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Iaeaaeaiea

Aaaaeaiea

1)Oai?ey oioiyooaeoa

2)Niaeo?aeueiua oa?aeoa?enoeee oioieaoiaea

3) ?aaioa auoiaea

4)?ani?aaeaeaiea yeaeo?iiia a iaoaeea

5)Naeaeoeaiue oioiyooaeo

6) Eaaioiiaoaie/aneay oai?ey oioiyooaeoa

7) I?eiaiaiea

Eeoa?aoo?a

Aaaaeaiea

N?aaee ?aciiia?aciuo yaeaiee a eioi?uo i?iyaeyaony aicaeaenoaea naaoa ia
aauanoai aaaeiia ianoi caieiaao oioiyeaeo?e/-aneee yooaeo o.a.enioneaiea
yeao?iiia aauanoaii iiae aeaenoaeai naaoa.Aiaeec yoiai yaeaiey i?eaae e
i?aaenoaaeaieth i naaoiauo eaaioao e nua?ae /?acao/aeii aaaeiaeueth
?ieue a ?acaeoee nia?aiaiuo oai?eoe/aneo i?aaenoaaeaiee.Aianoa n oai
oioiyeaeo?e/eneee yooaeo eniieuecoaony a oioiyeaiaioao iieo/eaoeo
eneeth/eoaeueii oe?ieia i?eiaiaiea a ?aciiia?aciaeueo iaeanoyo iaoee e
oaoieee e iaauathueo aua aieaa aiaaoua ia?niaeoeau.Ioe?uoea oioiyooaeoa
neaaeoao ioianoe e 1887 a.eiaaea Aa?oe iaia?oaeee /oi inaauaiea
oeueo?aoeieaoiaui naaoii yeaeo?iaeia ene?iaiai i?iiaaeooea iaoiaeyueainy
iiae iai?yaeaieai iaeaa/aao i?ineaeeaaiea ene?u iaaeaeo ieie. ssaeaiea
iaia?oaeaiia Aa?oeii iiaeii iaaethaeaoue ia neaaeothuai eaaei
inouanaeiii iiuoa (?en.1.). Aaee/eia ene?iaiai i?iiaaeooea (
iiaeae?aaony oaeei ia?acii, /oi a noaia ninoiyuae ec o?ainoi?iaoi?a O e
eiiaeainaoi?a N ene?a i?ineaeeaaao n o?oaeii (iaeei-aeaa ?aca a
ieiooo)Anee inaaoeoue yeaeo?iaeu ( naeaeaiiua ec /enoiai oeeiea naaoii
?oooiie eaiiu ((,oi ?ac?yae eiiaeainaoi?a cia/eoaeueii iaeaa/aaony:
ene?a ia/eiaao i?ineaeeaaoue aeiaieii /anoi, eiia/ii iiuiinoue
o?anoi?iaoi?a aeinoaoi/ii aeey auno?ie ca?yaeee eiiaeainaoi?a N .
Iiianoea iaaeaeo eaiiie e yeaeo?iaeaie ( noaeei ( iu i?aa?aaeaeaai
aeinooi oeueo?aoeieaoiaui eo/ai e yaeaiea i?ae?auaaony.Nenoaiaoe/aneia
eneaaeiaaiea Aaeueaaena, A.A. Noieaoiaa e ae?. (1885 a.)auynieee /oi a
iiuoa Aa?oea aeaei naiaeeony e inaiaiaeaeaieth ca?yaeia iiae aeaenoaeai
naaoa iiiaaeay a yeaeo?e/aneia iiea iaaeaeo yeaeo?iaeaie,ya?yaeu yoe
onei?ythony, eiiece?otho ie?oaeathuee aac e aucuaatho ?ac?yae. A.A.
Noieaoia inouanoaee iiuou ii oioiyooaeoo i?eiaiya aia?aua iaaieueoea
?aciinoe iioaioeeaeia iaaeaeo yeaeo?iaeaie.Noaia iiuoia i?eiaiyaiay
Noieaoiaui, ecia?aaeaia ia ?en.

Iniiaiuie ?acoeueoaie eneaaeiaaiee Noieaoiaa eiathuea cia/aiea e a iaoa
a?aiy, auee neaaeothuea caeeth/aiey:

1) Iaeaieaa yooaeoeaii aeaenoaoao oeueo?aoeieaoiaua eo/e, iiaeauaaiua
oaeii.

