Ee?anueeee oi?aa?neoao

?iai? Oa?ana Oaa/aiea

??aaeaiiaa A?ca?i Iaae?a?i?aia

OAeE 517.9

Iioeiaeuei? a??aiiaaaeai? noaie e?iaoe/ii? nenoaie

Iiii-???onaeeinueeiai oa ?o aiae?c

01.05.04 — Nenoaiiee aiae?c ? oai??y iioeiaeueieo ??oaiue

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a — 1999

1.Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? iaoaiaoe/ieo iaoiae?a
aeieiai-aeiiii?/-ieo aeine?aeaeaiue oaeoeueoaoo e?aa?iaoeee Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea.

Iaoeiaee ea??aiee — aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Eyoaiei ?ai? Ieeieaeiae/

(Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, caa.eaoaae?e)

Io?oe?ei? iiiiaioe:

1.- Aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Oona?iia Aeaien sso’?ae/

(Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, i?ioani?)

2. — Aeieoi? o?ceei-iaoaiaoe/ieo iaoe Iacei Ieaen?e A?eai?iae/

(?inoeooo iaoaiaoeee IAI Oe?a?ie, i?ia.iaoe.ni?a.)

I?ia?aeia i?aai?caoe?y — ?inoeooo E?aa?iaoeee ?iai? A.I.Aeooeiaa IAI
Oe?a?ie, a?aeae?e iioei?caoe?? ea?iaaieo i?ioeania

Caoeno a?aeaoaeaoueny “ 9 ” “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, Ee?a, i?.Aeooeiaa, 2, ei?i.6, aoae.40 i 15
aiaeei?

(oae./oaen 252 — 58 — 83, e-mail rada @ cyb.univ.kiev.ua.)

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

Aaoi?aoa?ao ?ic?neaiee “26” “eeiiy” 1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii? ?aaee

A.I.Oaa/aiei

Caaaeueia oa?aeoa?enoeea ?iaioe.

Aeooaeuei?noue oaie. A inoaii? aeanyoe??//y ieoaiiy iiaeaethaaiiy
e?iaoe/-iiai ?inoo a?ieia?/ieo iiioeyoe?e aeeeeeathoue ?ioa?an o
aaaaoueio a/aieo — iaoaiaoee?a oa a?ieia?a. E?euee?nia i?e?ia?ieia?y, ui
a?oioo?oueny ia iiaea-ethaaiii o?i?ei-eiiaoe/ieo i?ioean?a i?e?iaiiai
?inoo, ? aaeoccth aiieiia-oeee, yea oaeaeei ?icaeaa?oueny i ia? aaaaoi
ooiaeaiaioaeueieo ?acoeueoaoia oa i?aeoe/eo canoinoaaiue. Cie?aia,
aeine?aee c ae?iuoaaiiy i?e?ii?aai?c-i?a noaee iniiaith noai?aiiy
no/anieo a?ioaoiieia?/ieo i?ioean?a.

A ?icaeoie e?iaoe/iiai iiaeaethaaiiy a i?e?ia?ieia?? aaaiiee aia-nie
c?iaeee aeine?aeaeaiiy A??theiaa A.A.,Aaeyi?ia A.I.,Aa?oieii??aa N.Ae.,
?e?ca?iaa ?. ss., ???onaeeinueeiai I. Ae., Caneaanueeiai A. A., Eaioa?a
I. A., Ia/o?e?ia I.N., Iiciiaiai? ?. I., ?iaioiiai? ?. A.,
?iiaiianueeiai TH. I., Noaiaiiai? I. A., Na???aeaaa I. I., *a?iaanueeiai
Ae. N. oa aaaaoueio ?ioeo a/aieo.

