.

Моделювання нелінійних систем з імпульсними впливами: Автореф. дис… канд. фіз.-мат. наук / С.А. Волкова, Дніпропетр. держ. ун-т. — Д., 1999. — 19 с.

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Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao

Aieeiaa Na?oeaia Aiaoie??aia

OAeE 534.121:519.8

Iiaeaethaaiiy iae?i?eieo nenoai c

?iioeuenieie aieeaaie

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

Aei?i?iiao?ianuee – 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a Oe?a?inueeiio aea?aeaaiiio o?i?ei-oaoiieia?/iiio
oi?aa?neoao?, I?i?noa?noai ina?oe Oe?a?ie

Iaoeiaee ea??aiee:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?,

Ieeei/oe Aaea??e Ieeieaeiae/

Oe?a?inueeee aea?aeaaiee o?i?ei-oaoiieia?/iee oi?aa?neoao,

caa. eao. aeui? iaoaiaoeee.

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

I?oe?i TH??e Aieiaeeie?iae/

Oa?e?anueeee aea?aeaaiee iie?oaoi?/iee oi?aa?neoao,

i?ioani? eaoaae?e i?eeeaaeii? iaoaiaoeee.

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

Iaiaeai Iaoae?y ?ee?aia

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao,

i?ioani? eaoaae?e ia/enethaaeueii? iaoaiaoeee oa iaoaiaoe/ii?
e?aa?iaoeee.

I?ia?aeia onoaiiaa: Ee?anueeee aea?aeaaiee oi?aa?neoao ?iai? Oa?ana
Oaa/aiea, eaoaae?a iiaeaethaaiiy neeaaeaieo nenoai, oaeoeueoao
e?aa?iaoeee, I?i?noa?noai ina?oe Oe?a?ie, i. Ee?a.

Caoeno a?aeaoaeaoueny «9» aa?aniy 1999 ?. i 930 aiaeeie ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee

E 08.051.09 i?e Aei?i?iiao?ianueeiio aea?aeaaiiio oi?aa?neoao? ca
aae?anith:

320010, i. Aei?i?iiao?ianuee, i?. Ea?ea Ia?ena, 35, ei?i. 3, aoae. 42.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? Aei?i?iiao?ianueeiai
aea?aeaaiiai oi?aa?neoaoo,

320050, i. Aei?i?iiao?ianuee, aoe. Eicaeiaa, 8.

Aaoi?aoa?ao ?ic?neaiee «6» na?iiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ca?aaee
Oo?/eia A. A.CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. I?iaeaia aeine?aeaeaiiy iae?i?eieo nenoai c
?iioeuenieie aieeaaie, caeia? iaeia c oeaio?aeueieo i?noeue o aeeiai?oe?
nenoai. ?? ?ica’ycaiiy aaaeeeaa aeey i?aeoeee a ca’yceo c oe?ieei
aeei?enoaiiyi oaeeo nenoai o oai??? ca’yceo, aaoiiaoeciaaieo nenoaiao
ea?oaaiiy, iaaeeoeei? oa ?i.

I?iaeai? noai?aiiy iiaeaeae oa iaoiae?a ?ic?aooieo nenoai c ?iioeuenieie
aieeaaie i?enay/aii aiaaoi iaoeiaeo i?aoeue. Ua Ioaiea?a aoei
cai?iiiiiaaii iaoiaee iaoaiaoe/iiai iiaeaethaaiiy, o yeeo
aeei?enoiaothoueny i?e?iaei? oa ooo/ii aaaaeai? iae? ia?aiao?e, ui
i?enooi? o oi?ioethaaii? a?aeiia?aeii? caaea/?. Aeae? E?eeia I.I.,
Aiaiethaia I.I. oa Ieo?iiieueneee TH.I. iieacaee i?eaeaoi?noue
aneiioioe/ieo iaoiae?a iae?i?eii? iaoai?ee aeey aeine?aeaeaiiy nenoai c
?iioeuenieie aieeaaie. Ia?oeie ?iaioaie, i?enay/aieie ieoaiith no?eeino?
nenoai c ?iioeuenieie aieeaaie, i/aaeaeii aoee i?aoe? I?eueiaia A.Ae. oa
Ieoe?na A.Ae.

