IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?IAEAI IAOEIIAOAeOAAIIss ?i. A. I. I?aeai?iiai

IIAIAEEEIAA IA?EIA AIEIAeEIE??AIA

OAeE 519.859

IAOAIAOE*I? IIAeAE? ? IAOIAeE ?ICA’ssCAIIss

IAE?I?EIEO CAAeA* ?ICI?UAIIss

AAIIAO?E*IEO IA’?EO?A

01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

aeieoi?a o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a ?inoeooo? i?iaeai iaoeiiaoaeoaaiiy ?i. A.I.
I?aeai?iiai IAI Oe?a?ie.

Iaoeiaee eiinoeueoaio: /eai — ei?aniiiaeaio IAI Oe?a?ie, aeieoi?
oaoi?/ieo iaoe, i?ioani? Noiyi TH??e A?eai?iae/, ?inoeooo

i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie (i.Oa?e?a),
caa?aeoaa/ a?aeae?eo iaoaiaoe/iiai iiaeaethaaiiy ? iioeiaeueiiai
i?iaeooaaiiy.

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?
E?naeueiaa Ieaia Ieoaee?aia, Aei?i?iiao?ianueeee aea?aeaaiee
oi?aa?neoao, caa?aeoaa/ eaoaae?e ia/enethaaeueii? iaoaiaoeee ?
iaoaiaoe/ii? e?aa?iaoeee;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Eeoaei Ieaa Ieeieaeiae/,
Oe?a?inueea ?iaeaia?ii-iaaeaaia?/ia aeaaeai?y (i. Oa?e?a), caa?aeoaa/
eaoaae?e i?eeeaaeii? iaoaiaoeee

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? ?iaoeue Ieaa Ieaen?eiae/,
Iieoaanueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?i. TH.Eiiae?aothea,
caa?aeoaa/ eaoaae?e i?eeeaaeii? iaoaiaoeee ? iaoaiaoe/iiai
iiaeaethaaiiy.

I?ia?aeia onoaiiaa: ?inoeooo e?aa?iaoeee ?i. A.I.Aeooeiaa IAI Oe?a?ie,

a?aeae?e iaoiae?a ?ica’ycaiiy neeaaeieo caaea/ iioei?caoe??, i. Ee?a.

Caoeno a?aeaoaeaoueny «25» eenoiiaaea 1999 ?. i 14 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.180.01 a ?inoeooo?
i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith

310046, i. Oa?e?a, aoe. Aei. Iiaea?nueeiai, 2/10.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? ?inoeoooo i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith

310046, i. Oa?e?a, aoe. Aei. Iiaea?nueeiai, 2/10.

Aaoi?aoa?ao ?ic?neaiee «23» aeiaoiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee A.I.Caeoeaa

CAAAEUeIA OA?AEOA?ENOENOEEA ?IAIOE

Aeooaeuei?noue oaie. A aaaaoueio aaeocyo ethaenueei? ae?yeueiino?
aeieeathoue caaea/?, iia’ycai? c iioei?caoe??th no?oeoo?e ?
ooieoe?iioaaiiy aaaaoiia?aiao?e/ieo nenoai, o yeeo cae?enith?oueny
noi?nia ia?iaea neeaaeii? aaiiao?e/ii?, aiae?oe/ii? ? eia?/ii?
?ioi?iaoe?? c iaoith aeinyaiaiiy noaio iioeiaeueiiai ooieoe?iioaaiiy.

Iaeiei ?c iniiaieo ?ino?oiaio?a aea/aiiy ? iioei?caoe?? oaeeo nenoai ?
oai??y aeine?aeaeaiiy iia?aoe?e, cie?aia, iiaeae? ? iaoiaee
iaoaiaoe/iiai i?ia?aioaaiiy. A inoaii? aeanyoe??//y aia?ao iaoaiaoe/iiai
i?ia?aioaaiiy ye can?a aeai?o iioeiaeueii? eiio?ao?aoe?? aai iiiaeeie
ia?aiao??a aeey aeinyaiaiiy iaaii? iaoe ae?noaa iiaeaeueoee nooo?aee
?icaeoie cia/iith i??ith caaaeyee ooiaeaiaioaeueiei ?iaioai oaeeo
a?aeiieo oe?a?inueeeo o/aieo, ye aeaaeai?e Ieoaeaae/ A.N., aeaaeai?e IAI
Oe?a?ie Na?a??iei ?.A., aeaaeai?e IAI Oe?a?ie Oi? I.C., aeaaeai?e IAI
Oe?a?ie ?aa/ia A.E., aeaaeai?e IAI Oe?a?ie Ioaie/iee A.I.,
/eai-ei?aniiiaeaio IAI Oe?a?ie Aoaeee A.I., aeaaeai?e IAI Oe?a?ie
??iieue?a TH.I., /eai-ei?aniiiaeaio IAI Oe?a?ie Noiyi TH.A., i?ioani?
E?naeueiaa I.I. oa ?io?.

Iiiaeeia iioei?caoe?eieo caaea/, ui iia’ycai? c oe?eani?yiiaaiei
ia?aoai?aiiyi aaiiao?e/ii? ?ioi?iaoe?? ca?aeii c aeayeei e?eoa???i
iioeiaeueiino?, neeaaea? i?aaeiao oai??? aaiiao?e/iiai i?iaeooaaiiy.

Caaea/? aaiiao?e/iiai i?iaeooaaiiy aeieeathoue o ??ciiiai?oieo aaeocyo
iaoee ? oaoi?ee. Iaeaea an? aiie iia’ycai? c ia?iaeith aaiiao?e/ii?
?ioi?iaoe?? a o?e ?? /anoei?, aea eaeaoueny i?i ?ici?uaiiy aaiiao?e/ieo
ia’?eo?a aeia?eueii? i?inoi?iai? oi?ie, ? iieyaathoue o iiooeo
iioeiaeueiiai ?ici?uaiiy ne?i/aii? iiiaeeie aaiiao?e/ieo ia’?eo?a, ui
aecia/a?oueny aaeoi?ii ia?aiao??a ?ici?uaiiy ia’?eo?a, a caaeaieo
iaeanoyo ?ici?uaiiy i?e iayaiino? ??ciiiai?oieo iaiaaeaiue ? aeayeeo
e?eoa???a yeino? ?ici?uaiiy.

Noai?aiiy oai??? aaiiao?e/iiai i?iaeooaaiiy, iniiaith yei? ? iiaoaeiaa
? aeine?aeaeaiiy ??cieo aeae?a a?aeia?aaeaiue aaiiao?e/ii? ?ioi?iaoe??,
aeicaieeei iiaoaeoaaoe ?aeeio iaoaiaoe/io iiaeaeue oaeeo aaaeeeaeo
i?eeeaaeieo caaea/, ye caaea/? iioeiaeueiiai ?ice?ith i?iieneiaeo
iaoa??ae?a, caaea/? ?aoe?iiaeueiiai aeei?enoaiiy a?aeoiae?a, caaea/?
?ici?uaiiy iaeaaeiaiiy c o?aooaaiiyi iaiaaeaiue iae??ciiiai?oi?oiai
aeaeyaeo, caaea/? ?ici?uaiiy iiaeoe?a ia ?aae?iaeaeo?iii?e ieao?,
caaea/? oi?aae?iiy neeaaeieie oaoi?/ieie nenoaiaie, ?ic?iaea
aaia?aeueieo ieai?a i?iieneiaeo i?aei?e?inoa, i?iaeooaaiiy neeaaeieo
oaoi?/ieo nenoai c o?aooaaiiyi o?ceei-iaoai?/ieo iie?a ??ciiiai?oii?
i?e?iaee, yeui iin?? oeeo iie?a iathoue aeia?eueio i?inoi?iao oi?io
oiui. Aei caaea/? i?yiieooiiai ?ici?uaiiy caiaeyoueny aeaye? caaea/?
oai??? ?iceeaae?a ? ia’?iii-eaeaiaea?iiai ieaioaaiiy. Eean
iioei?caoe?eieo caaea/, iia’ycaieo c ia?aoai?aiiyi aaiiao?e/ii?
?ioi?iaoe??, i?noeoue oaeiae oae? caaea/?, ye caaea/? iie?eooy, caaea/?
?icaeooy aeayei? iiiaeeie ia i?aeiiiaeeie, ui iaia?aoeiathoueny oiui.

A inoaii? o?e aeanyoe??//y i?iaiaeyoueny ?ioaineai? iaoeia?
aeine?aeaeaiiy a aeai?e aaeoc? ciaiue, ui iiynith?oueny ye
neeaaei?noth iiaeaethaaiiy ? iiaoaeiae iaoiae?a ?ica’ycoaaiiy
iioei?caoe?eieo caaea/ aaiiao?e/iiai i?iaeooaaiiy, oae ? iaaecae/aeii
oe?ieei niaeo?ii i?aeoe/ieo canoinoaaiue.

Aeey oni?oiiai ?ica’ycaiiy iaoeiaeo ? i?aeoe/ieo caaea/, ui aeieeathoue
a i?ioean? ia?iaee ? iioei?caoe?? aaeeeeo ianya?a aaiiao?e/ii?
?ioi?iaoe??, iaiao?aei? ia o?eueee ?ic?iaea caaaeueieo i?eioeei?a
iiaeaethaaiiy caaea/ ?aaoey?iiai ? ia?aaoey?iiai ?ici?uaiiy aaiiao?e/ieo
ia’?eo?a, aea ? iiaoaeiaa ? aeine?aeaeaiiy i?iaeaiii-i???ioiaaieo
iaoaiaoe/ieo iiaeaeae eiie?aoieo eean?a caaea/ aeaii? i?aaeiaoii?
iaeano?, iaoiae?a ? aeai?eoi?a ?oiueiai ?ica’ycaiiy.

Eiioeaiooaeueiith caaea/ath ? iaoaiaoe/ia iiaeaethaaiiy iaiaaeaiue (ye
aaiiao?e/ieo, iia’ycaieo c o?aooaaiiyi i?inoi?iai? oi?ie ia’?eo?a, ui
?ici?uothoueny, ? iaeano? ?ici?uaiiy, oae ? iaiaaeaiue, ui iaoiiaeai?
oaoiieia??th i?ioeano, ui iiaeaeth?oueny), ye? aeae?eythoue iaeanoue
i?eionoeieo ?ica’yce?a iioei?caoe?eii? caaea/? aaiiao?e/iiai
i?iaeooaaiiy, ui ?icaeyaea?oueny.

I?e oeueiio iaei??th c iaea?eueo aeooaeueieo caaea/ ? i?i?i?caoe?y
ianyao aiae?oe/ii? ? eia?/ii? ?ioi?iaoe??, yea iio??aia aeey
aaeaeaaoiiai iieno ?aaeueiiai i?ioeano.

Neeaaei?noue aiae?oe/iiai iiaeaiiy iaeano? i?eionoeieo ?ica’yce?a ?
ooieoe?? iaoe caaea/ iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy,
aaaaoiaei??i?noue oa aaaaoiaeno?aiaeuei?noue caaea/, iae?i?ei?noue ?
iaaeeoa?aioe?eiaai?noue a caaaeueiiio aeiaaeeo ooieoe?e iaiaaeaiue
iaeano? i?eionoeieo ?ica’yce?a aeaiaeeoue aeaiee eean caaea/ ca ?aiee
eeane/ii? oai??? aeine?aeaeaiiy iia?aoe?e, oiio aeoaea aeooaeueiith ?
caaea/a noai?aiiy iaoiaeieia?? ?ica’ycaiiy caaea/ aaiiao?e/iiai
i?iaeooaaiiy.

A ca’yceo c oeei aaeeea iaoeiaa cia/aiiy iaaoaa? aeyaeaiiy caaaeueieo
caeiiii??iinoae iiaeaethaaiiy iioei?caoe?eieo caaea/ aaiiao?e/iiai
i?iaeooaaiiy, ui iia’ycaia c caaacia/aiiyi iiaeeeaino? canoinoaaiiy
iaoiae?a ?ica’ycaiiy iaeiiai eeano caaea/ aei ?ioiai, a?aei?iiiai ca
nai?th iaoi?iaeueiith iinoaiiaeith.

Iaea?eueoo neeaaei?noue c iaoaiaoe/ii? oi/ee ci?o i?aaenoaaey? eean
iioei?caoe?eieo caaea/ ia?aaoey?iiai ?ici?uaiiy ia’?eo?a aeia?eueii?
i?inoi?iai? oi?ie, na?aae yeeo iaeiaio aea/aieie ? caaea/? ia?aaoey?iiai
?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia’?eo?a (oiaoi ia’?eo?a,
iieiaeaiiy yeeo a iaeano? ?ici?uaiiy oa?aeoa?eco?oueny ia o?eueee
ia?aiao?aie o?aineyoe??, aea ? eooii iiai?ioo aeanieo nenoai eii?aeeiao)
a ?cio?iiieo ? ai?cio?iiieo iaeanoyo aeia?eueii? i?inoi?iai? oi?ie c?
ci?iieie iao?e/ieie oa?aeoa?enoeeaie. A?aenooi? aoaeoeai? caniae
?ica’ycaiiy oaeeo caaea/.

Ioaea, iiaeaethaaiiy oa ?ica’ycaiiy iioei?caoe?eieo caaea/
ia?aaoey?iiai ?ici?uaiiy ia’?eo?a aeia?eueii? i?inoi?iai? oi?ie ia?
caaaeueiioai?aoe/ia cia/aiiy.

Iacaaaeath/e ia oa, ui iioei?caoe?ei? caaea/? aaiiao?e/iiai
i?iaeooaaiiy iaeaaeaoue aei eeano NP-iiaieo caaea/, ? ia?aaaaeia
a?eueo?noue iaoiaeee ?ica’ycaiiy icia/aieo eean?a caaea/ ? aa?enoe/ieie,
oaeaeeee ?icaeoie ia/enethaaeueii? oaoi?ee iaaea? iiaeeea?noue
/enaeueii? ?aae?caoe?? caaea/ i?aeoe/ii? aei??iino?, oiio ? aeooaeueiei
i?iaeiaaeaiiy aeine?aeaeaiue o aaeoc? ?ic?iaee cania?a iiooeo
aeiaaeueii-iioeiaeueiiai ?ica’ycaiiy caaea/ ?ici?uaiiy, ui
?icaeyaeathoueny.

Ioaea, caaaeueia oai??y aaiiao?e/iiai i?iaeooaaiiy acaaae? ?
iiaeaethaaiiy ? ?ica’ycaiiy iioei?caoe?eieo caaea/ ia?aaoey?iiai
?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia’?eo?a a ?cio?iiieo ?
ai?cio?iiieo iaeanoyo ?ici?uaiiy cie?aia, iio?aao? iiaeaeueoiai
?icaeoeo, ui ? aecia/eei oaio aeaii? aeena?oaoe?eii? ?iaioe.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.

Aeena?oaoe?eia ?iaioa aeeiiaia a ia??iae c 1989 ?. ii 1999 ?. o
a?aeae?e? iaoaiaoe/iiai iiaeaethaaiiy ? iioeiaeueiiai i?iaeooaaiiy
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. I?aeai?iiai IAI Oe?a?ie ? ?
/anoeiith aeine?aeaeaiue, ui aeeiiothoueny i?ae ea??aieoeoaii /e.-ei?.
IAI Oe?a?ie TH. A. Noiyia ca?aeii c ieaiaie iaoeiai-aeine?aeieo ?ia?o ca
i?ia?aiaie:

-6.4.1. «?ioaa?iaai? eiii’thoa?i? oaoiieia?? i?iaeooaaiiy» ca ae/a
oaiaie:

—«?ioaa?iaaia eiii’thoa?ia oaoiieia?y aaiiao?e/iiai i?iaeooaaiiy
neeaaeieo oaoi?/ieo nenoai» (1992-1996??., NA?0193E020060);

—«?ioaeaeooaeuei? nenoaie aaiiao?e/iiai i?iaeooaaiiy» (1992-1993 ??., N
A?0193V020061), (Iinoaiiaa AeEIO Oe?a?ie);

-1.12.5 «I?iaeaie aaoiiaoecaoe?? i?iaeooaaiiy oaoi?/ieo nenoai» ca ae/a
oaiaie:

—«Iaoaiaoe/ia iiaeaethaaiiy neeaaeieo oaoi?/ieo nenoai iiaeoeueiiai
oeio», (1990-1993 ??., N A? 01900009448);

—«?ic?iaea ? aeine?aeaeaiiy ?ioaeaeooaeueii? nenoaie a?aeia?aaeaiiy
aaiiao?e/ii? ?ioi?iaoe?? aeey iioei?caoe?? ? iiaeaethaaiiy
o?ceei-iaoai?/ieo i?ioean?a ? oaoi?/ieo nenoai» (1994 — 1997 ??., N A?
0197V012281);

—1.7.2.2 «?ic?iaea ? aeine?aeaeaiiy iaoaiaoe/ieo iiaeaeae caaea/
iioei?caoe?? ?ici?uaiiy o?eaei??ieo aaiiao?e/ieo ia’?eo?a» (1998-2001
pp.);

— Aeiaiai?o c AeEIO Oe?a?ie (oiiae ooiaeaiaioaeueieo aeine?aeaeaiue) ?
12.3/66 «?ic?iaea iiaeo iaoiae?a ni?eueiiai caa?aaeaiiy oa ia?aoai?aiiy
neeaaeii? aiae?oe/ii? oa aaiiao?e/ii? ?ioi?iaoe?? a iaoaiaoe/iiio ?
eiii’thoa?iiio iiaeaethaaii?», (1994 — 1997 ??.).

— Aeiaiai?o c I?i?noa?noaii o ni?aaao iaoee ? oaoiieia?e Oe?a?ie N
2/847-97 «Aiaeioeei-aaiiao?e/ia oa eiii’thoa?ia iiaeaethaaiiy aenieeo
oaoiieia?e aeaioiaeaiiy oa aenieoaoaoe?? ia’?eo?a neeaaeii?
eiio?ao?aoe??, ui i?aeaeathoueny aenoeia?aaeiaioiei aieeaai».

Iaoith ?iaioe ? ?ic?iaea iaoiaeieia?? iaoaiaoe/iiai ? eiii’thoa?iiai
iiaeaethaaiiy ia?aaoey?iiai ?ici?uaiiy aeaiaei??ieo ? o?eaei??ieo
aaiiao?e/ieo ia’?eo?a c o?aooaaiiyi iiaeeeaino? ?o iiai?ioo a iaeanoyo
aeia?eueii? i?inoi?iai? oi?ie c? ci?iieie iao?e/ieie oa?aeoa?enoeeaie ?
noai?aiiy iiaeo cania?a ?ica’ycaiiy eeano iioei?caoe?eieo caaea/
aaiiao?e/iiai i?iaeooaaiiy, ui ?icaeyaea?oueny.

O aeena?oaoe?? aeey aeinyaiaiiy oe??? iaoe iinoaaeai? ianooii? iniiai?
iaoeia? caaaeaiiy:

1.Ia iniia? aiae?co ?nioth/eo cania?a oi?iae?caoe?? iniiaieo iaiaaeaiue
caaea/? ia?aaoey?iiai ?ici?uaiiy ia’?eo?a ?ic?iaeoe aia?ao
oi?iae?caoe?? oiia aca?iiiai iaia?aoeio a caaaeueiiio aeiaaeeo
iai???ioiaaieo aaiiao?e/ieo ia’?eo?a oa oiia ?o ?ici?uaiiy o iaeano?
?ici?uaiiy aeey ia’?eo?a ? iaeanoae aeia?eueii? i?inoi?iai? oi?ie c?
ci?iieie aaiiao?e/ieie oa?aeoa?enoeeaie.

