Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea

Aaoiyeia Ieaenaiae? Ieeieaeiae/

OAeE 517.977.5

Iioeiaeueia ea?oaaiiy io/eii o?a?eoi??e c iaaeeoa?aioe?eiaaieie
e?eoa??yie yeino?

01.05.04-nenoaiiee aiae?c ?

oai??y iioeiaeueieo ??oaiue

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy a/aiiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a-1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? iiaeaethaaiiy neeaaeieo nenoai Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea.

Iaoeiaee ea??aiee:aeieoi? oaoi?/ieo iaoe, i?ioani? Aa?auaiei Oaae??
Aai?a?eiae/ (Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, i?ioani?)

Io?oe?ei? iiiiaioe:1.aeieoi? o?ceei-iaoaiaoe/ieo iaoe Inoaiaiei Aaeaioei
Aieiaeeie?iae/ (IIE “?inoeooo i?eeeaaeiiai oa nenoaiiiai aiae?co”
I?iina?oe ? IAI Oe?a?ie, i?ia?aeiee iaoeiaee ni?a?ia?oiee)2.eaiaeeaeao
o?ceei-iaoaiaoe/ieo iaoe Iaoa?e/oe Einoyioei Naaiae/ (?inoeooo iaoai?ee
IAI Oe?a?ie, iaoeiaee ni?a?ia?oiee)

I?ia?aeia onoaiiaa:?inoeooo e?aa?iaoeee ?iai? A.I. Aeooeiaa IAI Oe?a?ie,
a?aeae?e ?ioaeaeooaeueieo nenoai ea?oaaiiy aeeiai?/ieie ia’?eoaie, i.
Ee?a.

Caoeno a?aeaoaeaoueny “09” aa?aniy 1999?. ia can?aeaii? niaoe?ae?ciaaii?
a/aii? ?aaee Ae 26.001.09 Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana
Oaa/aiea, i. Ee?a, i?. Aeaaeai?ea Aeooeiaa, 6, ei?i. 2, o-o e?aa?iaoeee,
aoae. 40 i 14 aiaeei?.

(Oae./oaen 252-58-83. E-mail: [email protected]).

C aeena?oaoe??th iiaeia iciaeiieoenue o Iaoeia?e a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea, i. Ee?a, aoe. Aieiaeeie?nueea, 58.

Aaoi?aoa?ao ?ic?neaiee “5” na?iiy 1999?.

A/aiee nae?aoa?

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

A.I. Oaa/aiei

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Iioei?caoe?y ?aaeueieo nenoai ia?aaeaa/a? caaeaiiy
e?eoa??th, yeee oa?aeoa?eco? ye?noue iiaaae?iee ia’?eoo. Aiae?c
eiie?aoieo caaea/ iieaco?, ui a aaaaoueio aeiaaeeao e?eoa??e yeino? ia ?
aeeoa?aioe?eiaaiei ca O?aoa. Oaea neooaoe?y aeieea? i?e aeine?aeaeaii?
aeeiai?/ieo i?ioean?a ia no?ee?noue, ioe?ithaaii? ia?aiao??a nenoai,
aiae?c? aa?aioiaaii? /ooeeaino?, a oaeiae a caaea/ao, aea iio??aii
iaenei?coaaoe ?acoeueoao i?e i?i?ioi? aeo?ao oa ?ioeo.

A iaoaiaoe/i?e iiaeae? aeioe?eueii a?aoiaoaaoe ?iceeae ia?aiao??a
ia’?eoo. Oiae? noai aeeiai?/ii? nenoaie iieno?oueny iiiaeeiaie. sseui
aiae?c yeino? ooieoe?iioaaiiy i?iaiaeeoueny a neeo aecia/aiiai ia
?ica’yceao iaaeeoa?aioe?eiaaiiai ooieoe?iiaeo, oi i?eoiaeeii aei
iaaeaaeei? caaea/? iioeiaeueiiai ea?oaaiiy io/eii o?a?eoi??e. Cie?aia,
aaaeeeai ioe?ithaaoe iaeanoue an?o ii/aoeiaeo aeaieo, aeey yeeo
a?aeiia?aei? o?a?eoi??? ia ii?oooaaee a caaeaieo oaciaeo iaiaaeaiue. A
aeayeeo aeiaaeeao iioei?caoe?y ioe?iee iiiaeei i?aeoe/ii? no?eeino?
caiaeeoueny aei ?ica’ycoaaiiy a?aeiia?aeii? caaea/? iioeiaeueiiai
ea?oaaiiy iao?e/ieie aeeoa?aioe?aeueieie ??aiyiiyie c
iaaeeoa?aioe?eiaaieie e?eoa??yie yeino?.

Canoinoaaiiy oai?aoe/ieo ?acoeueoao?a c iaaeaaeei? iioei?caoe?? ia
i?aeoeoe? oneeaaeith?oueny ca ?aooiie aaeeei? e?eueeino? ia/eneaiue.
?nioth/? ?oa?aoe?ei? i?ioeaaeo?e ?ica’ycoaaiiy oaeeo caaea/, ye i?aaeei,
ia ? ca?aeieie aei iioeiaeueiiai ?ica’yceo. Oiio aaaeeeai, c iaeiiai
aieo, ?ic?iaeyoe /enaeuei? iaoiaee, ye? iiaeia aoei a eaaei ?aae?coaaoe,
c ?ioiai, ioe?ieoe ?o ye?ni? oa?aeoa?enoeee : ii/aoeiaa iaaeeaeaiiy,
aaee/eio e?ieo, ai?ieneiaoeai? aeanoeaino? oiui.