Oe?iei iiaeai? a e?oa?aoo?? iaoiaee iiaeaethaaiiy neeaaeieo nenoai c
?iioeuenieie aieeaaie oeyoii i?yiiai /enaeueiiai aiae?co ( Oaeaiae O.,
Iaiaeai I.?., Aaenea? Ae.) oa iaoiaee aeine?aeaeaiiy no?eeino?
iae?i?eieo nenoai (?iaeei A.O., Oona?iia Ae.ss., Aiaoia I.I.).

Neeaaei?noue iaoaiaoe/iiai oi?ioethaaiiy i?iaeaie aeey aiae?oe/iiai
aeine?aeaeaiiy iaoiiaeaia iaaeaaee?noth a?aeiia?aeieo aeeiai?/ieo
i?ioean?a. Oea i?ecaiaeeoue aei iaiao?aeiino? ?icaeyaeaoe cai?noue
iaei??? nenoaie oe?eo na??th nenoai (o i?ii?aeeao i?ae ?iioeuenaie)
(Naiieeaiei A. I., Ia?anothe I. I., Aoiaoia I.O.). Aeueoa?iaoeaiee
oeyo neeaaea?oueny o aaaaeaii? a ??aiyiiy neiaoey?ieo ooieoe?e, ui
iiaeaeththoue ?iioeuene, ? ?icaeyaeo ??aiyiue ye ?ioaa?aeueieo
oioiaeiinoae o ?aieao oai??? ?iciiae?eo. A oea iio?aao? aeiaeaoeiaeo
iaoaiaoe/ieo iaa?oiooaaiue o iae?i?eiiio aeiaaeeo (Aeaaeeie?ia A.N.,
Ianeia A.I., Iiaeueyiia A. A., ?aaiia A.E.).

Iaeiae, iacaaaeath/e ia aaeee? aeine?aeaeaiiy, i?iaaaeai? a oe?e
iaeano?, caeeoeeeny ia ?icaeyiooeie ?yae aaaeeeaeo i?iaeai. Iaeia c ieo
– oea iiaeaethaaiiy ? ?ic?aooiie iae?i?eieo aeeiai?/ieo nenoai c iaeiei
oa aeaiia nooiaiyie aie? i?e ?iioeuenieo aieeaao, c iaoith iiaeeeaino?
iaea?aeaiiy ?aeeiiai aiae?oe/iiai ?ica’yceo ia anueiio /eneiaiio
?ioa?aae?.

Oaeei /eiii, ye ?c i?aeoe/ii?, oae ? oai?aoe/ii? oi/ie ci?o ?
aeooaeueiith ?ic?iaea iiaeo iiaeaeae, ui a?aoiaothoue oei/aniao
eieae?caoe?th aieea?a ??ciiai oeio oeyoii aeei?enoaiiy iaaeaaeeiai
ia?aoai?aiiy a?aoiaioo, a oaeiae aiae?c oeeo iiaeaeae oa aeine?aeaeaiiy
caeaaeiino? i?ae ia?aiao?aie iiaeae?.

O aeai?e ?iaio? aeey ?ica’yceo iinoaaeaii? caaea/? canoiniao?oueny
iaoiae iaaeaaeeiai ia?aoai?aiiy a?aoiaioo (/ano), ui ?ai?oa c oni?oii
aeei?enoiaoaaany aeey iiaeaethaaiiy aeaaeeeo neeueii iae?i?eieo
eieeaaeueieo i?ioean?a ? i?inoi?iaeo ia??iaee/ieo no?oeoo? (Iaiaae/
E.?., I?oe?i TH.A., Aaeaeen A.O., Naeaiaea? A.Ae., Noa?ooaiei A.A.,
Aiae??aiia ?.A.). A iniia? oeueiai iaoiaeo eaaeeoue niaoe?aeueia
i?aaenoaaeaiiy ?ica’yceo aeeoa?aioe?ei? ??aiyiue, yea aeei?enoiao?
ieeeiiiae?aio ooieoe?th oa a?aoiao? a?oiia? aeanoeaino? neiao???
ia??iaee/ieo i?ioean?a. I?enooi?noue iaaeaaeeiai a?aoiaioo aeyaeeany
oaeiae aeoaea ei?eniith i?e iiaeaethaaii? ?aaeei?a c eieae?ciaaieie
iniaeeainoyie /aniai? oi?ie. Iaoiae iaaeaaeeiai ia?aoai?aiiy a?aoiaioo
noi?ioeueiaaii Ieeei/oeii A.I.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa aeeiiaia
o a?aeiia?aeiino? c ieaiaie aea?aeathaeaeaoieo oai eaoaae?e aeui?
iaoaiaoeee Oe?a?inueeiai aea?aeaaiiai o?i?ei-oaoiieia?/iiai
oi?aa?neoaoo: «?ic?iaea iaoiae?a aeine?aeaeaiiy iae?i?eieo yaeu
o?ceei-iaoaiaoe/ieo oa iaoai?/ieo nenoai » (? 10970390/47),
«Aeine?aeaeaiiy a aeeiai?oe?, e?iaiaoeoe? oa no?eeino? e?i?eieo oa
iae?i?eieo nenoai» (? 47920190).

