I?I?NOA?NOAI INA?OE OE?A?IE
NAAANOIIIEUeNUeEEE AeA?AEAAIEE OAOI?*IEE OI?AA?NEOAO
E?aia?ue Aaaeei Ieaenaiae?iae/
OAeE 681.5
AEAAA?A?*I? OI?IE AIAE?CO ? NEIOACO A?OAEO
E?I?EIEO IAIA?A?AIEO NENOAI AAOIIAOE*IIAI
OI?AAE?IIss
05.13.03 – Nenoaie ? i?ioeane ea?oaaiiy
Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai
nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
Naaanoiiieue – 1999
Aeena?oaoe??th ? ?oeiien.
?iaioa aeeiiaia a Naaanoiiieuenueeiio Aea?aeaaiiio oaoi?/iiio
oi?aa?neoao? II Oe?a?ie.
Iaoeiaee ea??aiee – aeieoi? oaoi?/ieo iaoe,
Aa?aaaiia Ieaenaiae? O??oiiiae/,
i?ioani? aeaia?oaiaioo oaoi?/ii?
e?aa?iaoeee NaaAeOO
Io?oe?ei? iiiiaiou:
– aeieoi?. oaoi?/ieo iaoe, i?ioani?, I?yoieeia Oaaei? Aeieo???ae/,
Naaanoiiieuenueeee aea?aeaaiee oaoi?/iee oi?aa?neoao, aeaia?oaiaio
aeaeo?iaia?aaoeee, aee?aeoi?
– eaiaeeaeao o?ceei -iaoaiaoe/ieo iaoe ?aoia? TH??e Ai?eniae/, Ii?nueeee
a?ae?io?ce/iee ?inoeooo IAIO, noa?oee iaoeiaee ni?a?ia?oiee.
I?ia?aeia onoaiiaa – Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie «EI?»,
i. Ee?a.
Caoeno a?aeaoaeaoueny «_1_» _eeiiy____1999 ?. i _15__ aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae50. 052.02 a
Naaanoiiieuenueeiio Aea?aeaaiiio oaoi?/iiio oi?aa?neoao? ca aae?anith:
335053, i. Naaanoiiieue, No?aeaoeueea aaeea, nooaei?noa/ei, ei?ion
NaaAeOO.
Oaen (0692) 244530, e-mail:
C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? NaaAeOO.
Aaoi?aoa?ao ?ic?neaiee _25 o?aaiy___ 1999 ?.
A/aiee naeo?aoa? niaoe?ae?ciaaii? a/aii? ?aaee
e.o.i., aeioeaio ______________ I. I. Oa?aoaanueeee
CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE
Aeooaeuei?noue ?iaioe. Cia/ia i?noea a no/anieo aeine?aeaeaiiyo
caeiathoue o? aniaeoe i?iaeaie a?oaino?, ui ca’ycai? c ?ica?aii
ia?aiao??a a ?aaeueieo nenoaiao, a oaeiae iaieio/ath ?ica?aei?noth i?ae
ia?aiao?aie iiaeae? ? ?aaeueiiai ia’?eoo. Aa??aoe?? ia?aiao??a ?
iaa?ae’?iiith /anoeiith aeine?aeaeaiiy NAO, a i?iaeaia a?aooaaiiy oeeo
aa??aoe?e ? aecia/aiiy ?o aeiionoeieo iaae iaaeoi aeooaeueia i?e
aeine?aeaeaii? neeaaeieo ia’?eo?a. A iei?oi?e /an, ii?yae c oa?i?iii
«a?oa?noue» aeei?enoiao?oueny oa?i?i «?iaanoi?noue».
Aeanoea?noue a?oaino? (?iaanoiinoi), ia?aaeon?i, iiaeiii aeyaeyoeny a
no?eeino? nenoaie oi?aae?iiy. Caaea/a aiae?co no?eeino? nenoai
aaoiiaoe/iiai oi?aae?iiy c iaia?aiao?e/iith aaeeoeaiith aai
ioeueoeie?eaoeaiith iaicia/aii?noueth a iiaeae? ia’?eoo caeia? cia/ia
i?noi a no/ani?e oai??? oi?aae?iiy. Oaeei /eiii, aiae?c a?oaino?
aeanoeaino? aneiioioe/iie no?eeino? ? ca’ycai? c iei caaea/? neioaco
a?oaeo nenoai oi?aae?iiy, cie?aia, iaoiae D – iiae?ea, ? iaei?ie c
iaeaaaeeea?oeo caaea/ oai??? aaoiiaoe/iiai oi?aae?iiy. Iiyaa iiaeo ?
?icaeoie aaea ?nioth/eo iaoiae?a aiae?co ? neioaco ?iaanoieo NAO ia
ci?ia? aeooaeuei?noue oe??? i?iaeaie caaaeath/e ia ?? cia/aiiy ? oaeaeea
?icoe?aiiy iaeanoae canoinoaaiiy. Oeae oaeo i?aeoaa?aeaeo?oueny
iayai?noth cia/iiai /enea ioae?eaoe?e, ye a a?o/eciyi?e, oae ? a
ca?oa?aei?e ia/aooe?, i?e/iio e?euee?noue ?ia?o ,ui ioae?eothoueny ia
ciaioo?oueny ? a?eueoa ?o /anoeia a?aeiineoueny aei inoaii?o 10-15
?ie?a.
