Моделювання процесів управління інвестиційною компанією в умовах нестабільного економічного середовища: Автореф. дис… канд. екон. наук / В.В. Гриб,

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i?i?noa?noai ina?oe Oe?a?ie

Aeiiaoeueeee aea?aeaaiee oi?aa?neoao

A?ea Aaaeei Aaeaioeiiae/

OAeE 519.876.2:334.714 (477)

Iiaeaethaaiiy i?ioean?a oi?aae?iiy ?iaanoeoe?eiith eiiiai??th a oiiaao
ianoaa?eueiiai aeiiii?/iiai na?aaeiaeua

Niaoe?aeuei?noue 08.03.02 – Aeiiii?ei-iaoaiaoe/ia iiaeaethaaiiy

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa aeiiii?/ieo iaoe

Aeiiaoeuee – 1999

Aeena?oaoe??th ? ?oeiien

?iaioo aeeiiaii ia eaoaae?? aeiiii?/ii? e?aa?iaoeee Aeiiaoeueeiai
aea?aeaaiiai oi?aa?neoaoo I?i?noa?noaa ina?oe Oe?a?ie (i. Aeiiaoeuee)

Iaoeiaee ea??aiee –aeieoi? aeiiii?/ieo iaoe, aeioeaio

?ai?ia Iao?i Aieiaeeie?iae/,

Aeiiaoeueeee aea?aeaaiee oi?aa?neoao

I?i?noa?noaa ina?oe Oe?a?ie,

caa?aeoth/ee eaoaae?ith o?iain?a ? aaie?anueei? ni?aae (i.
Aeiiaoeuee)Io?oe?ei? iiiiaioe: aeieoi? aeiiii?/ieo iaoe, i?ioani?

Caa?iaenueeee Ay/aneaa Aaeaiiae/,

Oa?e?anueeee iaoe?iiaeueiee oi?aa?neoao ?iai? I.A. Ea?ac?ia

I?i?noa?noaa ina?oe Oe?a?ie;

caa?aeoth/ee eaoaae?ith aeiiii?/ii? e?aa?iaoeee (i. Oa?e?a)

eaiaeeaeao aeiiii?/ieo iaoe

E?a/eianueeee Aieiaeeie? A?eoi?iae/,

Aeiiaoeueeee aea?aeaaiee oi?aa?neoao aeiiii?ee oa oi?a?ae?

I?i?noa?noaa ina?oe Oe?a?ie

noa?oee iaoeiaee ni?a?ia?oiee eaoaae?e eiii’thoa?ieo oaoiieia?e (i.
Aeiiaoeuee)

I?ia?aeia onoaiiaa – Ee?anueeee iaoe?iiaeueiee aeiiii?/iee oi?aa?neoao
I?i?noa?noaa ina?oe Oe?a?ie, eaoaae?a aeiiii?ei-iaoaiaoe/ieo iaoiae?a
(i. Ee?a).

Caoeno aeena?oaoe?? a?aeaoaeaoueny 28 n?/iy 2000 ?ieo i 10 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee E 11.051.01 o Aeiiaoeueeiio
aea?aeaaiiio oi?aa?neoao? I?i?noa?noaa ina?oe Oe?a?ie ca aae?anith:
83015, i. Aeiiaoeuee, aoe. *aethne?ioe?a, 198-a, aoae. 101.

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? Aeiiaoeueeiai
aea?aeaaiiai oi?aa?neoaoo I?i?noa?noaa ina?oe Oe?a?ie (83055, i.
Aeiiaoeuee, aoe. Oi?aa?neoaonueea, 24)

Aaoi?aoa?ao ?ic?neaiee 25 a?oaeiy 1999 ?ieo

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Iaa/ei A.N.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie aeine?aeaeaiiy. O i?ioean? noaiiaeaiiy ia Oe?a?i?
?eieo oe?iieo iaia??a c’yaeeiny aaaaoi cian?i iaoa?aeoa?ieo aeey iaoi?
aeiiii?ee aeaiaio?a ? iaoai?ci?a ?iaioe ia oeueiio ?eieo. Iaeiei c oaeeo
aeaiaio?a, ui aeieeee ia oiiaeiaiio ?eieo Oe?a?ie, noaee o?iainia?
iina?aaeieee: ?iaanoeoe?ei? oiiaee ? eiiiai??, ui noaee oei ii/aoeiaei
aooa?ii, yeee ni?eya caeo/aiith a aeiiii?eo nii/aoeo eioo?a, a iio?i ?
i?eaaoecaoe?eieo cania?a a?iiaaeyi Oe?a?ie.

Aeine?aeaeaiiy ?acoeueoao?a ooieoe?iioaaiiy aaaaoueio a?o/eciyieo
o?iainiaeo ?inoeooo?a i?ioyaii inoaii?o ?ie?a iieacaee iecueeee
i?ioan?eiee ??aaiue iaiaaeaeiaioo ?iaanoeoe?eieo oiiae?a ? eiiiai?e. Oea
iiynith?oueny a?aenooi?noth aeina?aeo ?iaioe oaeeo o?iainiaeo
?inoeooo?a, oiane?aeie aeoaea ei?ioeiai oa?i?io ?o ?nioaaiiy. Aiie
c’yaeeeny oaeoe/ii iaeii/anii c iaaoooyi Oe?a?iith iacaeaaeiino?.
?iaanoeoe?ei? oiiaee ? eiiiai?? ii??aiyii c ?ioeie o?iainiaeie
?inoeoooaie iathoue naith niaoeeo?eo, ui iio??aii aeey caaacia/aiiy ?o
aoaeoeaiiai ooieoe?iioaaiiy, ?aoaeueiiai aea/aiiy i?eioeei?a ? iaoiae?a
?o ?iaioe c o?aooaaiiyi aeei?enoaiiy aeina?aeo ?icaeiooeo e?a?i na?oo.

Ianoaa?euei?noue ooieoe?iioaaiiy ?iaanoeoe?eieo oiiae?a ? eiiiai?e ?
iane?aeeii ianoaa?eueiino? aeiiii?ee a oe?eiio, ui iaoiiaeaii
iaieaoini?iiiaei?noth aaaaoueio ainiiaea?/eo noa’?eo?a ? neeaaei?noth a
iaea?aeaii? iiaii?, oi/ii? ? aeinoia??ii? o?iainiai? ?ioi?iaoe??.
O?oaeiiu? o aecia/aii? oi/ieo cia/aiue i?eaooeiaino? oe?iieo iaia??a,
oi?a?aey yeeie ? iaeiei c iniiaieo aeae?a ae?yeueiino? o?iainiaeo
?inoeooo?a, ia aea? iiaeeeaino? noi?ioaaoe iioeiaeueiee ii?ooaeue
oe?iieo iaia??a, ui aaaea aei cieaeaiiy aoaeoeaiino? ?iaioe
?iaanoeoe?eieo oiiae?a ? eiiiai?e.

A?aenooi?noue oai?aoe/ii? iniiae oi?ioaaiiy ? oi?aae?iiy ?iaanoeoe?eieie
eiiiai?yie (?E), aeai?eoi?/iiai ? i?ia?aiiiai caaacia/aiiy aecia/a?
aeooaeuei?noue aeine?aeaeaiiy i?iaeai oi?aae?iiy ?iaanoeoe?eiith
eiiiai??th ia iniia? canoinoaaiiy iiaeo aeinyaiaiue a iaeano?
iiaeaethaaiiy aeiiii?/ieo nenoai, canoinoaaiiy aeey oeeo oe?eae
aeiiii?ei-iaoaiaoe/ieo iaoiae?a oa ?ioi?iaoe?eieo oaoiieia?e.

Caycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?th
aeeiiaii ca iaoa??aeaie aea?aeathaeaeaoii? oaie AeiiAeO “Ainiiaea?nueeee
iaoai?ci ae?iaie/eo nenoai” (iiia? aea?ae?a?no?aoe?? – 01920005513).

I?aaeiaoii aeine?aeaeaiiy ? iiaeaethaaiiy i?ioean?a oi?aae?iiy
o?iainiaeie ?inoeoooaie a no/anieo oiiaao ia?aoiaeo aei ?eieiai?
aeiiii?ee.

Ia’?eoii aeine?aeaeaiiy ? i?ioeane oi?aae?iiy o?iainiaeie ?ano?naie
?iaanoeoe?eii? eiiiai??. Iniiai? ?acoeueoaoe aeine?aeaeaiiy io?eiaii i?e
aeine?aeaeaii? i?ioean?a oi?aae?iiy o?iainiaeie ?ano?naie ?iaanoeoe?eii?
eiiiai?? “OAEO” (i. Ee?a).

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith i?aaenoaaeaii? aeena?oaoe?eii?
?iaioe ? ?ic?iaea nenoaie oi?aae?iiy ?iaanoeoe?eiith eiiiai??th oeyoii
neioaco aeiiii?ei-iaoaiaoe/ieo iiaeaeae, ni?yiiaaieo ia iioeiaeueia
oi?aae?iiy o?iainiaeie ?ano?naie ?iaanoeoe?eii? eiiiai?? a oiiaao
ianoaa?eueiiai aeiiii?/iiai na?aaeiaeua.

Aeey aeinyaiaiiy cacia/aii? iaoe a ?iaio? iinoaaeaii ? ae??oaii oae?
caaea/?:

aeine?aeaeaii i?iaeaie ? i?eioeeie ooieoe?iioaaiiy ?iaanoeoe?eieo
oiiae?a ? eiiiai?e a Oe?a?i?;

i?iaaaeaii aiae?c ?nioth/eo iaoiae?a oi?aae?iiy o o?iainiaeo ?inoeoooao;

aecia/aii iniiai? iai?yiee no?aoaa?/iiai e iia?aoeaiiai oi?aae?iiy
?iaanoeoe?eiith eiiiai??th a oiiaao ianoaa?eueiiai aeiiii?/iiai
na?aaeiaeua;

?ic?iaeaii iiaeae? oi?aae?iiy o?iainiaeie ?ano?naie ?iaanoeoe?eii?
eiiiai?? c o?aooaaiiyi iaaecia/aiino? oa ?eceeo;

i?iaiae?ciaaii iaoiaee ??oaiiy noioanoe/ii? iiaeae? ?iaioe
?iaanoeoe?eii? eiiiai??.

Oai?aoe/iith ? iaoiaeieia?/iith iniiaith ? ?iaioe a?o/eciyieo ?
caei?aeiiieo aaoi??a a iaeano? oi?aae?iiy ?iaanoeoe?yie, i?eeiyooy
??oaiue, iiaeaethaaiiy a oiiaao iaaecia/aiino?.

Iaoeiaa iiaecia io?eiaieo ?acoeueoao?a. O ?iaio? aeeiiaii iinoaiiaeo ?
ae??oaiiy caaea/? oi?ioaaiiy iioeiaeueiiai ii?ooaey oe?iieo iaia??a
?iaanoeoe?eii? eiiiai?? c o?aooaaiiyi oa?i?i?a iiaa?iaiiy ?iaanoeoe?e.
I?e oeueiio io?eiaii oae? iia? iaoeia? ?acoeueoaoe, ui iathoue
ae??oaeueia cia/aiiy aeey oaeineiiaeaiiy nenoaie oi?aae?iiy
?iaanoeoe?eieie eiiiai?yie:

eiioeaioe?y oi?ioaaiiy ii?ooaeueii? no?aoaa??, yea iiaoaeiaaia ia
i?eioeeiao aaeaioeaiiai oi?aae?iiy oa yea caiacia/o? aoaeoeaia
aeei?enoaiiy on?o aeae?a ?iaanoeoe?eieo ?ano?n?a;

ocaaaeueiaii iiaeaeue no?aoaa?/iiai oi?aae?iiy o?iainiaeie ?ano?naie
?iaanoeoe?eii? eiiiai?? a oiiaao ianoaa?eueiiai aeiiii?/iiai
na?aaeiaeua, ui aeicaiey? ?ic?iaeyoe aio/e? no?aoaa?? oi?ioaaiiy
?iaanoeoe?eiiai ii?ooaey;

iiaeaeue oi?aae?iiy o?iainiaeie ?ano?naie ?iaanoeoe?eiith eiiiai??th, ui
a?aoiao? aeiaaeeia?noue cia/aiue iaeaooi?o iieaciee?a i?eaooeiaino?
o?iainiaeo ?ino?oiaio?a oa aeicaiey? cae?enieoe no?aoaa?/ia oi?aae?iiy
?iaanoeoe?eiith eiiiai??th;

iiaeaeue oi?ioaaiiy ii?ooaeth oe?iieo iaia??a, yeo iiaoaeiaaii ia iniia?
aeei?enoaiiy oai??? ia/?oeeo iiiaeei oa caaacia/o? anoaiiaeaiiy
aoaeoeaieo ?ici???a ?iaanooaaiiy;

iiaeaeue iia?aoeaiiai oi?aae?iiy ii?ooaeai oe?iieo iaia??a
?iaanoeoe?eiith eiiiai??th, ui caaacia/o? ?iaanoeoe?eii? eiiiai??
oaeaeeo ?aaeoe?th ia ci?io a ?eieo oe?iieo iaia??a.

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoao?a aeine?aeaeaiiy iieyaa? a oiio,
ui oai?aoe/i? ?ic?iaee, iaaaaeai? a ?iaio?, ?aae?ciaaii a ?iaanoeoe?ei?e
eiiiai?? “OAEO” (i. Ee?a). Ia iniia? aeaieo o?iainiai? ca?oiino? i?i
ae?yeuei?noue oe??? eiiiai?? ?aae?ciaaii noioanoe/io iiaeaeue oi?aae?iiy
o?iainiaeie ?ano?naie. Ia iniia? io?eiaieo ?acoeueoao?a ?ic?aoiaaii
aoaeoeai?noue iiaeae? ? cai?iiiiiaaii iai?yiee uiaei oaeineiiaeaiiy
?iaanoeoe?eii? no?aoaa?? oa ?nioth/eo iaoiae?a oi?aae?iiy c iaoith
i?aeaeuaiiy aoaeoeaiino? ?iaioe ?iaanoeoe?eii? eiiiai??.

Ai?iaaoe?y ?acoeueoao?a aeine?aeaeaiiy. Iniiai? iieiaeaiiy aeena?oaoe??
aeiiia?aeaeenue ? iaaiai?thaaeenue ia iaoeiaeo nai?ia?ao eaoaae?e
aeiiii?/ii? e?aa?iaoeee Aeiiaoeueeiai aea?aeaaiiai oi?aa?neoaoo
I?i?noa?noaa ina?oe Oe?a?ie (i. Aeiiaoeuee).