Iaoa ? caaea/? aeine?aeaeaiiy. Aieiaiith iaoith aeine?aeaeaiiy ?
?ic?iaea e aiae?c iae?i?eieo iaoaiaoe/ieo iiaeaeae aeey nenoai c
?iioeuenieie aieeaaie, noai?aiiy e iaa?oiooaaiiy iaoiae?a aiae?oe/iiai ?
/enaeueiiai aeine?aeaeaiiy iiaiaeaeaiiy cacia/aieo nenoai o caeaaeiino?
a?ae oa?aeoa?o ?iioeueniiai aieeao oa oeio iae?i?eiino?.

Iinoaaeaia iaoa aecia/eea oae? caaea/? aeine?aeaeaiiy:

?ic?iaeo iaoiaeeee iiaeaethaaiiy iae?i?eieo nenoai i?e ?iioeuenieo
aieeaao c eieae?ciaaieie iniaeeainoyie ??ciiai oeio;

noai?aiiy iiaeo iaoaiaoe/ieo iiaeaeae iae?i?eieo aeeiai?/ieo nenoai, ui
aaeaeaaoii iienothoue ?oi? iiaiaeaeaiiy i?e ?iioeueniiio aieea?;

noai?aiiy /enaeueiiai oa aiae?oe/iiai iaoiaeo ?ica’ycaiiy caaea/, ui
aeieeee a ?acoeueoao? iiaoaeiae iiaeaeae ye? iienothoue ia??iaee/iee,
eaac?ia??iaee/iee oa oaioe/iee ?oo;

aiae?c ia?aiao??a caaaeueii? iae?i?eii? iiaeae? aeeiai?/ii? nenoaie i?e
?iioeueniiio aieea? c iaoith iiaoaeiae eieaeueieo iiaeaeae, ui
oa?aeoa?ecothoue iiaaae?ieo aeine?aeaeoaaieo nenoai;

aaeaioaoe?th aneiioioe/ieo i?ioeaaeo? iaoiae?a Ioaiea?a e ina?aaeiaiiy
aeey aeine?aeaeaiiy iae?i?eieo iaoaiaoe/ieo iiaeaeae nenoai i?e
?iioeuenieo aieeaao.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a iieyaa?:

o noai?ai? iaoiaeeee iiaeaethaaiiy aeeiai?/ieo iae?i?eieo nenoai c
iaei??th oa aeaiia nooiaiyie aie? i?e ?iioeuenieo aieeaao.
Cai?iiiiiaaiee i?aeo?ae aeicaiey? iiaeaethaaoe ye aea?aeenoaioi?, oae ?
iaaea?aeenoaioi? ?iioeuene;

o iiaoaeia? iaoaiaoe/ieo iiaeaeae o aeaeyae? e?aeiaeo caaea/, ye? ia
i?noyoue ooieoe?e Ae??aea, ui aea? iiaeeea?noue aiae?oe/iei iaoiaeii
aea/eoe aeeiai?eo nenoaie ia anueiio oei/aniaiio ?ioa?aae?. Iiaoaeiaa
iiaeaeae a?oioo?oueny ia iaoiae? iaaeaaeeiai ia?aoai?aiiy a?aoiaioo;

o aeyaeaii? iiaeeeaeo aeeiai?/ieo ?aaeei?a oa iiaoaeoaaii? eieaeueieo
iiaeaeae cai?iiiiiaaiei /enaeueii-aiae?oe/iei caniaii;