Ia’?eoii aeine?aeaeaiiy a ?iaio? ? iaia?a?ai? e?i?ei? nenoaie oi?aae?iiy
c iaeeie/iei iaaaoeaiei cai?ioiei ca’yceii i?e iayaiino? iaia?aiao?e/iie
iaicia/aiiinoi a iiaeae? ia’?eoo ? iaia?a?ai? nenoaie oi?aae?iiy ye?
neioacothoueny iaoiaeii D – iiaeiea ii aauanoaaiiio ia?aiao?o ,ui
aoiaeeoue e?i?eii.
Iaoa aeena?oaoe?eiiai aeine?aeaeaiiy. Iaoith aeine?aeaeaiiy ? ?ic?iaea
aeaaa?a?/ieo iaoiae?a ? e?eoa???a aiae?co no?eeino? ? neioaco ia?aiao??a
?aaoeyoi?a e?i?eieo iaia?a?aieo nenoai oi?aae?iiy i?e iaia?aiao?e/iie
iaicia/aii?no? a iiaeae? ia’?eoo ? aeaaa?a?/ieo e?eoa???a ioe?iee yeino?
NAO, yea neioaco?oueny iaoiaeii D – iiaeieo ii aauanoaaiiio ia?aiao?o
,ui aoiaeeoue e?i?eii.
Aeey aeinyaiaiiy oe??? iaoe a aeena?oaoe?? ae??oothoueny ianooii?
caaea/?:
?ic?iaea iaoiae?a ? aeai?eoi?a aeaaa?a?/iiai aiae?co, ia iniia?
canoinoaaiiy ocaaaeueiaiiai iaoiaea ?aona, ?iaanoiie no?eino? e?i?eieo
iaia?a?aieo NAO c iaia?aiao?e/iith iaicia/aii?noueth a iiaeae? ia’?eoo;
?ic?iaea ia iniia? canoinoaaiiy ocaaaeueiaiiai iaoiaea Ao?a?oea cania?a
iiaoaeiae nenoai aeaaa?a?/ieo ia??aiinoae aeey neioaco ia?aiao??a
?aaoeyoi?a c caaeaiith no?oeoo?ith e?i?eii? iaia?a?aii? NAO ca iayaiino?
iaia?aiao?e/iie iaicia/aii?no? a iiaeae? ia’?eoo;
iiaoaeiaa ni?aa?aeiioaiue aeey aeaaa?a?/ii? ioe?iee yeino? NAO, yea
neioaco?oueny iaoiaeii D – iiae?eo ii aauanoaaiiiio ia?aiao?o ,ui
aoiaeeoue e?i?eii.
A ?aieao ??oaiiy iinoaaeaieo caaea/ ?ic?iaeai ?yae iiaeo aeai?eoi?a, a
oaeiae iiaeeo?eiaai? c o?aooaaiiyi niaoeeo?ee aeine?aeaeaiue aeaye? aaea
?nioth/? aeai?eoie ? iaoiaeeee. Eiaeiee c io?eiaieo ?acoeueoao?a
i?i?ethno?iaaiee i?eeeaaeii. ?ic?iaeai i?ia?aiiee eiiieaen, ca
aeiiiiiaith yeiai ?aae?cothoueny iniiai? ?acoeueoaoe ?iaioe.
Iaoiaee aeine?aeaeaiiy. Iinoaaeai? caaea/? ae??oothoueny ca aeiiiiiaith
iaoiae?a no/anii? oai??? oi?aae?iiy, e?i?eii? aeaaa?e ? canoinoaaiiy
i?aeoiae?a ocaaaeueiaiiai iaoiaea ?aona – Ao?a?oea.
Iaoeiao iiaecio neeaaeathoue ianooii? ?acoeueoaoe, ui aeiinyoueny ia
caoeno:
Iaoiaeeea ? aeai?eoie aeaaa?a?/iiai aiae?co ?iaanoiie no?eino? e?i?eieo
iaia?a?aieo nenoai oi?aae?iiy c iaia?aiao?e/iith iaicia/aii?noueth a
iiaeae? ia’?eoo;
Iaoiaeeea ? aeai?eoie neioaco ia?aiao??a ?aaoeyoi?a caaeaii? no?oeoo?e
e?i?eieo aacia?a?aieo nenoai oi?aae?iiy c iaia?aiao?e/iith
iaicia/aii?noueth a iiaeae? ia’?eoo;
Iaoiaeeea ? aeai?eoie aeaaa?a?/ii? ioe?iee yeino? nenoai aaoiiaoe/iiai
oi?aae?iiy yea neioaco?oueny iaoiaeii D – iiae?eo ii aauanoaaiiiio
ia?aiao?o.
Iniiaith aeai?eoi?a ,ui ?ic?iaeythoueny a aeena?oaoe?? ? ocaaaeueiaiee
iaoiae ?aona – Ao?a?oea.
I?aeoe/io oe?ii?noue ?iaioe neeaaea? i?ia?aiia caaacia/aiiy
cai?iiiiiaaiiai a i?e aeaaa?a?/iiai iaoiaea aiae?c ?iaanoiie no?eeino?,
neioaco ?iaanoii no?eeeo nenoai ? aeaaa?a?/iiai iaoiaea ioe?iee yeino?
NAO i?e neioac? ?? iaoiaeii D – iiae?eo. Ca aeiiiiiaith ?ic?iaeaiiai
i?ia?aiiiai caaacia/aiiy aeeiiaiee aiae?c nenoaie aaoiiaoe/iiai
oi?aae?iiy aaaeeiai e?oaea i?e caoiae? ia iinaaeeo ? nenoaie
aaoiiaoe/iiai oi?aae?iiy neeiaei a??ineii?/iei noaa?e?caoi?ii.
