?e oa
cai?iiiiiaaieo ?ioa?aaeueieo ia/enethaa/?a. ?icaeyioo? ieoaiiy
?icia?aeaethaaiiy caaaeueii? noaie ae??oaiiy e?aeiaeo caaea/.
Cai?iiiiiaai? i?aeoiaee aeei?enoiaothoueny i?e i?iaeooaaii? nenoai na???
«Iiea» aeey ia/enethaaeueieo eiiieaen?a ia?aeaeueii? ae??.

; iaae/eneth?ii ioe?ieo yeino? ?ica’yceo ca oi?ioeith

.

I?e aeinoaoi?e iiooaeiino? aea??ee (i>100) ioe?iea yeino? iiaeiia aooe
aeecueei? aei 1. I?iaaaeai? aenia?eiaioe aeey ??cieo i ? aeey ??cieo
aeai?ie. Aiae?c ?acoeueoao?a iieacaa aenieo no?ee?noue oa
aenia?eiaioaeueio ca?aei?noue i?ioeano.

Iniiai? ?acoeueoaoe oa aeniiaee

Ia iniia? oai??? R-ooieoe?e oa ia/?oei? eia?ee ?ic?iaeai?

eiino?oeoeai? iaoiaee oa aeai?eoie iiaeaethaaiiy o?ceei-iaoai?/ieo
iie?a, ye? aeicaieythoue a?aoiaoaaoe oaoi?/i? oa oaoiieia?/i? aeiionee
ia o?ce/io oa aaiiao?e/io ?ioi?iaoe?th, iioeaee aei???a, iiieeee
ie?oaeaiiy, oa ia iniia? aeyaeaiiy ?o eiiieaeniiai aieeao ia ?ica’ycie
?iaeoe aenia?oiee aeniiaie. Cai?iiiiiaai? iiaeae? o?ce/ieo iie?a, ui
a?aoiaothoue aeiionee ia o?ce/i? oa aaiiao?e/i? aeai?. Iaoiaeeea
aeicaiey? io?eioaaoe aeiionee ia ?ica’ycie ca aeiiiiiaith aa??thaaiiy
oeeo aaee/ei a iaaeao caaeaieo aeiione?a, a iio?i ?iaeoe aenia?oiee
aeniiaie i?i i?eeiyoi?noue ciaeaeaiiai ?ica’yceo.

2. Aeine?aeaeaii ca’ycie oai??? R-ooieoe?e oa ia/?oei? eia?ee.
Cae?eniaii aea?? eiino?oeoeaieo cania?a oai??? R-ooieoe?e aeey
iiaeaethaaiiy — iiiaeeia oiiaieo R[0,1] R-ooieoe?e, a ye?e aeeiiai?
iaiao?aei? ooieoe?iiaeuei? iiaoaeiae.

3. ?icaeyioo? i?aeoiaee aei canoinoaaiiy iaoiae?a ?ioa?aaeueii?
a?eoiaoeee.

Iiaoaeiaai? ?ioa?aaeuei? ia/enethaa/? a?eoiaoe/ieo iia?aoe?e c
a?aooaaiiyi iiieeie ie?oaeaiiy, ye? i?aeaeuothoue aoaeoeai?noue
?aae?caoe?? aeaaa?e aeeoa?aioe?eieo ei?oaae?a, yea eaaeeoue a iniia?
ia/enethaaeueiiai i?ioeano i?e ae??oaii? e?aeiaeo caaea/. Ia/enethaa/?,
ui cai?iiiiiaai?, aeicaieythoue eiino?othaaoe oi?ioee aeey aecia/aiiy
aa?oiuei? iaae? aaniethoiiai cia/aiiy iiieeie, ui ?icaeyaeathoueny.
Iaaaaeai? i?eeeaaee ia/eneaiiy ioe?iie iiieeie ie?oaeaiiy aeey iia?aoe?e
iiiaeaiiy aeaio ei?oaae?a, cai?ioiueiai aeaiaioo aeey iiiaeaiiy,
eaaae?aoiiai ei?aiy, noaiaiaai? oa eiaa?eoi?/ii? ooieoe??,
aeeoa?aioe?thaaiiy noia?iiceoe?? ooieoe?e.