2. Aeoiaey/e c iaoaiaoe/ii? iiaeae? iniiaii? caaea/? ia?aaoey?iiai
?ici?uaiiy ia’?eo?a, aiae?co ?nioth/eo cania?a ?ica’ycaiiy caaea/ c
eeano, ui ?icaeyaea?oueny, ?ic?iaeoe iaoiaeieia?th iiooeo ?ica’ycaiiy
iniiaii? caaea/?. Ia iniia? cai?iiiiiaaieo iaoiae?a noai?eoe
aeai?eoi?/ia ? i?ia?aiia caaacia/aiiy eeano caaea/ ia?aaoey?iiai
?ici?uaiiy ia’?eo?a a iaeanoyo aeia?eueii? i?inoi?iai? oi?ie.

3. I?iaiae?coaaoe iaoiaee ? aeai?eoie c oi/ee ci?o ?oiuei?
ia/enethaaeueii? neeaaeiino?.

4. ?ic?iaeoe ? aeine?aeeoe i?iaeaiii-i???ioiaai? iaoaiaoe/i? iiaeae?
caaea/ aaiiao?e/iiai i?iaeooaaiiy, aeae?eeoe ?oi? nooo?a? iniaeeaino?,
aeine?aeeoe iaeanoue i?eionoeieo ?ica’yce?a eean?a caaea/, ui
?icaeyaeathoueny.

Iniiai? iia? iaoeia? ?acoeueoaoe:

1. Ae?noaa iiaeaeueoee ?icaeoie aia?ao oi?iae?caoe?? oiia ?ici?uaiiy
ia’?eo?a a ?cio?iiieo ? ai?cio?iiieo iaeanoyo aeia?eueii? i?inoi?iai?
oi?ie o R2, iniiaaiee ia iiiyoo? F-ooieoe?? ia?e ia’?eo?a.

2. Iaea?aeaii iia? caniae aiae?oe/iiai iieno F-ooieoe?? i???ioiaaieo oa
iai???ioiaaieo ia’?eo?a, iia? aeanoeaino? F-ooieoe??.

3. Aeine?aeaeaii iaeanoue i?eionoeieo ?ica’yce?a caaea/? ?ici?uaiiy
iai???ioiaaieo aaaaoieooiee?a o iaeano? ?ici?uaiiy neeaaeii? i?inoi?iai?
oi?ie c? ci?iieie iao?e/ieie oa?aeoa?enoeeaie, aeae?eai? iia? nooo?a?
eiino?oeoeai? iniaeeaino? iaeano? i?eionoeieo ?ica’yce?a.

4. Aia?oa canoiniaaii aia?ao F-ooieoe?e aeey iieno oiia aca?iiiai
?ici?uaiiy aeaio iai???ioiaaieo aaaaoia?aiiee?a o R3.

5. Iiaoaeiaaii iia? oi/i? ? iaaeeaeai? caniae ?ica’ycaiiy iiaeo eean?a
iioei?caoe?eieo caaea/ ?ici?uaiiy o iaeanoyo ?ici?uaiiy c? ci?iieie
iao?e/ieie oa?aeoa?enoeeaie.

6. Ae?noaa iiaeaeueoee ?icaeoie iaoiae ?ica’ycaiiy eiia?iaoi?ii?
caaea/? ?ici?uaiiy i?yiieooiee?a ia iniia? canoinoaaiiy cania?a
iaia?a?aii? iioei?caoe??, a naia — cania?a aeoeaiiai iaai?o.
Iaoiaeieia?y ?ica’ycaiiy aeaiaei??ii? caaea/? i?yiieooiiai ?ici?uaiiy
canoiniaaia aei iiaiai eeano caaea/ — caaea/? iaeoaaiiy
a?ia?ia?aeaeai?iaae?a.

7. ?ic?iaeaii iiaee iaoiae ?ica’ycaiiy caaea/? ?ici?uaiiy
iai???ioiaaieo aaaaoieooiee?a, yeee iniiaaii ia iioei?caoe?? ca a?oiaie
ia?aiao??a o?aineyoe?? ia’?eo?a ? eooiaeo ia?aiao??a ?ici?uaiiy ? ui
a?aoiao? aaiiao?e/i? iniaeeaino? iaeano? i?eionoeieo ?ica’yce?a caaea/?.

8. ?ic?iaeaii iiaa aeai?eoi?/ia ? i?ia?aiia caaacia/aiiy eeano caaea/
ia?aaoey?iiai ?ici?uaiiy ia’?eo?a a iaeanoyo aeia?eueii? i?inoi?iai?
oi?ie c ioe?ieaie ia/enethaaeueii? neeaaeiino? aeai?eoi?a.

9. Io?eiaee iiaeaeueoee ?icaeoie i?iaeaiii-i???ioiaai? iaoaiaoe/i?
iiaeae? caaea/ aaiiao?e/iiai i?iaeooaaiiy, aeine?aeaeaii ?oi?
iniaeeaino?, ?ic?iaeaii iaoiaeieia?/ia oa i?ia?aiia caaacia/aiiy.

A??ia?aei?noue oa iaa?oioiaai?noue iaea?aeaieo ?acoeueoao?a
aecia/a?oueny aeei?enoaiiyi caaaeueiiaeciaieo cania?a iaoaiaoe/iiai
iiaeaethaaiiy ? aaiiao?e/iiai i?iaeooaaiiy, iaoaiaoe/ii? iiaeae?
iniiaii? caaea/? ia?aaoey?iiai ?ici?uaiiy ia’?eo?a. Aoaeoeai?noue
cai?iiiiiaaieo iaoiae?a, ?o aeai?eoi?/ii? ? i?ia?aiii? ?aae?caoe??
i?aeoaa?aeaeo?oueny aiae?cii ia/enethaaeueii? neeaaeiino? ? ii??aiyiiyi
io?eiaieo ?acoeueoao?a ye ca oaeaeeiae??th, oae ? ca ye?noth ?ica’ycaiiy
c aiaeia?/ieie ?acoeueoaoaie a?o/eciyieo ? ca?oa?aeieo aeine?aeiee?a.

Aaoi?ii ?ic?iaeaiee aaie i?ia?aiieo iiaeoe?a, ui noai?th? i?ia?aiia
caaacia/aiiy aeey ?ica’ycaiiy eeano caaea/ ia?aaoey?iiai ?ici?uaiiy
i???ioiaaieo ? iai???ioiaaieo aaiiao?e/ieo ia’?eo?a. Caaaeueiee ianya
i?ia?ai, ye? ?aae?cothoue iaoaiaoe/iee aia?ao, ui i?iiiio?oueny,
neeaaea? iiiaae 30000 iia?aoi??a.

Oai?aoe/ia cia/aiiy ?iaioe. An? oai?aoe/i? ?acoeueoaoe iiaeai? o
aeaeyae? aecia/aiue, oai?ai, aeanoeainoae, iien?a aeai?eoi?a, ui a
cia/i?e /anoei? i?eaiaeyoueny aia?oa aai ocaaaeueiththoue aaea a?aeii?.

I?aeoe/ia cia/aiiy ?iaioe. Iaoeia? ?acoeueoaoe aeena?oaoe?eii? ?iaioe ?
iiaeaeueoei ?icaeoeii oai??? aaiiao?e/iiai i?iaeooaaiiy, aeicaieythoue
caaaeyee aeae?eaiith caaaeueieo ooiaeaiaioaeueieo iniaeeainoae
iioei?caoe?eieo caaea/ ?ici?uaiiy, ??ciiiai?oieo ca nai?th
iaoi?iaeueiith iinoaiiaeith, ae??oeoe aaaaoi caaea/ aaiiao?e/iiai
i?iaeooaaiiy, ui ?ai?oa ia aoee ?ica’ycai?.

Noeoii?noue ?ic?iaeaieo iaoaiaoe/ieo iiaeaeae, iaoiae?a, aeai?eoi?a ?
i?ia?aiieo eiiieaen?a iiaea aeei?enoiaoaaoeny o aeaeyae?
iioei?caoe?eiiai yae?a a nenoaiao aaoiiaoeciaaiiai i?iaeooaaiiy ea?o
?ice?ith i?iieneiaeo iaoa??ae?a o acooo?a?e, oaenoeeuei?e ?
iaoaeiia?iai?e i?iieneiaino?, i?e noai?aii? ?ano?nicaa??aath/eo
oaoiieia?e, ye? aeicaieyoue i?aeiyoe aoaeoeai?noue aeei?enoaiiy
?ano?n?a. Inoaii?e oaeo iaaoaa? iniaeeaiai cia/aiiy a oiiaao aei?noeeo
iaiaaeaiue o?iainiaeo ? aia?aaoe/ieo ?ano?n?a a iao?e e?a?i?. E??i oiai,
?ic?iaeai? iaoiaee ? aeai?eoie iiaeooue aooe canoiniaai? i?e
i?iaeooaaii? a?aen?e?a o?ainii?oieo cania?a, aaia?aeueieo ieai?a
i?aei?e?inoa oiui.

Iaoaiaoe/ia, aeai?eoi?/ia ? i?ia?aiia caaacia/aiiy eeano caaea/
ia?aaoey?iiai ?ici?uaiiy ia’?eo?a iiaea aeei?enoiaoaaoeny a iaoeiaeo
aeine?aeaeaiiyo aeey oi?iae?caoe?? oiia ?ici?uaiiy a iaeanoyo
aeia?eueii? i?inoi?iai? oi?ie c? ci?iieie iao?e/ieie oa?aeoa?enoeeaie,
aeey ciaoiaeaeaiiy eieaeueii-iioeiaeueieo ? aeiaaeueii-iioeiaeueieo
?ica’yce?a a?aeiia?aeieo caaea/ ?ici?uaiiy.

Ie?ai? aeai?eoie ? i?ia?aie iiaeooue aeei?enoiaoaaoeny i?e ia?iaoe?
?ioi?iaoe?? a aeieia?/ieo caaea/ao ? a caaea/ao iii?oi?eiao Caie?.

?aae?caoe?y ? ai?iaaaeaeaiiy. Iiaeae?, iaoiaee, aeai?eoie oa i?ia?aiia
caaacia/aiiy caaea/ iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy, ui
?icaeyaeathoueny o aeena?oaoe?ei?e ?iaio?, aoei aeei?enoaii o iaoeiaeo
aeine?aeaeaiiyo ?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. I?aeai?iiai
IAI Oe?a?ie i?ae /an aeeiiaiiy aea?aeathaeaeaoieo oai ? aeiaiai??a c
AeEIO Oe?a?ie (oiiae ooiaeaiaioaeueieo aeine?aeaeaiue) ? c I?i?noa?noaii
o ni?aaao iaoee ? oaoiieia?e Oe?a?ie a ia??iae c 1991 ?. ii oaia??oi?e
/an.

Iniiai? caniae iaoaiaoe/iiai iiaeaethaaiiy, cai?iiiiiaai?
iaoiaee

?ica’ycaiiy caaea/ iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy
ai?iaaaeaeai? aei iaa/aeueiiai i?ioeano Oa?e?anueeiai aea?aeaaiiai
oaoi?/iiai oi?aa?neoaoo aoae?aieoeoaa ? a?o?oaeoo?e i?ae /an i?aeaioiaee
oa aeeeaaeaiiy oaeeo eaeoe?eieo eo?n?a: “Oaoi?/i? caniae a
a?o?oaeoo?iiio i?iaeooaaii?“, “Aeene?aoiee aiae?c“, “Iaoiaee
aeine?aeaeaiiy iia?aoe?e“ (1997-1999 ??.).

Ai?iaaoe?y ?acoeueoao?a aeine?aeaeaiiy. Iniiai? ?acoeueoaoe ?iaioe
aeiiia?aeaeeny oa io?eiaee noaaeaiiy ia: 18 i?aeia?iaeieo oa
iaoe?iiaeueieo eiioa?aioe?yo oa e?eueeio iaoeiaeo nai?ia?ao, a naia:

-Ananithciiio nai?ia?? «Iiaeaethaaiiy ?aa?iiaeueieo nenoai» (Ooa, 1990
?.); -Ananithci?e oeie? «Nenoaie i?ia?aiiiai caaacia/aiiy ?ica’yceo
caaea/ iioeiaeueiiai ieaioaaiiy» (Eino?iia, 1990 ?.); I?aeia?iaei?e
eiioa?aioe?? «Mathematical Optimization» (Aa?e?i, I?ia//eia, 1990 ?.);
?anioae?eainuee?e iaoeiai-oaoi?/i?e eiioa?aioe?? «NAI? oaoiieia?/ii? ?
eiino?oeoi?nueei? i?aeaioiaee ae?iaieoeoaa a iaoeiiaoaeoaaii?» (Oa?e?a,
1990 ?.); — Ananithci?e oeie? «Ieoaiiy iioei?caoe?? ia/eneaiue» (E?ei,
1991 ?.); — 12-e Ananithci?e eiioa?aioe?? «Nenoaie i?ia?aiiiai
caaacia/aiiy ?ica’ycaiiy aeiiii?/ieo caaea/» (Ia?aa-Ee?nnoo, 1992 ?.); —
I?aeia?iaei?e oeie? «I?iaeooaaiiy ANE ? ANO neeaaeieie ia’?eoaie»
(Ooaina, ?in?y, 1992 ?.); — 46-e iaoeia?e eiioa?aioe?? i?ioani??a ?
aeeeaaea/?a Iieoaanueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo (Iieoaaa,
1994 ?.); — 17-e I?aeia?iaei?e eiioa?aioe?? «System Modeling and
Optimization» (I?aaa, *ao?y , 1995 ?.); — I?aeia?iaei?e eiioa?aioe??
«Combinatorial Optimization’-96» (Eiiaeii, Aaeeea A?eoai?y, 1996 ?.); —
I?aeia?iaei?e eiioa?aioe?? «Iaoaiaoeea ? ienoaoeoai» (Nocaeaeue, ?in?y,
1996 ?.); — 18th International Conference on Software Engineering
(Aa?e?i, I?ia//eia, 1996 ?.); — I?aeia?iaei?e iaoeiai-oaoi?/i?e
eiioa?aioe?? «I?ia?aneai? oaoiieia?? iaoeiiaoaeoaaiiy ? no/ani?noue»
(Naaanoiiieue, 1996 ?.); — I?aeia?iaei?e eiioa?aioe?? «Cooperation and
Business Opportunities for Eastern/Western European countries in the IT
field» (Aoaeaiaoo, Oai?ueia, 1997 ?.); — 15-e I?aeia?iaei?e eiioa?aioe??
«Iaoaiaoeea. Eiii’thoa?, Ina?oa», (Iou?ii, ?in?y, 1997 ?.);- 1-io
I?aeia?iaeiiio Oi?oi? «Aeaeo?ii?ea ? iieiaeue a OOI noi??//?» (Oa?e?a,
1997 ?.); — 53-e iaoeiai-i?aeoe/i?e ? iaa/aeueii-iaoiaee/i?e
eiioa?aioe?? i?ioani??a ? aeeeaaea/?a Oa?e?anueeiai aea?aeaaiiai
oi?aa?neoaoo aoae?aieoeoaa ? a?o?oaeoo?e (Oa?e?a, 1998 ?.); — 16th
European Conference on Operational Research (A?thnnaeue, Aaeuea?y, 1998
?.); — iino?eii ae?th/iio nai?ia?? «Iaoaiaoe/i? iaoiaee aaiiao?e/iiai
i?iaeooaaiiy» (Oa?e?a, 1991-1999 ??.) i?e iaoeia?e ?aae? ca i?iaeaiith
«E?aa?iaoeea» IAI Oe?a?ie, iaoeiaiio nai?ia?? a?aeae?eo ? 120 ?inoeoooo
e?aa?iaoeee ?i. A. I. Aeooeiaa IAI Oe?a?ie (Ee?a, 1999 ?.).

Ioae?eaoe??. Ca oaiith aeena?oaoe?? iioae?eiaaii 30 iaoeiaeo ?ia?o, a
oiio /ene?: 1 iiiia?ao?y, 17 noaoae o iaoeiaeo aeaeaiiyo (aeo?iaeao oa
ca??ieeao iaoeiaeo i?aoeue), 2 aeaiiiiaaieo ?iaioe, 3 aeiiia?ae? a
iaoa??aeao i?aeia?iaeieo iaoeiaeo eiioa?aioe?e, 5 oac aeiiia?aeae ia
i?aeia?iaeieo ? iaoe?iiaeueieo iaoeiaeo eiioa?aioe?yo, 2 i?ai?eioa
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. I?aeai?iiai IAI Oe?a?ie.

O 1997 ?ioe? I?aceae?y IAI Oe?a?ie i?enoaeeea aaoi?o i?ai?th
Iaoe?iiaeueii? aeaaeai?? iaoe Oe?a?ie ca na??th e?aueo iaoeiaeo ?ia?o.

Iniaenoee aianie caeiaoaa/a. An? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
iaea?aeai? ca iniaenoith o/anoth aaoi?a. O iiiia?ao?? [1] aaoi?ii
iniaenoi iaienai? ?icae?ee 4.1, 4.2, 4.3.