Oai??y iaaeeoa?aioe?eiaaii? iioei?caoe?? iaaoea ?icaeoeo caaaeyee
i?aoeyi Aaneeue?aa O.I., Aoiaea A.I., Aeai?e?ia TH.I., Aeaiueyiiaa A.O.,
??iieue?aa TH.I., Eea?ea O., Iiena?aa I.I., Ioaie/iiai A.I.,
Oaaei?aiea ?.I., Oaaei?iaa A.A., Oi?a I.C. oa ?ioeo a/aieo. A aeai?e
aeena?oaoe?ei?e ?iaio? aeine?aeaeothoueny caaea/? iioeiaeueiiai
ea?oaaiiy io/eii o?a?eoi??e c iaaeeoa?aioe?eiaaieie ooieoe?iiaeaie.
Ie?ai? ieoaiiy a oe?e aaeoc? ?icaeyaeaeenue Aiaiue?iith O.O.,
Aa?auaieii O.A., Ianyii?eiaei Ae.A. Aea aaaeeea? eeane iaaeaaeeeo caaea/
iioeiaeueiiai ea?oaaiiy io/eii o?a?eoi??e oa iia’ycai? c ieie i?iaeaie
aiae?co aeeiai?/ieo nenoai caeeoeeenue a?aee?eoeie. Oiio oaia
aeena?oaoe?? ? aeooaeueiith c iaoaiaoe/ii? oi/ee ci?o ? aaciina?aaeiuei
iia’ycaia c ?ica’ycoaaiiyi i?eeeaaeieo i?iaeai.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa aeeiiaia
ca?aeii c ieaiaie iaoeiaeo aeine?aeaeaiue eaoaae?e iiaeaethaaiiy
neeaaeieo nenoai oaeoeueoaoo e?aa?iaoeee Ee?anueeiai oi?aa?neoaoo ?iai?
Oa?ana Oaa/aiea, a oaeiae iia’ycaia c iaoeiaeie a?aioaie ?97508
“?icaeoie eiino?oeoeaii? oai??? iiaeaethaaiiy oa iioeiaeueiiai ea?oaaiiy
neeaaeieo nenoai c iaiiaieie aeaieie” oa ?97544 “?ic?iaea
i?iaeaiii-i???ioiaaieo iaoaiaoe/ieo ? i?ia?aiieo cania?a iiaeaethaaiiy,
aiae?co oa neioaco ea?iaaieo o?ceei-iaoai?/ieo nenoai” I?i?noa?noaa
iaoee ? oaoiieia?e Oe?a?ie c ooiaeaiaioaeueieo oa i?eeeaaeieo
aeine?aeaeaiue.

Iaoa ?iaioe:

1) io?eiaoe oiiae iioeiaeueiino? aeey caaea/ iioeiaeueiiai ea?oaaiiy
io/eii o?a?eoi??e c ooieoe?iiaeaie oeio iaeneioio ca ii/aoeiaeie
aeaieie, iaeneioio ca iacaeaaeiith ci?iiith ? iaeneioio ca ii/aoeiaeie
aeaieie, iacaeaaeiith ci?iiith oa ?iaeaenii;

2) ?ic?iaeoe iaiao?aei? ? aeinoaoi? oiiae aeey caaea/ i?aeoe/ii?
no?eeino?;

3) aeine?aeeoe oiiae iioeiaeueiino? aeey caaea/? iioeiaeueiiai ea?oaaiiy
iao?e/iei aeeoa?aioe?aeueiei ??aiyiiyi. C ?o aeiiiiiaith iiaoaeoaaoe
/enaeuei? iaoiaee aeey ?ica’ycoaaiiy caaea/ iioei?caoe?? ioe?iie
i?aeoe/ii? no?eeino?;

4) aeei?enoiaoth/e io?eiai? oiiae iioeiaeueiino?, iiaoaeoaaoe aeai?eoie
ciaoiaeaeaiiy iioeiaeueiiai ea?oaaiiy oa ioe?ieoe ?o ye?ni?
oa?aeoa?enoeee;

5) ai?iaoaaoe ?ic?iaeai? aeai?eoie aeey ?ic?aooieo iioeiaeueieo
oa?aeoa?enoee a aeayeeo nenoaiao i?enei?aiiy oa oieonoaaiiy.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a iieyaa? a oiio, ui a
aeena?oaoe?? aia?oa:

 noi?ioeueiaaii ? aeiaaaeaii iaiao?aei?, a oaeiae aeinoaoi? oiiae
iioeiaeueiino? aeey caaea/ iioeiaeueiiai ea?oaaiiy io/eii o?a?eoi??e ?
iao?e/iei aeeoa?aioe?aeueiei ??aiyiiyi c ooieoe?iiaeaie oeio iaeneioio
ca ii/aoeiaeie aeaieie, iaeneioio ca iacaeaaeiith ci?iiith;

 iiaoaeiaaii aeai?eoie aeey ?ica’ycoaaiiy caaea/ iioeiaeueiiai ea?oaaiiy
io/eii o?a?eoi??e c iaaeeoa?aioe?eiaaieie e?eoa??yie yeino? oa
iioei?caoe?? ioe?iie i?aeoe/ii? no?eeino?;

 i?iaaaeaii aiae?c ye?nieo aeanoeainoae ?oa?aoe?eieo i?ioeaaeo?
iaoiaeaie i?aeoe/ii? no?eeino?;

 ?ic?iaeaii /enaeuei? iaoiaee aeey ?ica’ycoaaiiy caaea/ ciaoiaeaeaiiy
iioeiaeueiiai ea?oaaiiy io/eii ca?yaeaeaieo /anoeiie a aeayeeo nenoaiao
i?enei?aiiy oa oieonoaaiiy. I?iaaaeaii ia/enethaaeueiee aenia?eiaio ii
?ic?aooieo aiie?ooaee iai?oaeaiino? i?enei?thth/iai iiey aeey
iiacaeiaaeiueiai ?ooo, i?e ye?e aia?aaoe/iee ?iceeae io/ea ca?yaeaeaieo
/anoeiie a e?ioe? i?enei?thaa/a ? i?i?iaeueiei.

Iaoiaee aeine?aeaeaiiy. A ?iaio? aeei?enoaii iaoiaee iaoaiaoe/iiai
aiae?co, oai??? iioeiaeueiiai ea?oaaiiy, iioei?caoe?? oa no?eeino?,
/enaeuei? iaoiaee.

Oai?aoe/ia oa i?aeoe/ia oe?ii?noue. ?acoeueoaoe aeena?oaoe?? iiaeooue
aooe aeei?enoaieie aeey ?ica’ycoaaiiy caaea/ ciaoiaeaeaiiy iioeiaeueiiai
ea?oaaiiy aeeiai?/ieie nenoaiaie c iaaeeoa?aioe?eiaaieie
ooieoe?iiaeaie, i?e aeine?aeaeaii? caaea/ i?aeoe/ii? no?eeino?, a oaeiae
i?e iioei?caoe?? nenoai i?enei?aiiy oa oieonoaaiiy oa ?ioeo oaoi?/ieo
nenoai.

Iniaenoee aianie aaoi?a. A ?iaioao, ui aeeiiai? c? ni?aaaoi?aie,
iniaenoee aianie aaoi?a iieyaaa a iaaiai?aii? iinoaiiaie caaea/,
aeeiiaii? an?o iniiaieo aeiaaaeaiue, ?ic?aooie?a ? a oi?ioethaaii?
aeniiae?a.