4. Aeine?aeaeai? iiaeeeaino? ?icia?aeaethaaiiy ia/enethaaeueiiai
i?ioeano ia

iniia? y?onii-ia?aeaeueieo oi?i. Iiaoaeiaai? ia?aeaeuei? iia?aoi?i?
noaie aeey i?aeaeuaiiy oaeaeeiae??. Iaaaaeai? c?o/i? aeey
?icia?aeaethaaiiy ia/enethaaeuei? a?aoe aeey ?ioa?aaeueieo
ia/enethaa/?a, ui i?iiiiothoueny. Aea/ai? oaeiae iiaeeeaino?
aeei?enoaiiy iaoiae?a ?icia?aeaethaaiiy i?e ia/enethaaii?
aeeoa?aioe?eiiai ei?oaaea ooieoe??. ?icaeyioo? ??ci? i?aeoiaee aei
?icia?aeaethaaiiy aeai?eoi?a iiaeaethaaiiy o?ce/ieo iie?a:
?icia?aeaethaaiiy ii iioieai ii iioieai ?ioi?iaoe??, iia?aoi?ia oa
iia?aoe?eia ?icia?aeaethaaiiy. Cai?iiiiiaaii ii?aeiaiiy aeaieo
i?aeoiae?a ca aeiiiiiaith aeei?enoaiiy iaoiaeo iine?aeiaiiai
iiaeeaeaiiy.

5. I?iaaaeaiee ?yae /enaeueieo aenia?eiaio?a ii aeine?aeaeaiith
iaae?eiino? oa

aoaeoeaiino? ?ic?iaeaieo aeai?eoi?a oa i?ia?ai.

6. ?acoeueoaoe, ui io?eiai?, canoiniaothoueny aeey ?icoe?aiiy
iiaeeeainoae

nenoaie «Iiea» ia aeiaaeee ae??oaiiy e?aeiaeo caaea/, a iinoaiiaoe? yeeo
nooo?ao ?ieue a?athoue aeiionee ia o?ce/io oa aaiiao?e/io ?ioi?iaoe?th,
iia??oiino? aei???a oa iiieeee ie?oaeaiiy.

Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a oaeeo ?iaioao:

1. Oaa/aiei A.I., Oiieoea I.A. Iiaeaee?iaaiea oece/aneeo iieae n
eniieueciaaieai oai?ee R-ooieoeee e ia/aoeie eiaeee // Iaoiaeu
iioeiecaoeee oaoie/aneeo e eioi?iaoeeiiiuo nenoai : Na. iao/. o?. / IAI
Oe?aeiu. Ei-o eeaa?iaoeee ei. A.I. Aeooeiaa — Eeaa, 1995. — N. 64-67.

2. Oaa/aiei A.I., Oiieoea I.A. Iiaeaee?iaaiea aaiiao?e/aneeo iauaeoia a
nenoaiao aiaeeca oece/aneeo iieae // I?iaeaiu aeiieee. — 1998. — Aui.
49. — N. 130-134.

3. Oaa/aiei A.I., Oiieoea I.A. ?acaeoea eioaeeaeooaeueiuo
eioi?iaoeeiiiuo nenoai aiaeeca oece/aneeo iieae na?ee «Iiea» // I?iaeaiu
aeiieee. — 1998. — Aui. 49. — N. 135-140.

4. Oaa/aiei A.I., Oiieoea I.A. Ia iaeiie iaoiaeeea iiaeaee?iaaiey
?aaeueiuo oeceei-iaoaie/aneeo iieae — IAI Oe?aeiu. Ei-o i?iae.
iaoeiino?iaiey — Oa?ueeia, 1996. 17 n. — aeai. a AEIEOE 22.01.96, ?
241A-96.

5. Oiieoea I.A. I?eiaiaiea iaoiaeia eioa?aaeueiiai aiaeeca i?e ?aoaiee
e?aaauo caaea/ iaoaiaoe/aneie oeceee. — IAI Oe?aeiu. Ei-o i?iae.
iaoeiino?iaiey. — Oa?ueeia, 1997. — 22 n. — aeai. a AEIEOE 10.08.98, ?
2544-A98.

6. Oaa/aiei A.I., Oiieoea I.A. Aunieiyooaeoeaiua iaoiaeu, aeai?eoiu e
n?aaenoaa iiaeaee?iaaiey oeceei-iaoaie/aneeo iieae n eniieueciaaieai
iaoiaeia oai?ee R-ooieoeee, eioa?aaeueiiai aiaeeca e ia/aoeie eiaeee. —
IAI Oe?aeiu. Ei-o i?iae. iaoeiino?iaiey. — Oa?ueeia, 1997. — 38 n. —
aeai. a AEIEOE 21.08.98, ? 2624-A98.