O i?aoeyo, ui iaienai? o ni?aaaoi?noa?, aeena?oaioo iaeaaeaoue: [2] —
eiioeaioe?y iiaoaeiae nenoaie, ui i???ioiaaia ia ?ica’ycaiiy caaea/
i?yiieooiiai ?ici?uaiiy c iiaeeea?noth iiaeaethaaiiy ??cieo
oaoiieia?/ieo iaiaaeaiue; [6] — aiae?c aeai?eoi?a aioo??oiuei? oi/ee c
oi/ee ci?o ?oiuei? ia/enethaaeueii? neeaaeiino? ? iiaeeeaino?
canoinoaaiiy aei ?ica’ycaiiy caaea/ aaiiao?e/iiai i?iaeooaaiiy; [8] —
iiaeaethaaiiy ? aeine?aeaeaiiy iaeano? i?eionoeieo ?ica’yce?a caaea/?
?ici?uaiiy i???ioiaaieo aaaaoieooiee?a o aaaaoica’yci?e iaeano?
?ici?uaiiy; [9] — iiaoaeiaa iaoaiaoe/ii? iiaeae? iioei?caoe?eii? caaea/?
?ici?uaiiy iai???ioiaaiiai aaaaoia?aiieea o aaaaoia?aiieeo c? ci?iieie
iao?e/ieie oa?aeoa?enoeeaie; [10, 24] — aiae?c aoaeoeaiino? aeai?eoi?a
?ica’ycaiiy iioei?caoe?eieo caaea/ ?ici?uaiiy; [11] — iiaeaethaaiiy
caaea/? iioeiaeueiiai ?ici?uaiiy iai???ioiaaieo aaaaoieooiee?a o
aaaaoica’yci?e iaeano? ?ici?uaiiy ? aeeo/aiiy oiia eieaeueii?
ca?aeiino?; [13] — canoinoaaiiy iiiyooy F-ooieoe?? aei caaea/
aaiiao?e/iiai i?iaeooaaiiy, yeui ia’?eoe ?ici?uaiiy ? i?aea ia
u?eueieie; [14] — iinoaiiaea caaea/? aeine?aeaeaiiy, ?ic?iaea
i?eioeeiiaeo iniia canoinoaaiiy iaoiaeeee iaia?a?aii? iioei?caoe??, a
naia, no?aoaa?? aeoeaiiai iaai?o, aei eiia?iaoi?ii? caaea/? i?yiieooiiai
?ici?uaiiy; [17] — ii??aiyiiy, aiae?c ia/enethaaeueii? neeaaeiino? ?
canoinoaaiiy aeai?eoi?a, ui ?icaeyaeathoueny, aei ?ica’ycaiiy caaea/?
?ici?uaiiy iai???ioiaaieo aaaaoieooiee?a; [18] — canoinoaaiiy no?aoaa??
aeoeaiiai iaai?o aei ia?iaee ?ioi?iaoe?? i?i e?ioeaa? aa?oeie aea?aaa
?ica’yce?a caaea/? i?yiieooiiai ?ici?uaiiy, aeai?eoi?/ia oa i?ia?aiia
?aae?caoe?y; [19] — iiaeaethaaiiy caaea/? ?ici?uaiiy ne?i/aii? iiiaeeie
a?ia?ia?aeaeai?iaae?a o a?ia?ia?aeaeai?iaae?, can?a ?ica’ycaiiy caaea/?;
[20] — iiaeaethaaiiy ? aeine?aeaeaiiy eiino?oeoeaieo aeanoeainoae
iaeano? i?eionoeieo ?ica’yce?a caaea/? ?ici?uaiiy i???ioiaaieo
aaaaoieooiee?a o nioc? c aeaoaeoieie ciiaie; [21, 30] — iiaeaethaaiiy ?
aeine?aeaeaiiy iaeano? i?eionoeieo ?ica’yce?a caaea/? ?ici?uaiiy
iai???ioiaaiiai aaaaoia?aiieea a aaaaoia?aii?e iaeano?; [22] — iiaoaeiaa
iaoiaeo ?ica’ycaiiy, aiae?c iiiaeiee?a Eaa?aiaea c oi/ee ci?o
aaiiao?e/ieo iniaeeainoae caaea/? i?yiieooiiai ?ici?uaiiy; [23, 27] —
aeai?eoi?/ia ? i?ia?aiia ?aae?caoe?y iaoiaeo ?ica’ycaiiy caaea/?, ui
?icaeyaea?oueny; [25] — aeine?aeaeaiiy aeanoeainoae neiao??? iaeano?
i?eionoeieo ?ica’yce?a caaea/? i?yiieooiiai ?ici?uaiiy; [26] —
iiaeaethaaiiy caaea/?, ui ?icaeyaea?oueny, ye caaea/? iioeiaeueiiai
?ici?uaiiy aaaaoieooiee?a o nioc?; [27, 28] — iiaeeo?eaoe?y
no?aoaa?? aeoeaiiai iaai?o aeey ?ica’ycaiiy 2D caaea/ aaiiao?e/iiai
i?iaeooaaiiy.

Caaaeueiee ianya ioae?eaoe?e ca oaiith aeena?oaoe?? neeaaea? iiiaae 6
ae?oeiaaieo a?eoo?a. E??i oiai, a Oe??IOA? ca?a?no?iaaii 4
iaoeiai-oaoi?/ieo ca?oe ca aea?aeathaeaeaoieie oaiaie, ui aeeiiai? ca
oaiith aeena?oaoe?? i?e o/ano? aaoi?a.

No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?y i?noeoue anooi, i’youe
?icae?e?a, ae-

niiaee c ?iaioe, 2 aeiaeaoee, iiaiee ianya aeena?oaoe?? — 281 noi?., c
ieo 251 noi?.

iaoeiiieniiai oaenoo, 71 ?enoiie, 1 oaaeeoey, nienie aeei?enoaieo
aeaea?ae c 204 iaeiaioaaiue ia 20 noi?.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe??, iieacaia ??
iaoeiaa ni?yiiaai?noue, noi?ioeueiaaia iaoa ?iaioe oa caaea/?
aeine?aeaeaiiy, ye? iio??aii ae??oeoe aeey ?? aeinyaiaiiy. Iiaeaia
ei?ioea oa?aeoa?enoeea ?acoeueoao?a aeine?aeaeaiiy, nooiaith ?o
ai?iaaoe?? oa iioae?eoaaiiy.

Ia?oee ?icae?e aeena?oaoe?? i?enay/aii aiae?oe/iiio iaeyaeo e?oa?aoo?e
ca oaiith aeena?oaoe?? ? aeai?o iai?yie?a aeine?aeaeaiue.

Aiae?c no/aniiai noaio aeaii? i?iaeaie ca iaoa??aeaie a?o/eciyii? ?
ca?oa?aeii? iaoeiai? i?ane oa aea/aiiy i?aoeue oaeeo a?aeiieo a/aieo o
aaeoc? ?ica’ycaiiy caaea/ ?ici?uaiiy, ye i?io. Iooa/iaa A. I. (?in?y),
i?io. Dowsland W. (Aaeeea A?eoai?y), i?io. J.A.S. Ferreira
(Ii?ooaae?y), i?io. J. Terno (I?ia//eia), i?io. V. Milenkovic (NOA) oa
?i. iieacaee, ui iaea?eueo ?iciianthaeaeaiei niiniaii ? aai iineaaeaiiy
iaiaaeaiue caaea/?, aae aei iiaiiai ?aii?oaaiiy i?inoi?iai? oi?ie
ia’?eo?a, ui ?ici?uothoueny, oeyoii caaaeaiiy caaea/? aei caaea/?
iaeiiaei??iiai ?ici?uaiiy, oiaoi aei caaea/? e?i?eiiai i?ia?aioaaiiy,
aai o?enoaaiiy ia?aiao??a ?ici?uaiiy ia’?eo?a. Aiane?aeie oeueiai
?ica’ycie caaea/? eeoa aeiaaeeiai iiaea aeyaeoeny iioeiaeueiei.
Iaea?eueo aeine?aeaeaieie ? caaea/? e?i?eiiai (iaeiiaei??iiai)
?ici?uaiiy, oa caaea/? a?eueeioeiiiai i?yiieooiiai ?ici?uaiiy. Eiaeia
ie?aia caaea/a ?ici?uaiiy ?icaeyaea?oueny eeoa o eiioaeno? nai??
iaoi?iaeueii? iinoaiiaee. A?ae ooiaeaiaioaeueieo aeine?aeaeaiue a aeai?e
i?aaeiaoi?e iaeano? i?ecaiaeeoue aei oiai, ui iaeaea cian?i ia
?icaeyaeathoueny caaea/? ?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia’?eo?a
o aaaaoieooieo ?cio?iiieo oa ai?cio?iiieo iaeanoyo c? ci?iieie
iao?e/ieie oa?aeoa?enoeeaie. A ?iaio? iieacaii, ui oeae iaaeie?e iiaeia
e?ea?aeoaaoe ia iniia? ?aeeiiai i?aeoiaeo, ?aeeii? iaoaiaoe/ii? iiaeae?
caaea/ ?ici?uaiiy, yea ?icaeyaea?oueny a ?aieao oai??? aaiiao?e/iiai
i?iaeooaaiiy ? ?ic?iaey?oueny o iaoeia?e oeie? /eaia-ei?aniiiaeaioa IAI
Oe?a?ie i?ioani?a Noiyia TH.A.

Iniiai? ?acoeueoaoe ?icae?eo iioae?eiaaii a i?aoeyo [8, 6, 7, 21, 23].

O ae?oaiio ?icae?e? aeena?oaoe?? “Noai i?iaeaie ? iinoaiiaea caaea/?
aeine?aeaeaiiy” oi?ioeththoueny iaiaaeaiiy, ye? aeeo/athoue iniiaio aeey
aeaii? aeena?oaoe?eii? ?iaioe caaea/o aeine?aeaeaiiy na?aae an???
iiiaeeie caaea/ aaiiao?e/iiai i?iaeooaaiiy, iaaiaeeoueny iinoaiiaea
iniiaii? caaea/? aeine?aeaeaiiy ye caaea/? ?ici?uaiiy a oa?i?iao
aaiiao?e/ii? ?ioi?iaoe??.

Iioei?caoe?ei? caaea/? aaiiao?e/iiai i?iaeooaaiiy cia/iith i??ith
iia’ycai? c ia?iaeith ei?oaaeo aaiiao?e/ii? ?ioi?iaoe?? g i?i iaaio
oi/eiao iiiaeeio (aaiiao?e/iee ia’?eo) S, yea neeaaea?oueny c o?ueio
eiiiiiaio (o?eniaaieo aai ci?iieo)

g = (s1, s2 ,…,sq , m1 ,…,mi ,…, mq , v1 ,…,vi ,…,vq, v),

aea: q — /enei eiiiiiaio ca’yciino? iaae? ia’?eoa S.

s1, s2 ,…,sq -noeoii?noue i?inoi?iaeo oi?i eiiiiiaio ca’yciino? iaae?
S;

m1, m2 ,…, mq — iao?e/i? oa?aeoa?enoeee, eio??, cie?aia,
aecia/athoue ?ici??e oi/eiaeo iiiaeei, ui iathoue i?inoi?ia? oi?ie
{s};

v1 ,…,vi ,…,vq — ia?aiao?e ?ici?uaiiy eiiiiiaio ca’yciino? iaae?
S;

v — ia?aiao?e ?ici?uaiiy ia’?eoa S.

Ioaea, aaiiao?e/ia ?ioi?iaoe?y g ?iaeoeo? S o iaaiiio iao?e/iiio
i?inoi?? H. O ?iaio? acaaae? ?icaeyaeathoueny a?eoiaoe/i? aaee?aeiae
i?inoi?e R2 ? R3, oi/a ie?ai? ?acoeueoaoe ?iciianthaeaeothoueny ? ia
i?inoi?e a?eueoi? aei??iino?.

Iniiaia caaea/a aeaii? ?iaioe i???ioiaaia ia iaaiee eean oi/eiaeo
iiiaeei, a naia eean j*-aaaaoieooiee?a (j*-aaaaoia?aiiee?a).

O ?icae?e? aiae?cothoueny ?nioth/? caniae aecia/aiiy iaiioeeiai
aaaaoieooiiai (aaaaoia?aiiiai) j*-ia’?eoa. O i?inoi?? R2 iao?e/i?
oa?aeoa?enoeee m1, m2,…,mq iiaeooue aooe cia?aaeai? eii?aeeiaoaie
aa?oei a?aeiia?aeieo aaaaoieooieo eiioo??a o aeani?e nenoai? eii?aeeiao,
ia?aiao?e ?ici?uaiiy iathoue aeaeyae v=(x,y,f).

sseui iieeanoe ia?aiao? f — eoo iiai?ioo aeanii? nenoaie eii?aeeiao
j*-ia’?eoa a?aeiinii ioey i?inoi?o — o?eniaaiei, aaaaoieooia iaeanoue
oaeiae iiaea aooe caaeaia aiae?oe/ii ca aeiiiiiaith aia?aoo no?oeoo?
e?i?eieo ia??aiinoae ((F(x),(,m), aea F(x) — oii?yaeeiaaiee iaa??
e?i?eieo ia??aiinoae, ye? caaeathoue e?i?ei? /anoeie iaae?
j*-aaaaoieooieea S, (= (((qg((m(m- iao?eoey a?aeiioaiue, m- e?euee?noue
ia??aiinoae.

O ?icae?e? iaaaaeaii aiae?c aia?aoo no?oeoo? e?i?eieo ia??aiinoae ye
iioe?aiiy iiiyooy nenoaie e?i?eieo ia??aiinoae ? caniao aiae?oe/iiai
iieno iaiioeei? eiiiaeoii? oi/eiai? iiiaeeie.

— e?euee?noue aa?oei a?ai? gr, N — e?euee?noue a?aiae. Aaeoi?
ia?aiao??a ?ici?uaiiy ia’?eoa S ia? aeaeyae: {v} = (X,Y, Z, f, y, q).

Iaoaiaoe/ia iiaeaeue Ak(Rt) (t=2,3) — iioei?caoe?eii? caaea/?
aaiiao?e/iiai i?iaeooaaiiy, ui ?icaeyaea?oueny o ?iaio?, ia? aeaeyae:

aecia/eoe aaeoi? u* ? a?aeiia?aeiee eiio ia?ac Su ( Rt, ui
?iaeoeo?oueny aaiiao?e/iith ?ioi?iaoe??th
g(u*)=P(g0(u0),g1(u1),…,gn(un)), i?e yeiio

, (1)

aea gi=(si, mi, vi) — aaiiao?e/ia ?ioi?iaoe?y, ui ?iaeoeo? iaiaaeai?
iaeiica’yci? j*-aaaaoieooieee (j*-aaaaoia?aiieee) Si, i=0,1,…n a Rt;

S0-iaeanoue ?ici?uaiiy;

g(u)-aaiiao?e/ia ?ioi?iaoe?y i?i oi/eiao iiiaeeio Su=B(S0, S1,…Sn),

A — iia?aoi?, ui ? eiiiiceoe??th oai?aoeei-iiiaeeiieo iia?aoe?e
aeaeyaeo

Si)

P- iia?aoi? aeaeyaeo:

Si)}, {m0, m1 …mn}, {v0 v1…vn}),

ui — aaeoi? ci?iieo gi(Gi, i=0,1,…n;

D — iaeanoue i?eionoeieo ?ica’yce?a.

Caoaaaeaiiy 1. Aeoiaey/e c ?aaeueieo a?aeiioaiue iaoa??aeueieo ia’?eo?a
i?e ?ici?uaii? a aeai?e iaeano?, ui iiaeaeththoueny o ?iaio?, iaeanoue D
aecia/a?oueny:

a) oiiaaie ?ici?uaiiy ia’?eo?a Sj a iaeano? S0

, j=1,2,…n, (2)

— a?aeiioaiiy aeeth/aiiy,

S^0=R2\int S0 — aeiiiaiaiiy oi/eiai? iiiaeeie S0 aei anueiai i?inoi?o,
a yeiio ?icaeyaea?oueny oi/eiaa iiiaeeia S0.