Ai?iaaoe?y ?iaioe. Iaoa??aee aeena?oaoe?eii? ?iaioe aeiiia?aeaeenue ia
iaoeiaeo nai?ia?ao eaoaae?e iiaeaethaaiiy neeaaeieo nenoai oaeoeueoaoo
e?aa?iaoeee Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea, a oaeiae ia
eiioa?aioe?yo:

 Oe?a?inuee?e eiioa?aioe?? “Iiaeaethaaiiy ? aeine?aeaeaiiy no?eeino?
nenoai” (20-24 o?aaiy 1996?., Ee?a);

 I?aeia?iaei?e eiioa?aioe?? “Modeling and investigation of systems
stability” (19-23 o?aaiy 1997?., Ee?a).

Ioae?eaoe??. Ca oaiith aeena?oaoe?? aeeiiaii 5 ?ia?o [1-5]. Iniiai?
?acoeueoaoe iioae?eiaaii a noaooyo [1-3].

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa aeeeaaeaia ia 116
noi??ieao iaoeiiieniiai oaenoo, neeaaea?oueny ?c anooio, /ioe?ueio
?icae?e?a, aeniiae?a, nieneo aeei?enoaieo aeaea?ae c 104 iaeiaioaaiue,
aeiaeaoeo oa i?noeoue 1 ?ethno?aoe?th.

CI?NO ?IAIOE

O anooi? iaa?oioiao?oueny aeooaeuei?noue aea?aii? oaie, aecia/a?oueny
iaoeiaa iiaecia io?eiaieo ?acoeueoao?a oa aena?oeth?oueny ?o oai?aoe/ia
? i?aeoe/ia oe?ii?noue.

?icae?e 1 aeena?oaoe?? i?enay/aiee iiaoaeia? iaiao?aeieo ? aeinoaoi?o
oiia iioeiaeueiino? aeey caaea/ iioeiaeueiiai ea?oaaiiy io/eii
o?a?eoi??e c iaaeeoa?aioe?eiaaieie ooieoe?iiaeaie. Iaeyae e?oa?aoo?e c
oaiaoeee aeena?oaoe?eii? ?iaioe oa iinoaiiaee caaea/, ye?
aeine?aeaeothoueny a aeena?oaoe?? iaaaaeaii a i?ae?icae?e? 1.1. A
i?ae?icae?e? 1.2 io?eiaii iaiao?aei? oiiae iioeiaeueiino? a caaea/ao
i?i?i?caoe?? ooieoe?? iaeneioio ca ii/aoeiaeie oiiaaie.

Iaoae X — eiiiaeo c aaee?aeiaiai i?inoi?o Rn,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,  — i?ino?? m-aei??ieo
eoneiai iaia?a?aieo aaeoi?-ooieoe?e ia [t0,T], V — eiiiaeo c Rm,
picscalex100010009000003e20000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c024002a0041200000026060f001a00ffffffff00001000
0000c0ffffffb9ffffff60040000f90100000b00000026060f000c004d61746854797065
0000200017000000fb0240fe0000000000009001000000cc0002001054696d6573204e65
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7800d40009000000320a000270020100000052002e0117000000fb02c0fe000000000000
9001000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd04000000
2d01010004000000f001000009000000320a3701c603010000006e00a00010000000fb02
40fe0000000000009001000000020002001053796d626f6c0002040000002d0100000400
0000f001010009000000320a0002460101000000ce0039010a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f001000003000000000000000000 — aaeoi?
oaciaeo eii?aeeiao, n-aei??ia aaeoi?-ooieoe?y f(x,u,t) ? iaia?a?aiith
?acii c /anoeiieie iio?aeieie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, i,j=1,2,…,n ii x, u, oa eoneiai
iaia?a?aia ii t. ?icaeyiaii nenoaio aeeoa?aioe?aeueieo ??aiyiue
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09000000320ac002070e010000005400010110000000fb0240fe00000000000090010000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, (1)

ia o?a?eoi??yo yei? i?i?i?co?oueny ooieoe?iiae

picscalex100010009000003fa0100000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02800300101200000026060f001a00ffffffff00001000
0000c0ffffffb0ffffffc00f0000300300000b00000026060f000c004d61746854797065
0000f00017000000fb0240fe0000000000009001000000cc0002001054696d6573204e65
7720526f6d616e2043797200ccdd040000002d01000009000000320aa001320001000000
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7800d40009000000320aa001330b010000005400010109000000320aa001cc0c01000000
7800d40017000000fb02c0fe0000000000009001000000cc0002001054696d6573204e65
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01000000460044010a00000026060f000a00ffffffff01000000000010000000fb021000
070000000000bc02000000cc0102022253797374656d00cc040000002d01000004000000
f001010003000000000000000000. (2)

Ooo O(.) — aeeoa?aioe?eiaaia ooieoe?y, yea aecia/aia ia O,
picscalex100010009000003250100000200170000000000050000000902000000000400
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0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
000004000000f0010100030000000000f2fb00000000.

Iaoae u(t) — iioeiaeueia ea?oaaiiy caaea/? (1), (2). Aeei?enoiaoth/e
aie/aoo aa??aoe?th , aeiaaaeaii ianooiia oaa?aeaeaiiy.

Oai?aia 1.1. Aeey oiai, uia ea?oaaiiy uU aeinoaaeyei i?i?ioi
ooieoe?iiaeo (2) iaiao?aeii, uia

picscalex100010009000003ce0300000300170000000000050000000902000000000400
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f001010003000000000000000000

picscalex100010009000003000300000300170000000000050000000902000000000400
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040000002d01010004000000f00102000c000000320a20024000030000006d696e005b01
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e70009000000320a9f03c006010000007500a00009000000320a9002fe09010000007600
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c40a010000004800390109000000320a2002bb0c010000007800d40009000000320a2002
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0000000000009001000000020002001053796d626f6c0002040000002d01020004000000
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2a00a70010000000fb0200ff0000000000009001000000020002001053796d626f6c0002
040000002d01010004000000f001020009000000320a10037607010000002a0086001000
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020004000000f001010009000000320a2002db19010000003d00f60017000000fb0200ff
0000000000009001000000cc0002001054696d6573204e657720526f6d616e2043797200
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17000000fb02c0fe0000000000009001000000cc0002001054696d6573204e657720526f
6d616e2043797200ccdc040000002d01020004000000f001010009000000320a9002f115
010000003000a00017000000fb0240fe0000000000009001000000cc0002001054696d65
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0002001053796d626f6c0002040000002d01020004000000f001010009000000320a2002
be080100000044000c0109000000320a20022013010000005100440109000000320a2002
c517010000005100440109000000320a2002341101000000790044010a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01010004000000f001020003000000000000000000 (3)

aeey an?o [t0,T).