o iiaoaeia? eieaeueieo iiaeaeae, ui iienothoue ye?nii ??ci? oeie
iiaiaeaeaiiy nenoai oa aecia/aii? ?oi?o aeeiai?/ieo oa?aeoa?enoee;

o aiae?c? iaoaiaoe/ieo iiaeaeae nenoai c ?iioeuenieie aieeaaie
iaoiaeii Ioaiea?a oa ina?aaeiaiiy. Iaa?oioiaaia iiaeeea?noue ?o
canoinoaaiiy.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Io?eiai? a ?iaio?
?acoeueoaoe iiaeooue aeei?enoiaoaaoenue i?e iiaeaethaaii? iae?i?eieo
nenoai c eieae?ciaaieie /aniaeie iniaeeainoyie ??ciiai ?iaeo, i?e
?ica’ycaii? caaea/ aeeiai?/ii? no?eeino? oa aiae?co eieeaaeueieo
?aaeei?a iae?i?eieo iaoai?/ieo nenoai c iaei??th oa aeaiia nooiaiyie
aie? i?ae ae??th ?iioeueniiai iaaaioaaeaiiy. Cai?iiiiiaai? ?ica’ycee
iiaeooue aooe ei?enieie i?e aeine?aeaeaii? iiaeeeaeo aeeiai?/ieo aoaeo?a
o /anoeiai caiiaiaieo ??aeeiith no?oeoo?ao, ui ?ooathoueny, a oaeiae
?ic?aooieo aeaiaio?a i?oaeieo eiino?oeoe?e, iiaeaethaaii?
iae?iaeeiai?/ieo i?ioean?a oa aeaeo?iiieo nenoai.

Iniaenoee aianie caeiaoaa/a. I?ae ea??aieoeoaii aeieoi?a o?ceei –
iaoaiaoe/ieo iaoe, i?ioani?a Ieeei/oea A.I. ? i?e iniaeno?e o/ano?
aeena?oaioa io?eiaii iniiai? oai?aoe/i? ?acoeueoaoe oa i?iaaaeaii
/enaeueiee ?ic?aooiie iiaeeeaeo oei?a ?ica’yce?a iae?i?eieo nenoai c
ia??iaee/ieie ?iioeuenieie aieeaaie. A i?aoeyo [1], [2], [4], [5]
aeena?oaioia? iaeaaeeoue iiaoaeiaa eieaeueieo iiaeaeae; a i?aoeyo [6] –
[8] – /enaeueiee aiae?c nenoaie.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe ?iaioe
aeiiia?aeaeenue oa iaaiai?thaaeeny ia iaoeiaeo nai?ia?ao eaoaae?e aeui?
iaoaiaoeee Oe?a?inueeiai aea?aeaaiiai o?i?ei – oaoiieia?/iiai
oi?aa?neoaoo (i. Aei?i?iiao?ianuee, 1995-1999 ?.), ia i?aeia?iaei?e
eiioa?aioe?? ICBM’96 ” No?ieoaeueiua iaoa?eaeu e no?ieoaeueiua
eiino?oeoeee” (i. Aei?i?iiao?ianuee, 1996 ?.), i?aeia?iaeiiio neiiic?oi?
“Geomechanica” (i. Ono?iiue, Iieuenueea ?anioae?ea, 1997), ia
i?aeia?iaeiiio neiiic?oi? “Modelowanie w mechanice” (i. A?nea,
Iieuenueea ?anioae?ea, 1998 ?.), ia i?aeia?iaeiiio neiiic?oi?
“Theoretical foundation of civil engineering” (i. Aa?oaaa, Iieuenueea
?anioae?ea, 1998 ?.), ia iaoeiaiio nai?ia?? eaoaae?e i?eeeaaeii?
iaoaiaoeee Oa?e?anueeiai aea?aeaaiiai iie?oaoi?/iiai oi?aa?neoaoo (i.
Oa?e?a, 1998 ?.), ia iaoeiaiio nai?ia?? Aei?i?iiao?ianueeiai
aea?aeaaiiai oi?aa?neoaoo (i. Aei?i?iiao?ianuee, 1999 ?.), ia
?icoe?aiiio iaoeiaiio nai?ia?? oaeoeueoaoo e?aa?iaoeee Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea (i. Ee?a, 1999 ?.).