?aae?caoe?y ?acoeueoao?a ?iaioe. Aeena?oaoe?eia ?iaioa aeeiiaia a ?aieao
aaeocaaie i?ia?aie i?i?noa?noaa ina?oe Oe?a?ie “Ii?aoethaaiiy oai?i(,
caniaia, iiaeaeae oa aeai?eoiia aeey ooai?aiiy ?ioaeaeooaeueieo nenoai
ia?iaee ?ioi?iaoe??.” ?acoeueoaoe aeena?oaoe?? aoee aeei?enoai? i?e
aeeiiaii? IAe? “?ic?iaea iaoaiaoe/ieo iaoiae?a ? i?ia?aiieo cania?a
aeine?aeaeaiiy aiaeiai – oeeo?iaeo nenoai oi?aae?iiy aaaaoii??ieie
ia’?eoaie” (“A?ai?o”), “Iaoiaee ? i?ia?aii? caniae iaoeiiiai
aeine?aeaeaiiy aaaaoii??ieo nenoai oi?aae?iiy” (“Aeei?eo”) (Iaeac
I?i?noa?noaa Ina?oe Oe?a?ie ?37 a?ae 13.02.97a). Eiiieaen i?ia?ai
aeaaa?a?/iiai aiae?co ?iaanoiie no?eeino? ? ioe?iee yeino? nenoai
aeei?enoiao?oueny a iaa/aeueiiio i?ioean? aeaia?oaiaioo oaoi?/ii?
e?aa?iaoeee NaaAeOO a eaai?aoi?iiio i?aeoeeoii ii eo?no “Oai??y
aaoiiaoe/iiai oi?aae?iiy”. Ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe
i?aeoaa?aeaeai? a?aeiia?aeieie aeoaie.
Ai?iaaoe?y ?iaioe. Iniiai? iaoeia? ? i?aeoe/i? ?acoeueoaoe
aeena?oaoe?eii? ?iaioe aeiiia?aeaeenue ? iaaiai?thaaeenue ia 3-e
oe?a?inuee?e eiioa?aioe?? «Aaoiiaoeea-96» (Naaanoiiieue, 1996 ?.), 3-e ?
4-e e?einuee?e i?aeia?iaei?e iaoaiaoe/i?e oeie? «Iaoiae ooieoe??
Eyioiiaa ? eiai aeiaeaoee» (Aeoooa, 1997 ?., Aeoooa, 1998 ?.), 3-e
i?aeia?iaeiie iaoeiai – oaoi?/iie eiioa?aioe?? «Oi?aae?iiy aeei?enoaiiyi
aia?a??» (Naaanoiiieue, 1998 ?.).
Ioae?eaoe??. ?acoeueoaoe aeena?oaoe?? ui aeiinyoueny ia caoeno
iioae?eiaai? o 7 noaooyo iaoeiai – oaoi?/ieo ca??ie nieneo AAE Oe?a?ie.
No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio,
oanoe ?icae?e?a, aeniiae?a, niene?a e?oa?aoo?e ? aeiaeaoe?a. Caaaeueiee
ianya ?iaioe 168 noi??iie ae?oeiaaiiai oaenoo, i?noeoue 45 iaethie?a, 17
oaaeeoeue, nienie aeei?enoaieo aeaea?ae c 79 iaeiaioaaiue.
CI?NO ?IAIOE
A anooi? iaa?oioiao?oueny aeooaeuei?noue ?iaioe, noi?ioeueiaai? iaoa ?
iniiai? caaea/? aeine?aeaeaiiy, ia?a?aoiaai? ae??oai? a ?iaio? caaea/? ?
?acoeueoaoe ?o ??oaiiy ui caoeuathoueny, iaaaaeaia noenea aeeeaaeaiiy
oiai iiaiai, ui aiineoueny aaoi?ii a aeine?aeaeaiiy i?iaeaie, aecia/aia
i?aeoe/ia oe?ii?noue io?eiaieo ?acoeueoao?a.
A ia?oiio ?icae?e? i?eaiaeeoueny iaeyae e?oa?aoo?e ii i?iaeaiaoeoe?, ui
aeine?aeaeo?oueny, aeacothoueny iniiai? iai?yiee ? i?aeoiaee a ??oaii?
iinoaaeaieo caaea/. Cie?aia, iaeyae ?nioth/eo ioae?eaoe?e iieaco?, ui
caaea/a aiae?co no?eeino? nenoai aaoiiaoe/iiai oi?aae?iiy c
iaia?aiao?e/iie iaicia/aii?noueth a iiaeae? ia’?eoo ? iaei??th c
oeaio?aeueieo i?iaeai oai??? oi?aae?iiy ? i?iaeiaaeo? i?eaa?oaoe oaaao
aaeee? eieueeinoi aeine?aeiee?a. Oaeiae aeaco?oueny, ui caaea/a D –
iiaeieo ? /anoiei aeiaaeeii caaea/? ?iaanoiie no?eeino? ca iayaiino?
ia?aiao?e/ii? iaicia/aiino? a iiaeae? ia’?eoo ? caaea/a ioe?iee yeino?