7. Oaa/aiei A.I., Oiieoea I.A. Eioa?aaeueiua au/eneeoaee a n?aaea «Iiea»
// oac. aeiee. iaaeaeoia?iae. eiio. «Oai?ey e oaoieea ia?aaea/e, i?eaia
e ia?aaioee eioi?iaoeee», — Ooaina, 1995, N. 125.

8. Oiieoea I.A. Ia?aeeaeueiay ia?aaioea eioi?iaoeee a au/eneeoaeueiie
n?aaea «Iiea» // oac. aeiee. iaaeaeoia?iae. eiio. «Oai?ey e oaoieea
ia?aaea/e, i?eaia e ia?aaioee eioi?iaoeee», — Oa?ueeia — Ooaina, 1996,
/anoue 2. — N. 153 — 154.

9. Shevchenko A.N., Tonitsa O.V. R-functions, fuzzy logic and interval
analysis with POLYE system for simulation of fields // oace aeii.
anaoe?. iaoe. eiio. «?ic?iaea oa canoinoaaiiy iaoaiaoe/ieo iaoiae?a a
iaoeiai-oaoi?/ieo aeine?aeaeaiiyo», i?ena. 70-??//th a?ae aeiy
ia?iaeaeaiiy i?ioani?a I.N. Eac?i??nueeiai, Euea?a, 1995, /anoeia 2. —
N. 104.

10. Oaa/aiei A.I., Oiieoea I.A. Iiaeaee?iaaiea
oeceei-iaoaie/aneeo iieae iaoiaeaie oai?ee R-ooieoeee e ia/aoeie eiaeee
// oac. aeiee. iaaeaeoia?iae. eiio. «Iaoaiaoe/aneea iiaeaee e /eneaiiua
iaoiaeu iaoaieee nieioiuo n?aae», — Iiaineae?ne, 1996, N. 114-115.

11. Oiieoea I.A. Eniieueciaaiea aeaaa?u aeeooa?aioeeaeueiuo ei?oaaeae a
eioa?aaeueiuo iaoiaeao aeey ioeaiee ioeaie ie?oaeaiey a e?aaauo caaea/ao
// oac. aeiee. XIV Iaaeaeoia?iae. eiio. ii eioa?aaeueiie iaoaiaoeea, —
Iiaineae?ne, 1998. — N. 1-2.

12. Oiieoea I.A. I?eiaiaiea eioa?aaeueiie a?eoiaoeee i?e iino?iaiee
nenoai enneaaeiaaiey oece/aneeo iieae — EE ? 151-97. OA?IIOYE i?e
Ieienoa?noaa Oe?aeiu ii aeaeai iaoee e oaoiieiaee. — Oa?ueeia, 1997, 3
n.

13. Oaa/aiei A.I., Oiieoea I.A. Iaoiaeeea o/aoa aeiioneia i?e ?aoaiee
e?aaauo caaea/ iaoaiaoe/aneie oeceee. — EE ? 152-97. OA?IIOYE i?e
Ieienoa?noaa Oe?aeiu ii aeaeai iaoee e oaoiieiaee — Oa?ueeia, 1997, 3 n.

14. Oiieoea I.A. Iaoiaeu iino?iaiey iienaiee aaiiao?e/aneeo iauaeoia a
eeanna ooieoeee ia/aoeie eiaeee. — EE ? 12-98. OA?IIOYE i?e Ieienoa?noaa
Oe?aeiu ii aeaeai iaoee e oaoiieiaee. — Oa?ueeia, 1998, 3 n.

15. Oiieoea I.A. Ia?aeeaeueiia iiaeaee?iaaiea a nenoaiao aiaeeca
oeceei-iaoaie/aneeo iieae — EE 15-98. OA?IIOYE i?e Ieienoa?noaa Oe?aeiu
ii aeaeai iaoee e oaoiieiaee. — Oa?ueeia, 1998, 3 n.

16. Oiieoea I.A. Iino?iaiea aeai?eoiia au/eneaiey ooieoeee
i?eiaaeeaaeiinoe ia iniiaa eioaa?aeueiuo oa?aeoa?enoee — EE ? 63-98.
OA?IIOYE i?e Ieienoa?noaa Oe?aeiu ii aeaeai iaoee e oaoiieiaee. —
Oa?ueeia, 1998, 3 n.