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii 6 iaoeiaeo i?aoeue
caaaeueiei ianyaii 4.25 ae?oeiaaieo a?eoo?a, ?c yeeo aaoi?o iaeaaeeoue
2.2 ae?oeiaaieo a?eoo?a.

Ianya ? no?oeoo?a aeena?oaoe??. Iaoa, ia’?eo ? iaoiaeieia?y
aeine?aeaeaiiy aecia/eee eia?eo iiaoaeiae aeena?oaoe?eii? ?iaioe – a?ae
aiae?co i?eioeei?a ae?yeueiino? ?iaanoeoe?eieo oiiae?a ? eiiiai?e aei
oi?ioaaiiy nenoaie aeiiii?ei-iaoaiaoe/ieo iiaeaeae ?iaioe oeeo
o?iainiaeo ?inoeooo?a, ui caaacia/othoue oi?aae?iiy ?oi?i noaa?eueiei
ooieoe?iioaaiiyi.

Aeena?oaoe?y neeaaea?oueny c anooio, o?ueio ?icae?e?a, aeniiaeo, nieneo
e?oa?aoo?e c 116 iaeiaioaaiue, i?noeoue 6 oaaeeoeue, 3 ?enoiee, 8
aeiaeaoe?a ? aeeeaaeaia ia 162 noi??ieao iaoeiiieniiai oaenoo.

INIIAI? IIEIAEAIIss aeena?oaoe?eii? ?IAIOE

Aiae?c i?noey o?iainiaeo ?inoeooo?a o ?ano?oeoo?ecaoe?? aeiiii?ee
Oe?a?ie

?iaanoeoe?ei? oiiaee ? eiiiai?? i?ecia/aii aeey noeioethaaiiy a Oe?a?i?
iiaeo ?iaanoeoe?e o eiieo?aioi? aaeoc? ? i?aei?e?inoaa oa aeey
ianeoaiaoaaiiy i?ioeano i?eaaoecaoe?? aea?aeaaieo i?aei?e?inoa. Aea a
Oe?a?i? naia ?aeay i?eaaoecaoe?? aeoiaeeea ia c iaiao?aeiino?
i?eoyaiaiiy ?iaanoeoe?eieo ?ano?n?a a aeiiii?eo, a c iaiao?aeiino?
a?aeiiaeoe nioe?aeueio ni?aaaaeeea?noue oeyoii ia?aaea/? “oi?iaeueii
caaaeueiiia?iaeii? aeaniino?” ianaeaiith. Oiio eiioeaioe?y noai?aiiy
?iaanoeoe?eieo oiiae?a ? eiiiai?e noaaeeany a caeaaei?noue a?ae ae??aieo
?iaanoi??a, ui aaaeathoue ia no?eueee ?iaanooaaoe nai? caiuaaeaeaiiy a
aeiiii?eo, ne?eueee iaea?aeaoe iaeneiaeueio aeaiaeo a?ae aeei?enoaiiy
naiai i?aaa ia /anoeio a ?nioth/?e ? /anoi ia iaeaoaeoeai?o?e
aea?aeaai?e aeaniino?. Ae??ai? ?iaanoi?e aeae?athoue ?iaanoeoe?eio
eiiiai?th ia aeey oiai, uia cieceoe ?ecee ?iaanoeoe?e o iia? aaeoc?
ainiiaea?noaa, ui ?inoooue, ? ca?eueoeoe iiaeeea?noue i?eaooeo a?ae
oaeeo ?iaanoeoe?e, a ye aeanieee i?eaaoecaoe?eieo /ae?a ciaia’ycothoue
?iaanoeoe?ei? eiiiai?? i?eianoe i?eaooie, aea?aaeaioiee iaa?oue ia
caaaeuei?e na?aaei?e ?aioaaaeueiino? ainiiaea?noaa, a cia/ii aeuee.

A neeo aeuaneacaiiai aaeeea cia/aiiy ia? oaeineiiaeaiiy iaoiae?a
?aaoethaaiiy ae?yeueiino? o?iainiaeo ?inoeooo?a, cie?aia ?iaanoeoe?eieo
eiiiai?e, ?c iaoith ci?oeiaiiy oiiaeiaiai ?eieo ? noaa?e?caoe??
?iaanoeoe?eiiai i?ioeano a Oe?a?i?.

I?iaeaie oi?ioaaiiy ?iaanoeoe?eieo ?ano?n?a oiiae?a ? eiiiai?e

I?ioean oi?ioaaiiy ? ?ici?uaiiy ?ano?n?a ?iaanoeoe?eieo oiiae?a ?
eiiiai?e iaoiiaeaii anoaiiaeaiith oe?a?inueeei caeiiiaeaanoaii
i?aai?caoe?eii – i?aaiaith oi?iith ?nioaaiiy oeeo ?inoeoooe?iiaeueieo
?iaanoi??a. A?i ii/eia?oueny c oi?ioaaiiy noaoooiiai oiiaeo cae?eoiai
aeoe?iia?iiai oiaa?enoaa oeyoii iai?io cania?a caniiaiee?a ia aeoe??
aeaiiai ?iaanoeoe?eiiai oiiaeo.

I?ioa noi?iiaaiee noaoooiee oiiae iiaea? eeoa iaaaee/eo /anoeio
?iaanoeoe?eieo ?ano?n?a oiiaeo ? ? a?aei?aaiith oi/eith a i?ioean?
oi?ioaaiiy cania?a ?iaanoeoe?eiiai oiiaeo.

I?ney oi?ioaaiiy ii/aoeiaiai eai?oaeo (iiaii? iieaoe caniiaieeaie
aeoe?e) aei i?ioeano aeoioethaaiiy ?iaanoeoe?eieo ?ano?n?a
i?aeeeth/a?oueny iniaeeaa eaoaai??y ni?aaeaniee?a aeoea?a
?iaanoeoe?eiiai oiiaeo – eiai o/anieee, ye? ? iniiaiei aeaea?aeii
cania?a oiiaeo, ui iai?iththoueny ieie ia iniaeeao eaoaai??th oe?iieo
iaia??a – ?iaanoeoe?ei? na?oeo?eaoe. I?e oeueiio i???ioiai? ianyae
i?eoyaiaiiy ?ano?n?a o/aniee?a caeaaeaoue a?ae ?ici??o cania?a, aianaieo
o noaoooiee oiiae caniiaieeaie – aeoe?iia?aie.

Eiioeaioe?y aaeaioeaiiai oi?aae?iiy ?iaanoeoe?eiith eiiiai??th

?iaanoeoe?eia eiiiai?y, ye ? ?io? o?iainia? ?inoeoooe, ? neeaaeiith
aeiiii?/iith nenoaiith. ?, ye aoaeue-yea neeaaeia aeiiii?/ia nenoaia,
?iaanoeoe?eia eiiiai?y ia? iio?aao a noa?aiii i?aai?ciaaiiio e
aoaeoeaiiio oi?aae?ii?. I?ae oi?aae?iiyi a ?iaanoeoe?ei?e eiiiai?? ne?ae
?icoi?oe i?ioean, nooi?noue yeiai iiaeia aecia/eoe ye ae?iaeaiiy
ea?oth/eo aieea?a c aieo ea?oth/iai i?aaia eiiiai??, ni?yiiaaieo
aaciina?aaeiuei ia ?iaanoeoe?eiee i?ioean aeey aeinyaiaiiy iinoaaeaieo
ia?aae ?iaanoeoe?eiith eiiiai??th oe?eae ? caaea/.