picscalex100010009000003770300000300170000000000050000000902000000000400
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010000003d00f60009000000320adb02b509010000002d00f60009000000320a42063a07
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020009000000320a12025110010000002a00a70009000000320a12029012010000002a00
a70009000000320a7905660f010000002a00a70010000000fb0240fe0000000000009001
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320a4206690c01000000460044010a00000026060f000a00ffffffff0100000000001000
0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
010004000000f0010200030000000000000000000000 (4)

picscalex100010009000003ef0100000200170000000000050000000902000000000400
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4800390109000000320a00024602010000007800d40009000000320a0002b50301000000
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700009000000320a00029c04010000002c00700009000000320a00026e06010000002c00
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700009000000320a0002fa10010000002900910009000000320a0002f312010000002800
910009000000320a0002e514010000002c00700009000000320a00023e17010000002900
910010000000fb0240fe0000000000009001000000020002001053796d626f6c00020400
00002d01010004000000f001000009000000320a00021f05010000007900440109000000
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320a0002a50f010000005100440109000000320a00029013010000005100440109000000
320a00020f09010000003d00f60017000000fb02c0fe0000000000009001000000cc0002
001054696d6573204e657720526f6d616e2043797200ccdd040000002d01000004000000
f001010009000000320a70026916010000003000a0000a00000026060f000a00ffffffff
01000000000010000000fb021000070000000000bc02000000cc0102022253797374656d
00cc040000002d01010004000000f0010000030000000000000000ffffff — ooieoe?y
Aai?eueoiia.

Aeey aeiaaaeaiiy ianooiiiai oaa?aeaeaiiy nei?enoa?iiny aaaaoiaie/aoith
aa??aoe??th.

Oai?aia 1.2. Aeey oiai, uia ea?oaaiiy uU aeinoaaeyei i?i?ioi
ooieoe?iiaeo (2) iaiao?aeii, uia

picscalex100010009000003f80300000300170000000000050000000902000000000400
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0000000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc
040000002d01010004000000f001020003000000000000000000, (5)

aeey an?o iaai??a i[t0,T),
picscalex1000100090000033e0100000200170000000000050000000902000000000400
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53797374656d00cc040000002d01010004000000f001000003000000000000000000,
i0,
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000004000000f0010100030000000000fb2600000000, viV, i=2,3,…,r, aea
ni?yaeai? ooieoe?? (t,x0) caaeiaieueiythoue (4).

Ocaaaeueithth/e iiiyooy aaaaoiaie/aoi? aa??aoe??, io?eia?ii ?ioaa?aeueio
iaiao?aeio oiiao.

Oai?aia 1.3. Aeey oiai, uia ea?oaaiiy uU aeinoaaeyei i?i?ioi
ooieoe?iiaeo (2) iaiao?aeii, uia

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0000fb0200ff0000000000009001000000cc0002001054696d6573204e657720526f6d61
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000003000000000000000000, (6)

aea ni?yaeai? ooieoe?? (t,x0) caaeiaieueiythoue (4).

Na?aae iaiao?aeieo oiia, iaaaaeaieo a oai?aiao 1.1-1.3, oiiaa (6)
“neeuei?oa” a oiio ?icoi?ii?, ui aeey an?o uU, aeey yeeo aeeiio?oueny
oiiaa (6), iathoue i?noea (3), (5). Aeey iaiioeeeo caaea/ iaa?iaia
oaa?aeaeaiiy ia ni?aaaeaeo?oueny.

A aeaiiio i?ae?icae?e? iaiao?aei? oiiae io?eiai? oaeiae ia iniia?
iaeaoii?, aaaaoiiaeaoii?, eeane/ii? aa??aoe?e oa aa??aoe?? cnoao.

I?aaenoaaeii ooieoe?th ea?oaaiiy o aeaeyae?
picscalex100010009000003240200000200170000000000050000000902000000000400
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040000002d01000004000000f001010003000000000000000000. Ooo r —
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ciaoiaeaeaiiy iioeiaeueiiai ea?oaaiiy iieyaa? o aecia/aii? ooieoe?e i(t)
oa iao?eoe? ia?aiao??a . Aeey iioeiaeueiiai ea?oaaiiy
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f001010003000000000000000000 i?e aeayeiio >0 oa o?eniaaiiio iaai?? i(t),
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4003ad16010000004b00500111000000fb0240fe00000000000090010000000200020010
4d542045787472610002040000002d01030004000000f001020009000000320a40034921
010000004b00c0010a00000026060f000a00ffffffff01000000000010000000fb021000
070000000000bc02000000cc0102022253797374656d00cc040000002d01020004000000
f001030003000000000000000000. (7)

A i?ae?icae?e? 1.3 ?iaioe ?icaeyaeathoueny iaiao?aei? oiiae
iioeiaeueiino? a caaea/ao i?i?i?caoe?? ooieoe?? iaeneioio ca
iacaeaaeiith ci?iiith.

Iaoae ia o?a?eoi??yo nenoaie (1) i?e x(t0)=x0X i?i?i?co?oueny
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picscalex100010009000003730200000200170000000000050000000902000000000400
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000074007b0009000000320ac001590d010000007800d40017000000fb02c0fe00000000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. (8)

Oai?aia 1.11. Aeey oiai, uia ea?oaaiiy uU aeinoaaeyei i?i?ioi
ooieoe?iiaeo (8) iaiao?aeii, uia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,
aeey an?o [0,T).

Oaeiae aeiaaaeaii a?aeiia?aei? oiiae iioeiaeueiino?, ye? aacothoueny ia
?ioeo aa??aoe?yo ea?oaaiiy. A i?ae?icae?e? 1.4 a?aeiia?aei? iaiao?aei?
oiiae iioeiaeueiino? io?eiaii aeey ooieoe?iiaeo oeio iaeneioio ca
ii/aoeiaeie oiiaaie, iacaeaaeiith ci?iiith oa ?iaeaenii. Aeinoaoi? oiiae
iioeiaeueiino? ?icaeyiooeo caaea/ aeine?aeaeothoueny a i?ae?icae?e? 1.5.

Oai?aia 1.22. sseui a oiiaao oai?aie 1.1 O(.) — iioeea ooieoe?y,
f(x,u,t)=A(t)x+b(u,t), aea A(t) ? b(u,t) — iao?e/ia ooieoe?y i
aaeoi?-ooieoe?y ?ici??iino? a?aeiia?aeii nn oa n, oi oiiaa (3) aoaea ?
aeinoaoiueith oiiaith iioeiaeueiino?.