Ioae?eaoe??. Ca ?acoeueoaoaie aeeiiaieo aeine?aeaeaiue iioae?eiaaii 8
iaoeiaeo i?aoeue. C ieo: 3 noaoo? a iaoeiaeo aeo?iaeao, caoaa?aeaeaieo
AAE; 2 noaoo? iioae?eiaai? a iaoa??aeao eiioa?aioe?e; 1 aeaiiiiaaia
noaooy oa 2 oace.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny c
anooio, i’youeio ?icae?e?a, aeniiae?a oa nieneo aeei?enoaieo aeaea?ae.
Caaaeueiee ianya ?iaioe neeaaea? 145 noi??iie. Nienie aeei?enoaieo
e?oa?aoo?ieo aeaea?ae i?noeoue 215 iaeiaioaaiue. Oaeno aeena?oaoe??
i?noeoue 20 ?enoie?a.

INIIAIEE CI?NO AeENA?OAOe?EII? ?IAIOE

O anooi? iaa?oioiaaia aeooaeuei?noue oaie aeine?aeaeaiiy, noi?ioeueiaai?
iaoa, iniiai? caaea/? ?iaioe, iaoeiaa iiaecia io?eiaieo ?acoeueoao?a ?
?oiy i?aeoe/ia oe?ii?noue. Aeaia caaaeueia oa?aeoa?enoeea ?iaioe.

Ia?oee ?icae?e i?enay/aii aiae?co ?nioth/eo iaoiae?a aeine?aeaeaiiy
iiaiaeaeaiiy nenoai c ?iioeuenieie aieeaaie oa ?oiuei? no?eeino?.

Iieacaii, ui iiaeaethaaiiy nenoai c ?iioeuenieie aieeaaie i?iaiaeeoueny
a aeaio aniaeoao. A?aeiia?aeii aei ia?oiai, ?iioeueni? aieeae
iiaeaeththoueny oae, ui eii?aeeiaoe aai oaeaeeino? caaeiaieueiythoue
aeiaeaoeiaei oiiaai a ieieao oi/ie eieae?caoe?? ?iioeuen?a, iai?eeeaae,
caaeaiiyi no?eae?a oaeaeeinoae o iiiaio ae?? ?iioeuen?a.

Ae?oaee iai?yiie a?oioo?oueny ia oai??? ocaaaeueiaieo ooieoe?e. Ooo
?iioeueni? aieeae iiaeaeththoueny ca aeiiiiiaith aaaaeaiiy o ??aiyiiy
neiaoey?ieo /eai?a oeio SYMBOL 100 \f “Symbol” \s 12 d – ooieoe?e
Ae??aea.

Iniiaia ia?aaaaa ia?oiai caniao iiaeaethaaiiy iieyaa? a oiio, ui
aeeoa?aioe?ei? ??aiyiiy, ye? iienothoue nenoaio, oae? ae, ye ? i?e
a?aenooiino? ?iioeuen?a. I?ioa oe? ??aiyiiy iaiao?aeii ?icaeyaeaoe
ie?aii ia eiaeiiio c ?ioa?aae?a i?ae ?iioeuenaie, ? oaeei /eiii cai?noue
iaei??? nenoaie aiae?co?oueny oe?ea iine?aeiai?noue nenoai. Ae?oaee
niin?a iiaeaethaaiiy aea? ?aeeio nenoaio ??aiyiue ia onueiio /aniaiio
?ioa?aae? aac aaaaeaiiy caaaeaieo aeua oiia ia ci?ii?, aea a?aeiia?aeiee
aiae?c iiaeiai aooe ei?aeoiei a ?aieao oai??? ocaaaeueiaieo ooieoe?e. A
oea iio?aao? o iae?i?eieo aeiaaeeao aeiaeaoeiaiai iaoaiaoe/iiai
iaa?oiooaaiiy.

O aeai?e ?iaio? aeey iiaeaethaaiiy ?iioeuenieo i?ioean?a
aeei?enoiao?oueny iaoiae, noi?ioeueiaaiee Ieeei/oeii A.I. oa caniiaaiee
ia iaaeaaeeiio ia?aoai?aii? /ano. Oaeee i?aeo?ae aeicaiey?, c iaeiiai
aieo, iiaoaeoaaoe iaoaiaoe/io iiaeaeue, ui ia i?noeoue SYMBOL 100 \f
“Symbol” \s 12 d – ooieoe?e Ae??aea, a c ?ioiai – iaea?aeaoe ??
?ica’ycie o aeaeyae? ?aeeiiai aiae?oe/iiai ae?aco ia onueiio /aniaiio
?ioa?aae?.