a) oiiaaie aca?iiiai iaia?aoeio ia’?eo?a, ui ?ici?uothoueny, aeaeyaeo

, i < j =1,2,...n. (3) Iniiai? ?acoeueoaoe ?icae?eo iioae?eiaaii a i?aoeyo [1, 2, 7, 20, 21]. O o?aoueiio ?icae?e? “Iiaoaeiaa aiae?oe/iiai iieno aca?iieo iaiaaeaiue ia ia?aiao?e ?ici?uaiiy ia’?eo?a o iioei?caoe?eieo caaea/ao aaiiao?e/iiai i?iaeooaaiiy“ ?icaeyaeathoueny oai?aoe/i? iniiae ? caniae caaaeaiiy F-ooieoe??, aaaaeaii? /e.-ei?. IAI Oe?a?ie Noiyiii TH.A. aeey iieno oai?aoeei-iiiaeeiiiai a?aeiioaiiy aeeth/aiiy ? a?aeiioaiiy aca?iiiai iaia?aoeio ia?e aeaiaei??ieo (o?eaei??ieo) aaiiao?e/ieo ia'?eo?a. Ia iniia? iiaeaeueoiai aeine?aeaeaiiy aeanoeainoae F-ooieoe??, eeane/ia icia/aiiy yei? aoei aeaii aeey ia’?eo?a, ui iathoue iaii?iaeith aioo??oi?noue, ca- i?iiiiiaaii iioe?aiiy icia/aiiy F-ooieoe?? ia aeiaaeie, eiee iaeei /e aeaa aaiiao?e/ieo ia’?eoa ia?e (Si, Sj), ui ?icaeyaea?oueny, iathoue ii?iaeith aioo??oi?noue o i?inoi??, a yeiio aiie caaeai?, oiaoi eiee ii/aoeiaa ?ioi?iaoe?y i?i ia’?eoe, ui ?ici?uothoueny, aecia/a?oueny iiiaeeiith (iiaeeeai, iaaii?yaeeiaaaaiith) caieiaieo oa iacaieiaieo iie?e?i?e. A aaaaoueio caaea/ao iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy aeieea? iaiao?aei?noue iiaeaethaaoe iioei?caoe?ei? ia?aoai?aiiy iaae ia’?eoaie, ye? iathoue ci?ii? iao?e/i? oa?aeoa?enoeee. Oeiiaei i?aaenoaaieeii caaea/ oaeiai eeano ? caaea/a, a ye?e iaeanoue aai ia’?eoe ?ici?uaiiy iiaeooue c?ciaaaoe ao?iiiai ia?aoai?aiiy iiae?aiino?. O ?iaio? ?icaeyaea?oueny /anoeiiee aeiaaeie ao?iiiai ia?aoai?aiiy iiae?aiino? - aiiioao?y G aaiiao?e/iiai ia’?eoa Sj a?aeiinii oeaio?a eiai aeanii? nenoaie eii?aeeiao (aai, eiee oea c?o/ii, a?aeiinii ?ioi? oi/ee ieiueie R2): G(S) = S*, ui oa?aeoa?eco?oueny eiao?oe??ioii aiiioao?? K. Oiae? Sj* =KSj(vj). Aeae? ?icaeyaea?oueny a?aeiioaiiy aeeth/aiiy (2), yeui iaae iaeanoth ?ici?uaiiy - aaaaoieooieeii S0 - i?eionoeia aiiioao?y G(S0) = S0*, i?e/iio aaaaoieooiee Sj ia? caaeai? iao?e/i? oa?aeoa?enoeee, a ia?aiao?e ?ici?uaiiy iaeano? S0 o?eniaai?. O aeaiiio aeiaaeeo ye iaeanoue S0, oae ? ia'?eo ?ici?uaiiy Sj iathoue iaii?iaeith aioo??oi?noue ? oiiaa (2) caaea?oueny F0j(xj,yj,K)-ooieoe??th , , , , O ?iaio? iaaaaeaii iiaoaeiao aiae?oe/iiai iieno F0j(xj,yj,K)-ooieoe?? no?oeoo?ith e?i?eieo ia??aiinoae. Oeaio?aeueia i?noea o ?icae?e? caeia? iiaoaeiaa no?oeoo?e iae?i?eieo ia??aiinoae, ui iieno? iaeanoue iaa?ae’?iiino? F-ooieoe?? aeey ia'?eo?a, ye? iathoue eooiaee ia?aiao? ?ici?uaiiy. O oeueiio aeiaaeeo Fij(xi,yi,fi,xj,xj,fj)-ooieoe?y ye ooieoe?y, ui aeicaiey? caaeaaaoe iaia?aoei, aeioee ? ia?aoei caieiaieo j*-ia’?eo?a Si(xi,yi,fi) ? Sj(,xj,xj,fj) ?icaeyaea?oueny o i?inoi?? R6 ia?aiao??a ?ici?-uaiiy (xi, yi, fi, xj, xj, fj). Iiaa?oiy Tijlk 0-??aiy Fij(xi,yi,fi,xj,xj,fj) -ooieoe?? a R6 ? iae?i?eiith, eoneiai-aeeoa?aioe?eiaiith ? neeaaea?oueny c iaai?o aeaaeeeo iiaa?oiiue {Tijhlk},h=1,2, I. I?e iiaoaeia? no?oeoo?e iae?i?eieo ia??aiinoae aeei?enoiao?oueny aecia/aiiy iaeano? iaa?ae’?iiino? (-ooieoe?? ia?e i???ioiaaieo aaaaoieooiee?a (ia?aiao?e fi, fj ? o?eniaaieie) no?oeoo?ith e?i?eieo ia??aiinoae. I?e oeueiio iaiioee? aaaaoieooieee Si(xi,yi) ? Sj(xi,yi) cia?aaeothoueny o aeaeyae? ia’?aeiaiiy iioeeeo caieiaieo aaaaoieooiee?a: Sjk (4) O ?iaio? ?icaeyaeathoueny ? ii??aiththoueny caniae cia?aaeaiiy iaeiica’yciiai iaiioeeiai aaaaoieooieea o aeaeyae? (4). Iaoiaee, ui ?aae?cothoue oai?aoeei-iiiaeeiio iia?aoe?th (4), ii?yae ?c caniaaie ?aae?caoe?? iia?aoe?? noie I?ieianueeiai ? oai?aoeei-iiiaeeiiiai a?aei?iaiiy a?ae?a?athoue aeoaea aaaeeeao ?ieue o iiiaeei? iaoiae?a aaiiao?e/iiai i?iaeooaaiiy. Oiio caniae cia?aaeaiiy (4) ii??aiththoueny ia o?eueee c oi/ee ci?o i?i?i?caoe?? ianyao aaiiao?e/ii? ?ioi?iaoe?? i?i iiiaeeie ia’?eo?a {Sil} ? {Sjk} (4), ia/enethaaeueii? neeaaeiino? aeai?eoi?a, aea ? c oi/ee ci?o oieeiaiiy caeaeo iaoiaeieia?/ieo oneeaaeiaiue ia aoai? ?ica’ycaiiy eiie?aoii? iioei?caoe?eii? caaea/? aaiiao?e/iiai i?iaeooaaiiy, ui iiaeooue ii?iaeaeoaaoeny iaaiei caniaii cia?aaeaiiy (4). (Njk + Njk), aea Nil ? Njk - e?euee?noue aa?oei ia’?eo?a Sil ? Sjk a?aeiia?aeii, ii?iaeaeo?oueny iaeiei c o?ueio iiaeeeaeo aeiaaee?a aeioeeo ia’?eo?a (Sjk, Sil): Aeioee ia?oiai oeio: g-a noi?iia ia'?eoa Sil ? q-a aa?oeia ia'?eoa Sjk; Aeioee ae?oaiai oeio: q-a noi?iia ia'?eoa Sjk ? g-a aa?oeia ia'?eoa Sil; Aeioee o?aoueiai oeio: g-a noi?iia ia'?eoa Sil ? q-a noi?iia ia'?eoa Sjk. Oiiaa Fij (xil ,yil, xjk ,yjk) ( 0 (oiiaa aca?iiiai iaia?aoeio ia’?eo?a Sil ? Sjk ) cia?aaeo?oueny no?oeoo?ith e?i?eieo ia??aiinoae aeaeyaeo s(Flk (xil ,yil , xjk ,yjk), D, P), (5) aea ia??aiino? iaai?o Flk (xil ,yil , xjk ,yjk) e?euee?noth P iathoue aeaeyae Ap(xil - xjk ) + Bp(yil - yjk ) + Cp ( 0, p=1,2,...P, a eiao?oe??ioe Ap, Bp, Cp ? ooieoe?yie eii?aeeiao aa?oei, ui neeaaeathoue a?aeiia?aeio ia?o "aa?oeia - noi?iia" ia?oiai, ae?oaiai aai o?aoueiai oeio. Oiae? oiiaa aca?iiiai iaia?aoeio ia’?eo?a Si ? Sj o R4 c o?aooaaiiyi (5) aecia/a?oueny no?oeoo?ith sij e?i?eieo ia??aiinoae: s(Flk (xil, yil, xjk, yjk), D, ?). O i?inoi?? R6 an?o ia?aiao??a ?ici?uaiiy eii?aeeiaoe aa?oei ia'?eo?a Sil ? Sjk ? ooieoe?yie ia?aiao??a fi i fj. Oiio i?e ?icaeyae? iiaa?oi? Tijlk a R6 eiao?oe??ioe A, B, C noathoue iae?i?eieie ooieoe?yie aeaieo ia?aiao??a. R6 iaeaaeeoue iiaa?oi?, yea aecia/a?oueny ??aiyiiyi fijh=0, i?e/iio o aeiaaeeo ia?oiai oeio noi?iie Tp2 ooieoe?y fijh i?eeia? aeaeyae (Ahcosfi-Bhsinfi)(xil-xjk)+(Bhcosfi+Ahsinfi)(yil-yjk)+C1hcos(fi-fj) C2hsin(fi-fj)+ C3_h a o aeiaaeeo ae?oaiai oeio noi?iie Tp2 - (Ah cosfj - Bh sinfj)(xil - xjk)+ (Bhcosfj +Ahsinfj)(yil -yjk)+ +C1_h cos(fi - fj) C2_hsin(fi - fj) + C3_h , h=1,2,...H. Aeiaaeie o?aoueiai oeio caiaeeoueny aei iaeiiai c oeeo oei?a. Caoaaaeaiiy 2. Aiae?oe/iee iien Tijhlk i?noeoue oaeiae aecia/aiiy iiaeeeaeo iaae ci?ithaaiiy eooiaeo ia?aiao??a fi ? fj. Iaoae fi([0,2(], oiae? ia?aiao? fj iiaeiai caaeiaieueiyoe iaiaaeaiiy: fi - fj (-f ijhlk_2 , fj- fi ( fijhlk_1 , (6) aea {fijhlk_1, fijhlk_2} - iaai? eiinoaioe, ui caeaaeaoue a?ae ia?aii? ia?e "aa?oeia - noi?iia" (aeioee ia?oiai, ae?oaiai ? o?aoueiai oeio). Oiae? a caeaaeiino? a?ae oeio noi?iie Tp2 iiiaeeia Tijhlk ? /anoeiith a?ia?-iiaa?oi?, yea iieno?oueny nenoaiith iaiaaeaiue {fijh1=0; fi - fj (-f ijhlk_2 , fj - fi ( fijhlk_1 } (7) {fijh4=0; fi - fj ( -f ijhlk_2 , fj - fi ( fijhlk_1 } aeey noi?iie Tp2 ia?oiai ? ae?oaiai oeio a?aeiia?aeii. Caoaaaeaiiy 3. Ia’?eoe Sil ? Sjk o R2 iathoue aeia?eueio aca?iio i???ioaoe?th, oiio iiaa?oi? Tijhlk, h=1,2,...H, iiaeooue ii?iaeaeoaaoeny aeia?eueiith ia?ith aeaeyaeo "aa?oeia Sil - noi?iia Sjk " aai "aa?oeia Sjk - noi?iia Sil", oiaoi H= 2(Nil x Njk). I?e oeueiio, aeeiiaiiy iaei??? c oa?ia?ieo nenoai ia??aiinoae aeaeyaeo (7) caaea? oiiao aca?iiiai iaia?aoeio ia’?eo?a Sil ? Sjk a R6. Oiae? no?oeoo?a iae?i?eieo ia??aiinoae 3H) , ui aecia/a? oiiae aca?iiiai iaia?aoeio ia’?eo?a Sil ? Sjk, ia’?aeio? H oa?ia?ieo nenoai ia??aiinoae, ye? i?noyoue ia??aiino? aeaeyaeo (6-7). Iiaeaeueoee ?icaeoie aia?ao no?oeoo? iae?i?eieo ia??aiinoae ae?noa? aeey iieno a?aeiioaiiy aeeth/aiiy (3), yeui ia’?eo S1(x1,y1,f1) ?ici?uo?oueny a iaeano? S0 (x0, y0, f0, E) c o?aooaaiiyi ia?aoai?aiiy aiiioao?? iaae iaeanoth. A?aeiioaiiy (3) caaea?oueny no?oeoo?ith iae?i?eieo ia??aiinoae aeaeyaeo s(F0k (x0,y0,f0,E,xj,yj,fj), D,3H). (8) O ?icae?e? i?iaaaeaiee aiae?c aeanoeainoae F-ooieoe??, yea iieno? a?aeiioaiiy (3) ye aeey i???ioiaaieo, oae ? aeey iai???ioiaaieo iaiioeeeo o?eaei??ieo ia’?eo?a c o?aooaaiiyi ia?aoai?aiiy aiiioao?? iaae iaeanoth ?ici?uaiiy. Iaiaaeeiiny o aeai?e ?iaio? ?icaeyaeii aeioeeo o?eaei??ieo ia’?eo?a oeio 1. A?aiue gr ia'?eoa S0 - aa?oeia sp=(xp, yp, zp) ia'?eoa S1, 2. A?aiue gr oa'?eoa S1 - aa?oeia sk=(xk, yk, zk) ia'?eoa S0 . Aeaaeea /anoeia Tl, l=1,2....H, iiaa?oi? T 0-??aiy F-ooieoe??, ui ?icaeyaea?oueny, aecia/a?oueny nenoaiith 4 iaiaaeaiue aeaeyaeo }, (9) aea ooieoe?y fl o aeiaaeeo aeioeeo ia?oiai ? ae?oaiai oeio ia? aeaeyae a?aeiia?aeii fl=al x1+ bl y1+ cl z1+ dl (K)+ al xp((1) + bl yp((1)+ cl zp((1), fl=al ((1)x1+ bl((1) y1+ cl ((1)z1+ dl - K( al((1) xk + bl ((1)yk+ cl((1) zk), , g({k, p}, aecia/athoue ae?aiacii ci?ie eooiaeo ia?aiao??a (1=(f1, y1, q1) ia iaea?eueo? iiaeeea? eooe iiai?ioo c iioi/iiai iieiaeaiiy. O ?icae?e? ?icaeyiooi aiae?oe/iee iien oiiae aca?iiiai iaia?aoeio ia'?eo?a o aeiaaeeo ai?cio?iiii? iaeano? S0 ?ici?uaiiy, yea ? ai?cio?iiiith aiane?aeie iayaiino? a eiaei?e oi/oe? iaeano? naiai iai?yio iaeiaioi? oyao/ino? spoint, ui ?iciiae?eaiee, iai?eeeaae, ca ae?inii iai?oaeaiue, oiaoi eii?aeeiaoe (x,y) aeia?eueii? oi/ee iaeano? S0 caaeiaieueiythoue ni?aa?aeiioaiiy x=atcosf, y=btsinf, aea t - eiao?oe??io aiiioao??, a, b - cia/aiiy aeiaaeei i?ainae iaaiiai aaciaiai ae?ina. Ioaea, a eiaei?e oi/oe? iaeano? S0 iai?yi sobject iaeiaioi? oyao/ino? ia'?eoa Si, ui ?ici?uo?oueny, iiaeiai ca?aaoeny c iai?yiii ai?cio?ii?? spoint iaeano? ?ici?uaiiy, ui icia/a? ci?io i???ioaoe?? aeanii? nenoaie eii?aeeiao XiIiYi ia'?eoa a caeaaeiino? a?ae eii?aeeiaoe f eiai iiethna. ?icaeyaea?oueny aiae?oe/ia aecia/aiiy oiiae aca?iiiai iaia?aoeio ia'?eo?a ?ici?uaiiy no?oeoo?ith iae?i?eieo ia??aiinoae, a oaeiae can?a iiaoaeiae i?iaeoe?? 0-??aiy F-ooieoe?? aeaio iioeeeo aaaaoieooiee?a a iaeano? S0 (?en. 1). ?en.1 - I?iaeoe?y 0-??aiy F-ooieoe?? aeaio iioeeeo aaaaoieooiee?a (iieacaia oianoith e?i??th) o ai?cio?iii?e iaeano?. Iniiai? ?acoeueoaoe o?aoueiai ?icae?eo iioae?eiaai? o ?iaioao [1, 3, 5, 7-9, 12, 13, 18, 19, 21, 22, 24]. O /aoaa?oiio ?icae?e? ?icaeyaea?oueny ?aae?caoe?y caaea/? (1-3) ia iiiaeei? iai???ioiaaieo aaaaoieooieo ia'?eo?a ?ici?uaiiy, a naia iioei?caoe?eia caaea/a ia?aaoey?iiai ?ici?uaiiy ne?i/aiiai iaai?o iaiioeeeo iai???ioiaaieo aaaaoieooiee?a S={Si}, i=1,2,...,n o aaaaoieooi?e aaaaoica’yci?e iaeano? ?ici?uaiiy S0 c aeaoaeoieie ciiaie Wn, n=1,2,...K. Aiae?cothoueny iniaeeaino? iaeano? i?eionoeieo ?ica'yce?a caaea/?, i?iiiio?oueny iaoiae eieaeueii? iioei?caoe?? caaea/?, ui a?aoiao? iiaeeea?noue iioei?caoe?? ca a?oiaie ci?iieo, oiaoi ca a?oiaie ia?aiao??a o?aineyoe?? ia'?eo?a ? eooiaeo ia?aiao??a ?ici?uaiiy. ?icaeyaea?oueny oaeiae iiaeaethaaiiy caaea/? ?ici?uaiiy iai???ioiaaiiai aaaaoieooieea a iaiaaeai?e aaaaoieooi?e iaeano? c iaoith i?i?i?caoe?? ieiu? iaeano?, caaea/a ?ici?uaiiy iai???ioiaaiiai iaiioeeiai aaaaoia?aiieea a aaaaoia?aiieeo c iaoith i?i?i?caoe?? ia'?io inoaiiueiai, a oaeiae caaea/a ?ici?uaiiy i???ioiaaieo aaaaoieooiee?a o nioc?. Iaoaiaoe/ia iiaeaeue ?aae?caoe?? iniiaii? caaea/? (1-3), ui ?icaeyaea?oueny ia iiiaeei? iai???ioiaaieo aaaaoieooiee?a, ia? aeaeyae: aecia/eoe: min z, (10) R3n+1 aea O = (x1, y1, x2, y2, ..., xn, yn, z), f=( f1, f2, ...,fn), D3 aecia/a?oueny no?oeoo?ith ia??aiinoae sij}, (11) oiiaa (2) aecia/a?oueny no?oeoo?ith aeaeyaeo skt(F(X,f), 3, D1), i=1,2,...,n, oiiaa aca?iiiai iaia?aoeio ia’?eo?a Si oa Sj aecia/a?oueny no?oeoo?ith sgl (Flk (xil ,yil , fi, xjk ,yjk, fj), 3H, D), oiiaa aca?iiiai iaia?aoeio ia’?eo?a Sj ? Wn iieno?oueny no?oeoo?ith skl(F (xjk, yjk, fj, (acl, bcl),0), (Njk x Nnl), D). Aeeo/aii oae? iniiai? oa?aeoa?i? aeanoeaino? iaeano? D. 1. Iae?i?ei? iaiaaeaiiy, ui oi?iothoue D, a caaaeueiiio aeiaaeeo ia ? iioeeeie aai aaiooeie, i?e/iio ?o aann?aie ae?iaeaeai?, ai iathoue ia a?eueo i?ae 3 iaioeueiaeo aeanieo /enea. 2. Iaeanoue D iiaea aooe cia?aaeaia o aeaeyae? ia’?aeiaiiy ne?i/aiiai /enea iaiioeeeo iaeanoae Ds_nonlinear, eiaeia c yeeo caaea?oueny nenoaiith iae?i?eieo ? e?i?eieo iaiaaeaiue no?oeoo?e (11): Ds_nonlinear. (12) 3. Iie?eooy (12) ia ? ?icaeooyi, oiio aeey aeayeeo oi/ie X iaeano? D ia? i?noea ni?aa?aeiioaiiy: Dg_nonlinear, A ( (. 