NAO i?e neioac? ?? iaoiaeii D – iiae?eo ? iaaeoi aeooaeueiith. Iaeyae
e?oa?aoo?e iieaco?, ui ?nioth/? caniae iiae?aii? ioe?iee caniiaai? ia
/anoioiii i?aeoiae?. Ii ?yaeo i?e/ei, a aaaaoueio aeiaaeeao canoinoaaiiy
/anoioieo cania?a a aaoiiaoeciaaieo ?ic?aooieao iaaoaeoeaii. Oiio
aeieea? iaiao?aei?noue iiaoaeiae iie?iii?aeueieo oi?i ia??aiinoae,
?icaeyaeoaaieo i?e ??oaii? caaea/ aiae?co ? neioaco ?iaanoii no?eeeo NAO
i?e iaia?aiao?e/iie iaicia/aiino? a iiaeae? ia’?eoo ? ioe?iee yeino?
NAO, ye? neioacothoueny iaoiaeii D – iiae?eo ii aauanoaaiiio ia?aiao?o.
A ae?oaiio ?icae?e? ?icaeyaea?oueny canoinoaaiiy ocaaaeueiaiiai iaoiaea
?aona – Ao?a?oea aei aiae?co ?iciiae?eo ei?ai?a aauanoaaiiai iiiai/eaia,
ye can?a aeine?aeaeaiiy aeanoeainoae /anoioieo aiaeia?ao?a.
A o?aoueiio ?icae?e? i?iiiio?oueny iaoiae aeine?aeaeaiiy no?eeino?
e?i?eieo iaia?a?aieo NAO c iaia?aiao?e/iith iaicia/aii?noueth a iiaeae?
ia’?eoo, iniiaaiee ia aiae?c?, ca aeiiiiiaith ocaaaeueiaiiai iaoiaeo
?aona – Ao?a?oea, ?iciiae?eo aauanoaaieo ei?ai?a e??oa??aeueiiai
iiiai/eaia, ui oa?aeoa?eco? /anoioiee aiaeia?ao.
.
, yeui:
iathoue iaeiaeiaa /enei iano?eeeo iiethn?a;
,
(1)
iathoue iaeiaeiao eieueeinoue ei?ai?a ia iieiie in?.
, yeui:
iathoue iaeiaeiaa /enei iano?eeeo iiethn?a;
,
(2)
– caaeaia i?aaeeueia ?aoe?iiaeueia ooieoe?y, ui oa?aeoa?eco?
ioeueoeie?eaoeaio iaicia/aii?noue iiaeae?.
I?e /anoioiiio aiae?c? ?iaanoiie no?eeino? ?icaeyaeoaaieo nenoai
aeei?enoiaothoueny eaiie io?eiai? H. Kimura ? K. Wei, R. K. Yedavalli:
, aea
, (3)
? ?iaanoii no?eeei, yeui ? o?eueee yeui:
?
a) aeeiio?oueny ia??ai?noue
. (4)
aecia/a?oueny ni?aa?aeiioaiiyi (3), ? ?iaanoii no?eeei, yeui ? o?eueee
yeui:
.
(5)
Aeey ia?aoiaeo aei iie?iii?aeueieo oi?i ia??aiinoae aiae?co ?iaanoiie
no?eeino? i?e aaeeoeaiie iaicia/aii?no? aaiaeyoueny a ?icaeyae:
«?iaanoeciaaiiee» oa?aeoa?enoe/iee iiiai/eai caieiooi? nenoaie
, (6)
,
? «?iaanoeciaaiee» oa?aeoa?eno/iee iiiai/eai ?iciieiooi? nenoaie
.
(7)
Aiae?coth/e ia??ai?noue (4), iiaeaii caienaoe
(8)
aai, aeei?enoiaoth/e iiaeaiiy aeey eaaae?aoo iiaeoey, caieoaii
(9)
s=j(, oi aeey iiaeaeueoiai aiae?co (4) ?icaeyaea?oueny iiiai/eai
(10)
o aeaeyae?
, (11)
(12)
aeaeyaeo
(13)
x, caieoaii
, (14)
o./., aeey aeeiiaiiy ia??aiino? (9) iaiao?aeii ? aeinoaoiuei, uia
aeeiioaaeany ia??ai?noue
(15)
.
??oaiiy iinoaaeaii? caaea/? aecia/a?
aoa ?iaanoii no?eeei, iaiao?aeii ? aeinoaoiuei, uia:
;
aeeiioaaeinue ni?aa?aeiioaiiy
(16)
Aeey aiae?co ?iaanoiie no?eeino? NAO ca iayaiino? ioeueoeie?eaoeaiie
iaicia/aiiino? a iiaeae? ia’?eoo aaiaeyoueny a ?icaeyae «?iaanoeciaai?»
iiiai/eaie
(17)
, (18)
Oaeiae aaiaeeoueny iiiai/eai
. (19)
Aeeiioth/e iiaoaeiae aiaeia?/i? aeiaaeeo aaeeoeaii? iaicia/aiino?
iaea?aeo?ii, ui iaiao?aei? ? aeinoaoi? oiiae ?iaanoiie no?eeino?