I?e aiaeia?/ieo i?eiouaiiyo oiiae iioeiaeueiino? (5), (6) oaeiae ?
aeinoaoi?ie.

Oai?aia 1.23. sseui a oiiaao oai?aie 1.8 O(.) — iioeea ooieoe?y,
f(x,u,t) e?i?eia ii x(.) oa ii u(.), oi ni?aa?aeiioaiiy (7) aoaea ?
aeinoaoiueith oiiaith iioeiaeueiino?.

Iiae?ai? oai?aie ni?aaaaeeea? aeey caaea/ c ooieoe?iiaeaie oeio
iaeneioio ca iacaeaaeiith ci?iiith i iaeneioio ca ii/aoeiaeie oiiaaie,
iacaeaaeiith ci?iiith oa ?iaeaenii.

A ?icae?e? 2 aeena?oaoe?eii? ?iaioe aeine?aeaeothoueny caaea/?
iioeiaeueiiai ea?oaaiiy io/eii o?a?eoi??e ia iniia? iaiao?aeieo oa
aeinoaoi?o oiia i?aeoe/ii? no?eeino?. E?eoa??? i?aeoe/ii? no?eeino?
aeeiai?/ieo nenoai io?eiaii a i?ae?icae?e? 2.1.

?icaeyiaii nenoaio aeeoa?aioe?aeueieo ??aiyiue
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, t[t0,T], (9)

aea xRn — aaeoi? oaciaeo eii?aeeiao, f(x,t) — n-aei??ia aaeoi?-ooieoe?y,
yea caaeiaieueiy? oiiaai ?nioaaiiy oa ?aeeiino? ?ica’yceo caaea/? Eio?.
Iaoae x(t,x0,t0) — o?a?eoi??y nenoaie (9), ui a?aeiia?aea? ii/aoeia?e
oiia? o(t0)=o0,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, t[t0,T] —
eiiiaeoi? iiiaeeie,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.

Oai?aia 2.1 (iaiao?aeia oiiaa i?aeoe/ii? no?eeino?). Iaoae ioeueiaee
?ica’ycie nenoaie (9) ? G0,Ot,t0,T-no?eeei. Oiae? ?nio? ooieoe?y
Eyioiiaa V(x,t), yea ? iaia?a?aiith oa iac?inoath/ith ia ?ica’yceao
nenoaie (9), i?e oeueiio

1) x : V(x,t)1Ot, t[t0,T], (10)

2) G0x : V(x,t0)1. (11)

Aeey aeine?aeaeaiiy ioeueiaiai ?ica’yceo nenoaie (9) ia
G0,Ot,t0,T-no?ee?noue iiaeia aeei?enoiaoaaoe ooieoe?th Eyioiiaa aeaeyaeo

V(x,t)=picscalex10001000900000300050000020017000000000005000000090200000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aea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 — iaeneiaeueia ii aeeth/aiith iiiaeeia G0,Ot,t0,T-no?ee?no?
ioeueiaiai ?ica’yceo nenoaie (9),  — iao?eea, ui aea?aaeaioia
aaee?aeia?e. sseui G0 ? eiiiaeoii, oi ooieoe?y Eyioiiaa iiaea aooe
aea?aia o aeaeyae?

V(x,t)=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0a000000320a9705040e02000000292c910070000a000000320a9705fe0f02000000292c
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2e00700017000000fb02c0fe0000000000009001000000cc0002001054696d6573204e65
7720526f6d616e2043797200ccdd040000002d01000004000000f001010009000000320a
7a0316030100000079008f0009000000320a7a03fc04010000004700df0009000000320a
71013d1e010000006e00a00009000000320ad70614030100000079008f0009000000320a
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2e0109000000320a3a02ed1f010000004700390109000000320a9705150a010000007400
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d40009000000320a97050d14010000007800d40009000000320a97051417010000007400
7b0009000000320a970529180100000074007b0009000000320a97051c1a010000007800
d40009000000320a9705d91c010000004700390110000000fb02c0fe0000000000009001
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fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d010100
04000000f001000009000000320a3a02be06010000007200eb0009000000320a3a024d08
010000006a000c0109000000320a3a024c15010000006a000c0109000000320a9705bc06
010000007200eb0009000000320a97054b08010000006a000c0109000000320a97054a15
010000006a000c010a00000026060f000a00ffffffff01000000000010000000fb021000
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f001010003000000000000000000

Oai?aia 2.2 (aeinoaoiy oiiaa i?aeoe/ii? no?eeino?). Iaoae aeey nenoaie
aeeoa?aioe?aeueieo ??aiyiue (9) ciaeaeaoueny iaia?a?aia ? iac?inoath/a
ia ?ica’yceao (9) ooieoe?y Eyioiiaa V(x,t), yea caaeiaieueiy? oiiaai
(10), (11). Oiae? ioeueiaee ?ica’ycie nenoaie (9) ? G0,Ot,t0,T-no?eeei.

I?ae?icae?ee 2.2 oa 2.3 i?noyoue e?eoa??? i?aeoe/ii? no?eeino?
a?aeiia?aeii aeey e?i?eieo aeeiai?/ieo nenoai oa aeey iae?i?eieo nenoai
?c c??eiaith iiiaeeiith ii/aoeiaeo oiia.

A i?ae?icae?e? 2.4 aeena?oaoe?? ?icaeyaea?oueny caaea/a iioeiaeueiiai
ea?oaaiiy iao?e/iei aeeoa?aioe?aeueiei ??aiyiiyi

picscalex100010009000003a20100000300170000000000050000000902000000000400
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0000c0ffffffa2ffffff60100000020400000b00000026060f000c004d61746854797065
0000d00009000000fa02000010000000000000002200040000002d010000050000001402
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c002be02010000003d00f60009000000320ac0025e0b01000000ce00390117000000fb02
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7200ccdd040000002d01010004000000f001020009000000320ac002df04010000002800
910009000000320ac002d706010000002c00700009000000320ac0029c08010000002c00
70000a000000320ac002ab0902000000292c9100700009000000320ac002520c01000000
5b00910009000000320ac002660e010000002c00700009000000320ac002e50f01000000
5d00910017000000fb02c0fe0000000000009001000000cc0002001054696d6573204e65
7720526f6d616e2043797200ccdd040000002d01020004000000f001010009000000320a
30039d0d010000003000a0000a00000026060f000a00ffffffff01000000000010000000
fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d010100
04000000f001020003000000000000000000 (12)