Caaaeyee aeei?enoaiith ciaiioiueiai ea?oaaiiy aaeaeiny caaacia/eoe
iaia?a?aiinoue i?ioeano ae?iuoaaiiy iiioeyoei?, ui nooo?ai caaaaoeei
oai-?ith i i?aeoeeo no/anii? iie?iaiieiai?. Aea, a ca’yceo c
a?aenooi?noth iaoiae?a iioei?caoe?? oiia ?inoo iiioeyoe?? i?e
iaia?a?aiiio eoeueoeaoaaii? ia?aaa-ae ea?iaaiiai i?ioeano iiee ui
aeei?enoiaothoueny a aeinoaoi?e i???. Ia ia?oee ieai i?e oeueiio
aeieeaathoue caaea/? iioeiaeueiiai ea?oaaiiy oa ii-oei?caoe?? ia?aiao??a
a??aiiaaaeaieo noaoe?iia?ieo ?aaeei?a i?ioeano iaia-?a?aiiai
eoeueoeaoaaiiy. Iioei?caoe?y i?e aeei?enoaii? e?iaoe/ieo iiaea-eae
aeicaiey? ciaeoe ia eeoa iaa?? iioeiaeueieo oiia aaaeaiiy i?ioeano, aea
e iioeiaeueio i?ia?aio ci?ie ia?aiao??a. Naia oea i aecia/a?
aeooaeueiinoue iaoiaeo iioeiicaoei? ?inoo iie?ii?aaiiciia c
aeei?enoaiiyi eiiaoe/ii? nen-oaie Iiii-I??onaeeinueeiai. Caaea/a
iioeiaeueiiai cae?aiiy a?iaeath aeey e?iaoe/ii? nenoaie
Iiii-???onaeeinueeiai aia?oa aoea iinoaaeaia Ey-oaiei ?.I. ? Eyoaiei
I.I., a ?iaioao yeeo aeey /anoeiiiai aeiaaeeo a?ia?-aie?/ii? caeaaeiino?
oaeaeeino? ?inoo a?ae eiioeaio?aoe?e e?i?ooth/iai ii-aeeaiiai noano?aoo
oa ?ia?a??oth/eo iaoaaie?o?a aea/ai? iioeiaeuei? a??a-iiaaaeai? ?aaeeie
e?iaoe/ii? nenoaie Iiii-???onaeeinueeiai.

A aeaiie aeena?oaoeieiie ?iaio? i?iaaaeaii nenoaiiee aiae?c
iioe-iaeueieo naoe?iia?ieo ?ica’yce?a aeeoa?aioe?aeueieo ??aiyiue
nenoaie Iiii- I??onaeeinueeiai aeey caaaeueiiai aeiaaeeo iaeiieo?aioiiai
oa eiieo?aio-iiai ?ia?a??oaaiiy iiaeaiei noano?aoii oa iaoaaie?oaie.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa aeeiiaia
a?aeiia?aeii aei ieaio iaoeiaeo aeine?aeaeaiue eaoaae?e iaoa-iaoe/ieo
iaoiae?a aeieiai-aeiiii?/ieo aeine?aeaeaiue oaeoeueoaoo e?aa?ia-oeee
Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea.

Iaoa ?iaioe. Iaoith ?iaioe ? iinoaiiaea iiaeo caaea/ iioeiaeue-iiai
ea?oaaiiy aeey ocaaaeueiaii? iiaeae? Iiii-???onaeeinueeiai oa ?ic?ia-ea
iaoiaea aeine?aeaeaiiy iioeiaeueieo a??aiiaaaeaieo ?aaeei?a e?iaoe/ii?
nenoaie c oi/ee ci?o ?o ?nioaaiiy, ?aeeiino? oa no?eeino?.

Iaoeiaa iiaecia. A i?ioean? ?iaioe

· Cai?iiiiiaaii iaoiae aeine?aeaeaiiy iioeiaeueieo a??aiiaaaeaieo
?aaee-i?a e?iaoe/ii? nenoaie Iiii-???onaeeinueeiai, ui a?oioo?oueny ia
iin-oaiiaoe? a?aeiia?aeieo caaea/ iioeiaeueiiai cae?aiiy a?iaeath oa ia
ii-aoaeia? ? ?ica’ycaii? aeiiii?aeieo caaea/ ia?aiao?e/ii? iioei?caoe??.

· Iiaoaeiaaii iia? iiaeae? caaea/ iioeiaeueiiai cae?aiiy a?iaeath, ui
a?oioothoueny ia ocaaaeueiaii? iiaeae? Iiii-???onaeeinueeiai ia aeiaaeie
aeei?enoaiiy iaeo?ae?coth/iai eiio?aaaioa oa ia aeiaaeie cae?eniaiiy
ciai?oiuei? ?ioaineo?eaoe?? ae?iaieoeoaa.