2)Neea oioioiea i?iii?oeeiiaeueia nicaeaaaaiie inaauaiiinoe oaea
(?ac?yaeathuaa aeaenoaea i?e i?i/eo ?aaiuo oneiaeyo i?iii?oeeiiaeueii
yia?aee aeoeaiuo eo/ae,iaaeathueo ia ?ac?yaeaaioth iiaa?oiinoue.)

3)Iiae aeaenoaeai naaoa inaiaiaeaeaaony io?eoeaoaeueiua ca?yaeu.

aeieacaa /oi inaiaiaeaeaiiua naaoii io?eoeaoaeueiua ca?yaeu nooue
yeaeo?iiaie.

Oioiyeaeo?iiiay yienney iaoaeeia

Oioiyeaeo?iiiiie yienneae eee aiaoiei oioiyeaeo?e/aneei yoaeoii

iacuaaaony enioeaiey yeaeo?iiia iiaa?oiinoueth oaa?aeiai oaea iiae
aeaen-

aeai iaaeathuaai ia iaa yeaeo?iiaaieoiiai eceo/aiey.

Iniiaiuie caeiiaie oioiyooaeoa iiaeii n/eoaoue neaaeothuea

eioaineaiinoe naaoiaiai iioiea (,

( ) i?e oneiaee iaeciaiiinoe ni?aeo?aeueiiai

ninoaaa eceo/aiey (Caeii Noieaoiaa);

iaeanoe niaeo?a eceo/aiey

au?uaathuaai oioiyeaeo?iiu ec aeaiiai oioieaoiaea ; eeoue eceo/aiey n
aeeeiie

iiaoo au?uaaoue oioiyeaeo?iiu;

4) aacuia?oeeiiiinoue oioiyooaeoa. onoaiiaeaii, /oi oioioie iiyaeyaony e
en/acaao aianoa n inaauaieai, caiacaeuaay ia aieaa /ai

yeaeo?ii iiaea aeinoeaiooue iiaa?oiinoe iaoaeea e aueaoaoue ec
eaoiaea.

yeaeo?ii oianao n niaie eeiaoe/aneoth yia?aeth, ?aaioth

.

?aaiu ioetha o.a.

. (1)

, oi

(2)

ii?aaeaeyao iaeiaiueooth /anoioo oioiaeoeaiuo oioiiia (e?anioth
a?aieoeo oioiyooaeoa aeey aeaiiiai eaoiaea). O?aaiaiea (2) oaia?ue
iiaeii caienaoue a aeaea

. (3)

eaoiae-eieeaeoi?,i?e eioi?ie oioioie i?ae?auaaony . Aeaenoaeoaeueii (n
o/aoii eiioaeoiie ?aciinoe iioaioeeaeia )

neaaeiaaoaeueii,

ec niioiioaiey

eee

o.a.

(4)

Caeii Yeiooaeia eae iieacaea yenia?aiaioaeueiay i?iaa?ea, no?iai
auiieiyaony aeey ethauo

oioieaoiaeia, a oii /enea e aeey neiaeiuo ) Aeey iaoaeia caeii
Yeiooaeia aia?aua iiaeaa?aeee ia iiuoa ?.Ieeeeeai, ii iaeaieueoaa oi/iia
enneaaeiaaiea auei auiieiaii I.E.Eoee?neei e

N.N. I?eeaaeaaaui, eioi?ua i?eiaieee iaoiae oi?iicyuaai iiey iaaeaeo
noa?e/aneeie yeaeo?iaeaie, ?aiaa ?ac?aaioaiue I.E.Eoee?neei. Ionoue a
nenoaia aeaoo eiioeaio?e/aneeo noa?e/aneeo yeaeo?iaeia yieooa?ii neoaeeo
aiooa?iiyy noa?a ?anniio?ei yeaeo?ii,aueaoaaoee

, oiaiueoaaony, e a oi/ea i?eauoey A

(5)

, ?aaia

, (6)

aaea E—iieiay yia?aey yeaeo?iia. Oi?ioea aeaao /anoue iieiie yia?aee,
eioi?ay ia ecia?yaony

, e ecia?yaiay /anoue yia?aee ?aaia

, (7)

aoaeao iaeaieueoae aeey yeaeo?iiia, ia/aeueiay nei?inoue eioi?uo
iai?aaeaia ii eanaoaeueiie e iiaa?oiinoe yieooa?a.Aeey anao ae?oaeo
yeaeo?iiia ioeaea aoaeao aua iaiueoa. Oi?ioea (7) inoaaony aa?iie e
aeey nenoaiu, a eioi?ie aioo?aiiyy noa?a caiaiaia ianoa?e/aneei eaoiaeii
aeinoaoi/ii iaeiai ?acia?a.