c ii/aoeiaeie oiiaaie X(t0)=X0. Ooo t – iacaeaaeia ci?iia, X(t) –
iao?eoey noaio ??aiyiiy (12), U – iao?eoey ea?oaaiue,
F(X,U,t)=picscalex100010009000003730200000200170000000000050000000902000
000000400000002010100050000000102ffffff00040000002e011800050000003102010
00000050000000b0200000000050000000c020004c00d1200000026060f001a00fffffff
f000010000000c0ffffffa4ffffff800d0000a40300000b00000026060f000c004d61746
8547970650000c00010000000fb020dfd0301000000009001000000020002001053796d6
26f6c0002040000002d01000008000000320ace022700010000007b0010000000fb020df
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0f001000008000000320ace02f107010000007d0017000000fb0240fe000000000000900
1000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d0
1000004000000f001010009000000320a8002fb00010000004600f60009000000320a800
24403010000005800440109000000320a80020b05010000005500440109000000320a800
2d2060100000074007b0017000000fb02c0fe0000000000009001000000cc00020010546
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00a000000320af002c30102000000696a5700570009000000320a7703cc0801000000690
0570009000000320a7703960c010000006d00f70009000000320a4c01f408010000006a0
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1000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d0
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28d04010000002c00700009000000320a80025406010000002c00700009000000320a800
26507010000002900910017000000fb02c0fe0000000000009001000000cc00020010546
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009000000320a7703610a010000002c00500009000000320a7703650b010000002c00500
009000000320a7703a20b010000002e00500009000000320a7703d50b010000002e00500
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009000000320a4c01b60b010000002e00500009000000320a4c01e90b010000002e00500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 — iao?eoey ?ici??iino? mn, eiiiiiaioe yei? ?acii
c iio?aeieie
picscalex1000100090000030d0100000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600500041200000026060f001a00ffffffff00001000
0000c0ffffffaeffffffc00300000e0500000b00000026060f000c004d61746854797065
0000300109000000fa02000010000000000000002200040000002d010000050000001402
940240000500000013029402bb0310000000fb0240fe0000000000009001000000020002
001053796d626f6c0002040000002d01010009000000320aa201c50001000000b600d400
09000000320a6004550001000000b600d40017000000fb0240fe00000000000090010000
00cc0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d010200
04000000f001010009000000320aa2019901010000004600f60009000000320a60042901
010000007800d40017000000fb02c0fe0000000000009001000000cc0002001054696d65
73204e657720526f6d616e2043797200ccdd040000002d01010004000000f00102000a00
0000320a1202670202000000696a570057000a000000320ad0042b02020000007071a000
a0000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000
bc02000000cc0102022253797374656d00cc040000002d01020004000000f00101000300
00000000000000000000, i,p=1,2,…,m, j,q=1,2,…,n ? iaia?a?aieie
ooieoe?yie, X=(xij)mn, X0 — o?eniaaia iao?eoey. Ia o?a?eoi??yo (12)
?icaeyiooi ooieoe?iiaee
picscalex100010009000003480200000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00320111200000026060f001a00ffffffff00001000
0000c0ffffffafffffffe01000004f0300000b00000026060f000c004d61746854797065
0000f00010000000fb02a5fd0c01000000009001000000020002001053796d626f6c0002
040000002d01000008000000320ae601690901000000280010000000fb02a5fd0c010000
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08000000320ae6015e1001000000290017000000fb0240fe0000000000009001000000cc
0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d0100000400
0000f001010009000000320ac0013200010000004900910009000000320ac00182010100
00005500440109000000320ac001120a010000005800440109000000320ac001fc0b0100
00005400010109000000320ac001910d010000005800440117000000fb02c0fe00000000
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00002d01010004000000f001000009000000320a0003d304010000005800e70017000000
fb0240fe0000000000009001000000cc0002001054696d6573204e657720526f6d616e20
43797200ccdd040000002d01000004000000f001010009000000320ac001d30001000000
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6d6178005b01c900d40009000000320ac0015b0b010000002800910009000000320ac001
0d0d010000002c00700009000000320ac001bc0f010000002900910010000000fb0240fe
0000000000009001000000020002001053796d626f6c0002040000002d01010004000000
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9001000000020002001053796d626f6c0002040000002d01000004000000f00101000900
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fb02c0fe0000000000009001000000020002001053796d626f6c0002040000002d010100
04000000f001000009000000320a00032e07010000005800c80010000000fb0240fe0000
000000009001000000020002001053796d626f6c0002040000002d01000004000000f001
010009000000320ac001120801000000460044010a00000026060f000a00ffffffff0100
0000000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc
040000002d01010004000000f001000003000000000000ffffff,
picscalex1000100090000034b0200000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00380101200000026060f001a00ffffffff00001000
0000c0ffffffafffffff401000004f0300000b00000026060f000c004d61746854797065
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320a00038708010000005400b70009000000320a3002ce00010000003100a00009000000
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c001810301000000290091000c000000320ac0011806030000006d6178005b01c900d400
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17000000fb02c0fe0000000000009001000000cc0002001054696d6573204e657720526f
6d616e2043797200ccdd040000002d01000004000000f001010009000000320a00038006
010000005b00670009000000320a00033e08010000002c00500009000000320a00035409
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6f6c0002040000002d01010004000000f001000009000000320ac0014e04010000003d00
f60010000000fb02c0fe0000000000009001000000020002001053796d626f6c00020400
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fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d010100
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ffffffff01000000000010000000fb021000070000000000bc02000000cc010202225379
7374656d00cc040000002d01000004000000f0010100030000000000000000000000,
picscalex100010009000003960200000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a003e0161200000026060f001a00ffffffff00001000
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0000f001010009000000320ac0013200010000004900910009000000320ac0016a020100
00005500440109000000320ac0013a10010000005800440109000000320ac00132120100
00005800440109000000320ac001db140100000074007b0017000000fb02c0fe00000000
00009001000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd0400
00002d01010004000000f001000009000000320a0003b505010000005800e70009000000
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320a0003120c010000005400b70009000000320a3002e200010000003200a00009000000
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43797200ccdd040000002d01000004000000f001010009000000320a5003b70601000000
3000800009000000320a5003120b010000003000800017000000fb0240fe000000000000
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4e657720526f6d616e2043797200ccdd040000002d01000004000000f001010009000000
320a00030b0a010000005b00670009000000320a0003c90b010000002c00500009000000
320a0003df0c010000005d00670010000000fb0240fe0000000000009001000000020002
001053796d626f6c0002040000002d01010004000000f001000009000000320ac0018004
010000003d00f60010000000fb02c0fe0000000000009001000000020002001053796d62
6f6c0002040000002d01000004000000f001010009000000320a00035e0701000000ce00
df0009000000320a0003710901000000ce00df0009000000320a00030a08010000005800
c80010000000fb0240fe0000000000009001000000020002001053796d626f6c00020400
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26060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc
0102022253797374656d00cc040000002d01000004000000f00101000300000000000000
0000. Aeei?enoiaoth/e ??ci? aa??aoe?? ea?oaaiiy, aiaeia?/i? iienaiei o
?icae?e? 1, io?eiaii a?aeiia?aei? iaiao?aei? ? aeinoaoi? oiiae
iioeiaeueiino?. O i?ae?icae?e? 2.5 caaea/? iioei?caoe?? ioe?iie
i?aeoe/ii? no?eeino? caiaeyoueny aei caaea/ iioeiaeueiiai ea?oaaiiy
iao?e/iei aeeoa?aioe?aeueiei ??aiyiiyi c iaaeeoa?aioe?eiaaiei e?eoa???i
yeino?. Ia iniia? ?acoeueoao?a i?ae?icae?eo 2.4 iiaoaeiaaii a?aeiia?aei?
ooieoe?? Aai?eueoiia-Iiio?ya?ia oa ni?yaeai? nenoaie.