17. Oaa/aiei A.I., Oiieoea I.A. ?acaeoea eioaeeaeooaeueiuo
nenoai aiaeeca oece/aneeo iieae — EE ? 71-98. OA?IIOYE i?e Ieienoa?noaa
Oe?aeiu ii aeaeai iaoee e oaoiieiaee. — Oa?ueeia, 1998, 3 n.

18. Oiieoea I.A. Ieaie?iaaiea yenia?eiaioia i?e iiaeaee?iaaiee
oece/aneeo iieae — EE ? 147-98. OA?IIOYE i?e Ieienoa?noaa Oe?aeiu ii
aeaeai iaoee e oaoiieiaee. — Oa?ueeia, 1998, 3 n.

19. Oiieoea I.A. I?iaeoe?iaaiea nenoai aiaeeca oece/aneeo iieae a
nia?aiaiiuo eioi?iaoeeiiiuo oaoiieiaeyo — EE ? 151-98. OA?IIOYE i?e
Ieienoa?noaa Oe?aeiu ii aeaeai iaoee e oaoiieiaee. — Oa?ueeia, 1998, 3
n.

AIIOAOe?ss

Oii?oea I.A. Iiaeaethaaiiy o?ce/ieo iie?a iaoiaeaie oai??? R-ooieoe?e

oa ia/?oei? eia?ee. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo

iaoe ca niaoe?aeuei?noth 01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa
ia/enethaaeuei? iaoiaee. — ?inoeooo i?iaeai iaoeiiaoaeoaaiiy ?i.
A.I.I?aeai?iiai IAI Oe?a?ie, Oa?e?a, 1999.

?ic?iaeai? eiino?oeoeai? iaoiaee oa aeai?eoie iiaeaethaaiiy
o?ceei-iaoai?/ieo iie?a ia iniia? oai??? R-ooieoe?e oa ia/?oei? eia?ee,
ye? aeicaieythoue a?aoiaoaaoe oaoi?/i? oa oaoiieia?/i? aeiionee ia
aaiiao?e/io oa o?ce/io ?ioi?iaoe?th, iia??oiino? aei???a, iiieeee
ne?oaeaiiy, oa ia iniia? aiae?co ?o eiiieaeniiai aieeao ia ?ica’ycie
?iaeoe aenia?oiee aeniiaie. Cai?iiiiiaai? iiaeae? o?ce/ieo iie?a, ui
i?noyoue aeiionee ia aaiiao?e/i? oa o?ce/i? oa?aeoa?enoeee ca
aeiiiiiaith a?aooaaiiy ooieoe?? iaeaaeiino? aaee/ei, ui
?icaeyaeathoueny, a iaaeao caaeaieo aeiione?a. Iaoiaeeea, ui ?ic?iaeaia,
aeicaiey? io?eioaaoe aeiionee ia ?ica’ycie ca aeiiiiiaith aa??thaaiiy
oeeo aaee/ei a iaaeao caaeaieo aeiione?a, a iio?i ca aeiiiiiaith
io?eiaieo aeiione?a ?iaeoe aenia?oiee aeniiaie i?i i?eeiyoi?noue
ciaeaeaiiai ??oaiiy. Iiaoaeiaai? ?ioa?aaeuei? ia/enethaa/? a?eoiaoe/ieo
iia?aoe?e c a?aooaaiiyi iiieeie ie?oaeaiiy, ye? i?aeaeuothoue
aoaeoeai?noue ?aae?caoe?? aeaaa?e aeeoa?aioe?aeueieo ei?oaae?a, ui
eaaeeoue a iniia? ia/enethaaeueiiai i?ioeano. Aeine?aeaeai? iiaeeeaino?
?icia?aeaethaaiiy ia/enethaaeueiiai i?ioeano ia iniia?
y?onii-ia?aeaeueieo oi?i. ?acoeueoaoe, ui io?eiai?, canoiniaothoueny
aeey ?icoe?aiiy iiaeeeainoae nenoaie «Iiea» ia aeiaaeee ae??oaiiy
e?aeiaeo caaea/, a iinoaiiaoe? yeeo nooo?ao ?ieue a?athoue aeiionee ia
aaiiao?e/io oa o?ce/io ?ioi?iaoe?th, iia??oiino? aei???a oa iiieeee
ie?oaeaiiy.