· Aeiaaaeaii ?aeei?noue oa aneiioioe/io no?ee?noue iioeiaeueiiai noaio
iiaea-e? Iiii-???onaeeinueeiai o aeiaaeeo, eiee iiaeeaiee noano?ao ia?
iae-ii/anii e?i?ooth/ee oa ?ia?a??oth/ee aieea ia oaeaee?noue ?inoo
iiioey-oe??. I?e oeueiio aeine?aeaeai? aeiaaeee ye iaeiieo?aioiiai, oae
? eiieo-?aioiiai ?ia?a??oaaiiy noano?aoii oa iaoaaie?oaie.

· Anoaiiaeaii oaiooinoue caaea/? ia?aiao?e/ii? iioei?caoe?? aeey iiaeae?
Iiii — ???onaeeinueeiai c iaeo?ae?coth/ei eiio?aaaioii oa ciaeaeai?
iaeaeaa eieaeuei? aneiioioe/ia no?ee? iioeiaeuei? a??aiiaaaeai? noaie
(i?e oeueiio aeine?aeaeai? aeiaaeee iaeiieo?aioiiai oa eiieo?aioiiai
?ia?a??oaaiiy).

· Anoaiiaeaii iioee?noue caaea/? ia?aiao?e/ii? iioei?caoe?? aeey iiaeae?
Iiii-???onaeeinueeiai c oaeoi?ii ?ioaineo?eaoe?? ae?iaieoeoaa a?iiane oa
aeiaaaeaii ?aeei?noue oa aneiioioe/io no?ee?noue iioeiaeueiiai
a??aii-aaaeaiiai noaio (aeine?aeaeai? iaeaeaa aeiaaeee — iaeiieo?aioia
oa eiieo-?aioia ?ia?a??oaaiiy).

Iaoiaee aeine?aeaeaiiy. A ?iaio? aeei?enoiaothoueny oai??y
iioe-iaeueiiai ea?oaaiiy, oai??y iae?i?eii? iioei?caoe??, iaoiaee
ia?aiao?e/ii? iioei?caoe??, oai??y no?eeino? aeey aeeoa?aioe?aeueieo
??aiyiue.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Anoaiiaeaia a aeena?oaoe??
?aeei?noue aneiioioe/ii no?eeeo iioeiaeueieo a??aiiaaaeaieo noai?a
e?iaoe/ii? nenoaie Iiii-???onaeeinueeiai aea? iaoaiaoe/ia ia-a?oiooaaiiy
aeai?o iioeiaeueiiai ?aaeeio ?iaioe eoeueoeaaoi?a iaia-?a?aii? ae?? i?e
ae?iuoaaii? i?e?ii?aai?ci?a. Caeeaaeaiee a iniiao i?i-oeana iioei?caoe??
e?eoa??e caaaeueiiai aeiiiie/iiai i?eaooeo aea? iiaeee-a?noue ioe?ieoe
aeiiii?/io aoaeoeai?noue a?aeiia?aeiiai iioeiaeueiiai ?aaee-io ?iaioe
eoeueoeaaoi?a.

Ai?iaaoe?y ?acoeueoao?a ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?eii?
?iaioe aeiiia?aeaeenue ia iaoeiaeo nai?ia?ao oaeoeueoaoo e?aa?iaoeee
Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea, ?inoeoooo e?aa?iaoeee
Iaoe?iiaeueii? aeaaeai?? iaoe Oe?a?ie, a oaeiae ia:

— Anaoe?a?inuee?e eiioa?aioe?? “Iiaeaethaaiiy oa aeine?aeaeaiiy
no?eeino? nenoai” (15 — 19 o?aaiy 1995 p., Ee?a);

— Anaoe?a?inuee?e eiioa?aioe?? “Iiaeaethaaiiy oa aeine?aeaeaiiy
no?eeino? nenoai” (20 — 24 o?aaiy 1996 p., Ee?a).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a /ioe?ueio
noaooyo oa a o?ueio oacao eiioa?aioe?e.

No?oeoo?a oa ianya. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio,
/ioe?ueio aeaa, aeniiae?a oa nieneo e?oa?aoo?e. ?iaioa aeeeaaeaia ia 122
noi??ieao oaenoo, nienie aeei?enoaieo aeaea?ae i?noeoue 110
iaeiaioaaiue.

Iniiaiee ci?no.