4. Iaeanoue D a caaaeueiiio aeiaaeeo ? iaca’yciith iiiaeeiith ? eiaeia ?? eiiiiiaioa ca’yciino? ia? “y?oaeiee” oa?aeoa?. 5.O ia?a??c? iaeano? D a?ia?ieiueiith fconst={fi}i=1,2,...,n=const ia?ii iaaio aaaaoia?aiio iaiioeeo iiiaeeio R2n+1, aea Dg_linear - eiiiiiaioa e?i?eii? ca’yciino? iaeano? Dlinear, Dg_s_linear - iioeea aaaaoia?aiia i?aeiiiaeeia. 6. Iaeanoue Dlinear ? iaeanoth i?eionoeieo ?ica’yce?a caaea/? aeaeyaeo z. (13) Caaea/a (13) ? caaea/ath iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy ia no?oeoo?? e?i?eieo ia??aiinoae, aeey yei? a ?iaio? i?iiiio?oueny iaoiae eieaeueii? i?i?i?caoe?? ooieoe?? iaoe z ia iaai?e eiiiiiaio? e?i?eii? ca’yciino?. *a?ac aeanoeaino? 1-4 iaeano? D, caaea/a (10-11) eeaneo?eo?oueny ye aaaaoiaei??ia aaaaoiaeno?aiaeueia iioei?caoe?eia caaea/a c e?i?eiith ooieoe??th iaoe ?, a caaaeueiiio aeiaaeeo, iae?i?eieie iaiioeeeie iaiaaeaiiyie. O ?icae?e? ?icaeyaeathoueny e?eueea i?aeoiae?a aei iiaoaeiae ii/aoeiaiai iaaeeaeaiiy O0 (fconst=const), ye? aiae?cothoueny c oi/ee ci?o yeino? O0 ? ia/enethaaeueii? neeaaeiino? aeai?eoi?a. Ia i?aenoaa? iiaeeaeaiiai aiae?co aea?? ?iaeoueny ia ei?enoue aeey iaoiaeo eieaeueii? iioei?caoe?? caaea/? (12). Oi/ea O0 ? aa?oeiith iaeano? Dlinear ? aecia/a?oueny nenoaiith ?aiao (2n+1) aeoeaieo o oi/oe?. e?i?eieo iaiaaeaiue F(fconst)O0+ C(fconst)=0, (14) aea e?a? /anoeie ??aiyiue nenoaie (14) i?eeiathoue aeaeyae -Ck (15) +Ce }, g=1,2,...m1; k= m1+1, ...,m2, l= m2+1,..., m3, w= m3 +1,..., m4, e= m4 +1,...,2n+1. A caaaeueiiio aeiaaeeo oi/ea O0 ? ae?iaeaeaiith ? iaeaaeeoue a?eueo i?ae iaei?e iaeano? Dg_s_linear, ui aecia/a?oueny nenoaiith ia??aiinoae ii?yaeeo n(n-1)/2 +4n +(E-1)n G(f const)X+C(f const) ( 0, (16) aea e?a? /anoeie ??aiyiue nenoaie (16) iathoue aeaeyae (15). Iaoith ?ica'ycaiiy caaea/? (10-11) ? ciaoiaeaeaiiy iaeiiai eieaeueiiai i?i?ioio, oiio iae?athoueny iaaia i?aeiaeanoue Dg_s_linear(Dlinear, yea i?noeoue O0 ? aecia/a?oueny nenoaiith (16), iaaia nenoaia ??aiyiue (14), ui caaea? O0, ? cae?enith?oueny caio?aiiy o i?ino?? an?o ci?iieo R3n+1, o yeiio ?icaeyaea?oueny caaea/a aecia/eoe (X*,f*) = arg min z , R3n+1 aea iiiaeeia Dnonlinear, caaea?oueny nenoaiith iaiaaeaiue aeaeyaeo , (17) aea nenoaia G(f)X-C(f) ( 0 ii?iaeaeo?oueny nenoaiith (16), i?noeoue n(n-1)+8n+2(E-1)n ia??aiinoae aeaeyaeo (6). ?icaeyaea?oueny oaeiae i?aeiaeanoue Dequation iaae? iaeano? D, ui caaea?oueny nenoaiith iaiaaeaiue ii?yaeeo (2n+1), .... (3n) aeaeyaeo (18) aea nenoaia F(f)O+ C(f)=0 ii?iaeaeo?oueny nenoaiith (14). Caaaeueia noaia iaoiaea eieaeueii? iioei?caoe?? caaea/? (10-11) ? ?oa?aoe?eiei i?ioeanii, k-a ?oa?aoe?y yeiai iieyaa? a noeoiiino? oaeeo ae?e: 1. O ieie? iaaii? ii/aoeiai? oi/ee (Xk, fk) ?ica’ycaoe caaea/o: ciaeoe (Xk*, fk*) = arg min z , (19) Ds_nonlinear aea i?aeiaeanoue Ds_nonlinear iieno?oueny nenoaiith aeaeyaeo (17). 2. Ia?aa??eoe oiiao (Xk*, fk*) = arg min z , (20) Dg_nonlinear (=1,2,...,(. sseui oiiaa (20) aeeiiaia, oi/ea (Xk*, fk*) ? eieaeueiei ?ica’yceii caaea/? (10-11). sseui i?, aeeo/a?oueny ianooiia iaeanoue D(g+1)_nonlinear, ui i?noeoue (Xk*, fk*), oi/ea (Xk*, fk*) iicia/a?oueny ye (Xk+1,fk+1) ? aeeiio?oueny (k+1)-a ?oa?aoe?y. O ?icae?e? cai?iiiiiaaii ?icaeyaeaoe caaea/o (19) a aeaeyae? aeaio i?aecaaea/: Caaea/a 1. Aecia/eoe: . (21) Caaea/a 2. Aecia/eoe ianooiio nenoaio aeaeyaeo (18) oeyoii aeiiiaiaiiy aai iiiiaeaiiy nieneo aeoeaieo iaiaaeaiue. Caaea/a (21) ?icaeyaea?oueny ye caaea/a iae?i?eiiai i?ia?aioaaiiy c iaiaaeaiiyie-??aiinoyie (iaiaaeaiiy-ia??aiino? aeaeyaeo (6) o?aoiaothoueny o?eueee ia aoai? aecia/aiiy aaee/eie e?ieo bk), aeey ?ica’ycaiiy yei? canoiniao?oueny iiaeeo?eiaaia ?aae?caoe?y no?aoaa?? aeoeaiiai iaai?o, ui caiaeeoueny aei aacoiiaii? i?i?i?caoe?? a?aeiia?aeii? ooieoe?? Eaa?aiaea L(l,X,f). A?aoiaoth/e, ui iao?eoey Aanna Hxx(l,X,f) ooieoe?? Eaa?aiaea caaea/? (21) ? ciaeiiaaecia/aiith, iiooe iai?yio nioneo aeeiio?oueny a caaaeueiiio aeiaaeeo acaeiaae e?eai?: C={X (a): X (a) =X1+q1 (a) s+q2 (a) d, 0}, yea aa?aioo? ca?a iine?aeiaiino? Xi{a} aei iaaii? oi/ee (X*, f*), a ye?e NL(l,X*, f*) =0 ? Hxx (l, X*, f*) ? aeiaeaoii iai?aaecia/aiith. Aaeoi? s ? ?ica’yceii iaaii? nenoaie ??aiyiue Bksk=-gk c aeiaeaoii aecia/aiith neiao?e/iith iao?eoeath Bk. Aaeoi? d yaey? niaith iai?yi a?ae’?iii? e?eaeie, gk ? a?aae??ioii ooieoe?? Eaa?aiaea caaea/? (21). O ?iaio? aeei?enoaii oaeoi?ecaoe?th Oieanueeiai aeey ia/eneaiiy iai?yio d ? iiaoaeiae aeiaeaoii aecia/aii? iao?eoe?, yea ai?ieneio? iaaecia/aio iao?eoeth Hxx(l,X,f). Caoaaaeaiiy 4. Oaeoi?ecaoe?y Oieanueeiai ci?ith? o?eueee cia/aiiy ae?aaiiaeueieo aeaiaio?a ii/aoeiai? iao?eoe? Hxx(l, X, f). Ioaea, cai?iiiiiaaii iaoiaeeeo, yea aeicaiey? caaacia/eoe caeiaoooy noaoe?iia?ii? oi/ee caaea/? (21). O ?aieao ?ic?iaeaii? ia oaia??oi?e /an oai??? aeine?aeaeaiiy iia?aoe?e aeiaeaoia iai?aaecia/ai?noue iao?eoe? Hxx(l*,X*,f*) o caaaeueiiio aeiaaeeo ? iieacieeii noaoe?iia?iino? oi/ee (X*,f*). Iaeiae, oa?aeoa? ioeueiaeo aeanieo /enae, ui ii?iaeaeothoueny ae?oaeie iio?aeieie ca ia?aiao?aie o?aineyoe?? ia'?eo?a ?ici?uaiiy, a oaeiae ia??ai?noue ioeth ae?oaeo iio?aeieo ca eooiaeie ia?aiao?aie ?ici?uaiiy i?e aeeiiaii? aeoaea neaaeeo aaiiao?e/ieo iaiaaeaiue aea? i?aenoaae i?eioneaoe, ui a oi/oe? (X*,f*) aoaea iaoe i?noea iano?ia?e eieaeueiee i?i?ioi. Oai?aia 1. Iao?eoey Aanna Hxx(l, X, f) ooieoe?? Eaa?aiaea L (l,X,f) caaea/? (21) ia? ?aia ia a?eueo 2n, aea n - e?euee?noue ia'?eo?a, ui ?ici?uothoueny. ?ioeie neiaaie, iiooe iai?yio ?ooo pk iiaeia cae?enithaaoe o ia?a??c? iiaa?oi?, ui caaea?oueny nenoaiith (14), ieiueiith Iy1 y2... yn. Oai?aia 2. Aeey caaea/? (21) iaoiae i?i?i?caoe?? ca a?oiaie eooiaeo ia?aiao??a ?ici?uaiiy ? ia?aiao??a o?aineyoe?? i?eaiaeeoue aei noaoe?iia?ii? oi/ee caaea/?. O ?icae?e? ?icaeyiooi ieoaiiy aecia/aiiy ioe?iie ? oi/ieo cia/aiue iiiaeiee?a Eaa?aiaea. Caoaaaeaiiy 5. sseui nienie aeoeaieo iaiaaeaiue i?noeoue (2n+1) ??aiinoae, aeinoaoiuei acyoe aaeoi? iiiaeiee?a Eaa?aiaea, ui aecia/aiee aeey iioeiaeueii? oi/ee caaea/? aeaeyaeo (13). I?e oeueiio eiiiiiaioe aaeoi?a gTk ca ci?iieie o?aineyoe?? aei??aiththoue ioeth, oiaoi ? iaiao?aeiith i?i?i?caoe?y o?eueee ca eooiaeie ia?aiao?aie, ui ? ua iaeiei i?aeoaa?aeaeaiiyi iniiaii? ?aea? aeai?eoio - aeeo/aiiy aeaio a?oi ci?iieo ? iioei?caoe?? ca a?oiaie ci?iieo. I?e aecia/aii? aaee/eie e?ieo bk a?aoiao?oueny, ui oi/ee (Xk,fk) ? (Xk+1, fk+1) iaeaaeaoue iaae? iaeano? D. ?icaeyiaii aeayeo ??ai?noue nenoaie iaiaaeaiue (18) ? i?eionoeii, ui ia?a “aa?oeia - noi?iia“ (aeea. ?icae. 3), yea oi?io? eiao?oe??ioe iaiaaeaiue nenoaie, caeeoa?oueny iaci?iiith. Oiae? ? a??iith Oai?aia 3. O caaea/? (21) aecia/aiiy iaeneiaeueii? aaee/eie e?ieo bk ca eooiaeie ia?aiao?aie {fi}, i=1, 2,..., n ?ici?uaiiy ia caeaaeeoue a?ae cia/aiue ia?aiao??a o?aineyoe?? (x1, y1, x2, y2,... , xn, yn). O ?icae?e? cai?iiiiiaaii caaaeueiee can?a aecia/aiiy aaee/eie e?ieo bk. Aeiaaaeaii eiino?oeoeaio oai?aio, ui aeicaiey? cia/ii ciaioeoe ianya ia/enethaaiue ia iniia? aeei?enoaiiy neiao??e ?ici?uaiiy. Aeieeaaeii ?icaeyiooi aeiaaeie ae?iaeaeaiino? - aeioee o?aoueiai oeio. ?acoeueoaoii ae?? caniao aecia/aiiy aaee/eie bk ? iaaiee i?ii?aeiee aaeoi? ci?iieo caaea/? (Xk, fk+1), ui aecia/a? aai aioo??oith, aai iai?eionoeio oi/eo iaeano? D caaea/? (10-11). Iaeaaei?noue oi/ee (Xk+1,fk+1) iaeano? D caaacia/o?oueny i?eianoaaiiyi aa??aoe?e aaeoi?a iacaeaaeieo ci?iieo X. Aeey oeueiai ca iiaeie cia/aiiyie fk+1 ia?aia/eneththoueny eiao?oe??ioe iaiaaeaiue nenoaie (14) i?ney /iai cia/aiiy eooiaeo ia?aiao??a o?enothoueny. Nenoaia ??aiyiue ?c ciia noai?aiith iao?eoeath eiao?oe??io?a (aai ?? e?i?eii-iacaeaaeia i?aenenoaia, yeui ii?yaeie nenoaie (14) a?eueoa i?ae 2n+1) ?ica'yco?oueny c iaoith aecia/aiiy ia?aiao??a o?aineyoe?? ? z. A?aecia/eii, ui a caaaeueiiio aeiaaeeo i?ioeaaeo?a i?eianoaaiiy ? aaeaioeaiith i?aecaaea/ath. Iaeiae i?e ?ica'ycaii? i?aeoe/ieo caaea/ ?ici?uaiiy oey i?ioeaaeo?a neeaaeaeanue c iaeiiai e?ieo, iacaaaeath/e ia oa, ui iaia? oi/iiai aeiaaaeaiiy, ui iao?eoey eiao?oe??io?a nenoaie (14) (aai ?? i?aeiao?eoey ?aiao 2n+1) caaaeaee aoaea noi?niith. Iaiao?aeiei aoaiii ?ica’ycaiiy caaea/? (21) ? ia?aa??ea iaeaaeiino? oi/ee (Xk+1,fk+1) iaeano? D. Iiaeeea? ianooii? aeiaaeee. 1. (Xk+1,fk+1) ( Dnonlinear (Xk+1,fk+1) ( D. 2. (Xk+1,fk+1) ( Dnonlinear (Xk+1,fk+1) ( D. 3. (Xk+1,fk+1) ( Dnonlinear (Xk+1,fk+1) ( D. Iaea?eueo oe?eaaei ? ae?oaee aeiaaeie, eiee ? iiaeeea?noue nioneo ii aioo??oiueino? iaeano? D. Ia ?en. 2 iaaaaeaii i?eeeaae ?ica'ycaiiy caaea/? iioeiaeueiiai ?ici?uaiiy iiiaeeie 16 aaaaoieooiee?a o i?aiane?i/ai?e nioc?. a) a) a) ?en. 2. I?eeeaae ?iaioe aeai?eoio eieaeueii? i?i?i?caoe?? a) - iaaia ii/aoeiaa ?ici?uaiiy; a) - oi/ea X0 ; a) - oi/ea eieaeueiiai i?i?ioio caaea/? (19). ?icaeyiaii oaeo ?aae?caoe?th iniiaii? caaea/? (1-3). Iaoae ? iaiaaeai?, caieiai?, a caaaeueiiio aeiaaeeo iaiioee? aaaaoia?aii? ia'?eoe Si, i=0,1, ui iathoue caaeaio i?inoi?iao oi?io, i?e/iio iao?e/i? oa?aeoa?enoeee ia'?eoa S1 oaeiae caaeai?. Iieiaeaiiy ia'?eo?a o i?inoi?? R3 oa?aeoa?eco?oueny ia?aiao?aie ?ici?uaiiy (xi,yi,zi,fi,yi,qi), i=0,1. Iaae ia'?eoaie i?eionoei? ao?ii? ia?aoai?aiiy o?aineyoe??, iiai?ioo, a iaae ia'?eoii S0 - ? ia?aoai?aiiy aiiioao??, ui caaea?oueny eiao?oe??ioii aiiioao?? E. Caaea/a iieyaa? a ?ici?uaii? ia'?eoa S1 o aaaaoia?aiieeo S0 ?c iaoith i?i?i?caoe?? ia'?io V0(S0) ia'?eoa S0. Aeei?enoaiiy aeanoeainoae ao?iieo ia?aoai?aiue aeicaiey? ciaioeoe ?ici??i?noue caaea/? aaea?/? o?enaoe??th ia?aiao??a ?ici?uaiiy iaeano? S0. O ?icae?e? ia iniia? aecia/aiiy ia’?io aaaaoia?aiieea ye ooieoe?? eii?aeeiao aa?oei oa eiao?oe??io?a ??aiyiue, ui caaeathoue eiai a?ai? ? aeei?enoaiiy aeanoeainoae ia?aoai?aiiy aiiioao??, iieacaii, ui iaoaiaoe/ia iiaeaeue caaea/? ia? aeaeyae: min E3 V0, (22) S0 ( S1 = S1 (23) aea V0* ? ii/aoeiaei cia/aiiyi ia'?io ia'?eoa S0. Oiiaa (22), ui aecia/a? iaeanoue D i?eionoeieo ?ica'yce?a caaea/? (22-23), caaea?oueny oiiaith O01(x1,y1,z1,f1,y1,q1)(0, iiaa?oiy 0-??aiy yei? iieno?oueny iaai?ii iae?i?eieo iiaa?oiiue aeaeyaeo (9). Aiae?c iaeano? D caaea/? (22-23) ia iniia? aecia/aiiy iao?eoeue Aanna ooieoe?e iaiaaeaiue caaea/? iieacaa, iaiaaeaiiy iaeano? D ia ? iioeeeie aai oa?aiooeie. A?eueo oiai, iaeanoue i?eionoeieo ?ica'yce?a D caaea/? ? o caaaeueiiio aeiaaeeo iaca'yciith. Oiio aeaia caaea/a ? aaaaoiaeno?aiaeueiith caaea/ath c iae?i?eieie iaiioeeeie iaiaaeaiiyie, ui caaaaea? aaciina?aaeiueiio canoinoaaiith iaoiae?a eeane/iiai iioeeiai iae?i?eiiai i?ia?aioaaiiy. Ca oiiae, ui ii/aoeiaa aca?iia ?ici?uaiiy, i???ioaoe?y, a oaeiae ni?aa?aeiioaiiy ia'?i?a ia'?eo?a iiaeooue aooe aeia?eueieie, cai?iiiiiaaii ? i?ia?aiii ?aae?ciaaii aeaiaoaiiee iaoiae ?ica'ycaiiy caaea/?. 1. Iiaoaeiaa ii/aoeiaiai i?eionoeiiai ?ici?uaiiy ia'?eo?a, ui caaea?oueny aaeoi?ii w1=(x1,y1,z1,f1,y1,q1,K), caniiaaia ia aecia/aii? aca?iii? ia?niaeoeaii? i???ioaoe?? ia'?eo?a ca aeiiiiiaith ioe?iee ?oi?o iiiaio?a ?ia?oe?? oa ?ic?aooieo ae?ini?ae?a ?ia?oe?? aeey eiaeiiai c ia'?eo?a (?en.3.a). Aaeoi? w1 caaea? oi/eo iaeano? D, ui iaeaaeeoue iaai?e iaiioee?e eiiiiiaio? ca'yciino? Dp iaeano? D, o ye?e aeae? ?icaeyaea?oueny caaea/a (22-23). 