Eeth/ia? neiaa: iiaeaethaaiiy o?ce/ieo iie?a, R-ooieoe??, ia/?oea
eia?ea, aeiionee ia aaiiao?e/io oa o?ce/io ?ioi?iaoe?th, iia??oiino?
aei???a, iiieeee ie?oaeaiiy, ooieoe?y iaeaaeiino?, aenia?oiee aeniiaie,
?ioa?aaeueia a?eoiaoeea, aeaaa?a aeeoa?aioe?aeueieo ei?oaae?a,
?icia?aeaethaaiiy ia/enethaaeueiiai i?ioeano.

AIIIOAOeEss

Oiieoea I.A. Iiaeaee?iaaiea oece/aneeo iieae iaoiaeaie oai?ee
R-ooieoeee e ia/aoeie eiaeee. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.05.02 — iaoaiaoe/aneia
iiaeaee?iaaiea e au/eneeoaeueiua iaoiaeu. — Einoeooo i?iaeai
iaoeiino?iaiey ei. A.I.Iiaeai?iiai IAI Oe?aeiu, Oa?ueeia, 1999.

I?e iino?iaiee nenoai enneaaeiaaiey caaea/ ?an/aoa iieae aaaeai o/ao
noioanoe/aneiai oa?aeoa?a iia?aoiinoae ecia?aiee, aeiioneia ia
aaiiao?e/aneoth e oece/aneoth eioi?iaoeeth e iia?aoiinoae ie?oaeaiey. A
nayce n yoei aicieeaao iaiaoiaeeiinoue a ?acaeoee nouanoaothueo nenoai
?an/aoa iieae aeey iiiaiaa?eaioiuo caaea/ n oeaeueth iieo/eoue aeiionee
ia ?aoaiea e iineaaeothuaa yenia?oiia caeeth/aiea. Au/eneaiey a nenoaiao
?an/aoa iieae, eae i?aaeei, iinyo aeaoa?ieie?iaaiiue oa?aeoa?, a oi
a?aiy eae ?aaeueiua i?ioeannu a ii?aaeaeaiiie noaiaie yaeythony
noioanoe/aneeie, niaea?aeao a naaa iaeioi?oth ia/aoeinoue. Aeey o/aoa
iineaaeiae ioaeii oae i?aia?aciaaoue nouanoaothuoth noaio enneaaeiaaiey
oece/aneeo iieae, /oiau a ?acoeueoaoa iiiaiaa?eaioiiai n/aoa iieo/eoue
aieaa oi/iia «ia/aoeia» ?aoaiea, eioi?ia aoaeao aeeaea e ?aaeueiinoe.
Oeaeaniia?acii aaanoe a noaio ?aoaiey o/ao aeiioneia, o. a. enoi/ieeia
ia/aoeinoe, iaeaieaa neeueii aeeythueo ia ?acoeueoe?othuaa ?aoaiea.
I?aeoeea iieacuaaao, /oi oaeeo enoi/ieeia, eae i?aaeei, o?e: aeiionee
iiaeaee (ia aaiiao?e/aneea e oece/aneea oa?aeoa?enoeee), ioeaee iaoiaea
(«ona/aiea» ?yaea, ioeaee eioaa?e?iaaiey, ?aoaiey nenoai eeiaeiuo
o?aaiaiee) e iia?aoiinoe ie?oaeaiey. Iaiaoiaeeii onoaiiaeoue eiiieaeniia
aeeyiea aa?uee?iaaiey aaee/ei a i?aaeaeao aeiioneia e enneaaeiaaoue
aiciiaeiinoe iino?iaiey aeiioneia ia ?aoaiea. A nayce n yoei aieueoie
eioa?an i?aaenoaaeyao ?ac?aaioea nenoai enneaaeiaaiey iieae,
i?eaioe?iaaiiuo ia iiiaiaa?eaioiia ?aoaiea e?aaauo caaea/ n oeaeueth
o/anoue aa?uee?iaaiea ii?aaeaeaiiuo aaee/ei a i?aaeaeao caaeaiiuo
aeiioneia.