Ne?ae cacia/eoe, ui aeiyoie “aioo??oi?o” oaea??a ca aeiiiiiaith
iaaeaaeeeo ia?aoai?aiue i?inoi?iaeo eii?aeeiao canoiniaoaaa AEo?aaeueia
A.O. Iaeiae oeae iaoiae, nei??oa ca ana, aaciina?aaeiuei
aeei?enoiao?oueny o?eueee aei a?a?ioaea?ieo nenoai oa nenoai c
iaeiia?/ieie ia oo?eioth/eie ca’yceaie. I?e oeueiio ia?aoai?aiith
i?aeaea?oueny i?inoi?iaa eii?aeeiaoa, a ia /an. O aeei?enoiaoaaiiio ooo
iaoiae? iniiaiee ia’?eo ia?aoai?aiiy – /an, a ia ooeaia ooieoe?y.

A ae?oaiio ?icae?e? noaaeoueny caaaeueia caaea/a iiaeaethaaiiy
iae?i?eieo nenoai c eieae?ciaaieie /aniaeie iniaeeainoyie,
aeeeaaeathoueny i?eioeeie ?aae?caoe?? oaeeo iiaeaeae, a oaeiae
i?iaiaeeoueny iiaoaeiaa iaoaiaoe/ieo iiaeaeae aac neiaoey?iinoae.

Iiaeaethaaiiy nenoai c eieae?ciaaieie /aniaeie iniaeeainoyie caniiaaii
ia ia?aoai?aii? /ano, o ?acoeueoao? /iai i?inoi?iaa eii?aeeiaoa iaaoaa?
no?oeoo?o aeaaa?e aac ?iciiae?eo

, (symbol 116 \f “Arial” \s 12tsymbol 174 \f “Symbol”
\s 12®symbol 116 \f “Symbol” \s 12t symbol 125 \f “Arial” \s 12,
(1)

– eoneiai-e?i?eia ia??iaee/ia ii t, c ia??iaeii T=4 ieeeiiiae?aia
ooieoe?y

– ?? ia?oa iio?aeia. Ia?aiao? SYMBOL 81 \f “Symbol” \s 12 Q ,
oa?aeoa?eco? oei ?iioeueniiai aieeao. I?e SYMBOL 81 \f “Symbol” \s 12 Q
SYMBOL 185 \f “Symbol” \s 12 ? 0 ooieoe?y SYMBOL 116 \f “Symbol” \s 12
t (t; SYMBOL 81 \f “Symbol” \s 12 Q ) ? einineiao?e/iith, ?iioeuene
ae?thoue ia?aie. I?e SYMBOL 81 \f “Symbol” \s 12 Q = 0 ooieoe?y
SYMBOL 116 \f “Symbol” \s 12 t (t; SYMBOL 81 \f “Symbol” \s 12 Q ) –
neiao?e/ia, ?iioeuene ae?thoue /a?ac ??ai? i?ii?aeee /ano.

Iaiao?aeia ni?aa?aeiioaiiy

io?eiaii oi?iaeueiei aeeoa?aioe?thaaiiyi iaio /anoei ??aiino? (1).

Iieacaii, ui iaaeaaeea ia?aoai?aiiy /ano {t SYMBOL 174 \f “Symbol” \s 12
® SYMBOL 116 \f “Symbol” \s 12 t } ? aoaeoeaiei caniaii iiaeaethaaiiy
nenoai c ?iioeuenieie aieeaaie, yea aeicaiey? iiaoaeoaaoe caaaeueio
iiaeaeue o aeaeyae? e?aeiai? caaea/? ia noaiaea?oiiio ?ioa?aae? (-1
SYMBOL 163 \f “Symbol” \s 12 F SYMBOL 116 \f “Symbol” \s 12 t SYMBOL
163 \f “Symbol” \s 12 F 1) aac SYMBOL 100 \f “Symbol” \s 12 d –
ooieoe?e. Aacoth/enue ia ia??iaee/iino? ooieoe?? SYMBOL 116 \f “Symbol”
\s 12 t (t; SYMBOL 81 \f “Symbol” \s 12 Q ) ?ica’ycie, io?eiaiee ia
i?aia??iae?, iiaeia i?iaeiaaeeoe ia anth /eneiao a?nue.