Ia?oi/a?aiaei aoaiii o i?ioean? oi?aae?iiy ?iaanoeoe?eiith eiiiai??th ?
ae?iaeaiiy ?iaanoeoe?eii? no?aoaa??. ?iaanoeoe?eia no?aoaa?y eiiiai??
aaco?oueny ia iiiyooyo oe?eae ? iaiaaeaiue. Aoaeue-yeo caaea/o aeai?o
iaea?eueo aoaeoeaieo ?iaanoeoe?e iiaea aooe ?aoe?iiaeueii ae??oaii ia
iniia? iiia?aaeiueiai /?oeiai oi?ioethaaiiy iaoe. Ui noino?oueny
iaiaaeaiue, oi aiie, ye i?aaeei, aeeeoothoueny ?eieii.

Oiio a oiiaao ianoaa?eueiino? ia ?eieo oe?iieo iaia??a a ?iaanoeoe?ei?e
eiiiai?? aeieea? iaiao?aei?noue aeinoaoiuei /anoiai ei?eaoaaiiy
?iaanoeoe?eii? no?aoaa?? c o?aooaaiiyi ciai?oi?o aieea?a. Ei?eaoaaiiy
?iaanoeoe?eii? no?aoaa?? c iaeiaioeie aeo?aoaie aac iia??oaiiy
iieaciee?a aoaeoeaiino? iiaeia caaacia/eoe, aeei?enoiaoth/e nenoaio
aaeaioeaiiai oi?aae?iiy ?iaanoeoe?eiith eiiiai??th.

Eiioeaioe?y aaeaioeaiiai oi?aae?iiy ?iaanoeoe?eiith eiiiai??th
oa?aeoa?eco?oueny oaeeie iieiaeaiiyie:

aeeaiea aea/aiiy iaoai?cio e oiia ?aae?caoe?? no?aoaa?/ieo ieai?a ca
iiia?aaei? ia??iaee e i?aai?caoe?y iaa/aiiy nenoaie no?aoaa?/iiai
oi?aae?iiy;

i?aeaeuaiiy iaae?eiino? iieaciee?a ooieoe?iioaaiiy ?iaanoeoe?eii?
eiiiai?? (i?ae iaae?ei?noth iieacieea ?icoi??oueny ?iia??i?noue eiai
noaa?eueiino?);

aeoeaia o/anoue niaoe?ae?no?a o oi?ioaaii? no?aoaa?/iiai ieaio
(?aae?caoe?y i?eioeei?a ?ioa?aeoeaiiai no?aoaa?/iiai oi?aae?iiy);

i?aai?caoe?y iaoai?cio ei?eaoaaiiy no?aoaa?? i?e ci?i? oiia ??
?aae?caoe??.

Aaeaioeaia no?aoaa?/ia oi?aae?iiy aecia/a?oueny aeaiia aeaeaie
aaeaioaoe??: ianeaia e aeoeaia no?aoaa?/ia aaeaioaoe?y.

Ianeaia aaeaioaoe?y a nenoai? aaeaioeaiiai no?aoaa?/iiai ieaioaaiiy
i?aaenoaaey? niaith aaeaioeai? yeino? no?aoaa??, ui caeeaaeathoueny i?e
?? oi?ioaaii? (aoaeo aioeneiaoe??). Oea icia/a?, ui aaeaioeai? yeino?
?aca?aothoueny a no?aoaa?/iiio ieai? o oi?i? iaeano? iaiaa?oaaiiy
no?aoaa?/iiai ieaio. Aaeaioeai? yeino? no?aoaa?? oiai /e ?ioiai nooiaiy
aecia/athoue iaea?eueo aoaeoeaio ?aaeoe?th ?iaanoeoe?eii? eiiiai?? ia
ci?io oiia ?aae?caoe?? no?aoaa?/iiai ieaio.

Aeoeaia aaeaioaoe?y – oea iaoai?ci ?aae?caoe?? aaeaioeaieo yeinoae
no?aoaa?/iiai ieaio, ui aaco?oueny ia iioaioe?eieo iiaeeeainoyo ianeaii?
aaeaioaoe??. Aeoeaia aaeaioaoe?y ?aae?co?oueny /a?ac iaoai?ci
?aaoethaaiiy a i?ioean? ei?eaoaaiiy no?aoaa??.

Oaeei /eiii, aaeaioeaia no?aoaa?/ia oi?aae?iiy ? i?ioean, caniiaaiee ia
?aae?caoe?? iiaeaeae oi?ioaaiiy iioeiaeueiiai no?aoaa?/iiai ieaio, ui
aieiae?? aaeaioeaieie yeinoyie, ? ?aae?caoe?? aaeaioeaieo yeinoae
no?aoaa?/iiai ieaio. I?ioean

aaeaioeaiiai no?aoaa?/iiai oi?aae?iiy ?iaanoeoe?eii? eiiiai?? iiaeia
i?aaenoaaeoe o aeaeyae? oaei? noaie (?en.1):

?enoiie 1. Noaia aaeaioeaiiai oi?aae?iiy ?iaanoeoe?eiith eiiiai??th

Iicia/aiiy aei ?en. 1 :

O – oe?e? oa iaiaaeaiiy ?iaanoeoe?eii? eiiiai??;

— ciai?oi? aieeae, iaoiiaeai? noaiii ?eieo;

— iaiaaeaiiy, ui aeeeoothoueny ?eieii;

Ui — oi?aaeyth/? aieeae, ye? ae?iaeththoueny i–i aeieii, (i
=wmetafile8? ??C????????????
???????????yyy????.????1?????? ???????
?`???&??yyyy?????Ayyy1/2yyy ??1/2?? ???&?
?MathType??P????u y??????Y — ?acoeueoao ?iaanoeoe?eii? ae?yeueiino?
(i?eaooie).

O aeioe? (AN) cae?enith?oueny ae?iaeaiiy ?iaanoeoe?eii? no?aoaa?? ia
iniia? oe?eae ? iaiaaeaiue ae?yeueiino? ?E, a oaeiae iiaeeeainoae,
iaaeaieo ?eieii. Oe? iiaeeeaino? ioe?iththoueny a aeioe? aiae?co
?iaanoeoe?e (A?): aiae?c ?eieo a oe?eiio, eiai naaiaio?a ? ie?aieo
oe?iieo iaia??a. O aeioe? oi?ioaaiiy ?iaanoeoe?eiiai ii?ooaey (OI)
cae?enith?oueny ??oaiiy caaea/? aeiai?o ia’?eo?a ?iaanooaaiiy. O aeioe?
(OA) ?aae?co?oueny oi?aae?iiy aeoeaaie. O aeioe? (IA) ?aae?co?oueny
ioe?iea aoaeoeaiino? ?iaanoeoe?eii? ae?yeueiino? ?E. Aeie aaeaioaoe??,
oiaoi ei?eaoaaiiy ?iaanoeoe?eii? no?aoaa?? (EN) ? aieiaiei o aeai?e
noai?, oiio ui a iueiio ?aae?co?oueny eiioeaioe?y aaeaioeaiiai
oi?aae?iiy ?E.