Ia ?en. naa?oo ecia?aaeaia noaia iiuoia Eoee?neiai e I?eeaaeaaaa, a
aieco ia oii aea ?en. iieacaiu ?acoeueoaou ecia?aiey aieueo-aiia?iie
oa?aeoa?enoee aeey iaaee i?e o?ao aeeeiao aiei. Ec niaeo?aeueii
?aceiaeaiiiai iioiea eceo/aiey auaeaeythony iiiio?iiaoe/aneee io/ie
eo/ae, eioi?ue iai?aaeyaony ia aiooa?iithth noa?o. Oie (i/aiue neaaue)
ecia?yaony yeaeo?iia?ii. Oi?io ecia?aiiuo aieueo-aiia?iuo
oa?aeoa?enoee enoieeiaaoue iao?oaeii. Ai?eciioaeueiue o/anoie — yoi
oie ianuuaiey, oaeouee a onei?ythuai iiea. Ia ?en. ianooaa aua?ai oae,
/oi i?aeeiaoa, eca?aaeathuay oie ianuuaiey aeey anao aeeei aiei,
iaeeiaeiaa.A oi/ea, aaea ia/eiaaony iiieaeaiea e?eauo, i?ienoiaeeo
ia?aoiae io onei?ythuaai iiey e oi?iicyuaio, e a yoie oi/ea iai?yaeaiea
aaoa?ae eiiiaine?oao eiioaeoioth ?aciinoue iioaioeeaeeia e enoeiia
iai?yaeaiea

.

Aeey oi/ae ia?ana/aiey oa?aeoa?naee n inueth aanoeenn auiieiyaony
niioiioaiea

Oyi

aaea Ucai – aaee/eia caie?athuaai iai?yaeaiey e Oyi- ?aaioa auoiaea
yieooa?a.

y?a( nae, o.a. i?eainoiaeiia iiaeoaa?aeaeaiea caeiia Yeiooaeia.

aieueo-aiia?iay oa?aeoa?enoeea aeey Cu ?en
3.

/a?ac Uca , oi

Oyi,

(Oa-Oyi),

oi

Oa),

e iaeiii e oii aea iaoaeea eieeaeoi?a-aiiaea aieueo-aiia?iua
oa?aeoa?enoeee aeey ?acee/iuo iaoaeee/aneeo yieooa?ia ia/eiathony ec
iaeiie e oie aea oi/ee ia ine aanoeenn.

Aieueo-aiia?iay oa?aeoa?enoeea ia o/anoea oi?iicyuaai iiey i?aaenoaaeyao
niaie eioaa?aeueioth e?eaoth ?ani?aaeaeaiey yeaeo?iiia ii yia?aeyi.A
naiii aeaea, aanoeennu yoie e?eaie a iaeioi?ii ianooaaa ?aaiu yia?aeee
yeaeo?iia, a aiiaeiue oie, ioeiaeaiiue ii ine i?aeeiao:

,

aaea dNW -/enei yeaeo?iiia n yia?aeyie a eioa?aaea io W aei
W+dW.Aiiaeiue oie Ia, oaeei ia?acii, i?iii?oeeiiaeai /eneo yeaeo?iiia,
yia?aee eioi?uo i?aa?auatho aaee/eioW1=eUa. E?eaay, au?aaeathuay naycue
iaaeaeo yia?aeae W1 e /eneii /anoeoe, eiathueo yia?aeth, i?aauoathuoth
W1, iacuaaaony eioaa?aeueiie e?eaie ?ani?aaeaeaiey, *oiau iieo/eoue
iau/ioth e?eaoth ?ani?aaeaeaiey, ioaeii i?iaeeooa?aioee?iaaoue
a?aoe/anee eioaa?aeueioth e?eaoth ?ani?aaeaeaiey. Yoi naeaeaii ia ?en.

Eae aeaeii, iaeneiaeueiua yia?aee oioiyeaeo?iiia aeey iaoaeea, aeaaea
i?e inaauaiee oeueo?aoeieaoiaui naaoii, oieueei iaiiiai i?aauoatho 1ya,
a iaeaieaa aa?iyoiay yia?aey (iaeneioi e?eaie), a?oai aiai?y, aaeaia
iaiueoa.