?ac?aaioaiu eiino?oeoeaiua iaoiaeu e aeai?eoiu iiaeaee?iaaiey
oeceei-iaoaie/aneeo iieae ia iniiaa oai?ee R-ooieoeee e ia/aoeie eiaeee,
iicaieythuea o/eouaaoue oaoie/aneea e oaoiieiae/aneea aeiionee ia
aaiiao?e/aneoth e oece/aneoth eioi?iaoeeth, iia?aoiinoe ecia?aiee,
ioeaee ie?oaeaiey e ia iniiaa aiaeeca eo eiiieaeniiai aeeyiey ia ?aoaiea
aeaeaoue yenia?oiia caeeth/aiea. I?aaeeiaeaiu iiaeaee oece/aneeo iieae,
niaea?aeauea aeiionee ia aaiiao?e/aneea e oece/aneea oa?aeoa?enoeee i?e
iiiiue o/aoa ooieoeee i?eiaaeeaaeiinoe ?anniao?eaaaiuo aaee/ei a
i?aaeaeao caaeaiiuo aeiioneia. ?ac?aaioaiiay iaoiaeeea iicaieyao
iieo/aoue aeiionee ia ?aoaiea i?e iiiiue aa?uee?iaaiey yoeo aaee/ei a
i?aaeaeao caaeaiiuo aeiioneia, a caoai aeaeaoue yenia?oiia caeeth/aiea
i i?eaieaiinoe iaeaeaiiiai ?aoaiey.

Iino?iaiu eioa?aaeueiua au/eneeoaee a?eoiaoe/aneeo iia?aoeee n o/aoii
ioeaie ie?oaeaiey, iiauoathuea yooaeoeaiinoue aeaaa?u
aeeooa?aioeeaeueiuo ei?oaaeae, eaaeauae a iniiaa au/eneeoaeueiiai
i?ioeanna aeaiiuo iaoiaeia.

Enneaaeiaaiu aiciiaeiinoe ?ania?aeeaeeaaiey au/eneeoaeueiiai i?ioeanna
ia iniiaa y?onii-ia?aeeaeueiuo oi?i. Iieo/aiiua ?acoeueoaou i?eiaiythony
aeey ?anoe?aiey aiciiaeiinoae nenoaiu «Iiea» ia neo/ae ?aoaiey e?aaauo
caaea/, a iinoaiiaea eioi?uo nouanoaaiioth ?ieue ea?atho aeiionee ia
aaiiao?e/aneoth e oece/aneoth eioi?iaoeeth, iia?aoiinoe ecia?aiee e
ioeaee ie?oaeaiey.

Eeth/aaua neiaa: iiaeaee?iaaiea oece/aneeo iieae, R-ooieoeee, ia/aoeay
eiaeea, aeiionee ia aaiiao?e/aneoth e oece/aneoth eioi?iaoeeth,
iia?aoiinoe ecia?aiee, ioeaee ie?oaeaiey, ooieoeey i?eiaaeeaaeiinoe,
yenia?oiia caeeth/aiea, eioa?aaeueiay a?eoiaoeea, aeaaa?a
aeeooa?aioeeaeueiuo ei?oaaeae, ?ania?aeeaeeaaiea au/eneeoaeueiiai
i?ioeanna.

SUMMARY

Tonitsa O.V. Modelling of physical fields by means of R-functions
theory and fuzzy logics. — Manuscript.

The thesis for a Physical-Mathematical Sciences Candidate’s degree,
speciality 01.05.02 — mathematical modelling and computational methods.
— Institute for problems in machinery by A.N. Podgorny National academy
of sciences of the Ukraine, Kharkiv, 1999.

The constructive methods and algorithms for simulation of
physical-mechanical fields based on the R-functions theory and fuzzy
logics are elaborated which allow us take into account technical and
technological assumptions on geometrical and physical information,
measuring errors, rounding errors, and draw expert conclusion by
analysis their complex influence on the solution. The models of physical
fields, containing assumptions on geometrical and physical
characteristics by account the fuzzy membership function of values
reviewed in bounds of the assumptions are proposed. The technique
presented enables us to receive assumption on the solution by changing
of this values in bounds of the assumptions and draw expert conclusion
about acceptability of solving finding. The interval calculators for
arithmetical operators with accounting of rounding errors estimates are
created which increases effisiency of algebra of differential tuples.
The possibilities of paralleling computation process is investigated.
The results obtained is applicated for widening of possibilities of the
POLYE system.

Key words: modelling of physical fields, fuzzy logic, R-functions,
assumptions of geometrical and physical information, measuring errors,
rounding errors, fuzzy membership function, interval arithmetics,
algebra of differential tuples, paralleling of computational process.

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