Iaeiei ?c iaea?eueo aaaeeeaeo aoai?a oi?aae?iiy ?iaanoeoe?eiith
ae?yeuei?noth ? oi?aae?iiy ?iaanoeoe?eiei ii?ooaeai. ?ic??ciythoue aeaa
i?aeoiaee aei oi?aae?iiy ?iaanoeoe?eiei ii?ooaeai: aeoeaiee ? ianeaiee.

Aeoeaia oaeoeea i?eionea?, c iaeiiai aieo, ieeueia a?aene?aeaeaiiy ?
i?eaeaaiiy iaea?eueoa aoaeoeaieo oe?iieo iaia??a, a c ?ioiai aieo –
iaeneiaeueii oaeaeeee caoeno a?ae iecueeii?eaooeiaeo aeoea?a. Oae?e
oaeoeoe? a?aeiia?aea? niaoeeo?/iee iaoiae aeoeaiiai ea?oaaiiy – naii?ia,
ui icia/a? iino?eiee iai?i oa ?ioaoe?th oe?iieo iaia??a /a?ac o?iainiaee
?eiie.

Ianeaia oi?aae?iiy caniiaaia ia oyaeaii?, ui ?eiie aeinoaoiuei
aoaeoeaiee aeey aeinyaiaiiy oni?oo o aeai?? oe?iieo iaia??a aai a
o?aooaaii? /ano. Nooue ianeaii? oaeoeee neeaaea?oueny a noai?aii? aeia?a
aeeaa?neo?eiaaieo ii?ooae?a ?c cacaeaeaa?aeue aecia/aiei ??aiai ?eceeo ?
o?eaaeiio oo?eiaii? ii?ooaey a iaci?iiiio noai?.

A caeaaeiino? a?ae ia?aiiai i?aeoiaeo canoiniaothoueny o? aai ?io?
iaoiaee oi?aae?iiy ?iaanoeoe?eiei ii?ooaeai.

Ocaaaeueiaia iiaeaeue no?aoaa?/iiai oi?aae?iiy ?iaanoeoe?eiith
eiiiai??th

?iaanoeoe?eia eiiiai?y ciaoiaeeoueny a iino?ei?e aca?iiae?? c ciai?oi?i
na?aaeiaeuai. C iaeiiai aieo, aiia caeo/a? c ciai?oiueiai na?aaeiaeua
a?euei? o?iainia? ?ano?ne, c ?ioiai aieo – ?iaanoo? oe? ?ano?ne a
??ciiiai?oi? oe?ii? iaia?e (iai?eeeaae, aeoe?? i?aei?e?inoa). Oaeei
/eiii, ae?yeuei?noue ?iaanoeoe?eii? eiiiai?? i?aaenoaaey? niaith
ocaiaeaeaiee o /an? iio?e o?iainiaeo ?ano?n?a, ui noai?th? eiioo? ?c
iiceoeaieie ? iaaaoeaieie cai?ioieie ca’yceaie; ioaea, ?iaanoeoe?eia
eiiiai?y ? iacaieiooith nenoaiith, ui iiynith?oueny aeainoi?iiiueith
aca?iiae??th c iaaeieeoi?i na?aaeiaeuai.

sse?noue iacaieiooino? ? iaiao?aeiith c aeaio i?e/ei: ii-ia?oa,
aacoieiia aeaeeaaiiy ?iaanoeoe?eii? eiiiai?? caeaaeeoue a?ae ??
ni?iiiaeiino? caaacia/eoe iaaeoiaeaeaiiy ?ano?n?a ?c ciai?oiueiai
na?aaeiaeua, a ii-ae?oaa, aeeaaeaiiy i?eoyaiooeo cania?a o ??ciiiai?oi?
o?iainia? ?ino?oiaioe caaacia/o? iaea?aeaiiy iaeneiaeueiiai i?eaooeo, ui
oaeiae ni?ey? ?icaeoeo ?eieo oe?iieo iaia??a ? a oe?eiio iiceoeaii
aieeaa? ia aeiiii?eo.

?iaanoeoe?eia eiiiai?y i?aoeth? c /ioe?ia iioieaie eioo?a:

— caeo/aiiy o?iainiaeo ?ano?n?a;

— aeeaaeaiiy oeeo ?ano?n?a o oe?ii? iaia?e;

— iaea?aeaiiy i?eaooe?a a?ae oe?iieo iaia??a;

— iiaaoaiiy ciaia’ycaiue (ianea?a).

?ioi?iaoe?th i?i o?iainia? iioiee iieeaaeaii a iniiao iiaoaeiae iiaeae?
no?aoaa?/iiai oi?aae?iiy o?iainiaeie ?ano?naie ?iaanoeoe?eii? eiiiai??.

I?ioean i?eeiyooy ??oaiue i?i aeeaaeaiiy cania?a o i?eaooeia? aeoeae a
iiaeae? ?icaeyaea?oueny ye aeene?aoiee, o yeiio ci?ii? ci?iththoueny
o?eueee a ie?ai? iiiaioe /ano, ui iaceaathoueny iaaeae? noaae?yie
?iaanoeoe?eiiai i?ioeano. Iaoae oeae i?ioean ?icaeyaea?oueny i?ioyaii
aeayeiai a?ae??ceo /ano [I,O], ui ?icaeaa?oueny ia n ?ioa?aae?a,
o?eaae?noue eiaeiiai c ieo aei??aith? . Ioaea, n* = T, aea ?
iaeeieoeath aei??o /ano, ui ci?ith?oueny aeene?aoii.

Aeey iiaoaeiae iiaeae? ae?yeueiino? ?iaanoeoe?eii? eiiiai?? aaaaeaii
oae? iicia/aiiy:

Rij – ?ano?ne, ui caeo/athoueny ia i-e noaae??, c oiiaith iiaa?iaiiy ia
noaae?? j;

Aki – aeoeae, ?iaanoiaai? ia k-e noaae??, iiaa?iaiiy yeeo
ia?aaeaa/a?oueny ia i-e noaae??;

Pki – ianeae (ciaia’ycaiiy), caeo/ai? ia k-e noaae??, iiaaoaiiy yeeo
ia?aaeaa/a?oueny ia i-e noaae??;

ylij – ?ano?ne, ye? ?ici?uai? a l-e aeoea ia noaae?? i c iaoiiaeaiei
iiiaioii iiaa?iaiiy ia noaae?? j;

rlii – /anoeia ?ano?n?a R, ui caeo/athoueny oa eaea ia aeeaaeaiiy a l-e
aeoea ia noaae?? i c iaoiiaeaiei iiiaioii iiaa?iaiiy ia noaae?? j;

alij – /anoeia ?ano?n?a A, ui ?a?iaanoo?oueny o l-e aeoea ia noaae?? i c
iaoiiaeaiei iiiaioii iiaa?iaiiy ia noaae?? j;

xki – /anoeia ?iaanoiaaieo ia k-e noaae?? ?ano?n?a A, ui eaea ia
iiaaoaiiy ciaia’ycaiue ia i-e noaae??;

pki – /anoeia ?ano?n?a R, ui caeo/athoueny ia i-e noaae?? oa eaea ia
iiaaoaiiy ciaia’ycaiue k-e noaae??.

Aeey iai/iino? i?ioeano ?iaanooaaiiy ia ?en. 2 i?eaaaeaii noaio ?iaioe
?iaanoeoe?eii? eiiiai??.