?icaeyaeoaaii? NAO i?e caaeaiie ioeueoeie?eaoeaiie iaicia/aiino?
aecia/a?
aoa ?iaanoii no?eeei iaiao?aeii ? aeinoaoiuei, uia:
;
2. Aeeiioaaeinue ni?aa?aeiioaiiy
(20)
. Ia?aa??ea oiia (16) ? (20) cae?enith?oueny ca aeiiiiiaith
iaoaiaoe/iiai aia?aoo caaaeueii? i?iaeaie ?aona, cie?aia, oeyoii
iiaoaeiae i?inoi? ocaaaeueiaii? oaaeeoe? ?aona ii aeaii ao?aeiei
?yaeeai, ui oi?iothoueny ii eiao?oe?aioai caaeaiiai iiiai/eaia, ?
canoinoaaiiy i?aaeea ia/eneaiiy /enea ??ciiiai?oieo iaaaoeaieo ei?ai?a
aauanoaaiiai iiiai/eaia.
a neiaieueiiio aeaeyae? canoinoaaiiyi Ao?a?oeaaeo oi?i aiae?co
?iciiae?eo aauanoaaieo ei?ai?a iiiai/eaia iaea?aeo?ii nenoaie
aeaaa?a?/ieo ia??aiinoae, aeica?e yeeo i?ecaiaeeoue aei iiaoaeiae
iaeanoae ?iaanoiie no?eeino? NAO a i?inoi?? ia?aiao??a ?aaoeyoi?a.
A /aoaa?oiio ?icae?e? i?iiiio?oueny aeaaa?a?/iee i?aeo?ae aeine?aeaeaiiy
yeino? nenoai, yea neioaco?oueny iaoiaeii D – iiaeieo ii aauanoaaiiio
ia?aiao?o, ui cae?enith?oueny canoinoaaiiyi iaoaiaoe/iiai aia?aoo
caaaeueii? i?iaeaie ?aona ? naiaeyu?eny aei aiae?co aauanoaaieo ei?ai?a
iiiai/eai?a, a oaeiae ?iaeaen?a Eioe ?aoe?iiaeueieo ooieoe?e, ui
oa?aeoa?ecothoue a?aeiia?aei? /anoioi? aiaeia?aoe ? e?eoa???.
A yeino? nenoai c ia?aiao?e/iith iaicia/aii?noueth ?icaeyaea?oueny NAO,
yea neioaco?oueny iaoiaeii D – iiaeieo ii aauanoaaiiio e?i?eiiio
ia?aiao?o. A yeino? ao?aeieo aeei?enoiaothoueny /anoioi? e?eoa???
ioe?iee yeino? ?icaeyaeoaaieo nenoai A. A. Iaa?iaa.
ia? aeaeyae
. (21)
Aeey io?eiaiiy iieeiii?aeueieo ia??aiinoae aeei?enoiao?oueny iiaeaiiy
aeey aauanoaaiie ? ii?iie /anoeie /anoioiiai aiaeia?aoa
, (22)
, (23)
aea
A (s2)=(1/2) [R (s) Q (-s) +R (-s) Q (s)] =/ao [R (-s) Q (s)],
(24)
)=(1/2) [sQ (s) R (-s)+(-s) Q (-s) R (s)] =/ao [-sQ (-s) R (s)].
(25)
Aeei?enoiaoth/e icia/ai? iiaeaiiy ? iiaeaiiy aeey eaaae?aoo iiaeoey
iaea?aeo?ii aeaaa?a?/i? oi?ie aiae?co ye?nieo iieaciee?a ?icaeyaeoaaieo
NAO.
Oae, iayai?noue a nenoai? caiano no?eeino? ii oac? ia iaioa caaeaiiai
aecia/a?oueny ae?aaeaiiyi
(E/A+) =0,
(26)
aea ae?aaeaiiy a e?a?e /anoei? (26) icia/a? /enei iaaaoeaieo ei?ai?a
iiiai/eaia E (x) ui aeinoaaeythoue iiceoeaia cia/aiiy iiiai/eaio A(x), a
iiiai/eaie E(x) ? A(x) oa?aeoa?ecothoue aiaeia?ao D – iiaeieo.
Aiaeia?/ii io?eiai? aeaaa?a?/i? ae?ace aeey ioe?iee iiiioiiino?
ia?ao?aeiiai i?ioeano, aaee/eie ia?a?aaoethaaiiy, /ano ?aaoethaaiiy ?
aiae?co iieiaeeoaeuei?no? aauanoaaiie /anoioiie oa?aeoa?enoeee nenoaie
yea neioaco?oueny. An? io?eiai? ni?aa?aeiioaiiy aeneiaeththoueny /a?ac
oae? /enea, ui oa?aeoa?ecothoue ?iciiae?e ei?ai?a iiiai/eai?a, ye /enei
on?o ??ciiiai?oieo aauanoaaieo, /enei an?o ??ciiiai?oieo iaaaoeaieo
(iiceoeaieo) aauanoaaieo ei?ai?a, /enei ??ciiiai?oieo iaaaoeaieo
(iiceoeaieo) aauanoaaieo ei?ai?a caaeaii? e?aoiino?, /enei ??ciiiai?oieo
aauanoaaieo ei?ai?a a caaeaiiio ?ioa?aae?. Icia/ai? /enea
ia/eneththoueny ca aeiiiiiaith iaoaiaoe/iiai aia?aoo caaaeueii?
i?iaeaie ?aona oeyoii iiaoaeiae i?inoi? ? ?icoe?aii? oaaeeoeue ?aona ?
canoinoaaiiy a?aeiia?aeieo aeai?eoi?a.
A i’yoiio ?icae?e? ?icaeyaeathoueny ieoaiiy, ca’ycai? c ?ic?iaeith
e?iaa?noe/iiai ? i?ia?aiiiai caaacia/aiiy.