2. Aecia/aiiy iioeiaeueiiai ?ici?uaiiy, oiaoi ?ica'ycaiiy oaei? i?aecaaea/e: ciaeoe: min E3 V0, (24) G( D(R7 aea i?aeiaeanoue G aecia/a?oueny nenoaiith ?aiao m({1,2,...,7} aeoeaieo a iioi/i?e oi/oe? X(D iaiaaeaiue iaeano? D, oiaoi iaiaaeaiue, ui iienothoue aeioee ia'?eo?a. Iiooe eieaeueiiai i?i?ioio caaea/? (24) yaey? niaith iiiioiiiee ?oa?aoe?eiee i?ioean, o yeiio oeyoii ai?ieneiaoe?? ciaeiiaaecia/aiiai aann?aia aeayeith aeiaeaoii aecia/aiith iao?eoeath ia eiaeiiio e?ioe? i?ioeano ?ica'ycaiiy ? aeai?o iai?yio nioneo iiaeia iaea?aeaoe iine?aeiai?noue Xj, j=1,2,..., ui ca?aa?oueny, o caaaeueiiio aeiaaeeo, aei noaoe?iia?ii? oi/ee X* (?en.3.a). Aea?? aaeoi?a iai?yio ?ooo cae?enith?oueny oeyoii caaaeaiiy caaea/? ia eiaei?e ?oa?aoe?? i?ioeano aei iine?aeiaiino? aeiiii?aeieo i?aecaaea/ ?c e?i?eieie iaiaaeaiiyie ca aeiiiiiaith iaoiaea ni?iaeoiaaiiai eaa?aiae?aia, aea ooieoe?? iaoe aeiiii?aeii? caaea/? eaaae?aoe/ii ai?ieneiothoue ooieoe?th Eaa?aiaea caaea/? (24). ?en. 3 - ?ici?uaiiy iai???ioiaaieo aaaaoia?aiiee?a a) - ii/aoeiaa ?ici?uaiiy. Ia'?eoe ia?aoeiathoueny. a) - ?acoeueoao ?iaioe i?ia?aie eieaeueii? iioei?caoe?? O ?icae?e? ?icaeyaea?oueny ua iaeia ?aae?caoe?y caaea/? (1-3) o R2. ? aeaa iaiioeeeo aaaaoieooieee S0 ? S1, ui oa?aeoa?ecothoueny nai?th ieiuath si, ?=0,1, (s1=const). Ao?ii? ia?aoai?aiiy ?ooo i?eionoei? iaae ia'?eoaie S0 ? S1, iaae S0 i?eionoeia oaeiae aiiioao?y. Iaiao?aeii aecia/eoe oae? iao?e/i? oa?aeoa?enoeee ia'?eoa S0 i?e caa??aaii? i?inoi?iai? oi?ie ia'?eo?a, uia caaeiaieueiyeeny oae? oiiae: min s0 (25) S1 ( S0 = S0, Aiae?c ooieoe?? iaoe (25) aeicaieea caienaoe iiaeaeue caaea/? o aeaeyae? min K2 s0* (26) D( R4 aea s0* - ii/aoeiaa cia/aiiy ieiu? iaeano? S0, iaeanoue D iieno?oueny no?oeoo?ith iae?i?eieo ia??aiinoae aeaeyaeo (8). Iiia?aaei?e aiae?c ooieoe?e iaiaaeaiue nenoai ia iniia? ?oi?o iao?eoeue Aanna iieaco?, ui a caaaeueiiio aeiaaeeo oe? ooieoe?? ia ? iioeeeie /e oaiooeie. I?ioa c o?aooaaiiyi oa?aeoa?o aeanieo eiia?oaioieo ia?aoai?aiue iaae ia’?eoaie, ? a??iith oaea oai?aia. Oai?aia 4. Ooieoe?? iaiaaeaiue caaea/?, ui iaeeaaeathoueny ia iaeanoue i?eionoeieo ?ica'yce?a, iioee? (a ie?aiiio aeiaaeeo e?i?ei?), a iaeanoue D - oa?aiooa iiiaeeia. Oai?aia 5. Aeiaaeueiee i?i?ioi caaea/? aeinyaa?oueny a e?aei?e oi/oe? iaeano? i?eionoeieo ?ica'yce?a. Eiaeia e?aeiy oi/ea iaeano? D aecia/a?oueny nenoaiith /ioe?ueio e?i?eieo ? iae?i?eieo ??aiyiue. Ia iniia? ?noioiiai aiae?co aaiiao?e/ieo iniaeeainoae caaea/? ioe?iea I /enea an?eyeeo nenoai ??aiyiue neeaaea? I=I(N0xN1)2. Cai?iiiiiaaiee iaoiae iiaea aooe canoiniaaii, iai?eeeaae, o oae?e oeiia?e iioei?caoe?ei?e caaea/? ?ici?uaiiy, yea aeieea? o acooo?a?e i?iieneiaino?. Iaoae ? ii/aoeiaa ?ici?uaiiy (?en. 4.a) a ?cio?iii?e i?yiieooi?e iaeano? ?ici?uaiiy S0, yea iiaea aooe iaea?aeaii aoaeue-yeei iaoiaeii aaiiao?e/iiai i?iaeooaaiiy. Iaoae oaeiae ? iaa?? ia'?eo?a {S}, ye? ? ua ia?ici?uaieie. (?en. 4.a). Aaaaea?ii, ui iaa?? {S} ia? iane?i/aio iiooaei?noue. Iaiao?aeii ?ici?noeoe ia'?eoe c iaai?o {S} o iacaeiyoeo /anoeiao iaeano? ?ici?uaiiy S0. Iaoiaeeea ?ica'ycaiiy oe??? caaea/? neeaaea?oueny c aeaio aoai?a. Aoai 1. Aeeo/aiiy oae caaieo a?eueieo iaeanoae (ia ?en. 4.a oe? iaeano? iioa?aiaai? n??ei eieuei?ii). Caaea/a ?ica'yco?oueny ca aeiiiiiaith aeai?eoio, ui ?aae?co? iia?aoe?th oai?aoeei-iiiaeeiiiai a?aei?iaiiy c o?aooaaiiyi iaaii? iioeaee, aaee/eia yei? iia'ycaia c iao?e/ieie oa?aeoa?enoeeaie iaeiaioiai ia'?eoa c iaai?o {S}. Can?a o?aooaaiiy iioeaee iieyaa? o cae?eniaii? iaae ia'?eoaie ii/aoeiaiai ?ici?uaiiy ia?aoai?aiiy aiiioao?? ia?aae aeeiiaiiyi iia?aoe?? a?aei?iaiiy. Aoai 2. Iioeiaeueia ?ici?uaiiy o a?eueieo iaeanoyo ia'?eo?a iaai?o {S}, aeey /iai ?aae?ciaaiee can?a ?ica'ycaiiy caaea/? (35). I?e oeueiio c iaai?o ia'?eo?a {S} aeae?a?oueny ia'?eo c oaeeie iao?e/ieie oa?aeoa?enoeeaie, yeee iiaea aooe ?ici?uaiee o iioi/i?e a?euei?e iaeano?. a) a) a) ?en. 4 - ?acoeueoao ?ica'ycaiiy caaea/? ?ici?uaiiy ia iaai?? ii/aoeiaeo aeaieo ?c acooo?ai? i?iieneiaino?. Iniiai? ?acoeueoaoe ?icae?eo iioae?eiaai? a ?iaioao [2, 4, 5, 7, 8, 10-13, 16-18, 19, 21, 24, 29]. I’yoee ?icae?e “Iaoiaee iiooeo aeno?aioio caaea/ ?ici?uaiiy i?yiieooieo aaiiao?e/ieo ia’?eo?a o i?yiieooi?e iaeano?” i?enay/aii ?aae?caoe?? iniiaii? caaea/? (1-3) ia iiiaeei? i?yiieooieo ia’?eo?a ?ici?uaiiy. Oey caaea/a oi?ioeth?oueny ye caaea/a eiia?iaoi?ii? iioei?caoe??. ?icaeyioo? eiino?oeoeai? aeanoeaino? iaeano? i?eionoeieo ?ica’yce?a caaea/?, ui aeicaieythoue canoinoaaoe iaoiaeeeo no?aoaa?? aeoeaiiai iaai?o aeey ciaioaiiy iiiaeeie oi/ie, ui ? i?aeic??eeie ia aeno?aioi. Iaoiaeeea ?ica’ycaiiy caaea/? canoiniao?oueny oaeiae aei caaea/? ?ici?uaiiy a?ia?ia?aeaeai?iaae?a o a?ia?ia?aeaeai?iaae?. W, W=const} c iaoith i?i?i?caoe?? aeiaaeeie z caeiyoi? /anoeie nioae. Iaoaiaoe/ia iiaeaeue caaea/? ia? aeaeyae , (27) aea iaeanoue i?eionoeieo ?ica’yce?a D iieno?oueny no?oeoo?ith . (28) aea iaa?? Fi0(vi,z) i?noeoue ia??aiino? aeaeyaeo {xi(0; yi(0; z-xi - ai (0; W - yi - bi (0}, iaa?? F(vi,vj) i?noeoue ia??aiino? aeaeyaeo {xi - xj - aj(0; xj - xi - ai(0; yi - yj - bj(0; yj - yi - bi(0}, i,j=1,2,...,n, i(j. A caaaeueiiio aeiaaeeo iaeanoue D ? iaca’yciith aaaaoia?aiiith iiiaeeiith, caaaeyee /iio oa e?i?eiino? ooieoe?? iaoe aeiaaeueiee i?i?ioi caaea/? aeinyaa?oueny o iaai?e aa?oei? X* iaeano? D. Aa?oeia X* aecia/a?oueny iaei??th aai e?eueeiia nenoaiaie ??aiyiue FX+C=0, ui iaeaaeaoue iiiaeei? on?eyeeo e?i?eii-iacaeaaeieo nenoai ??aiyiue Q, iiaoaeiaaieo c ia??aiinoae iaai??a Fi0(vi,z) i F(vi,vj) no?oeoo?e (28). Caaea/a (27-28) ? NP-iiaiith iioei?caoe?eiith caaea/ath, oiio aeey ?? ?ica’yceo canoiniaaiee can?a aeene?aoii? iioei?caoe??, yeee iniiaaiee ia i?aai?caoe?? iioei?caoe?eiiai i?ioeano ca aea?aaii ?ica’yce?a A ? iieyaa? a on?/aiiio ia?aai?? iiiaeeie Q. Iiaoaeiaaia ia inoaiiueiio ??ai? aea?aaa ?ica’yce?a A nenoaia ??aiyiue FX+C=0, yeui aiia noi?nia, iieno?: 1) aa?oeie iaeano? D; 2) oi/ee, ui iaeaaeaoue iaae? iaeano? D; 3) oi/ee iica iaeanoth D, oiaoi oi/ee, ui aecia/athoue ia?aiao?e ?ici?uaiiy, i?e yeeo aeaye? ia?e i?yiieooiee?a ia?aoeiathoueny. E??i oiai, aa?oeie aea?aaa ?ica’yce?a iiaeooue neiaie?coaaoe ? 4) ianoi?ni? nenoaie. I?iaaaeaiee ia iaoiaee/iiio, aeai?eoi?/iiio ? i?ia?aiiiio ??ai? aiae?c oa?aeoa?o ? caaaeueii? e?eueeino? nenoai ??aiyiue, ui aecia/athoue eiaeio c /ioe?ueio aeuaiaaaaeaieo iiiaeei iieacaa, ui cia/io /anoeio iiiaeeie Q neeaaeathoue naia ianoi?ni? nenoaie ??aiyiue, ye? aeoaea aaaee? aeey aiae?co ia aeioe?euei?noue iiaeaeueoiai aaeoaeaiiy ? canoinoaaiiy aoaeoeaieo i?aaee a?aeoeiaiiy. O ?icae?e? i?iiiio?oueny iiaeaeueoee ?icaeoie iaoiaeo ?ica’ycaiiy caaea/? (27-28) c iaoith onoiaiiy iaiao?aeiino? aiae?co ianoi?nieo nenoai ??aiyiue. Aeey oeueiai aea?aai ?ica’yce?a A ?icaeaa?oueny ia aeaa i?aeaea?aaa: A1 ? A2. I?aeaea?aai A1 i?noeoue on? aa?oeie aea?aaa A, ia yeeo ia eiaeiiio ??ai? aea?aaa ?ica’yce?a i?e aeeth/aii? a nenoaio ??aiyiue /a?aiaiai iaiaaeaiiy a nienie ci?iieo aeiaea?oueny o?eueee iaeia ci?iia, oiaoi, ia eiaeiiio ??ai? i?aeaea?aaa A1 iiaoaeiaaia nenoaia ??aiyiue iieno? oi/eo a i?inoi?? aei??iino? iiia?a ??aiy aea?aaa. C ?ioiai aieo, yeui a nenoaio ??aiyiue, ui aoaeo?oueny, aeiaea?oueny iaiaaeaiiy, a?aeiia?aeia aa?oei? aea?aaa ?ica’yce?a A2, oi a nienie ci?iieo aiaeii/an c oaeei iaiaaeaiiyi aeiaeathoueny aea? ci?ii?, ? oaea nenoaia ??aiyiue iieno? e?i?eiee iiiaiaeae aei??iino?, a?eueoi? ioey. Caoaaaeaiiy 6. On? ianoi?ni? nenoaie ??aiyiue aeinyaathoueny ia aa?oeiao aea?aaa A2. Can?a aiae?co aa?oei aea?aaa A1 caaacia/o? i?yiee ii?yaeie ia?aaeyaeo aa?oei ? ?aae?co? iiiaeeio N i?aaee a?aeoeiaiiy e?ioeaaeo aa?oei aea?aaa, o oiio /ene? aa?oei aea?aaa A1, ye? aecia/athoue oi/eo XoutD ( D (aeiaaeie 3), aaeoaeaiiy c yeeo ? iaaeioe?eueiei. Iaeiae, i?iaaaeai? aeine?aeaeaiiy aeiaaee, ui caeiaooa aiae?oe/ia ?ioi?iaoe?y i?i oi/eo XoutD iiaea aooe aeei?enoaia aeey iiaeaeueoiai ia?aaeyaeo aea?aaa A. Canoinoaaiiy iaoiaeo iaia?a?aii? iioei?caoe??, a naia, iaoiaeeee aeoeaiiai iaai?o ia iaaieo e?ieao ?ica’ycaiiy eiia?iaoi?ii? caaea/?, yeee cai?iiiiiaaii o ?icae?e?, aeicaiey? aeei?enoaoe nenoaio ??aiyiue FoutX-B=0, ui aecia/a? oi/eo (aaeoi? ia?aiao??a ?ici?uaiiy) XoutD, o ye?e (-ooieoe?? aeayeeo ia? i?yiieooiee?a i?eeiathoue a?ae'?ii? cia/aiiy. ?ioeie neiaaie, o oi/oe? XoutD, caeiaooi? ia ??ai? 2k aea?aaa ?ica’yce?a A1 ? iiiaeeia Fbroken={fik1, fik2, fik3, f ik4}, i < k, i({1,2,...,k-1} ii?ooaieo iaiaaeaiue (/ioe?e aeey eiaeii? F-ooieoe??, ui i?eeia? a?ae’?iia cia/aiiy). Aecia/aiiy 1. Iacaaii iaeaeeae/eie a?aie/i? oi/ee iaeano? D2k, io?eiai? c aeaii? oi/ee XoutD ca aeai?eoiii, ui ?aae?co? no?aoaa?th aeoeaiiai iaai?o. A?aecia/eii, ui oaeeo iaeaeeae/eo oi/ie aeey eiaeii? oi/ee XoutD iiaea aooe aeae?eueea. Oaea iaiaeiicia/i?noue aeieea? o ca'yceo c iaiaeiicia/iei aecia/aiiyi ii?ooaieo ia??aiinoae, ui oi?iothoue ooieoe?th iaoe caaea/? aecia/aiiy iaeaeeae/i? oi/ee. A?ae’?ii?noue iaei??? (-ooieoe??, eio?a aiae?oe/ii iieno?oueny no?oeoo?ith ia??aiinoae, icia/a? ii?ooaiiy /ioe?ueio ia??aiinoae. Aeeiiaiiy oi/a a iaei??? c oeeo ia??aiinoae aa?aioo? iaa?ae’?ii?noue (-ooieoe??. I?e oeueiio iaeaeeae/? oi/ee aoaeooue aa?oeiaie ??cieo iioeeeo i?aeiaeanoae iaiioeei? iaeano? i?eionoeieo ?ica’yce?a caaea/?, a?eueo oiai, aa?oeiaie ??cieo eiiiiiaio ca'yciino? iaeano? D. O ?iaio? i?iaaaeaii aiae?c iiiaeeie ooieoe?e iaoe caaea/? aecia/aiiy iaeaeeae/i? i?eionoeii? oi/ee. Cai?iiiiiaaii can?a ciaioaiiy iiooaeiino? iiiaeeie ooieoe?e iaoe caaea/? aecia/aiiy iaeaeeae/i? oi/ee. Iaoiae iiooeo iaeaeeae/i? oi/ee iniiaaiee ia ia?aaeyae? ciae?a eiiiiiaio?a aaeoi?a iiiaeiee?a Eaa?aiaea ia eiaei?e ?oa?aoe??. A caaaeueiiio aeiaaeeo a caeaaeiino? a?ae aea?aiiai ia aeai?e ?oa?aoe?? iiiaeieea (iai?yio ?ooo) ?acoeueoao iioei?caoe?? (i?eionoeia oi/ea) iiaea aooe a?aei?iiei. C iaoith onoiaiiy oe??? iaiaeiicia/iino? i?e caaeai?e ooieoe?? iaoe ia iniia? ci?noiaiiai aiae?co iiaeeeainoae aeai?o a?ae`?iieo iiiaeiee?a cai?iiiiiaaii can?a iaeiicia/iiai aeai?o iiiaeiee?a Eaa?aiaea: Oai?aia 6. Iaoae nenoaia ??aiyiue FX+C=0, ui aecia/a? ii/aoeiao iai?eionoeio oi/eo XoutD, ia? oaeo aeanoea?noue: eiaei?e iacaeaaei?e ci?ii?e caaea/? a?aeiia?aea? o?eueee iaeia ??ai?noue nenoaie, yea i?noeoue oeth ci?iio c eiao?oe??ioii 1. Oiae? ca oiiae, ui aeaia aeanoea?noue iiaeiia caa?aaoeny ? a i?eionoei?e oi/oe?, ia eiaei?e ?oa?aoe?? iaoiaeo ?ica’ycaiiy a?ae’?iiee iiiaeiee Eaa?aiaea aeae?a?oueny iaeiicia/ii. Ioaea, aeey ?ica’ycaiiy caaea/? (27-28) iaiao?aeii iiaoaeoaaoe an? nenoaie ??aiyiue, ui aecia/athoue aa?oeie iaeano? i?eionoeieo ?ica’yce?a caaea/?. *anoeia oaeeo nenoai ??aiyiue aoaeo?oueny i?e ia?aaeyae? aa?oei aea?aaa ?ica’yce?a A1, ?ioa /anoeia iiaea aooe io?eiaia ye ?ica’ycie noeoiiino? e?i?eieo caaea/ ?ica’yce?a iiiaeeie iaeaeeae/eo oi/ie c aeayei? oi/ee OoutD. A?aecia/eii oaeo aaaeeeao aeanoea?noue Aeanoea?noue 1. Aeai?eoi aecia/aiiy iaeaeeae/i? oi/ee aeicaiey? ciaeoe aa?oeie (a?aie/i? oi/ee) iaeano? Dk (k - iiia? ??aiy aea?aaa ?ica’yce?a), ui caaeathoueny nenoaiaie ??aiyiue, ye? iiaeia iiaoaeoaaoe o?eueee i?e ia?aaeyae? aa?oei aea?aaa A2. ?ioeie neiaaie, c oi/ee OoutD iica iaeanoth i?eionoeieo ?ica’yce?a, ui ciaeaeaia i?e ia?aaeyae? aea?aaa A1, aoaeothoueny aa?oeie (a?aie/i? oi/ee) iaeano? i?eionoeieo ?ica’yce?a, ui oi?iothoueny, acaaae? eaaeo/e, ia aa?oeiao aea?aaa A2, i?e/iio aeaiee i?ioean ne?i/aiee ? i?aeaea?oueny oii?yaeeoaaiith. Ioaea, iiaoaeiaaiee iaia?a?aiee oeyo i?ae a?aei?iieie eiiiiiaioaie ca'yciino? iaeano? i?eionoeieo ?ica’yce?a iniiaii? caaea/?. O ?icae?e? cai?iiiiiaaii iaoiae oii?yaeeoaaiiy aa?oei aea?aaa A, ui ? a?aei?iiei a?ae caaaeueiia?aeiieo cania?a ia?aaeyaeo aa?oei aea?aaa ?ica’yce?a o?aoiao? ye iiaeeea?noue aaeoaeaiiy ca aeiiiiiaith iaoiaeo i?yiiai ii?yaeeo, oae ? iiaeeea?noue canoinoaaiiy aeai?eoio aecia/aiiy iaeaeeae/i? oi/ee. Oaeee can?a ia?aaeyaeo aa?oei aea?aaa A aeicaiey? oieeiooe iaiao?aeiino? aiae?coaaoe ianoi?ni? nenoaie ??aiyiue. A?aecia/eii, ui o oa?i?iao caaea/? i?yiieooiiai ?ici?uaiiy oi?ioeththoueny iioei?caoe?ei? caaea/?, a yeeo ?ioi?iaoe?y i?i ia'?eoe aeine?aeaeaiiy ia ? aaiiao?e/iith, iai?eeeaae, caaea/? oai??? ?iceeaae?a, caaea/? oai??? ia'?iii-eaeaiaea?iiai ieaioaaiiy oiui. E??i oiai, cai?iiiiiaaiee iaoiae ?ica'ycaiiy caaea/? i?yiieooiiai ?ici?uaiiy eaaei iiaea aooe ?iciianthaeaeaiee ia oae? eeane caaea/ iioeiaeueiiai i?yiieooiiai ?ici?uaiiy, ye caaea/?, a yeeo i?eionea?oueny iiai?io ia'?eo?a ia 90 a?aaeon?a aai caaea/?, a yeeo ia'?eoe ?ici?uaiiy ? neeaaeaieie i?yiieooieeaie. Iacaaaeath/e ia iia? aeanoeaino? iaoi?iaeueieo iinoaiiaie oaeeo caaea/, ?o iaoaiaoe/ia iiaeaeue caa??aa? na?e nooo?ai aeene?aoiee oa?aeoa? ? oiio aeey ?ica'ycaiiy caaea/? iiaeia canoiniaoaaoe cai?iiiiiaaiee can?a c iaaaeeeeie iiaeeo?eaoe?yie. Ia ?en. 5 iaaaaeaiee ?ica’ycie caaea/? i?yiieooiiai ?ici?uaiiy 25 i?yiieooiee?a. *an ?ica’ycaiiy neeaa 21 oaeeeio ia PC AT 486. ?en. 5 ?ica’ycie caaea/? i?yiieooiiai ?ici?uaiiy 25 i?yiieooiee?a O ?icae?e? oaeiae aeeeaaeaii can?a iiooeo aeiaaeueiiai iioeioio ua iaei??? ?aae?caoe?? caaea/? (1-3) - caaea/? ?ici?uaiiy i?yiieooieo a?ia?ia?aeaeai?iaae?a, ui ? iiaeeo?eiaaiei caniaii a?eie ? iaae ? ?icaeaa? ?aea?, cai?iiiiiaai? i?e ?ica’ycaii? caaea/? ?ici?uaiiy i?yiieooiee?a. Iaoae ? iai?aiane?i/aia iaeanoue Ak, k=2,...,p}. , k=1, 2,..., p acaeiaae a?aeiia?aeieo inae eii?aeeiao a iaeano? S0 oae, uia aeiaaeeia caeiyoi? /anoeie iaeano? acaeiaae eii?aeeiaoii? in? IO1 aoea i?i?iaeueiith. Iaoaiaoe/ia iiaeaeue caaea/? ia? aeaeyae, aiaeia?