Ia i?aenoaa? c?iaeaieo aeua i?eiouaiue ? iicia/aiue iiaoaeo?ii
iaoaiaoe/io iiaeaeue ?iaioe ?iaanoeoe?eii? eiiiai??:

wmetafile8? ??U???????????
???????????yyy????.????1?????? ???????  
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?MathType??a????uya?????wmetafile8? ??U???????????
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?MathType???????u?th??????wmetafile8? ??b???????????
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Aa#???&??yyyy?????Ayyy?yyy #??r?? ???&?
?MathType???????u?th??????wmetafile8? ??q???????????
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A?%???&??yyyy?????Ayyy«yyy@%??k?? ???&?
?MathType???????uya?????wmetafile8? ??u???????????
???????????yyy????.????1?????? ???????
@?(???&??yyyy?????Ayyy±yyy@(??n?? ???&?
?MathType??a????u©ya?????wmetafile8? ??B???????????
???????????yyy????.????1?????? ???????
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???u?th??????aea wmetafile8? ?????????????
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A ???&??yyyy?????Ayyy©yyy`??i?? ???&?
?MathType??p????uAy??????

?enoiie. 2. Noaia ?iaioe ?iaanoeoe?eii? eiiiai??.

I?ioa c oeueiai oaa?aeaeaiiy ia aeieeaa? i?ioeeaaeia. ?iaeoa eaaeo/e, c
iaeiiai aeaea?aea iiaea a?aeaoaaoeny ?iaanooaaiiy a ??ciiiai?oi? oe?ii?
iaia?e, aea a iaeei aeae oe?iieo iaia??a ia iiaea a?aeaoaaoeny
?iaanooaaiiy c aeae?eueeio aeaea?ae. Ae?enii, ?icoaoiaoth/e caniae
iaeiiai aeeaaeieea (aai aeae?eueeio aeeaaeiee?a, eiinie?aeiaaieo ii
oa?i?iao aeeaaeaiiy), ?iaanoeoe?eia eiiiai?y iiaea ?icii?yaeaeaoeny ieie
oaeei /eiii, uia ni?aa?aeianoe /an iiaa?iaiiy ?iaanoeoe?e ?c oa?i?iaie
iiaaoaiiy ciaia’ycaiue.

?iaeaen i i?e Li iieaco?, ui /enei ?iaanoeoe?eieo iai?yie?a ia eiaeiiio
aoai? iiaea aooe ??ciiiai?oiei ? caeaaeeoue a?ae i?iiiceoe?e ia ?eieo
oe?iieo iaia??a.

Oe?eueiaa ooieoe?y (1) aecia/a? iaenei?caoe?th i?eaooeo ?iaanoeoe?eii?
eiiiai??, io?eiaiiai a?ae aeeaaeaiiy cania?a o ??ciiiai?oi? oe?ii?
iaia?e ca a?ae?aooaaiiyi aeo?ao, iia’ycaieo ?c aeieaoith a?aenioe?a ?
aeea?aeaiae?a ii ciaia’ycaiiyo ia?aae ?iaanoi?aie.

Iaiaaeaiiy (2) iieaco?, ui caeo/ai? ?ano?ne ?iaanoeoe?eii? eiiiai??
?iciiae?eythoueny ia aeeaaeaiiy a aeoeae ? ia iiaaoaiiy iioi/ieo aeiia.

Iaiaaeaiiy (3) a?aeia?aaea? aeeaaeaiiy cania?a a aeoeae: /anoeia cania?a
caeo/a?oueny ia aeaiiio aoai?, a /anoeia cania?a ?a?iaanoo?oueny c
i?eaooeo.

Iaiaaeaiiy (4) iieaco? iai?yiee aeei?enoaiiy i?eaooeo, io?eiaiiai a?ae
?iaanooaaiiy: /anoeia eaea ia iiaaoaiiy iioi/ieo ianea?a, a /anoeia
ciiao ?a?iaanoo?oueny a aeoeae.

Iaiaaeaiiy (5) aeiaaa?, uia on? iioi/i? ciaia’ycaiiy aoee a/anii
iiaaoai?. Caniae ia iiaaoaiiy ciaia’ycaiue aa?ooueny ye ?c i?eaooeo, oae
? c? ciiao caeo/aieo cania?a.

Iaiaaeaiiy (6) ? oiiaith iaa?ae’?iiino? ci?iieo.

Ooieoe?y Clij(y) ae?aaea? i?eaooie ?iaanoeoe?eii? eiiiai?? a?ae
?ici?uaiiy cania?a y a i?eaooeia? aeoeae. Oeae i?eaooie iiaea aooe
io?eiaiee o aeaeyae? aeea?aeaiae?a, yeui aeeaaeaiiy a?aeaoaa?oueny a
aeoe??, aai ae o aeaeyae? a?aenioe?a, yeui aeeaaeaiiy a?aeaoaa?oueny a
iae?aaoe?? aai ?io? ai?aia? oe?ii? iaia?e.

Ooieoe?y C’ij(R) icia/a? aeo?aoe ?iaanoeoe?eii? eiiiai??, ui aeieeee a
?acoeueoao? caeo/aiiy cania?a R ? iaeeaaei? aeo?aoe a ca’yceo c
ianeoaiaoaaiiyi ?iaanoeoe?eiiai i?ioeano.

O iaei?ino?oiio e?i?eiiio aeiaaeeo, eiee ia?aooaaiiy a?aenioe?a
cae?enith?oueny ca oi?ioeith neeaaeieo a?aenioe?a, ooieoe?? Clij(y) ?
C’ij(R) iathoue aeaeyae:

wmetafile8? ??2???????????
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??Q??????????? ???????????yyy????.????1??????
??????? @????&??yyyy?????Ayyy±yyyA??n?? ???&?
?MathType??aea n — /enei ia??iae?a, ui ciaoiaeyoueny a ?ioa?aae? /ano
(i,j);

hi — oe?ia i?iaeaaeo ?ano?n?a, ui ae?? ia iiiaio /ano i oa ae?aaeaia a
??/ieo a?aenioeao;

h’i — oe?ia caeo/aiiy ?ano?n?a, ui ae?? ia iiiaio /ano i oa ae?aaeaia a
??/ieo a?aenioeao;

S — iaeeaaei? aeo?aoe.

Oaeei /eiii, noi?ioeueiaaia caaea/a oi?aae?iiy aeoeaaie ? ianeaaie
?iaanoeoe?eii? eiiiai?? (1) – (6) yaey? niaith caaea/o e?i?eiiai
i?ia?aioaaiiy, aeey ??oaiiy yei? iiaeooue aooe cai?iiiiiaai? oe?iei
a?aeii? iaoiaee.

Noioanoe/ia iiaeaeue no?aoaa?/iiai oi?aae?iiy ?iaanoeoe?eiith eiiiai??th

Aoaeue-yea aeiiii?ei-iaoaiaoe/ia iiaeaeue i?noeoue ea?iaai? ? iaea?iaai?
ia?aiao?e. Ea?iaai? ia?aiao?e (ci?ii?) aecia/athoueny a ?acoeueoao?
ae??oaiiy caaea/?, ca aeiiiiiaith yei? oi?ioeth?oueny iiaeaeue.
Iaea?iaai? ia?aiao?e (ao?aeia ?ioi?iaoe?y) caaeathoueny. Aiie iienothoue
ciai?oi? ? aioo??oi? oa?aeoa?enoeee nenoaie, ui iiaeaeth?oueny.
Iaea?iaai? ia?aiao?e ia ci?iththoueny a i?ioean? ??oaiiy caaea/?.