*oanoaeoaeueiinoue oioieaoiaea iiaeii oaeaea au?aceoue a aeaea
ioiioaiey /enea yeieo?iiia na enioneaaiuo oioieaoiaeii ,e /eneo oioiiia
n ? ,oiaaoeo ia aai iiaa?oiinoue ca oi aea a?aiy .Aaee/eio n e(n ?
iacuaatho eaaioiaui auoiaeii ( ,o.a.

iacuaathony niaeo?aeueiuie oa?aeoa?enoeeaie oioieaoiaea .

I?aeoe/anee aeey oioiyeaiaoia aieueuee eioa?an i?aaenoaaeyao
iieiue oioioie ,aicieeathuee i?e inaauaiee nieioiui niaeo?ii ,
aeaaaaiui ?aneaeaiiui oaeii ,iaei?eia? , nie?aeueth eaiiu iaeaeeaaiey .
Oa?aeoa?enoeea oioieaoiaea a yoii neo/aa iacuaaaony eioaa?aeueiie
/oanoaeoaeueiinoueth e aeaaony iau/ii a iee?iaiia?ao ia ethiueai (iee(ei
-1) .Eioaa?aeueiay /oanoaeoaeueiinoue , i/aaeaeii ,ii?aaeaeyaony
niaeo?aeueiie oa?aeoa?enoeeie oioieaoiaea e niaeo?aeueiui ninoaaii
eceo/aiey.Iau/ii eioaa?aeueiay /oanoaeoaeueiinoue oioieaoiaea
ii?aaeaeyaony i?e eniieueciaaiee noaiaea?oiiai enoi/ieea iaeo/aiey
.Oaeei enoi/ieeii yaeyaony aieueo?aiiaay ieoue iaeaea eaiiu i?e
oaiia?aoo?a aa, ?aaiie 2770E (y?einoiay oaiia?aoo?a i?e yoii ?aaia
2848E ).

) ;

; ieiei e?aniie a?aieoeu ?ino oioioiea ii?aaeaeyaony caaeneiinoueth

i?eiyoi iacuaaoue ii?iaeueiie oa?aeoa?enoeeie, a oioiyooaeo a yoii
neo/aa (ii?iaeueiui.Anee aea niaeo?aeueiay oa?aeoa?enoeea eiaao
iaeneioi, oioiyooaeo iau/ii iacuaatho naeaeoeaiui.

ya ii?yaeea 10-2 – 10-1 ye/ea e, neaaeiaaoaeueii ,a (10(100) ?ac
i?aauoatho aaee/eiu ( a aeaeeiie e aeeaeiae oeueo?aoaieaoiaie iaeanoyo
niaeo?a. Iaeanoe aunieeo cia/aiee ( i?aaeoanoaoao neeueiue ?ino ( a
eioa?aaea h(((((((( ya.Niaeanii ia/aei yoiai ?inoa ( i?e h(((((((( ya
niaiaaeaao n iaeanoueth, a eioi?ie caiaoii oiaiueoaaony io?aaethuay
niiniaiinoue iaoaeeia e ia/eiaaony cia/eoaeueiue ?ino iiaeauaiey. Iinea
auno?iai ?inoa ( , eae i?aaeei, iaaethaeaaony aeiaieueii iieiaee
iaeneioi, iinea eioi?iai neaaeoao niaae e?eaie (( h(( ; a iniaaiiinoe
io/aoeeai yoio iaeneioi iaia?oaeeaaaony aeey oioiyooaeoa n
ieaiie.Ia/aei niaaea ( niaiaaeaao i?eia?ii n iaeanoueth, aaea
iiaeiuaiea ia/eiaao oiaiueoaoueny e nouanoaaiii aic?anoaao
niiniaiinoue iaoaeeia i?iioneaoue eceo/aiea.