O anooi? ia??oioiao?oueny aeooaeuei?noue aeine?aeaeaiue c iioei?caoe??
i?e?ia?ieia?/ieo i?ioean?a, ui iienothoueny e?iaoe/iith nenoaiith
Iiii-???onaeeinueeiai, iiaeaii noeneee iaeyae iaea?eueo aaaeeeaeo
?acoeueoao?a noiniaii aeaii? oaiaoeee. I?eaaaeai? iniiai? ?acoeueoaoe
aeena?oaoe?? oa noeneee ci?no aeena?oaoe?? ii aeaaao.

Ia?oa aeaaa ?iaioe neeaaea?oueny c /ioe?ueio ?icae?e?a.

?icae?e 1.1 i?noeoue ?aoa?aoeai? ?acoeueoaoe c ?nioth/eo iiaeaeae
oa-iinoaoiiai eoeueoeaoaaiiy ee?oeiieo iiioeyoe?e. Oai??y oaiinoaoiiai
eoeueoeaoaaiiy aeoiaeeoue c oiai, ui ??no eoeueoo?e oa?aeoa?eco?oueny
oaiin-oaoiith e?eaith, ui cia?aaea? caeaaei?noue aonoeie iiioeyoe?? O,
eiioeaio?a-oe?? iiaeeaiiai noano?aoa S, eiioeaio?aoe?? i?iaeoeo?a
aeeoo?ae?yeueiino? (iaoa-aie?o?a) ? a?ae oaeaeeino? i?ioieo D a
eoeueoeaaoi??:

wmetafile0 wmetafile0

wmetafile0 (1)

wmetafile0

Ooo ac,bc,S0- caaeai? aeiaeaoi? eiinoaioe, ac ? 1+bc, m = m (S,P) —
ie-oiia oaeaee?noue ?inoo i?e?ii?aai?ci?a, ui a iaei?ino?oiio aeiaaeeo
ia? a?ia?aie?/io caeaaei?noue

wmetafile0 (2)

yea a?aeia?aaea? e?i?ooaaiiy ?inoo noano?aoii oa ?ia?a??oaaiiy
iaoaaie?oaie.

A aaaaoueio aeiaaeeao iiaeeaiee noano?ao i?e aaeee?e eiioeaio?aoe?? ia?
oaeiae ?ia?a??oth/ee aieea ? oiae? cai?noue (2) ia?ii

wmetafile0 (3)

aai

wmetafile0
(4)

Oi?ioee (3) oa (4) ? iiaeaeyie a?aeiia?aeii iaeiieo?aioiiai oa
eii-eo?aioiiai ?ia?a??oaaiiy noano?aoii ? iaoaaie?oaie. Naia oe? aeaa
aeiaaeee aeaoaeueii aeine?aeaeothoueny a aeena?oaoe??.

A ?icae?e? 1.2 aeathoueny iinoaiiaee iiaeo iiaeaeae — caaea/
iioeiaeue-iiai cae?aiiy a?iaeath aeey e?iaoe/ii? nenoaie Iiii —
?a?onaeeinueeiai

wmetafile0
(5)

oa ?? aeaio ocaaaeueiaiue:

— 1) nenoaie c iaeo?ae?coth/ei eiio?aaaioii:

wmetafile0
(6)

— 2) nenoaie c ciai?oiueith ?ioaineo?eaoe??th ae?iaieoeoaa:

wmetafile0
(7)

Ooo o(t) ? 0,0 y(t) F y0, z(t) ? 0 — oacia? o?a?eoi???; u(t) ? 0, v(t)
? 0, w(t) ? 0 -iioeiaeuei? ea?oaaiiy.

E?eoa??e — caaaeueiee a?iaeae ca o?eniaaiee i?ii?aeie /ano [0,T] aeey
nenoaie (5) ia? aeaeyae

wmetafile0

?icaeyaeathoueny a??aiiaaaeai? noaie, eiee wmetafile0 a u ? 0, v
? 0, w ? 0 — /eneia? ia?aiao?e. Aeey a?aeooeaiiy iioeiaeueieo
a??aiiaa-aeaieo noai?a ?icaeyaeathoueny o?e caaea/? ia?aiao?e/ii?
iioei?caoe??, eiee aeey aei?aee?a (5), (6), (7) a?aeiia?aeieie
e?eoa??yie ?

ux ® max
(8)

ux — gv ® max, g > 0
(9)

ux — (1 + r)w ® max, r > 0
(10)

aea g > 0, oa r > 0 — aa?o?ni? ia?aiao?e.