O iiaeae? (1) – (6) iaea?iaaieie ia?aiao?aie ? ?ici?? i?eaooeiaino? a?ae
?iaanooaaiiy a oe?ii? iaia?e Clij(y) ? noia caeo/aieo ia i-i aoai?
cania?a aeeaaeiee?a Rij. *a?ac oa, ui oe? ?ici??e caeaaeaoue a?ae noaio
oiiaeiaiai ?eieo ? a?ae i?iiiceoe?? ?iaanoi??a, oe? ia?aiao?e ?
aeiaaeeiaeie. Oey ianoaaeia i?aee?aneth?oueny oeyoii aeacoaaiiy ia
caeaaei?noue oeeo ia?aiao??a a?ae . Oaeei /eiii, ? aeiaaeeia? ?ici??e
Clij(y,) ? Rij(), i?aenoaaeaoe ye? o aeaoa?i?iiaaio iiaeaeue (1) – (6),
iaea?aeeii:

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???u™ya?????O caaaeueiiio aeiaaeeo caaea/a ia? aeaeyae:

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Aa%???&??yyyy?????Ayyy3/4yyy %??~?? ???&?
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???&??yyyy?????Ayyy?yyy?

??u?? ???&? ?MathType?? ???utha?????aea I – ciae iaoaiaoe/iiai
i/?eoaaiiy.

*a?ac oa, ui aeaia caaea/a ? aaaaoiaoaiiith, oiaoi iaiao?aeii aecia/aoe
no?oeoo?o iioeiaeueiiai ii?ooaey oe?iieo iaia??a ia eiaeiiio aoai?
caeo/aiiy o?iainiaeo ?ano?n?a, ??oaiiy aeaii? caaea/? iiaea aooe
io?eiaia ca aeiiiiiaith iaoiaeo noioanoe/ieo eaac?a?aae??io?a.

Iiaeaeue oi?ioaaiiy ii?ooaey oe?iieo iaia??a

ia iniia? aeei?enoaiiy oai??? ia/?oeeo iiiaeei

sse no?aoaa?/ia oe?eue ooieoe?iioaaiiy ?iaanoeoe?eii? eiiiai??
?icaeyaea?oueny caaea/a i?aeaeuaiiy ?iaanoeoe?eii? i?eaaaeeaino?
eiiiai?? aeey nai?o aeeaaeiee?a. O ca’yceo c oeei aoaeo?oueny
iaoaiaoe/ia iiaeaeue, o ye?e e?eoa???i iioeiaeueiino? ? nai?/ania
aeeiiaiiy ciaia’ycaiue ia?aae aeeaaeieeaie.

Ioaea, iaoae yj Y, j=1,…,m – iiiaeeia aa??aio?a iai?yie?a ?iaanooaaiiy
eioo?a ?iaanoi??a ri R, i=1,…,n. Eiaeiee yj ia’?aeio? a nia? iiiaeeio
aa??aio?a aaniethoii noiaeeo i?ae niaith o oa?i?i? iiaa?iaiiy,
i?eaooeiaino? ? nooiaith ?eceeo ?iaanoeoe?e, a eiaeiee ri ia’?aeio? a
nia? e?euee?noue ?iaanoi??a, o yeeo ca?aathoueny aaaeaiiy c oa?i?io
iiaa?iaiiy ?oi?o eioo?a. Aiane?aeie oeueiai iiaeia eiaei?e eiae?oe??
?iaanoi??a iinoaaeoe o a?aeiia?aei?noue aaaeaiee oa?i?i iiaa?iaiiy
cania?a i=1,…,n. Oiae? eiaeiiio aa??aioo iai?yieo ?iaanooaaiiy (iaaeae?
aoaeaii iaceaaoe aa??aioii ?iaanoeoe?eiiio i?iaeoo) iiaeia iinoaaeoe o
a?aeiia?aei?noue oa?i?i iiaa?iaiiy ?iaanoeoe?e j=1,…,m. ?ic?a’?ii
iiiaeeio ?iaanoeoe?eieo i?iaeo?a Y ia k i?aeiiiaeei. ?iaanoeoe?ei?
i?iaeoe ia’?aeiothoueny a aeai? i?aeiiiaeeie ca i?eioeeiii iaeiaeiaiai
??aiy i?eaooeiaino? aai nooiaiy ?eceeo. Oaeei /eiii, ia?oi/a?aiaith
iaoith ?iaanoeoe?eii? eiiiai?? ? caaeiaieaiiy aaaeaiue ?iaanoi??a c
oa?i?io iiaa?iaiiy eioo?a. Ae?oai?yaeiith iaoith ?iaanoeoe?eii?
eiiiai?? ? iaenei?caoe?y i?eaooeo a?ae ?iaanooaaiiy. C oeueiai aeieeaa?,
ui ooieoe?y oe?e? iiaeiia iaenei?coaaoe caaaeueio ei?eni?noue aeey
?iaanoi??a c oa?i?i?a iiaa?iaiiy cania?a.

Aaaaeaii ooieoe?th iaeaaeiino? R(V) oiai /e ?ioiai ?iaanoeoe?eiiai
i?iaeoo, ui ae?aaea? nooi?iue iaaeaiiy ia?aaaae ?iaanoi?ii aeaiiai
i?iaeoo. Cia/aiiy ooieoe?? “ia?aaaae” ci?ith?oueny a ?ioa?aae? [0,1].
Aiii aoaea aei??aithaaoe 1, yeui oa?i?ie aeeaaeaiiy cania?a ?iaanoi?a ?
oa?i?ie iiaa?iaiiy ?iaanoeoe?e ca?aathoueny, aai inoaii? iaioa ia?oeo.
sseui ae oa?i?ie iiaa?iaiiy ?iaanoeoe?e ia?aaeuothoue aaaeai? oa?i?ie
iiaa?iaiiy cania?a ?iaanoi?a, oi cia/aiiy ooieoe?? “ia?aaaae” aoaea
iaioei ca 1. ? /ei a?eueoa oey ??cieoey a oa?i?iao, oei iaioa cia/aiiy
oe??? ooieoe??.

Iiaoaeo?ii iao?eoeth ooieoe?e iaeaaeiino? (ia?aaaae) i-i ?iaanoi?ii
j-ai ?iaanoeoe?eiiai i?iaeoo:

Oaaeeoey 1. Iao?eoey ooieoe?e iaeaaeiino?