/iee (27-28). Iaoiae iiooeo aeiaaeueiiai i?i?ioio caiaeeoueny aei ia?aai?o iiiaeeie P={pl}, l=1, 2,..., n! ia?anoaaeaiue pl iiia??a ia'?eo?a, ui ?ici?uothoueny, ? caei aoooy aa??aio?a ?ici?uaiiy ca aea?aaii ?ica’yce?a A aeey eiaeiiai ia?anoaaeaiiy. Cai?iiiiiaaii i?aaeea a?aeoeiaiiy e?ioeaaeo aa?oei aea?aaa A, ui iniiaai? ia aaiiao?e/ieo aeanoeainoyo caaea/? oa iiaeeeainoyo aiae?oe/iiai cia?aaeaiiy iiiaeeie aeno?aiaeueieo oi/ie o ?aieao aeaiiai caniao ?ica’ycaiiy. Aeey iiaeaeueoiai ciaioaiiy e?eueeino? aa?oei aea?aaa ?ica’yce?a, ui a?aeiia?aeathoue aa??aioo ?ici?uaiiy ia'?eo?a o i?inoi?? Rp, o ?iaio? cai?iiiiiaaii canoinoaaiiy oaeiai ii?yaeeo ia?aaeyaeo aa?oei aea?aaa ?ica’yce?a, ui aeei?enoiao? eaeneeia?ao?/ia oii?yaeeoaaiiy ia?anoaaeaiue. O ?icae?e? oaeiae ?icaeiooa ?aeay aeei?enoaiiy aeanoeaino? neiao??e ia iiiaeei? ?ici?uaiue. Iaoae ? iiiaeeie P1 ? P2 ia?anoaaeaiue c n aeaiaio?a 1,2,..., n oae?, ui iiiaeeia P1 i?noeoue n!/2 ia?acoaaeaiue, na?aae yeeo iaia? ?iaa?nieo a?aeiinii ae?oa ae?oaa ia?anoaaeaiue, ? iiiaeeia P2 i?noeoue n!/2 ia?anoaaeaiue, ?iaa?nieo aei ia?anoaaeaiue iiiaeeie P1. Oiae?, yeui aeayea ia?anoaaeaiiy p'=(a1,..., ai,...,an)I P1, oi ia?anoaaeaiiy p"=(an, ...,an-i,...,a1) I P2. Oai?aia 7. Iiiaeeie P1 ? P2 ia?anoaaeaiue iiia??a ia'?eo?a aecia/athoue iaeia ? oa aea cia/aiiy i?i?ioio ooieoe?? iaoe caaea/?, ui ? ?? aeiaaeueiei i?i?ioiii. Ne?aenoai. sseui a ia?anoaaeaii? (a1, ..., ai,...,an) c n /enae 1.2,..., n cia/aiiy an < a1, oiae? aeey aecia/aiiy i?i?iaeueiiai cia/aiiy ooieoe?? iaoe caaea/? aeaia ia?anoaaeaiiy iiaeia ia ?icaeyaeaoe. Oai?aia 8. Iaoae i?e aeayeiio ?ici?uaii? Qi an?o n ia'?eo?a a iaeano? S0 ia'?eo Si ciaoiaeeoueny a aa?oei? V aeaii? iaeano?. Oiae? ?nio? 2p a?aei?iieo aa??aio?a ?ici?uaiiy n ia'?eo?a a iaeano? S0, neiao?e/ieo ?ici?uaiith Qi . Aeaiee can?a ae?noaa aeai?eoi?/io oa i?ia?aiio ?aae?caoe?th aeey aeiaaeeo o?eaei??ii? caaea/? ?ici?uaiiy ia?aeaeai?iaae?a o ia?aeaeai?iaae?. Iniiai? ?acoeueoaoe ?icae?eo aeeeaaeaii o i?aoeyo [1, 2, 10, 14, 18, 19, 22, 25, 29]. INIIAI? ?ACOEUeOAOE OA AENIIAEE 1. O aeena?oaoe?? i?iaaaeaii nenoaiiee aiae?c no/aniiai noaio ?nioth/eo cania?a iaoaiaoe/iiai iiaeaethaaiiy ? ?ica'ycaiiy aeaiaei??ieo ? o?eaei??ieo ia?aaoey?ieo caaea/ ?ici?uaiiy ? ia oe?e iniia? aeae?eaii eiioeaiooaeueii aaaeeeaee eean caaea/ ia?aaoey?iiai ?ici?uaiiy aaiiao?e/ieo ia'?eo?a c iiaeeea?noth o?aooaaiiy eooiaeo ia?aiao??a ?ici?uaiiy, ui ? iaeiaio aea/aiei, iacaaaeath/e ia aaeeea i?aeoe/ia cia/aiiy. Iaoith aeaii? aeena?oaoe?eii? ?iaioe ? iiaeaeueoee ?icaeoie caaaeueii? oai??? aaiiao?e/iiai i?iaeooaaiiy acaaae? oa iiaeaethaaiiy ? ?ica'ycaiiy iioei?caoe?eieo caaea/ ia?aaoey?iiai ?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia'?eo?a a ?cio?iiieo ? ai?cio?iiieo iaeanoyo ?ici?uaiiy cie?aia. A i?ioean? aeine?aeaeaiue io?eiai? oae? iia? ?acoeueoaoe. 2. Noai?aii oai?aoe/iee aacen oa ?ino?oiaioa??e iaoaiaoe/iiai iiaeaethaaiiy caaea/ aeaiaei??iiai ? o?eaei??iiai ?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia'?eo?a o iaeanoyo ?c ci?iieie iao?e/ieie oa?aeoa?enoeeaie. 3. Noai?aii aia?ao no?oeoo? iae?i?eieo ia??aiinoae aeey iieno iniiaieo aaiiao?e/ieo iaiaaeaiue caaea/ ?ici?uaiiy - oai?aoeei-iiiaeeiiiai a?aeiioaiiy aeeth/aiiy ? a?aeiioaiiy aca?iiiai iaia?aoeio aeaiaei??ieo aaiiao?e/ieo ia'?eo?a, ye? iathoue eooiaee ia?aiao? ?ici?uaiiy. 4. Noai?aii can?a aiae?oe/iiai iiaeaiiy oai?aoeei-iiiaeeiiiai a?aeiioaiiy aeeth/aiiy aeey ia?e aeaiaei??ieo iai???ioiaaieo aaiiao?e/ieo ia'?eo?a, iaeei c yeeo c?cia? ao?iiiai ia?aoai?aiiy iiae?aiino?. 5. Aia?ao O-ooieoe?e canoiniaaii aeey iieno oiia aca?iiiai ?ici?uaiiy aeaio iai???ioiaaieo aaaaoia?aiiee?a o R3. 6. ?icaeyiooi aiae?oe/iee iien oiiae aca?iiiai iaia?aoeio ia'?eo?a ?ici?uaiiy o aeiaaeeo ai?cio?iiii? iaeano? ?ici?uaiiy. 7. Cai?iiiiiaaii iaoiaeeeo iiaoaeiae i?iaeoe?? 0-??aiy F-ooieoe?? aeaio iai???ioiaaieo aaaaoieooiee?a a ai?cio?iii?e iaeano?. 8. Neioaciaaii oi?aa?naeueio iaoaiaoe/io iiaeaeue eeano iioei?caoe?eieo caaea/ ia?aaoey?iiai ?ici?uaiiy ne?i/aiiai iaai?o iaiioeeeo iai???ioiaaieo aaaaoieooiee?a o aaaaoieooi?e iaeano? ?ici?uaiiy. 9. I?iaaaeaii aiae?c iniaeeainoae iaeano? i?eionoeieo ?ica'yce?a iioei?caoe?eii? caaea/? ia?aaoey?iiai ?ici?uaiiy iaiioeeeo iai???ioiaaieo aaaaoieooiee?a. Iieacaii iai?enoiniaai?noue aeey ?ica'ycaiiy oe??? caaea/? eeane/ieo iaoiae?a iaoaiaoe/iiai i?ia?aioaaiiy oa iaa?oioiaaia iaiao?aei?noue ?ic?iaee iiaiai oai?aoe/iiai aaceno aeey noai?aiiy cania?a ?ica'ycaiiy caaea/ icia/aiiai eeano. 10. Cai?iiiiiaaii iiaee iaoiae eieaeueii? iioei?caoe?? caaea/? ia?aaoey?iiai ?ici?uaiiy iaiioeeeo iai???ioiaaieo aaaaoieooiee?a, yeee a?aoiao? iiaeeea?noue iioei?caoe?? ca a?oiaie ci?iieo, oiaoi ca a?oiaie ia?aiao??a o?aineyoe?? ia'?eo?a ? eooiaeo ia?aiao??a ?ici?uaiiy. 11. ?ic?iaeaii iaoaiaoe/i? iiaeae? oaeeo ?aae?caoe?e iniiaii? caaea/? iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy ye caaea/a ?ici?uaiiy iai???ioiaaiiai aaaaoieooieea a iaiaaeai?e aaaaoieooi?e iaeano? c iaoith i?i?i?caoe?? ieiu? iaeano?, caaea/a ?ici?uaiiy iai???ioiaaiiai iaiioeeiai aaaaoia?aiieea a aaaaoia?aiieeo c iaoith i?i?i?caoe?? ia'?io inoaiiueiai, a oaeiae caaea/a ?ici?uaiiy i???ioiaaieo aaaaoieooiee?a o nioc?. Aeae?eai? caaaeuei? nooo?a? aeanoeaino? oeeo caaea/, ui aeicaiey? canoiniaoaaoe ?aeaieia?/ii aeecuee? iaoiaeeee ?ica'ycaiiy. 12. ?ic?iaeaii iaoiaeeee ?ica'ycaiiy iaaaaeaieo ?aae?caoe?e iniiaii? caaea/? iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy. Oe? iaoiaee ? iiaeie aai aaeineiiaeththoue ? ocaaaeueiththoue a?aeii? ?ai?oa. 13. Cai?iiiiiaaii aeai?eoi?/i? oa i?ia?aii? ?aae?caoe?? iaoiae?a c ioe?ieaie ia/enethaaeueii? neeaaeiino? aeai?eoi?a. 14. Iaea?aeaa iiaeaeueoee ?icaeoie iaoiae ?ica'ycaiiy ?aae?caoe?? iniiaii? caaea/? aeine?aeaeaiiy ia iiiaeei? i?yiieooieo ia'?eo?a ?ici?uaiiy. Aeae?eai? eiino?oeoeai? aeanoeaino? iaeano? i?eionoeieo ?ica’yce?a caaea/?, ui aeicaieythoue canoinoaaoe iaoiaeeeo iiiaeiee?a Eaa?aiaea o caaea/? eiia?iaoi?ii? iioei?caoe??, yeith ? oey ?aae?caoe?y o ii/aoeia?e iinoaiiaoe?. 15. Cai?iiiiiaaii iaoaiaoe/io iiaeaeue ? iaoiae iiooeo aeiaaeueiiai i?i?ioio caaea/? ?ici?uaiiy a?ia?ia?aeaeai?iaae?a a a?ia?ia?aeaeai?iaae?, aeeo/ai? eiino?oeoeai? iniaeeaino? iaeano? i?eionoeieo ?ica’yce?a aeaii? ?aae?caoe?? iniiaii? caaea/? aeine?aeaeaiiy. ?ic?iaeaii aaie i?ia?aiieo iiaeoe?a, ui noai?th? i?ia?aiia caaacia/aiiy aeey ?ica'ycaiiy eeano caaea/ ia?aaoey?iiai ?ici?uaiiy i???ioiaaieo ? iai???ioiaaieo aaiiao?e/ieo ia'?eo?a. Noeoii?noue ?ic?iaeaieo iaoaiaoe/ieo iiaeaeae, iaoiae?a, aeai?eoi?a ? i?ia?aiieo eiiieaen?a iiaea aeei?enoiaoaaoeny o aeaeyae? iioei?caoe?eiiai yae?a a nenoaiao aaoiiaoeciaaiiai i?iaeooaaiiy ea?o ?ice?ith i?iieneiaeo iaoa??ae?a i?e noai?aii? no/anieo ?ano?nicaa??aath/eo oaoiieia?e, nenoaiao i?iaeooaaiiy aaia?aeueieo ieai?a i?aei?e?inoa oiui. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a ianooiieo iaoeiaeo i?aoeyo. 1. Yeaiaiou oai?ee aaiiao?e/aneiai i?iaeoe?iaaiey / Aeeue I.E., sseiaeaa N.A., Iiaiaeeeiaa I.A. e ae?.: Iiae ?aae. aeaae. IAI Oe?aeiu ?aa/aaa A.E. - E.: Iaoe. aeoiea, 1995. - 248n. 2. Iiaiaeeeiaa I.A., Eiaeooia I.A. Nenoaia ?aoaiey iiaeeeanna caaea/ aaiiao?e/aneiai i?iaeoe?iaaiey // I?ia?aiiiia iaania/aiea oaoie/aneeo nenoai, E.: Ei-o eeaa?iaoeee AI ONN?. - 1991. - N. 26-30. 3. Iiaiaeeeiaa I.A. Iaoaiaoe/aneay iiaeaeue e iniaaiiinoe iaeanoe aeiionoeiuo ?aoaiee iaeeiaeiie caaea/e ?aciauaiey // Iaoiaeieiaey ?aoaiey i?eeeaaeiuo iioeiecaoeeiiiuo caaea/.-E.:Ei-o eeaa?iaoeee IAI Oe?aeiu.-1992. - N. 15-21. 4. Iiaiaeeeiaa I.A. Iaoiae ?aoaiey caaea/e iioeiecaoeee eeiaeiie ooieoeee oeaee ia no?oeoo?a iaeeiaeiuo ia?aaainoa // Iaoaiaoe/aneia iiaeaee?iaaiea e iioeiecaoeey oaoie/aneeo nenoai e i?ioeannia.-E.:Ei-o eeaa?iaoeee IAI Oe?aeiu. - 1993. - N.25-30. 5. Iiaiaeeeiaa I.A. Iiaeaee?iaaiea e ?aoaiea caaea/e ?aciauaiey iaauioeeuo iiiaioaieueiuo iauaeoia a ia?aie/aiiie iaeanoe // Aaoiiaoecaoeey a?oeoaeoo?ii-no?ieoaeueiiai i?iaeoe?iaaiey.- ?inoia- ia-Aeiio: ?inoianeee ain. a?oeoaeoo?iue ei-o. - 1994. - N.120-129. 6. 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Biro M., Stoyan Yu., Novozhilova M. et al. The State of Software Best Practice in Central and Eastern Europe // IEEE Software Process Newsletter.-1998, N 12.- P.19-21. 11. Noiyi TH.A., Iiaiaeeeiaa I.A. Oneiaey eieaeueiie iioeiaeueiinoe a ia?aaoey?iuo iaeeiaeiuo caaea/ao aaiiao?e/aneiai i?iaeoe?iaaiey // Aeieeaaeu IAI Oe?aeiu.-1998.- N 12.-N.40-45. 12. Iiaiaeeeiaa I.A. Iiaeaee?iaaiea e ?aoaiea caaea/e ?aciauaiey iai?eaioe?iaaiiiai iauaeoa a iaeanoe n ia?aiaiiuie iao?e/aneeie oa?aeoa?enoeeaie // I?iaeaiu aeiieee.- Oa?ueeia: OAOO?Y.- 1998.-Aui. 49. - N.95-98. 13. Iiaiaeeeiaa I.A., Iaiaei?ii I.E. Aeei?enoaiiy iiiyooy F-ooieoeii a 2D caaea/ao aaiiao?e/iiai i?iaeooaaiiy // Ainiee AEIOI; Ooiaeaiaioaeuei? iaoee. - 1998. - N 8. - N. 328-331. 14. Iiaiaeeeiaa I. A., Eaca?aaa E.A. I?eiaiaiea iaoiaeieiaee iiiaeeoaeae Eaa?aiaea a eiiaeiaoi?iie caaea/a ?aciauaiey i?yiioaieueieeia // Eeaa?iaoeea e nenoaiiue aiaeec.- 1999. - N 3. - N. 141-147. 15. Iiaiaeeeiaa I. A. Iaoiaeieiaiy ?ica’ycaiiy iioeiicaoeieieo iaeiiieieo caaea/ aaiiao?e/iiai i?iaeooaaiiy // Ainiee Caii?icueeiai aea?aeaaiiai oiiaa?neoaoo. - Caii?iaeaey: CAeO.-1999.- N 1. - N. 79-82. 16. Iiaiaeeeiaa I. A. Iiaeaethaaiiy iniiaieo iaiaaeaiue a iaeiiieieo caaea/ao iioeiicaoeieiiai aaiiao?e/iiai i?iaeooaaiiy // I?eeeaaeia aaiiao?iy i iiaeaia?ia a?aoiea. - E.:EAeOOAA. - 1999. - N 65. - N.82-86. 17. Iaiaei?ii I.E., Iaie?aoia I.A., Iiaiaeeeiaa I. A. Aiaeic i neeaaeiinoue aeai?eoio cia?aaeaiiy iaeiicayciiai iaiioeeiai iiiaieooieea o aeaeyaei ia’?aeiaiiy iioeeeo iiiaieooieeia // Ainiee Caii?icueeiai aea?aeaaiiai oiiaa?neoaoo. - Caii?iaeaey: CAeO. -1999. - N 2. - N. 79-83. 18. Stoyan Yu.G., Novozhilova M.V. Nonguillotine placement of rectangles into a strip of given width // Pesquisa Operacional: Special Issue on Cutting and Packing problems.- 1999. - N 3. - P. 63-74. 