A oinoiio ?icae?e? iaaaaeai ?ic?aooiie nenoaie aaoiiaoe/iiai oi?aae?iiy
aaaeeiai e?oaea i?e caoiae? ia iinaaeeo ? nenoaie aaoiiaoe/iiai
oi?aae?iiy neeiaei a??ineii?/iei noaa?e?caoi?ii ca aeiiiiiaith
cai?iiiiiaaieo a aeena?oaoe?? i?aeoiae?a.
INIIAI? ?ACOEUeOAOE ? AENIIAEE
?ic?iaeai? aeaaa?a?/i? caniae aiae?co ? neioaco a?oaeo e?i?eieo
iaia?a?aieo NAO c iaicia/ai?noueth a iiaeae? ia’?eoo.
?iciianthaeaeaii canoinoaaiiy ocaaaeueiaiiai iaoiaeo ?aona – Ao?a?oea ia
caaea/? aiae?co ? neioaco a?oaeo nenoai oi?aae?iiy c iaia?aiao?e/iith
iaicia/aii?noueth a iiaeae? ia’?eoo.
Io?eiai? iaiao?aei? ? aeinoaoi? oiiae ?iaanoiie no?eeino? e?i?eii?
iaia?a?aii? NAO ca iayaiino? iaia?aiao?e/iie iaicia/aiino? a iiaeae?
ia’?eoo a oi?i? aiae?co ?iciiae?eo aauanoaaieo iaaaoeaieo ei?ai?a
e??oa??aeueieo iiiai/eai?a canoinoaaiiyi ocaaaeueiaiiai iaoiaea ?aona.
Io?eiaia iaoiaeeea oi?ioaaiiy oiia a aeaeyae? nenoaie aeaaa?a?/ieo
ia??aiinoae neioaco ia?aiao??a ?aaoeyoi?a caaeaii? no?oeoo?e ?iaanoii
no?eei? e?i?eii? iaia?a?aii? NAO c iaia?aiao?e/iith iaicia/aii?noueth a
iiaeae? ia’?eoo. Icia/aia iaoiaeeea caniiaaia ia aiae?c? iiceoeaii?
aecia/aii?no? iiiai/eaia a neiaieueiiio aeaeyae? canoinoaaiiyi
Ao?a?oeaaeo oi?i aiae?co ?iciiae?eo aauanoaaieo ei?ai?a iiiai/eaia.
Io?eiai? oiiae ioe?iee yeino? NAO yea neioaco?oueny iaoiaeii D – iiaeio
ii aauanoaaiiio ia?aiao?o a oi?i? aiae?co ?iciiae?eo aauanoaaieo ei?ai?a
iiiai/eai?a, ui oa?aeoa?ecothoue /anoioio e?eao D – iiaeieo.
Cai?iiiiiaai? a aeena?oaoe?ei?e ?iaio? aeaaa?a?/i? i?aeoiaee
aeicaieythoue ?noioii i?aeaeueoe aoaeoeai?noue aaoiiaoeciaaiiai
aeine?aeaeaiiy ? i?iaeooaaiiy NAO ca ?aooiie nei?i/aiiy ia aeae?eueea
ii?yaee?a caaaeueiiai /enea iia?aoe?e a iiaoaeiaao ? canoinoaaiiyo
?icaeyaeoaaieo e?eoa???a ?iaanoiie no?eeino? ? yeino?, a oaeiae ca
?aooiie nenoaiii? ?aae?caoe?? aeai?eoi?/ieo cania?a a iaoeiieo
aeine?aeaeaiiyo.
?ic?iaeaiee i?ia?aiiee eiiieaen «MULTI-ROUTH» neeaaea?oueny c iniiaii?
i?ia?aie ? a?ae?ioaee i?ia?aiieo iiaeoeae, ui aeicaieeoue aaoiiaoeciaaia
ae??ooaaoe iinoaaeai? a aeena?oaoe?ei?e ?iaio? caaea/?. ssae?ii
?ic?iaeaiiai i?ia?aiiiai eiiieaeno ? caniae ? aeai?eoie ocaaaeueiaiiai
iaoiaea ?aona.
Aeei?enoiaoth/e cai?iiiiiaai? iaoiaee ? aeai?eoie aeeiiaii
aeine?aeaeaiiy a?oaino? ?aaeueieo nenoai oi?aae?iiy.
?acoeueoaoe i?iaaaeaieo aeine?aeaeaiue iiaeooue aooe aeei?enoai? i?e
aaoiiaoeciaaieo aeine?aeaeaiiyo neeaaeieo nenoai aaoiiaoe/iiai
oi?aae?iiy.
NIENIE IIOAE?EIAAIEO ?IA?O
Iniiai? iieiaeaiiy aeena?oaoe?? aeeeaaeai? a ianooiieo ?iaioao:
Aa?aaaiia A.O., E?aia?ue A.A. Aeaaa?ae/aneea oi?iu /anoioiuo e?eoa?eaa
ea/anoaa eeiaeiuo nenoai oi?aaeaiey // Aanoiee NaaAOO. Aaoiiaoecaoeey
i?ioeannia e oi?aaeaiea. -1996. -Aui.2. -N.3-17.
Aa?aaaiia A.O., E?aia?ue A.A. Aeaaa?ae/aneea ioeaiee ea/anoaa nenoaiu ia
iniiaa e?eaie D – ?acaeaiey ii aauanoaaiiiio ia?aiao?o // Aanoiee
NaaAOO. Aaoiiaoecaoeey i?ioeannia e oi?aaeaiea. -1997. -Aui.7. -N.9-17.