A ?icae?e? 1.3 aeine?aeaeothoueny oiiae ?nioaaiiy oa ?aeeiino?
iioeiaeue-ii? o?a?eoi??? aeey caaea/? iioeiaeueiiai cae?aiiy
a?iaeath.Nii/aoeo aeine?ae-aeo?oueny aeiiii?aeia caaea/a iioeiaeueiiai
cae?aiiy a?iaeath

wmetafile0

wmetafile0 (11)

aea Vt — aeiionoeiee i?ioean caaea/?; u(t) — eoneiai — iaia?a?aia
ea?oaaiiy;s, x0, x1- caaeai? noae?, i?e/iio 0 < x0 < x1. E?eoa??e iiaeia caienaoe oaeiae a aea?aaeaioi?e oi?i? wmetafile0 (12) I/aaeaeii, ui iioeiaeueiith o?a?eoi???th caaea/? (10) i?e m = const >0 aoaea:

a) wmetafile0 i?e wmetafile0

a) wmetafile0 i?e wmetafile0

I?e m = m (o), aea m (o) — iaia?a?aii aeeoa?aioe?eiaia ooieoe?y,
i/aaeaeii, ui iioeiaeueiith o?a?eoi???th aoaea :

a) i?e wmetafile0 , u(t) = 0, x(t) — ?ica’ycie caaea/? Eio? wmetafile0

wmetafile0

a) i?e wmetafile0

yeui i?e oeueiio ooieoe?y m (o) ia? aeanoeaino?:

1) wmetafile0 (aeaionoi?iiiy iaiaaeai?noue),

2)wmetafile0 (iiiioiiia niaaeaiiy),

3) wmetafile0 — no?iai iioeea aai?o.

Caaaeyee o?ao?e aeanoeaino? ia a?ae??ceo 0 F x F x1 caaaeaee ?nio?
?aeeiee iaeneioi ooieoe?? m (o) o:

wmetafile0

I?e oeueiio 0 < o* F x1. Iioeiaeueiee a?iaeae aeey caaea/? (10) aoaea wmetafile0 Aeae? ?icaeyaea?oueny ieoaiiy i?i neioac iioeiaeueii? o?a?eoi??? ca-aea/? iioeiaeueiiai cae?aiiy a?iaeath aeey e?iaoe/ii? nenoaie Iiii - ??-?onaeeinueeiai wmetafile0 wmetafile0 (13) wmetafile0 wmetafile0 A?aeiinii ooieoe?? m (y,z) aaiaeyoueny oae? oiiae: 1) m (y,z) - iaiaaeaia ? iaia?a?aia a wmetafile0 ooieoe?y, i?e/iio wmetafile0 wmetafile0 2) m (y,z) - iaia?a?aii aeeoa?aioe?eiaia a wmetafile0 ooieoe?y, i?e/iio (14) wmetafile0 aeey wmetafile0 Eiia?ioth/e ia?oa ? ae?oaa aeeoa?aioe?aeuei? ??aiyiiy nenoaie (13), a oaeiae ia?oa oa o?ao? ??aiyiiy oe??? ae nenoaie, i?eoiaeeii aei aeniiaeo, ui aiia aieiae?? aeaiia aneiioioe/ii no?eeeie ?iaa??aioieie ieiueiaie wmetafile0 (15) ui ?acii ooai?ththoue ?iaa??aioio i?yio. Oe? ?ioaa?aee caaeathoue caeii caa?aaeaiiy ?a/iaeie ? aeicaieythoue a ieie? noaoe?iia?ii? oi/ee nenoaie aeeoa?aioe?aeueieo ??aiyiue (13) aeeeth/eoe c ?icaeyaeo aeeiai?eo iiaeeaiiai noano?aoa y oa iaoaaie?o?a z. A ?acoeueoao? ia ?iaa??aioi?e i?yi?e (15) i?eoiaeeii aei iiaiai aeaeyaeo caaea/? iioeiaeue-iiai cae?aiiy a?iaeath: wmetafile0 aea m0(x) = m(y0 - ax, bx ); u(t) - eoneiai - iaia?a?aia ea?oaaiiy. Iaea?aeaia caaea/a ? aeiiii?aeiith caaea/ath iioeiaeueiiai cae?aiiy a?iaeath (11), yea i?e aeeiiaii? oiia (14), oa aeiaeaoeiai? oiiae, ui ooieoe?y m0(x)o -no?iai iioeea aai?o, ia? iioeiaeueio o?a?eoi??th, yea neeaaea?oueny c aeaio ae?eyiie: a) i?e 0 F t F T0 aoaea u(t) = 0, a x(t) - ?ica’ycie caaea/? Eio? wmetafile0 a) i?e T0 F t F T aoaea wmetafile0 Ciaoiaeaeaiiy iaa?no?ae?, ye iniiaii? ae?eyie? iioeiaeueii? o?a?e-oi??? caaea/? iioeiaeueiiai cae?aiiy a?iaeath (13), ui ?icaeyaea?oueny ia ?i-aa??aioi?e i?yi?e (15), caiaeeoueny aei ciaoiaeaeaiiy oaeeo iioeiaeueieo noa-oe?iia?ieo oi/ie nenoaie aeeoa?aioe?aeueieo ??aiyiue (13), ye? iaenei?cothoue i?iaeoeoeai?noue a?ieia?/ii? nenoaie: wmetafile0 Oey caaea/a ?ica’yco?oueny o ae?oa?e aeaa? aeena?oaoe??. A?aeiinii ?nio-aaiiy noaoe?iia?ieo ?ica'yce?a nenoaie aeeoa?aioe?aeueieo ??aiyiue (13) i?e u = const aeiaaaeaia. Oai?aia 1. Iaoae aeeiiothoueny oiiae (14). Aeey oiai, uia nenoaia aeeoa?aioe?aeueieo ??aiyiue (13) i?e u = const iaea iao?ea?aeueiee noaoe?iia?iee ?ica’ycie, iaiao?aeii oa aeinoaoiuei, uia aeeiioaaeanue ia??ai?noue wmetafile0 Oeae noaoe?iia?iee ?ica’ycie ?aeeiee. A ?icae?e? 1.4 ?icaeyaea?oueny caaea/a iioeiaeueiiai cae?aiiy a?iaeath, eiee ia ??no iiioeyoe?? aieeaa? ?aeeiee oaeoi? - iiaeeaiee noano?ao, yeee ia? iaeii/anii e?i?ooth/ee oa ?ia?a??o/ee aieea. A?aeooeaiiy iioeiaeue-ieo a??aiiaaaeaieo noai?a caiaeeoueny aei caaea/? oiiaii? iioei?caoe??: wmetafile0 (16) aea wmetafile0 Aeiaaaeai? oae? oai?aie. Oai?aia 2. A?aeiia?aeia (16) caaea/a iioeiaueiiai cae?aiiy a?iaeath ia? ?aeeiee iioeiaeueiee a??aiiaaaeaiee noai: wmetafile0 wmetafile0 Oai?aia 3 Iioeiaeueiee a??aiiaaae?iee noai wmetafile0 caaea/? iioeiaeueiiai cae?aiiy a?iaeath, ui a?aeiia?aea? (16), i?e oiia?wmetafile0 ? aneiioioe/ii no?eeei ca Eyioiiaei. Iienai? iniiai? aoaie ?ic?iaeaiiai iaoiaea ciaoiaeaeaiiy oa aiae?co iioeiaeueieo a??aiiaaaeaieo ?aaeei?a eoeueoeaoaaiiy iiioeyoe??. Ae?oaa aeaaa ?iaioe i?enay/aia ?icaeyaeo aeaio caaea/ iioeiaeueiiai cae?aiiy a?iaeath aeey e?iaoe/ii? nenoaie Iiii - ???onaeeinueeiai (5) c e?eoa???i (8) oa iaiaaeaiiyie wmetafile0 wmetafile0 wmetafile0 Ia?oa caaea/a a?aeiia?aea? aeiaaeeo iaeiieo?aioiiai ?ia?a??oaaiiy wmetafile0 (17) ae?oaa caaea/a, a?aeiia?aea? aeiaaeeo eiieo?aioiiai ?ia?a??oaaiiy wmetafile0 (18) Aeey ciaoiaeaeaiiy iioeiaeueieo a??aiiaaaeaieo ?aaeei?a e?iaoe/ii? nenoaie Iiii - ???onaeeinueeiai (5), (17) noi?ioeueiaaia caaea/a ia?aiao-?e/ii? iioei?caoe?? o aeaeyae? wmetafile0 Oai?aia 4 Caaea/a