19. Iiaiaeeeiaa I. A., *a?iiii?aoe A. A. Ia iaeiii niiniaa iienea iioeiaeueiiai ?aciauaiey i?yiioaieueiuo aeia?ia?aeeaeaieiaaeia. - Oa?ueeia: 1992. - 27 n.(I?ai?./IAI Oe?aeiu. Ei-o i?iae. iaoeiino?iaiey; N 365). 20. Noiyi TH.A., Iiaiaeeeiaa I. A., Ea?oaoia A.A. Iaoaiaoe/aneay iiaeaeue e iioeiecaoeey eeiaeiuo Ee(R2) caaea/ ?aciauaiey.-Oa?ueeia: 1991.-25 n. (I?ai?. / IAI Oe?aeiu. Ei-o i?iae. iaoeiino?iaiey; N 353). 21. Iino?iaiea ia/aeueiiai i?eaeeaeaiey aeey caaea/e ?aciauaiey auioeeiai iiiaia?aiieea a auioeeie iiiaia?aiiie iaeanoe n ia?aiaiiuie iao?e/aneeie oa?aeoa?enoeeaie // Iiaiaeeeiaa I.A., Ioaie/iay A.Ae.; Ei-o i?iae. iaoeiino?. AI Oe?aeiu. I., 1996 - 18c. - ?on. - Aeai. AEIEOE 16.08. 96, N 2694-A 96. 22. I?eiaiaiea iaoiaeieiaee iai?a?uaiie iioeiecaoeee a iaeiie eiiaeiaoi?iie caaea/a aaiiao?e/aneiai i?iaeoe?iaaiey n eeiaeiuie ia?aie/aieyie e ooieoeeae oeaee // Iiaiaeeeiaa I.A., Eaca?aaa E.A. ; Ei-o i?iae. iaoeiino?. AI Oe?aeiu. I., 1997 - 29c. - ?on. - Aeai. AEIEOE, 15.04.97,- N 1257-1397. 23. Stoyan Yu. G., Novozhilova M.V. Modelling and solving of the allocation problem of non-convex polygons with rotations // Pric. of 17 International Conf. “System Modelling”. -London: Charman & Hall Publisher. - 1996.- P. 559-565. 24. Stoyan Yu., Loyko A., Novozhilova M. The State of Software Best Practice in Central and Eastern Europe // Proceedings of International Conf. “Cooperation and Business Opportunities for Eastern/Western European countries in the IT field”. - 1997. - P. 1-15. 25. Noiyi TH.A., Iiaiaeeeiaa I.A. Ceiiao?ey a caaea/ao aaiiao?e/aneiai i?iaeoe?iaaiey // O?oaeu Iaaeae. eiio. “Iaoaiaoeea. Eiiiuethoa?. Ia?aciaaiea”. - Ioueii: IAO.-1997.-N.261-264. 26. Iiaiaeeeiaa I.A., A?enoiaa E.A. ?ac?aaioea oaoiieiaee eiiiiiiai/iiai neioaca yia?aaoe/aneeo nenoai n o/aoii ?enea aicieeiiaaiey aaa?ee e eaoano?io // Aiiio. aeiee. Iaaeaeoia?. oeieu "I?iaeoe?iaaiea aaoiiaoece?iaaiiuo nenoai eiio?iy e oi?aaeaiey neiaeiuie iauaeoaie". -Ooaina: Oa?uee.ei-o ?aaeeiyeaeo?iieee.- 1992.- N.13. 27. Iiaiaeeeiaa I.A., Ea?oaoia A.A. Iioeiecaoeey i?e iino?iaiee ?ane?ieiuo ieaiia a NO AAI // Oac. Iaaeaeoia?. oeieu “I?iaeoe?iaaiea aaoiiaoece?iaaiiuo nenoai eiio?iy e oi?aaeaiey neiaeiuie iauaeoaie”.- Ooaina: Oa?ueeianeee ei-o ?aaeeiyeaeo?iieee.-1992.- C.12. 28. Iiaiaeeeiaa I.A., Ea?oaoia A.A., ?iciiuaiiy aaaaoieooieeia a iaeanoyo c ia?anoaieie a?aieoeyie // Oac.aeii. 46 iaoe. eiio. aeeeaaea/ia.- Iieoaaa:IAI.- 1994.-N.42. 29. Iiaiaeeeiaa I.A., Eaca?aaa E.A. Iaoiae iienea aeiaaeueiiai ieieioia iaeiie caaea/e aaiiao?e/aneiai i?iaeoe?iaaiey // Oac. aeiee. 1-ai Iaaeaeoia?iaeiiai iieiaeaaeiiai oi?oia "Yeaeo?iieea e iieiaeaaeue a OOI aaea".- Oa?ueeia.-OOO?Y.- 1997.-N. 183. 30. Iiaiaeeeiaa I.A., Ioaie/iay A.Ae. ?aoaiea caaea/e ?aciauaiey iaauioeeiai iiiaia?aiieea a iaauioeeie iiiaia?aiiie iaeanoe // Oac. aeiee. 1-ai Iaaeaeoia?iaeiiai iieiaeaaeiiai oi?oia "Yeaeo?iieea e iieiaeaaeue a OOI aaea ".- Oa?ueeia.-OOO?Y.- 1997.-N. 182. AIIOAOe?ss Iiaiaeeeiaa I.A. ”Iaoaiaoe/i? iiaeae? ? iaoiaee ?ica’ycaiiy iae?i?eieo caaea/ ?ici?uaiiy aaiiao?e/ieo ia’?eo?a“. - ?oeiien. Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy aeieoi?a o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.05.02-iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee. - ?inoeooo i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie, Oa?e?a, 1999. I?iaaaeaii ocaaaeueiaiiy ? ?icaeoie oai??? ? iaoiae?a iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy a iaeano? iiaeaethaaiiy ? ?ica'ycaiiy iioei?caoe?eieo caaea/ ia?aaoey?iiai ?ici?uaiiy 2D ? 3D i???ioiaaieo ? iai???ioiaaieo aaiiao?e/ieo ia'?eo?a a ?cio?iiieo ? ai?cio?iiieo iaeanoyo ?ici?uaiiy ?c ci?i ieie iao?e/ieie oa?aeoa?enoeeaie. Noai?aii ? aeine?aeaeaii aia?ao no?oeoo? iae?i?eieo ia??aiinoae aeey iieno iniiaieo aaiiao?e/ieo iaiaaeaiue caaea/ ?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia'?eo?a. Cai?iiiiiaaii iiaee iaoiae eieaeueii? iioei?caoe?? caaea/? ?ici?uaiiy iai???ioiaaieo aaaaoieooiee?a. Ae?noaee iiaeaeueoee ?icaeoie iaoiaee ?ica’ycaiiy eeano caaea/ i?yiieooiiai ?ici?uaiiy. Cai?iiiiiaaii aeai?eoi?/i? oa i?ia?aii? ?aae?caoe?? iaoiae?a c ioe?ieaie ia/enethaaeueii? neeaaeiino? aeai?eoi?a. Eeth/ia? neiaa: iaoaiaoe/ia iiaeaethaaiiy, iioei?caoe?eia aaiiao?e/ia i?iaeooaaiiy, iioeiaeueia ?ici?uaiiy, aaiiao?e/iee ia’?eo. ABSTRACT Novozhilova I.V. ”Iathematical models and solution methods for nonlinear problems of placement of geometric objects “. The dissertation is the manuscript presented for the scientific degree of the Doctor of Physical-Mathematical Sciences on the specialty 01.05.02 - mathematical modeling and computational methods. - Institute for Problems in Machinery named after A.N.Podgorny, National Academy of Sciences of Ukraine, Kharkov, 1999. Theory and methods of optimization geometric design in the field of modeling and solving optimization problems of non-regular placement of oriented and non-oriented 2D and 3D geometric objects in isotropic and non-isotropic placement regions having variable metric characteristics have been generalized and developed. Created and analyzed is the apparatus of structures of non-linear inequalities describing basic geometric restrictions of the optimization placement problems of non-oriented geometric objects. New method searching for local minimum of the placement has been proposed. Developed are solution methods for the rectangular placement problems. Algorithmic and program implementations of the solution methods accompanied with computation complexity evaluations have been described. Key words: mathematical modeling, optimization geometric design, optimal placement, geometric object. AIIIOAOeEss Iiaiaeeeiaa I.A. ”Iaoaiaoe/aneea iiaeaee e iaoiaeu ?aoaiey iaeeiaeiuo caaea/ ?aciauaiey aaiiao?e/aneeo iauaeoia“. - ?oeiienue. Aeenna?oaoeey ia nieneaiea o/aiie noaiaie aeieoi?a oeceei-iaoaiaoe/anneeo iaoe ii niaoeeaeueiinoe 01.05.02 - iaoaiaoe/aneia iiaeaee?iaaiea e au/eneeoaeueiua iaoiaeu. - Einoeooo i?iaeai iaoeiino?iaiey ei. A.I. Iiaeai?iiai IAI Oe?aeiu, Oa?ueeia, 1999. A aeenna?oaoeeiiiie ?aaioa i?iaaaeaii iaiauaiea e ?acaeoea oai?ee e iaoiaeia iioeiecaoeeiiiiai aaiiao?e/aneiai i?iaeoe?iaaiey a iaeanoe iiaea ee?iaaiey e ?aoaiey iioeiecaoeeiiiuo caaea/ ia?aaoey?iiai ?aciauaiey 2D e 3D i?eaioe?iaaiiuo e iai?eaioe?iaaiiuo aaiiao?e/aneeo iauaeoia a ecio?iiiuo e aiecio?iiiuo iaeanoyo ?aciauaiey n ia?aiaiiuie iao?e/aneeie oa?aeoa?enoeeaie. Aeooaeueiinoue enneaaeiaaiey naycaia n oai, /oi n iaeiie noi?iiu o?oaeiinoe, aicieeathuea i?e iaoaiaoe/aneii e eiiiuethoa?iii iiaeaee?iaaiee aeaiiiai eeanna caaea/, iinyo eiioeaiooaeueiue oa?aeoa? e auaiaeyo aeaiiue eeann caaea/ ca ?aiee eeanne/aneie oai?ee enneaaeiaaiey iia?aoeee, a n ae?oaie noi?iiu /?acau/aeii oe?ieei niaeo?ii i?eeeaaeiuo caaea/. Eniieueciaaiea iiiyoey ei?oaaea aaiiao?e/aneie eioi?iaoeee aeey oi?iaeecaoeee aeaiiuo i i?iecaieueiii aaiiao?e/aneii iauaeoa e aiia?aoa F-ooieoeee aeey iienaiey iniiaiuo oai?aoeei-iiiaeanoaaiiuo ioiioaiee iaaeaeo iauaeoaie ?aciauaiey iicaieeei ?ac?aaioaoue oai?aoe/aneee aacen e eino?oiaioa?ee aeey iiaeaee?iaaiey e ?aoaiey ?anniao?eaaaiiai eeanna caaea/ aaiiao?e/aneiai i?iaeoe?iaaiey. Aiia?ao F- ooieoeee iieo/ee aeaeueiaeoaa ?acaeoea aeey neo/ay ieaaea ia ieioiuo aaiiao?e/aneeo iauaeoia, aeey ia?u iauaeoia, iaeei ec eioi?uo iiaeaa?aaaony aooeiiiio i?aia?aciaaieth iiaeiaey. I?aaeeiaeaia iaoiaeeea i?eiaiaiey F-ooieoeee aeey iienaiey oneiaee acaeiiiai ia?ana/aiey iai?eaioe?iaaiiuo iiiaia?aiieeia a R3 . Nicaeai e enneaaeiaai eiino?oeoeaiue aiia?ao no?oeoo? iaeeiaeiuo ia?aaainoa aeey iienaiey iaeanoe iaio?eoeaoaeueiuo cia/aiee F-ooieoeee, caaeathueo oneiaea iaia?ana/aiey ?aciauaaiuo iauaeoia, eiathueo oaeiaie ia?aiao? ?aciauaiey. ?anniio?aii aiaeeoe/aneia iienaiea oneiaey acaeiiiai ia?ana/aiey iauaeoia ?aciauaiey a neo/aa aiecio?iiiie iaeanoe ?aciauaiey. I?aaeeiaeaia iaoiaeeea iino?iaiey i?iaeoeee 0-o?iaiy F-ooieoeee aeaoo iai?eaioe?iaaiiuo iiiaioaieueieeia a aiecio?iiiie iaeanoe, eioi?ay yaeyaony iniiaie aeey ?aoaiey iioeiecaoeeiiiuo caaea/ ?aciauaiey iauaeoia a aiecio?iiiuo iaeanoyo. Neioace?iaaia oieaa?naeueiay iaoaiaoe/aneay iiaeaeue eeanna iioeiecaoeeiiiuo caaea/ ia?aaoey?iiai ?aciauaiey eiia/iiai iaai?a iaauioeeuo iai?eaioe?iaaiiuo iiiaioaieueieeia a iiiaioaieueiie iiiainayciie iaeanoe ?aciauaiey. I?iaaaeai aiaeec iniaaiiinoae iaeanoe aeiionoeiuo ?aoaiee aeaiiie caaea/e, iieacaia iai?eiaieiinoue eeanne/aneeo iaoiaeia iaoaiaoe/aneiai i?ia?aiie?iaaiey aeey ?aoaiey aeaiiie caaea/e. I?aaeeiaeai iiaue iaoiae eieaeueiie iioeiecaoeee caaea/e ia?aaoey?iiai ?aciauaiey iaauioeeuo iai?eaioe?iaaiiuo iiiaioaieueieeia, eioi?ue o/eouaaao aiciiaeiinoue iioeiecaoeee ii a?oiiai ia?aiaiiuo, oi anoue ii a?oiiai ia?aiao?ia o?aineyoeee e oaeiauo ia?aiao?ia ?aciauaiey. ?ac?aaioaiu e enneaaeiaaiu iaoaiaoe/aneea iiaeaee oaeeo ?aaeecaoeee iniiaiie caaea/e iioeiecaoeeiiiiai aaiiao?e/aneiai i?iaeoe?iaaiey eae caaea/a ?aciauaiey iai?eaioe?iaaiiiai iiiaioaieueieea a ia?aie/aiiie iiiai oaieueiie iaeanoe n oeaeueth ieieiecaoeee ieiuaaee iaeanoe, caaea/a ?aciauaiey iai?eaioe?iaaiiiai iaauioeeiai iiiaia?aiieea a iiiaia?aiieea n oeaeueth ieieiecaoeee iauaia iineaaeiaai, a oaeaea caaea/a ?aciauaiey i?eaioe?iaaiiuo iiiaioaieueieeia a iieina. Auaeaeaiu iauea nouanoaaiiua iniaaiiinoe ?anniao?eaaaiuo ?aaeecaoeee iniiaiie caaea/e enneaaeiaaiey, /oi iicaieyao i?eiaiyoue eaeaieiae/anee aeeceea iaoiaeeee ?aoaiey. ?ac?aaioaiiua iaoiaeeee ?aoaiey oeacaiiuo ?aaeecaoeee yaeythony iiauie eee nouanoaaiii ?acaeaatho ecaanoiua. I?aaeeiaeaiu aeai?eoie/aneea e i?ia?aiiiua ?aaeecaoeee iaoiaeia n ioeaieaie au/eneeoaeueiie neiaeiinoe aeai?eoiia. Iieo/ee aeaeueiaeoaa ?acaeoea iaoiae ?aoaiey ?aaeecaoeee iniiaiie caaea/e enneaaeiaaiey ia iiiaeanoaa i?yiioaieueiuo iauaeoia enneaaeiaaiey. Auaeaeaiu eiino?oeoeaiua iniaaiiinoe iaeanoe aeiionoeiuo ?aoaiee caaea/e, eioi?ua iicaieytho i?eiaieoue ia ii?aaeaeaiiuo yoaiao ?aoaiey ii nouanoao eiiaeiaoi?iie caaea/e eaeae no?aoaaee aeoeaiiai iaai?a e nouanoaaiii nie?aoeoue /enei enneaaeoaiuo aa?eaioia ?aoaiey. Enneaaeiaaia iiaeaeue e i?aaeeiaeai iaoiae ?aoaiey aeiaaeueiiai ieieioia caaea/e ?aciauaiey aeia?ia?aeeaieiaaeia a aeia?ia?aeeaieiaaea, auaeaeaiu e i?iaiaeece?iaaiu eiino?oeoeaiua iniaaiiinoe iaeanoe aeiionoeiuo ?aoaiee aeaiiie ?aaeecaoeee iniiaiie caaea/e. A niaieoiiinoe i?aaeeiaeaiiua iiaeaee e iaoiaeu ?aoaiey yaeythony eiino?oeoeaiui aiia?aoii iaoaiaoe/aneiai e eiiiuethoa?iiai iiaeaee?iaaiey, enneaaeiaaiey e ?aoaiey iiauo eeannia caaea/ aaiiao?e/aneiai i?iaeoe?iaaiey. ?ac?aaioaiu eiiieaenu i?ia?aii (iauaa eiee/anoai iia?aoi?ia enoiaeiiai eiaea ieiei 30000), eioi?ua ninoaaeytho iaoaiaoe/aneia iaania/aiea aeey ?aoaiey eeanna caaea/ ?aciauaiey i?eaioe?iaaiiuo e iai?eaioe?iaaiiuo aaiiao?e/aneeo iauaeoia. Iiiaeanoai ?ac?aaioaiiuo iaoaiaoe/aneeo iiaeaeae, iaoiaeia, aeai?eoiia e i?ia?aiiiuo eiiieaenia iiaeao auoue eniieueciaaii a ea/anoaa ooieoeeiiaeueiie /anoe nenoai aaoiiaoece?iaaiiiai i?iaeoe?iaaiey ea?o ?ane?iy i?iiuoeaiiuo iaoa?eaeia a eaaeie i?iiuoeaiiinoe, i?e nicaeaiee iaeiiooiaeiuo oaoiieiaee, i?e i?iaeoe?iaaiee caeaiee e nii?oaeaiee e o. ae. A aeenna?oaoeee ?ac?aaioai ii?aaeaeaiiue eioaeeaeooaeueiue aiia?ao, eioi?ue iicaieyao nicaeaaaoue ia?niaeoeaiua NAI?, i?eaioe?iaaiiua ia nicaeaiea nia?aiaiiuo oaoiieiaee. Eeth/aaua neiaa: iaoaiaoe/aneia iiaeaee?iaaiea, iioeiecaoeeiiiia aaiiao?e/aneia i?iaeoe?iaaiea, iioeiaeueiia ?aciauaiea, aaiiao?e/aneee iauaeo.

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