Ae?y ?iioeuenieo ii?ooaiue ia iiaeaeue iieno?oueny ca aeiiiiiaith
ae?oai? ocaaaeueiaii? iio?aeii? ooieoe?? SYMBOL 116 \f “Symbol” \s 12
t (t; SYMBOL 81 \f “Symbol” \s 12 Q ).

O aeiaaeeo iaia?a?aiiai ?ica’yceo x(t) a?i aoaea aeeeth/aiee ca ?aooiie
oiiae Y SYMBOL 189 \f “Symbol” \s 12 1/2 SYMBOL 116 \f “Symbol” \s 12
t = SYMBOL 177 \f “Symbol” \s 12 ± 1=0.

o ae?ac? aeey ae?oai? iio?aeii? aeicaiey? aeeeth/eoe neiaoey?i? /eaie
c aeo?aeiiai aeeoa?aioe?eiiai ??aiyiiy, yea iieno? iiaeaeue, ui
?icaeyaea?oueny.

Iieacaii iiaeeea?noue iiaeaethaaiiy ?iioeuenieo aieea?a ??ciiai oeio,
oiaoi iiaeaethaaiiy ia o?eueee aea?aeenoaioieo, aea e
iaaea?aeenoaioieo ?iioeuenieo aieea?a, ui cia/ii ?icoe?th? eiei
?ica’ycaieo caaea/.

Iniiai? aoaie iiaeaethaaiiy ?ethno?othoueny ia o?ueio oeiiaeo nenoaiao.

, ui ia?aaea?oueny /a?ac aaniethoii aei?noeo iaaaioaaeoaaeueio aaeeo.
Iiaiaeaeaiiy ieanoeie iieno?oueny ??aiyiiyi

aea SYMBOL 68 \f “Symbol” \s 12 D – aeeoa?aioe?aeueiee iia?aoi?;

D – oeee?iae?e/ia aei?noe?noue;

m – iana ieanoeie, a?aeianaia aei iaeeieoe? ieiu?;

Ny, Nz, Nyz – coneeey a na?aaeeii?e iiaa?oi?.

c ianooiiei canoinoaaiiyi iaoiaeo Aaeuei?e?ia i?ecaiaeeoue aei
iae?i?eii? iiaeae? o aeaeyae? aeeoa?aioe?eiiai ??aiyiiy ae?oaiai
ii?yaeeo oeio Aeoo?iaa c ia??iaee/ieie ?iioeuenieie aieeaaie

(2)

, p ? q – ia?aiao?e;

SYMBOL 101 \f “Symbol” \s 12 e – ia?aiao? iae?i?eiino?.

Aei aiaeia?/iiai aeaeyaeo iiaeooue aooe caaaeai? ? caaea/? aeeiai?ee
?iioeuenieo no?eeeo nenoai.

Iaaeaaeea ia?aoai?aiiy /ano (1) aeicaieeei ?ic?iaeoe caaaeueio iiaeaeue
o aeaeyae? nenoaie aeeoa?aioe?eieo ??aiyiue

(1- SYMBOL 81 \f “Symbol” \s 12 Q 2)X SYMBOL 178 \f “Symbol” \s 12 ? –
2 SYMBOL 81 \f “Symbol” \s 12 Q Y SYMBOL 178 \f “Symbol” \s 12 ? +(1-
SYMBOL 81 \f “Symbol” \s 12 Q 2)2pX = – SYMBOL 101 \f “Symbol” \s 12 e
(1- SYMBOL 81 \f “Symbol” \s 12 Q 2)2Rf ,
(3)