ia?aiao?e/ii? iioei?caoe?? (19) ia? ?aeeiee iaeneioi: wmetafile8010009000003c3010000040015000000000005000000090200000000040000 0002010100050000000102ffffff00040000002e01180005000000310201000000050000 000b0200000000050000000c026003200f1200000026060f001a00ffffffff0000100000 00c0ffffffa9ffffffe00e0000090300000b00000026060f000c004d6174685479706500 00800009000000fa02000010000000000000002200040000002d0100000500000014025c 02060a0500000013024002370a09000000fa02000020000000000000002200040000002d 0101000500000014024802370a05000000130201037e0a040000002d0100000500000014 020103860a050000001302f200e40a050000001402f200e40a050000001302f200100e15 000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d 616e000084040000002d01020008000000320a6002220e02000000292e08000000320a60 026809010000002c0009000000320a6002f604040000006d696e2808000000320a600234 0001000000300015000000fb0220ff0000000000009001000000000402001054696d6573 204e657720526f6d616e000084040000002d01030004000000f001020008000000320ab4 01c70801000000300015000000fb0220ff0000000000009001010000000402001054696d 6573204e657720526f6d616e000084040000002d01020004000000f00103000800000032 0ac002260d010000006d0008000000320ac002d50b01000000790015000000fb0280fe00 00000000009001010000000402001054696d6573204e657720526f6d616e000084040000 002d01030004000000f001020008000000320a6002610c010000006b0008000000320a60 02fc0a010000006b0008000000320a6002f60701000000790008000000320a6002aa0201 000000790010000000fb0280fe0000000000009001000000020002001053796d626f6c00 02040000002d01020004000000f001030008000000320a6002be03010000003c00080000 00320a60024e01010000003c0010000000fb0220ff000000000000900100000002000200 1053796d626f6c0002040000002d01030004000000f001020008000000320a0201b40201 0000002d000a00000026060f000a00ffffffff01000000000010000000fb021000070000 000000bc02000000cc0102022253797374656d00cc040000002d01020004000000f00103 00030000000000 A?aeiia?aeii, aeey e?iaoe/ii? nenoaie Mono - ???onaeeinueeiai (5) oa ooieoe?? ieoiii? oaeaeeino? (18) noi?ioeueiaaia caaea/a ia?aiao?e/ii? ii-oei?caoe??: wmetafile0 (20) Oai?aia 5 Caaea/a ia?aiao?e/ii? iioei?caoe?? (20) ia? ?aeeiee iaeneioi wmetafile0 .I?e oiia? wmetafile0 caaea/a (20) ? caaea/ith iioeeiai i?ia?aioaaiiy. Oai?aia 6 An? iioeiaeuei? noaoe?iia?i? oi/ee wmetafile0 nenoaie aeeoa?aioe?aeueieo ??aiyiue (5), (17) oa (5), (18), ui ? ?ica’yceaie caaea/ ia?aiao?e/ii? iioei?caoe?? (19) oa (20), ? aneioioe/ii no?eeeie ca Eyioiiaei (no?eeeie a?aeiinii cao?aiue a i?aaeo /anoeiao aeeoa?aioe?aeueieo ??aiyiue). ?c aneiioioe/ii? no?eeino? iioeiaeueieo noaoe?iia?ieo oi/ie e?ia-oe/ii? nenoaie Iiii-???onaeeinueeiai (5) i?e m(y,z), ui aecia/athoueny ni?aa?aeiioaiiyie (17) aai (18), aeieeaa? aneiioioe/ia no?ee?noue iioe-iaeueieo a??aiiaaaeaieo ?aaeei?a a iaio aeiaaeeao (iaeiieo?aioiiai oa eiieo?aioiiai) ?ia?a??oaaiiy iiaeeaiei noano?aoii oa iaoaaie?oaie. O o?ao?e aeaa? ?iaioe aeine?aeaeaia a?eueo caaaeueia iiaeaeue Iiii -???onaeeinueeiai - nenoaia c iaeo?ae?coth/ei eiio?aaaioii: wmetafile0 (21) sse ? ?ai?oa, ?icaeyaea?oueny oaiinoaoiee ?aaeei ?iaioe eoeueoeaaoi?a iaia?a?aii? ae??, eiee ieoiiee ??no i?e?ii?aai?ci?a ?ia?a??o?oueny iaaeeeo-eii noano?aoa. Aea nenoaia ia? aeiaeaoeiao iniaeea?noue. A eoeueoeaaoi? ii-aea?oueny eiio?aaaioia ?a/iaeia, yea iiai?noth aai /anoeiai iaeo?ae?co? ia-oaaie?oe, ui i?ecaiaeeoue aei c?inoaiiy oaiio m(y,z) ia?iuoaaiiy a?iiane. sse e?eoa??e iioeiaeueiino? ?icaeyaea?oueny iaeneioi caaaeueiiai i?eaooeo ca iaia?aae aecia/aiee /aniaee i?ii?aeie [0,T]: wmetafile0 (23) aea g > 0 — aa?o?niee ia?aiao?, ui ni?aaei??th? aa?o?noue i?iaeoeoe??
a?iiane iiioeyoe?? ux oa aeo?aoe iaeo?ae?coth/iai eiio?aaaioa v; Vt —
aeiionoeiee i?ioean, ui iieno?oueny caaea/ith Eio? (21), (22) oa
nenoaiith iaiaaeaiue