Y Yk1 Yks Ykm R y1 yj…yk1y1yj…yksy1yj…ykm r1 1(1)
1(j)…1(k1)1(1)1(j)…1(kS)1(1)1(j)…1(km) ri i(1)
i(j)…i(k1)i(1)i(j)…i(kS)i(1)i(j)…i(km)…………………………………rnn(1)n(j)…n(k1)n(1)n
(j)…n(kS)n(1)n(j)…n(km)

?yaeee aeaii? oaaeeoe? yaeythoue niaith iaiaaeaiiy caaea/?. Oiae? iaoith
caaea/? ? aea?? iaee?auiai aa??aioa ?iaanoeoe?eiiai i?iaeoo a eiaei?e c
i?aeiiiaeei Yks. Noeoii?noue iaee?aueo aa??aio?a o eiaei?e i?aeiiiaeei?
aoaea ae??oaiiyi caaea/? caaeiaieaiiy aaaeaiue ?iaanoi??a c oa?i?i?a
iiaa?iaiiy eioo?a. I?ioean ??oaiiy aeaii? caaea/? iiaeia ?icaeoe ia oae?
aoaie:

1. I?iaaaeeoueny ia?aoeiaiiy iaiaaeaiue (?yaee?a iao?eoe?) Ri o eiaei?e
c i?aeiiiaeei Yks: wmetafile8? ??A???????????
???????????yyy????.????1?????? ???????
`a???&??yyyy?????Ayyy?yyy ???? ???&?
?MathType??P???u?th??????2. C io?eiaiiai aaeoi?a DS ooieoe?e
iaeaaeiino? (ia?aaaae) aeae?a?oueny iaeneiaeueiee aeaiaio o eiaei?e c
i?aeiiiaeei Yks: d=maxDS aai wmetafile8? ??3. I?iaaaeeoueny
ia’?aeiaiiy d, s=1,…,m iaee?aueo aa??aio?a ?c eiaeii? i?aeiiiaeeie Yks;
oaeei /eiii, io?eia?ii aaeoi? D=(d1,…,dS,…,dm), yeee neeaaea?oueny ?c
iaeneiaeueieo aeaiaio?a oeeo i?aeiiiaeei.

Caaaeueiee aeae ??oaiiy aeaii? caaea/? iiaeia caienaoe o oaeiio
aeaeyae?:

wmetafile8? ??k???????????
???????????yyy????.????1?????? ???????
@A???&??yyyy?????Ayyy!yyy???a?? ???&?
?MathType??@???u?th???????acoeueoaoii ??oaiiy aeaii? iiaeae? ? aaeoi?
D=(d1,…,dS,…,dm), yeee neeaaea?oueny c iaee?aueo aa??aio?a ?iaanooaaiiy
a?ioiaeo cania?a, oiaoi oeae aaeoi? i?aaenoaaey? niaith ?iaanoeoe?eiee
ii?ooaeue. Iaee?auei aa??aioii ?iaanooaaiiy a eiaei?e i?aeiiiaeei?
aaaaea?oueny oie aa??aio, aea?? yeiai caaeiaieueiy? caaaeueiei ?ioa?anai
?iaanoi??a c oa?i?i?a iiaa?iaiiy eioo?a. I?e oeueiio iaoa iaenei?caoe??
i?eaooeo ?iaanoeoe?eii? eiiiai?? iinoa? ia ae?oaa i?noea.

Iiaeaeue iia?aoeaiiai oi?aae?iiy ?iaanoeoe?eiith eiiiai??th

Ia iaio aaaeeeaei aeey o?iainiaeo iina?aaeiee?a ? cae?eniaiiy
aoaeoeaiiai iia?aoeaiiai oi?aae?iiy. Ia a?aei?io a?ae no?aoaa?/iiai
oi?aae?iiy, ui ni?yiiaaia ia caaacia/aiiy aeeoo?caeaoiino? eiiiai??, a
oaeiae i?aeaeuaiiy ?iaanoeoe?eii? i?eaaaeeaino? aeey aeeaaeiee?a, ui
ni?ey? ca?eueoaiith ianya?a o?iainiaeo ?ano?n?a, ye? caeo/athoueny, ?
?icoe?aiith nai?? ae?yeueiino? ia oiiaeiaiio ?eieo, iia?aoeaia
oi?aae?iiy ?iaanoeoe?eiith eiiiai??th noaaeoue nai?th iaoith aeinyaiaiiy
iioi/ieo oe?eae. Iniiaieie oe?eyie iia?aoeaiiai oi?aae?iiy ? iaea?aeaiiy
i?eaooeo a?ae iia?aoe?e ?c oe?iieie iaia?aie, i?aeo?eiea e?ea?aeiino?
aeanieo aeoea?a.

Ia’?eoii iia?aoeaiiai oi?aae?iiy ? ei?ioeino?ieia? aeeaaeaiiy a
??ciiiai?oi? o?iainia? aeoeae, ui, ye i?aaeei, ia ? aenieii?eaooeiaeie.
Uia iaenei?coaaoe i?eaooie, ea??aieoeoai eiiiai?? iae/ano?oa aeeaaea?
eiooe a a?eueo ?eceeiaai? oe?ii? iaia?e.

*a?ac oa, ui a no/anieo oiiaao aeiiii?/ii? ianoaa?eueiino? oaeoeea
?iaanooaaiiy a ?eceeiaai? aeoeae iiaea i?ecaanoe aei iaaaoeaieo
iane?aee?a, iniiaiith caaea/ath iia?aoeaiiai oi?aae?iiy ?iaanoeoe?eiith
eiiiai??th ? i?i?i?caoe?y ?eceeo iaio?eiaiiy i/?eoaaiiai i?eaooeo. Oiio
i?e aeai?? e?eoa??th iioeiaeueiino? iaoaiaoe/ii? iiaeae? iia?aoeaiiai
oi?aae?iiy ?iaanoeoe?eiei ii?ooaeai eiiiai?? caaea/a i?i?i?caoe?? ?eceeo
? aecia/aeueiith.

Iiaoaeo?ii iaoaiaoe/io iiaeaeue iia?aoeaiiai oi?aae?iiy ?iaanoeoe?eii?
eiiiai??, iaoith yei? ? i?i?i?caoe?y caaaeueiiai ?eceeo ci?ie
i?eaooeiaino? oe?iieo iaia??a aeey ?iaanoeoe?eii? eiiiai?? a i?ioean?
aaaaoiaoaiiiai ?iaanooaaiiy a ??ciiiai?oi? aeoeae.

Iaoae ytmj – noia eioo?a, ui ?iaanoothoueny a j-e aeoea (j=1,…,n), oa
caeo/athoueny ia t-io aoai? c oiiaith iiaa?iaiiy cania?a ia m-i (m>t)
aoai?. Ci?iia atm ae?aaea? noio eioo?a, ui ?a?iaanoo?oueny ia t-oii
aoai? c oiiaith iiaa?iaiiy a ia??iae m. Aaee/eia ctmj – iieaciee
i?eaooeiaino? j-ai aeoeao a ??ci? ia??iaee /ano. I?eionoeii, ui
i/?eoaaia cia/aiiy cj iiaea i?eaeecii aooe ??aiei na?aaeiueiio ca
ia??iae:

wmetafile8? ??x???????????
???????????yyy????.????1?????? ???????  ?
???&??yyyy?????AyyyAyyy@ ??a?? ???&? ?MathType??P
???u?????????»????-?????o???U???u?y??????aea t=1,2,…
,T-1.

??cieoey i?ae cj ? ctmj iiaea aooe ae?aaeaia ye rtmj = ctmj – cj, ?
i?aaenoaaey? niaith a?aeoeeaiiy aaee/eie i?eaooeiaino?, ui
niinoa??aa?oueny, a?ae i/?eoaaii?.

Caaaeueia e?euee?noue cania?a aeeaaeiee?a ui caeo/athoueny ia t-i aoai?
c oiiaith iiaa?iaiiy ia m-oii aoai? iiaeaii ci?iiith Rtm. Aaee/eia Rkt
ae?aaea? noio caeo/aieo ia k-io (k

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