E?aia?ue A.A. E?eoa?ee iieiaeeoaeueiinoe aauanoaaiiuo /anoioiuo
oa?aeoa?enoee nenoaiu neioace?oaiie iaoiaeii D – ?acaeaiey // Aanoiee
NaaAOO. Aaoiiaoecaoeey i?ioeannia e oi?aaeaiea. -1997. -Aui.7.
-N.124-128.
Aa?aaaiia A.O., E?aia?ue A.A., Iao?ooeia I.A. Aeai?eoie/aneee e
i?ia?aiiiue eiiieaen Multi – Routh aiaeeca e neioaca eeiaeiuo e
iaeeiaeiuo nenoai // Aanoiee NaaAOO. Eioi?iaoeea, yeaeo?iieea e naycue.
-1998. -Aui.10.-N.9-15.
Aa?aaaiia A.O., E?aia?ue A.A. Aeaaa?ae/aneay oi?ia aiaeeca onoie/eainoe
eeiaeiuo iai?a?uaiuo nenoai aaoiiaoe/aneiai oi?aaeaiey n
iaia?aiao?e/aneie aaeaeeoeaiie iaii?aaeaeaiiinoueth // Aanoiee NaaAOO.
Aaoiiaoecaoeey i?ioeannia e oi?aaeaiea. -1998. -Aui.14.-N.3-10.
E?aia?ue A.A. Aeaaa?ae/aneay oi?ia aiaeeca onoie/eainoe eeiaeiie
iai?a?uaiie nenoaiu i?e ioeueoeieeeaoeaiie iaii?aaeaeaiiinoe // Aanoiee
NaaAOO. Aaoiiaoecaoeey i?ioeannia e oi?aaeaiea. – 1998.
-Aui.14.-N.76-80.
Aa?aaaiia A.O., E?aia?ue A.A. Aeaaa?ae/aneea oi?iu ioeaiee caiania
onoie/eainoe eeiaeiuo nenoai oi?aaeaiey // Aeeiaie/aneea nenoaiu.-
1998.- Aui.14.- N.-10-18.
E?aia?ue A.A. Aeaaa?ae/aneea oi?iu aiaeeca e neioaca a?oauo eeiaeiuo
iai?a?uaiuo nenoai aaoiiaoe/aneiai oi?aaeaiey. – ?oeiienue.
Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.13.03 – Nenoaiu e i?ioeannu oi?aaeaiey, –
Naaanoiiieueneee ainoaea?noaaiiue oaoie/aneee oieaa?neoao, Naaanoiiieue,
1999.
A aeenna?oaoeee i?aaeeaaathony iiaua iaoiaeu aeaaa?ae/aneiai aiaeeca e
neioaca nenoai aaoiiaoe/aneiai oi?aaeaiey i?e iaee/ee iaia?aiao?e/aneie
iaii?aaeaeaiiinoe a iiaeaee iauaeoa e NAO, neioace?oaiie iaoiaeii D –
?acaeaiey ii i?iecaieueiiio aauanoaaiiiio ia?aiao?o.
Iieo/aiu niioiioaiey, iicaieythuea enneaaeiaaoue ?iaanoioth
onoie/eainoue i?e iaee/ee aaeaeeoeaiie eee ioeueoeieeeaoeaiie
iaii?aaeaeaiiinoe a iiaeaee iauaeoa ia iniiaa aiaeeca ?ani?aaeaeaiey
ei?iae e?eoa?eaeueiuo iiiai/eaiia iaiauaiiuie iaoiaeaie ?aona –
Ao?aeoea. ?ac?aaioaia iaoiaeeea iino?iaiey nenoai aeaaa?ae/aneeo
ia?aaainoa aeey neioaca ia?aiao?ia ?aaoeyoi?a caaeaiiiai aeaea eeiaeiie
iai?a?uaiie NAO i?e iaee/ee iaia?aiao?e/aneie iaii?aaeaeaiiinoe a
iiaeaee iauaeoa . A iniiaa oeacaiiie iaoiaeeee eaaeeo i?eiaiaiea
iaiauaiiiai iaoiaea Ao?aeoea e aiaeeco ?ani?aaeaeaiey ei?iae
e?eoa?eaeueiuo iiiai/eaiia, niaea?aeaueo neioace?oaiua ia?aiao?u
?aaoeyoi?a. ?ac?aaioaiu niioiioaiey, iicaieythuea ioeaieaaoue
ea/anoaaiiua ia?aiao?u nenoaiu aaoiiaoe/aneiai oi?aaeaiey neioace?oaiie
iaoiaeii D – ?acaeaiey ii aauanoaaiiiio eeiaeii aoiaeyuaio ia?aiao?o eee
eiyooeoeeaioo oneeaiey i?yiie oeaie a /anoiii neo/aa. Aeey ?aoaiey
iinoaaeaiiie caaea/e iieo/aiu iieeiiieaeueiua oi?iu /anoioiuo ia?aaainoa
A.A. Iaa?iaa. ?aoaiea iieo/aiiuo iieeiiieaeueiuo ia?aaainoa
inouanoaeyaony iooai i?eiaiaiey iaiauaiiiai iaoiaea ?aona – Ao?aeoea e
aiaeeco ciaeiii?aaeaeaiiinoe ?aoeeiiaeueiie ooieoeee.