wmetafile0

Iioeiaeuei? noaoe?iia?i? oi/ee iaea?aeothoueny o aeaeyae? ?ica’yceo
ia-?aiao?e/ii? caaea/? iae?i?eii? iioei?caoe??:

wmetafile0 (24)

wmetafile0 (25)

aeey aeiaaeeo iaeiieo?aioiiai ?ia?a??oaaiiy (17) oa

wmetafile0 (26)

ia iiiaeei? (25) aeey aeiaaeeo eiieo?aioiiai ?ia?a??oaaiiy (18) ?inoo
iiioeyoe??.

Ooo aaaaeaii iicia/aiiy wmetafile0 . Aeiionoeia iaeanoue wmetafile0
yaey? niaith i?yii-eooiee o?eeooiee, aea oe?eaa? aeey ian aeiaaeee
iicia/ai? oeeo?aie:

1. wmetafile0

2. wmetafile0

3. wmetafile0

Oe? o?e aeiaaeee iathoue oaeo aeiiii?/io ?ioa?i?aoaoe?th. A ia?oiio
aeiaaeeo iioeioi aeinyaa?oueny ia a?aieoe? z=0, aea v > 0, eiio?aaaio
aeei?enoiao?oueny aeey iiaiiai cieuaiiy i?iaeoeo?a iai?io (oea
a?aeaoaa?oueny i?e aeineoue iecue-e?e oe?i? eiio?aaaioa). A ae?oaiio
aeiaaeeo iioeioi ? aioo??oiueith oi/eith aeiionoeii? iiiaeeie D, aea v >
0, z > 0, eiio?aaaio aeei?enoiao?oueny eeoa aeey /anoeiaiai cieuaiiy
i?iaeoeo?a iai?io (oea a?aeaoaa?oueny, eiee oe?ia eiio?aaaioa ia ?
iaeith). A o?aoueiio aeiaaeeo iioeioi aeinyaa?oueny ia a?a-ieoe?
wmetafile0 , aea v > 0, eiio?aaaio ia aeei?enoiao?oueny (oea
a?aeaoaa?oueny i?e aeinoaoiuei aenie?e oe?i? eiio?aaaioa).

Oai?aia 7 Ia?aiao?e/ia caaea/a iae?i?eii? iioei?caoea? (24). (25) ?
aeaioaeno?aiaeueiith ? ia? oi/ee aeno?aioio, ui eaaeaoue a?aeiia?aeii ia
a?aieoeyo aeiionoeii? iaeano? (z = 0) oa (v = 0).

Oai?aia 8 Ia?aiao?e/ia caaea/a iae?i?eii? iioei?caoea? (26), (25) ?
aeaioaeno?aiaeueiith ? ia? oi/ee aeno?aioio eeoa ia a?aieoeyo
aeiionoeii? iaeano?, oiaoi i?e z = 0 (v > 0) oa wmetafile0 (v = 0).

Aeey iaio e?eoa???a (24) oa (26) ciaeaeai? oi/ee ia?aieeaiiy g = g0, i?e
yeeo aeiaaeueiee iaeneioi ci?ith? nai? i?noeaciaoiaeaeaiiy. Ia?ii
a?aeiia?aeii:

wmetafile0

wmetafile0

?

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