Ieoaiiy iiaoaeiae aeai?eoi?a ia iniia? oai?aoe/ieo ?acoeueoao?a
?icae?e?a 1, 2 aena?oeth?oueny a ?icae?e? 3 aeena?oaoe?eii? ?iaioe. A
i?ae?icae?e? 3.1 iieno?oueny caaaeueiee i?aeo?ae, yeee aaco?oueny ia
iaoiae? oneeaaeiaiiy iiaeae?. I?e oeueiio ca ii/aoeiaa iaaeeaeaiiy ia
aeayeiio aoai? aeae?a?oueny iioeiaeueia ooieoe?y ea?oaaiiy, ui aoea
io?eiaia ia iiia?aaeiueiio aoai?. Oae, o i?ae?icae?e? 3.2 ia iniia?
oai?aoe/ieo ?acoeueoao?a ?icae?eo 1, iaoiaeaie no?oeoo?ii-ia?aiao?e/ii?
iioei?caoe?? ia/eneth?oueny iioeiaeueia ea?oaaiiy a eean? ?aeaeieo. O
i?ae?icae?e? 3.3 i?iaiaeeoueny iiaeaeueoa iioei?caoe?y a
ooieoe?iiaeueiiio i?inoi??. Aeey oeueiai i?iiiio?oueny aeei?enoaoe
?oa?aoe?eio i?ioeaaeo?o u(s+1)(t)=Puu(s)(t)-sG(s)(t), aea Pu. — iia?aoi?
i?iaeooaaiiy ia aeiionoeio iiiaeeio ea?oaaiue,
s[0;picscalex100010009000003ab000000020012000000000005000000090200000000
0400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02600260011200000026060f001a00ffffffff0000
10000000c0ffffffbbffffff200100001b0200000b00000026060f000c004d6174685479
70650000600011000000fb0240fe000000000000900100000002000200104d5420457874
72610002040000002d01000009000000320a69016300010000002400910010000000fb02
40fe0000000000009001000000020002001053796d626f6c0002040000002d0101000400
0000f001000009000000320aa0012a00010000007200eb000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01000004000000f001010003000000000000a000000000] —
e?ie, yeee aecia/a?oueny oae, uia ooieoe?iiae I(u(s+1)) io?eiaa iaeiaioa
cia/aiiy, G(s)(.) — iai?yiie iaeoaeaeoiai nioneo a ooieoe?iiaeueiiio
i?inoi?? ea?oaaiue. Iaoae ia e?ioe? s ciaeaeaii u(s)(t). sseui iiiaeeia
picscalex100010009000003630300000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
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0000000109000000fa02000010000000000000002200040000002d010000050000001402
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020008000000320a5803ce1801000000280010000000fb0291fc04010000000090010000
00020002001053796d626f6c0002040000002d01020004000000f001010008000000320a
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Iaoae W — i?ino?? eoneiai iaia?a?aieo ia [t0,T] ooieoe?e, ooieoe?iiae picscalex1000100090000030c0100000200170000000000050000000902000000000400 000002010100050000000102ffffff00040000002e011800050000003102010000000500 00000b0200000000050000000c02c00280071200000026060f001a00ffffffff00001000 0000c0ffffffb9ffffff40070000790200000b00000026060f000c004d61746854797065 0000600010000000fb0240fe0000000000009001000000020002001053796d626f6c0002 040000002d01000009000000320a00023200010000006d00f60017000000fb0240fe0000 000000009001000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd 040000002d01010004000000f001000009000000320a00023501010000003a007b000900 0000320a0002b801010000005700a90109000000320a000281050100000052002e011000 0000fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d01 000004000000f001010009000000320a0002800301000000ae00b40117000000fb02c0fe 0000000000009001000000cc0002001054696d6573204e657720526f6d616e2043797200 ccdd040000002d01010004000000f001000009000000320a3701be06010000003100a000 0a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02 000000cc0102022253797374656d00cc040000002d01000004000000f001010003000000 000000000000 caaeiaieueiy? oiiaai : a) [w]0, aeey aeia?eueieo wW; a) [w]=[w], aeey aoaeue-yeeo wW, R1; a) [v][w], aeey wW, vW oaeeo, ui |v(t)||w(t)|, t[t0,T]; a) [w+v][w]+[v], aeey aeia?eueieo wW, vW. ?icaeyiaii ?oa?aoe?eio i?ioeaaeo?o ciaoiaeaeaiiy iioeiaeueiiai ea?oaaiiy uU caaea/? (1)-(2) aeaeyaeo us+1=us-sGs, s=0,1,... (14) Ooo u0 — caaeaia ii/aoeiaa ea?oaaiiy, picscalex100010009000003ee0100000200170000000000050000000902000000000400 000002010100050000000102ffffff00040000002e011800050000003102010000000500 00000b0200000000050000000c020004a00f1200000026060f001a00ffffffff00001000 0000c0ffffffafffffff600f0000af0300000b00000026060f000c004d61746854797065 0000b00010000000fb02b1fc0001000000009001000000020002001053796d626f6c0002 040000002d01000008000000320a0103a70301000000280010000000fb02b1fc00010000 00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000 08000000320a0103040e01000000290017000000fb0240fe0000000000009001000000cc 0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d0100000400 0000f001010009000000320aa0023200010000004700390109000000320aa00242040100 00004700390109000000320aa002d506010000004700390109000000320aa002a40b0100 00004700390117000000fb02c0fe0000000000009001000000cc0002001054696d657320 4e657720526f6d616e2043797200ccdd040000002d01010004000000f001000009000000 320ad7019e010100000073007f0009000000320ad701ae050100000073007f0009000000 320ad70141080100000073007f0009000000320a10031a0d010000006b00a00009000000 320ad701100d0100000073007f0009000000320a4101aa0e010000005400b70010000000 fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d010000 04000000f001010009000000320aa0028002010000003d00f60017000000fb02c0fe0000 000000009001000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd 040000002d01010004000000f001000009000000320a10039a05010000003100a0000900 0000320a10034108010000003200a00017000000fb0240fe0000000000009001000000cc 0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d0100000400 0000f001010009000000320aa0025b06010000002c00700009000000320aa00220090100 00002c00700009000000320aa0022a0b010000002c00700011000000fb0240fe00000000 