(1+3 SYMBOL 81 \f “Symbol” \s 12 Q 2)Y SYMBOL 178 \f “Symbol” \s 12 ? –
2 SYMBOL 81 \f “Symbol” \s 12 Q (1- SYMBOL 81 \f “Symbol” \s 12 Q 2)X
SYMBOL 178 \f “Symbol” \s 12 ? +(1- SYMBOL 81 \f “Symbol” \s 12 Q 2)2pY
= – SYMBOL 101 \f “Symbol” \s 12 e (1- SYMBOL 81 \f “Symbol” \s 12 Q
2)2If,

c e?aeiaeie oiiaaie

(X’+qX) SYMBOL 189 \f “Symbol” \s 12 1/2 SYMBOL 116 \f “Symbol” \s 12
t = SYMBOL 177 \f “Symbol” \s 12 ± 1= [2 SYMBOL 81 \f “Symbol” \s 12 Q
Y’+ SYMBOL 81 \f “Symbol” \s 12 Q 2(X’+qX)] SYMBOL 189 \f “Symbol” \s 12
1/2 SYMBOL 116 \f “Symbol” \s 12 t = SYMBOL 177 \f “Symbol” \s 12 ± 1,

Y SYMBOL 189 \f “Symbol” \s 12 1/2 SYMBOL 116 \f “Symbol” \s 12 t =
SYMBOL 177 \f “Symbol” \s 12 ± 1=0.
(4)

Iacaaaeath/e ia oi?iaeueii a?eueo neeaaeiee aeaeyae, io?eiaia iiaeaeue
(3)-(4) ia i?noeoue neiaoey?ieo /eai?a. O oeueiio ?? iniiaia ia?aaaaa.
Ae?y ?iioeueniiai aieeao aeyaey?oueny a e?aeiaeo oiiaao c ia?aiao?ii q.
I?e q=0 ?iioeueni? aieeae ia nenoaio ia ae?thoue.

I?ney iiaeaethaaiiy iaaea?aeenoaioii? nenoaie i?iaaaeaii iiaeaethaaiiy
aea?aeenoaioiiai ( SYMBOL 81 \f “Symbol” \s 12 Q =0) i?ioeano. Iiaa eaea
i?i ?ic?iaeo iaoaiaoe/ii? iiaeae? aeey aeiaaeeo ??aiia?aeaeaeaieo
?iioeuen?a. I?e oeueiio ?iioeuene iiaeaeththoueny ca aeiiiiiaith
neiao?e/ii? ieeeiiiae?aii? ooieoe?? SYMBOL 116 \f “Symbol” \s 12 t
(t). No?iai eaaeo/e, oaea caaea/a ? ie?aiei aeiaaeeii
iaaea?aeenoaioiiai i?ioeano. I?ioa caaea/a ? oe?eaaith, ine?eueee
?aae?caoe?y iaoaiaoe/ii? iiaeae? aac ooieoe?e Ae??aea iiaeeeaa ca
aeiiiiiaith ia?aoai?aiiy, ui i?noeoue o?eueee X – eiiiiiaioo (Y=0).
?acoeueoaoii iaaeaaeeiai ia?aoai?aiiy ? iaoaiaoe/ia iiaeaeue o aeaeyae?
e?aeiai? caaea/?, ui i?eionea? oi/iee ?ica’ycie ??oaiiy a ae?ioe/ieo
ooieoe?yo.

2. Iae?i?eia iiaeaeue nenoaie c aeaiia nooiaiyie aie? oeio ??aeeia –
aaniethoii oaa?aea o?ei. I?iaaaeaii aeine?aeaeaiiy iiaeae?,
iiaoaeiaaii? Ieeei/oeii A.I. oa ?a?aa?iii ?.A., ui iieno? aca?iiae?th
??aeeie c aeeiai?/iith no?oeoo?ith.

Ia?aaeaa/a?oueny, ui iaieiiea ? aaniethoii aei?noeith. Iiaeaeeth
??aeeie, ui a?eueii eieeaa?oueny , ? iayoiee aeiaaeeie L. Iayoiee
aeinyaa? no?iee iaieiiee, eiee eoo c aa?oeeaeueiith neeaaeiaith
aei??aith? SYMBOL 113 \f “Symbol” \s 12 q = SYMBOL 177 \f “Symbol” \s
12 ± SYMBOL 113 \f “Symbol” \s 12 q 0. Oaea?e iayoieea ia no?iee o?ea
iienai? oaiiiaiieia?/ii iioaioe?eiei iieai, neaaeei a iaeano? SYMBOL
231 \f “Symbol” \s 12 c SYMBOL 113 \f “Symbol” \s 12 q SYMBOL 231 \f
“Symbol” \s 12 c SYMBOL 60 \f “Symbol” \s 12

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