Aeey i?eia?a ia ?en. i?eaaaeaiu caaeneiinoe eaaioiaiai auoiaea ( ,
eiyooeoeeaioa io?aaeaiey R eeiyooeoeeaioa i?iioneaiey T eceo/aiey io
yia?aee iaaeathueo eaaioia aeey Al . A iaeanoe aaeooiiiai oeo?aoaieaoa
eaaioiaue auoiae cia/eoaeueii iaiaa /oanoaeoaeai e ninoiyieth
iiaa?oiinoe , /ai a iaeanoe , i?eeaaathuae e e?aniie a?aieoea .I?ia?aa
iaoaeeia iau/ii oiaiueoaao Y eeoue i?eia?ii a 10 ?ac. ieaiee ,iaiueaiiua
a ecia?eoaeueiii i?eai?a , a aieueoeinoaa neo/aaa oa?aeoa?ecothony a
1,5(2 ?aca aieaa ieceeie cia/aieyie Y , /ai ieaiee oao aea iaoaeeia
, iiauaaaoea a aoiinoa?a.Oae aea eae e a aeeeiiiaieiiaie iaeanoe ,
eiaaony ?aca?in (i?eia?ii a i?aaeaeao iaeiiai ii?yaeea ) a cia/aieyo Y,
ecia?aiiuo ?aciuie aaoi?aie.

Oeaeue ?yae enneaaeiaaiee iinayuai auyniaieth aeeyiey oaiia?aoo?u
eaoiaea ia oioioie. Ia?aiia/aeueiua iiuou ni niaeo?aeueii
ia?aceiaeaiiui naaoii aeaaaee iayniua ?acoeueoaou e a iauai
onoaiaaeeaaee neaaoth caaeneiinoue io io O,anee eciaiaiea oaiia?aoo?u ia
aucaaei eciaiaiey ninoiyiey iiaa?oiinoe, aa?aaaoiiai ninoiyiey eee
oaciauo i?aa?auaiee. Eco/aiea oioiyooaeoaa aucuaaaiiai iiiio?iiaoe/aneei
naaoii,ia niiiaiii,onoaiiaeei oaiia?aoo?iue yooaeo.I?eo yoii oioioie io
neaai iaiyaony n O aeey ( ( (i e ?acei aic?inoaao n iiauoaieai
oaiia?aoo?u i?e (~(o(e a iniaaiiinoe aeey (((o). I?eia?ii iiaoo
neoaeeoue aeaiiua aeey ?d ,i?eaaaeaiiua ia ?en.

?en

Ii aaaeaieaoiea auei oaeiai eae aoaeoi (o oiaiueoaeinue n ?inoii
oaiia?aoo?u.Yooaeoeaiay e?aniay a?aieoea niauaeanue a iaeanoue iaiueoeo
( n ?inoii O , e aeae niaeo?aeueiie oa?aeoa?enoeee a iaeanoe (((o
nooanoaaiii iaiyeny ; e?eaay io((( a yoie iaeanoe niaeo?a aeaeaeanue
iieiaea e ii?aaeaeaiea (i noaiiaeeanue aanueia ia ii?aaeaeaiiui .

Oeaiioth eioi?iaoeeth i iaoaiecia oioiyooaeoa iiaoo aeaoue ?acoeoaou
enneaaeiaaiee ii yia?aaoe/aneei ?ani?aaeaeaieyi oioiyeaeo?iiia. Yoe
enneaaeiaaiey i?iaiaeeeenue eeai iaoiaeii ioeeiiaiey a iaaieoiii iiea,
eeai iaoiaeii caaea?aeeaathuaai iioaioeeaea.Eae iieacaee aua ?aiiea
eneaaeiaaiey a aeaeeiie e aeeaeiae oeueo?aoeieaoiaie iaeanoyo niaeo?a ,
eia?aaoe/aneee niaeo? oioiyeaeo?iiia yieooe?iaaiuo ianneaiuie iaoaeeaie
iai?a?uaai e caieiaao iaeanoue io ioey aei iaeo?iai iaeneiaeueiiai
cia/aiey Aiao , ii?aaeaeyaiiai niioiioaieai Yiooaeia. Auei iieacaii ,
/oi i?e h( , aeeceeo e h(o , yia?aaoe/aneee niaeo? oioiyeaeo?iiia neaai
caaeneo io i?e?iaeu iaoaeea. Ii ecia?aaeaaony ieaaiie e?eaie n
iaeneioiii ?en.C ?inoii h( iinoaiaiii oaaee/eaaaony ioiineoaeueiia
/enei iaaeeaiiuo yeaeo?iiia, ii iauee oa?aeoa? e?eaie nio?aiyaony

(ni. ?en. E?eaua 1,2 e 3).