0000900100000002000200104d542045787472610002040000002d01010004000000f001 000009000000320aa0027709010000004b00c0010a00000026060f000a00ffffffff0100 0000000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc 040000002d01000004000000f001010003000000000000ffffff — iai?yiie nioneo, yeee ii?iiaaiee oae, ui picscalex100010009000003fe0100000300170000000000050000000902000000000400 000002010100050000000102ffffff00040000002e011800050000003102010000000500 00000b0200000000050000000c02600520091200000026060f001a00ffffffff00001000 0000c0ffffffa4ffffffe0080000040500000b00000026060f000c004d61746854797065 0000200109000000fa02000010000000000000002200040000002d010000050000001402 4701ce030500000013022104ce0305000000140247011a0605000000130221041a061000 0000fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d01 010009000000320a20033200010000006d00f60017000000fb0240fe0000000000009001 000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d01 020004000000f001010009000000320a2003f303010000004700390117000000fb02c0fe 0000000000009001000000cc0002001054696d6573204e657720526f6d616e2043797200 ccdd040000002d01010004000000f001020009000000320a90035b050100000069005700 09000000320a57025b050100000073007f0009000000320aec040c020100000069005700 09000000320a6d018202010000006b00a00010000000fb02c0fe00000000000090010000 00020002001053796d626f6c0002040000002d01020004000000f001010009000000320a ec047102010000003d00af0010000000fb02c0fd00000000000090010000000200020010 53796d626f6c0002040000002d01010004000000f001020009000000320a6e0306020100 0000e500920110000000fb0240fe0000000000009001000000020002001053796d626f6c 0002040000002d01020004000000f001010009000000320afa01530101000000e900a800 09000000320ae904530101000000eb00a80009000000320aab03530101000000ea00a800 09000000320afa01450601000000f900a80009000000320ae904450601000000fb00a800 09000000320aab03450601000000fa00a80009000000320a2003220701000000a300f600 17000000fb02c0fe0000000000009001000000cc0002001054696d6573204e657720526f 6d616e2043797200ccdd040000002d01010004000000f001020009000000320aec041603 010000003100a00017000000fb0240fe0000000000009001000000cc0002001054696d65 73204e657720526f6d616e2043797200ccdd040000002d01020004000000f00101000900 0000320a20032b08010000003100e0000a00000026060f000a00ffffffff010000000000 10000000fb021000070000000000bc02000000cc0102022253797374656d00cc04000000 2d01010004000000f001020003000000000000ffffff, s — aeiaeaoia /enei, ui caaeiaieueiy? oiiaai : a) spicscalex100010009000003ab000000020012000000000005000000090200000000040 0000002010100050000000102ffffff00040000002e01180005000000310201000000050 000000b0200000000050000000c02600260011200000026060f001a00ffffffff0000100 00000c0ffffffacffffff200100000c0200000b00000026060f000c004d6174685479706 50000600011000000fb0240fe000000000000900100000002000200104d5420457874726 10002040000002d01000009000000320a6e015f00010000002400910010000000fb0240f e0000000000009001000000020002001053796d626f6c0002040000002d0101000400000 0f001000009000000320aa0012a00010000007200eb000a00000026060f000a00fffffff f01000000000010000000fb021000070000000000bc02000000cc0102022253797374656 d00cc040000002d01000004000000f0010100030000000000410000000000, s=0,1,..., aea picscalex100010009000003ab0000000200120000000000050000000902000000000400 000002010100050000000102ffffff00040000002e011800050000003102010000000500 00000b0200000000050000000c02600260011200000026060f001a00ffffffff00001000 0000c0ffffffacffffff200100000c0200000b00000026060f000c004d61746854797065 0000600011000000fb0240fe000000000000900100000002000200104d54204578747261 0002040000002d01000009000000320a6e015f00010000002400910010000000fb0240fe 0000000000009001000000020002001053796d626f6c0002040000002d01010004000000 f001000009000000320aa0012a00010000007200eb000a00000026060f000a00ffffffff 01000000000010000000fb021000070000000000bc02000000cc0102022253797374656d 00cc040000002d01000004000000f0010100030000000000000000000000 — iaia?aae caaeaia aeiaeaoia /enei; a) (us-sGs)U, s=0,1,... ?icaeyiaii iine?aeiai?noue ea?oaaiue v0,v1,...,picscalex100010009000003e0000000020017000000000005000000090200 0000000400000002010100050000000102ffffff00040000002e01180005000000310201 000000050000000b0200000000050000000c024002e0021200000026060f001a00ffffff ff000010000000c0ffffffb9ffffffa0020000f90100000b00000026060f000c004d6174 68547970650000200017000000fb0240fe0000000000009001000000cc0002001054696d 6573204e657720526f6d616e2043797200ccdd040000002d01000009000000320a000240 00010000007600d40017000000fb02c0fe0000000000009001000000cc0002001054696d 6573204e657720526f6d616e2043797200ccdd040000002d01010004000000f001000009 000000320a37014201010000007000a00017000000fb0200ff0000000000009001000000 cc0002001054696d6573204e657720526f6d616e2043797200ccdd040000002d01000004 000000f001010009000000320a8701000201000000300080000a00000026060f000a00ff ffffff01000000000010000000fb021000070000000000bc02000000cc01020222537973 74656d00cc040000002d01010004000000f001000003000000000000000000,...,vP,.. ., yea io?eiaia iaoiaeii (14). Oai?aia 3.3. 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aea Q — aeayea aeiaeaoii aecia/aia neiao?e/ia iao?eoey, ui, vi — a?aeiia?aei? aeaiaioe aaeoi??a u oa v, n oa ns, s=p0,...,P — aeiaeaoi? /enea. Oiae? aeey ,s,p0,P-ca?aeiino? ?oa?aoe?eii? i?ioeaaeo?e (14) aeinoaoiuei, uia 0

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