Iieo/aiu aeaaa?ae/aneea au?aaeaiey, iicaieythuea ioeaieaaoue caian
onoie/eainoe ii oaca nenoaiu, iiiioiiiinoue ia?aoiaeiiai i?ioeanna,
aaee/eio ia?a?aaoee?iaaiey, a?aiy ?aaoee?iaaiey e aiaeece?iaaoue
iieiaeeoaeueiinoue aauanoaaiiie /anoioiie oa?aeoa?enoeee neioace?oaiie
nenoaiu. Ana iieo/aiiua a aeenna?oaoeee niioiioaiey au?aaeathony
iin?aaenoaii /eneiauo oa?aeoa?enoee ?ani?aaeaeaiey ei?iae aauanoaaiiuo
iiiai/eaiia, oaeeo eae /enei anao ?acee/iuo aauanoaaiiuo, /enei anao
?acee/iuo io?eoeaoaeueiuo (iieiaeeoaeueiuo) aauanoaaiiuo ei?iae, /enei
?acee/iuo io?eoeaoaeueiuo (iieiaeeoaeueiuo) aauanoaaiiuo ei?iae
caaeaiiie e?aoiinoe, /enei ?acee/iuo aauanoaaiiuo ei?iae a caaeaiiii
eioa?aaea. Oeacaiiua /enea au/eneythony i?e iiiiue iaoaiaoe/aneiai
aiia?aoa iauae i?iaeaiu ?aona, iooai iino?iaiey i?inouo e ?anoe?aiiuo
oaaeeoe ?aona – Ao?aeoea e i?eiaiaiey niioaaonoaothueo aeai?eoiia.
Eeth/aaua neiaa: iaia?aiao?e/aneay iaii?aaeaeaiiinoue, ?iaanoiay
onoie/eainoue, iaiauaiiue iaoiae ?aona – Ao?aeoea, aeaaa?aecaoeey, D –
?acaeaiea, iieacaoaee ea/anoaa.
E?aia?ue A. A. Aeaaa?a?/i? oi?ie aiae?co ? neioaco a?oaeo e?i?eieo
iaia?a?aieo nenoai aaoiiaoe/iiai oi?aae?iiy. – ?oeiien.
Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ii niaoe?aeueiino? 05.13.03 – Nenoaie ? i?ioeane oi?aae?iiy, –
Naaanoiiieuenueeee aea?aeaaiee oaoi?/iee oi?aa?neoao, Naaanoiiieue,
1999.
A aeena?oaoe?? i?iiiiothoueny iia? iaoiaee aeaaa?a?/iiai aiae?co ?
neioaco nenoai aaoiiaoe/iiai oi?aae?iiy ca iayaiino? iaia?aiao?e/iie
iaicia/aii?no? a iiaeae? ia’?eoo ? NAO, yea neioaco?oueny iaoiaeii D –
iiaeieo ii aauanoaaiiio ia?aiao?o. Io?eiai? ni?aa?aeiioaiiy, ui
aeicaieyoue aeine?aeaeoaaoe ?iaanoioth no?ee?noue NAO c aaeeoeaiie aai
ioeueo?ie?eao?aiie iaicia/aiinoueth a iiaeae? ia’?eoo ia iniia?
aiae?co ?iciiae?eo ei?ai?a e??oa?eaeueiiai iiiai/eaia ocaaaeueiaiei
iaoiaeii ?aona. Ia iniia? ocaaaeueiaiiai iaoiaeo Ao?a?oea io?eiai? oiiae
a oi?i? nenoaie aeaaa?a?/ieo ia??aiinoae aeey neioaco ia?aiao??a
?aaoeyoi?a NAO c iaia?aiao?e/iie iaicia/aii?noueth a iiaeae? ia’?eoo.
?iciianthaeaeaii canoinoaaiiy ocaaaeueiaiiai iaoiaeo ?aona – Ao?a?oea ia
aiae?c ?yaeo iieaciee?a yeino? nenoai, ye? neioacothoueny iaoiaeii D –
?aca??i?y.
Eeth/ia? neiaa: iaia?aiao?e/ia iaicia/aii?noue, ?iaanoia no?ee?noue,
ocaaaeueiaiee iaoiae ?aona – Ao?a?oea, aeaaa?a?caoe?y, D – ?aca??i??,
iieacieee yeino?.
Kramar V. A. The algebraic forms of the analysis and synthesis of rough
linear continuous systems of automatic control. – Manuscript.
Dissertation on competition of a scientific degree of the candidate of
engineering science on a speciality 05.13. 03 – System and control
procedures, – Sevastopol state engineering university, Sevastopol, 1999.
In a thesis the new methods of the algebraic analysis and synthesis of
systems of automatic control are offered at presence of nonparametric
uncertainty in a model of plant and system, synthesized by a method D –
partition on a real parameter. The relations permitting to investigate
system’s robust stability with additive or multiplicate uncertainty in a
model of plant are
obtained analysing distribution of the roots of a criteria polynomial on
a generalized Routh table. The conditions in the form of a system of
algebraic inequalities, for synthesis of parameters of the governor of a
system with nonparametric uncertainty in a model of plant are obtained,
with help of generalized method of the Hurwitz. The application of a
generalized Routh – Hurwitz method to the analysis of a series of
indexes of quality of systems synthesized by the method D – of a
partition is spreaded.
Key word: nonparametric uncertainty, robust stability generalized a
Routh – Hurwitz method, algebraization, D – partition, indexes of
quality.
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