?en

Ia/eiay n iaeioi?iai cia/aiey h(, oa?aeoa? e?eauo ?ani?aaeaeaiey
oneiaeiyaony , cia/eoaeueii aic?anoaao ioiineoaeueiay aeiey iaaeeaiiuo
yeaeo?iiia e nouanoaeiii oiaiueoaaony eiee/anoai oioiyeaeo?iiia n
yia?aeyie e aeeceeie e iei. Aeey E, iai?eia? , oaeia eciaiaiea
yia?aaoe/aneiai niaeo?a ii iaaethaeaaony i?e h( ~ – E1 . Iiyaeaiea
aieueoiai ioiineoaeueiiai eiee/anoai iaaeeaiuo yeaeo?iiia a niaeo?a
oioiyeaeo?iiia i?e aeinoaoi/ii aieueoeo h( iauyyniyaony iau/ii
ianeieueeeie aiciiaeiuie i?e/eiaie:

1) Aieueoeie iioa?yie yia?aee, naycaiiuie n aicaoaeaeaieai
oioiyeaeo?iiaie i?e eo aeaeaeaiee e iiaa?oiinoe ieaciaiuo eieaaaiee

2) Iioa?yie yia?aee i?e acaeiiaeaenoaee n yeaeo?iiaie i?iaiaeeiinoe ,
i?aa?auathueie auno?ua aiooaiiee ia?ae/iua oioiyeaeo?iiu a iaaeeaiiua ;
iaeioi?ua ec aicaoaeaeaiiuo yeaeo?iiia i?iaiaeeiinoe oaeaea i?eieiaoue
o/anoea a oioiyiennee a ea/anoaa iaaeeaiiuo oioiyeaeo?iiia; oaeei
ia?acii, i?e yoii iaoaiecia iaeei iiaeiuaiiue oioii aeinoaoi/iie
yia?aee iiaeao niinianoaiaaoue aicieeiiaaieth aeaoo iaaeeaiiuo
oioiyeaeo?iiia;

3) Iaeia?aiaiiii aicaoaeaeaieai i?e iiaeiuaiee iaeiiai eaaioa eceo/aiey
aeaoo yeaeo?iiia; a yoii neo/aa, eae e a i?aaeuaeouai, iaeioi?ua ec
oioiiia aeinoaoi/iie yia?aee iiaoo nicaeaaaoue aeaa
oioiyeaeo?iia.Yia?aeoe/aneee niaeo? oioiyeaeo?iiia ii aeaiiui
iiaeoaa?aeaeaiiui a iineaaeiea aiaeu a ?aaioa, oaeaea nouanoaaiii
iaiyaony i?e ia?aoiaea e i/aiue oiiueeei iaoaeee/aneei ieaieai. Oae,
niaeanii i?e h(=3,38 ya yia?aeoa/aneee niaeo? yeaeo?iiia aeey ieaiee
oieueiie a 8 aoiiiuo neiaa caiaoii ioee/aaony io oaeiaiai aeey ieaiee
oieueiie 40 aoiiiuo neiaa ?en.

?en

Aeey oiieeo ieaiie eiee/anoai iaaeeaiiuo yeaeo?iiia oiaiueoaaony e
aic?anoaao /enei yeaeo?iiia n yia?aeyie, aeeceeie e iaeneiaeueiie, oae
eae iioa?e yia?aee, i?eaiaeyuea e i?aa?auaieth auno?uo oioiyeaeo?iiia a
iaaeeaiiua,ia aieaa ei?ioeii iooe e iiaa?oiinoe a oiieii oiioeaoiaea
oiaiueoaathony .

Aii?inu i aeaea niaeo?aeueiuo oa?aeoa?enoee oioieaoiaeia , i
?ani?aaeaeaiee oioiyeaeo?iiia ii yia?aeyi e i oaiia?aoo?iie caaeneiinoe
oioioiea eaaeao aia ?aiie ia?aiia/aeueiie oai?ee Yeiooaeia .
?anniio?aiea eo o?aaoao ooi/iaiey oai?ee oioiyooaeoa . ?aoaiea caaea/e
iino?iaiey oaeie aeaoaeueiie oai?ee i?eioeeieaeueii aeieaeii auei au
aanoenue ii neaaeothuaio ieaio : i?aaeaea anaai neaaeoao auynieoue i?e
aeaiiie oaiia?aoo?a O ?ani?aaeaeaiea yeaeo?iiia a iaoaeea ii ?acee/iui
ninoiyieyi ; aeaeaa , auynieoue aa?iyoiinoue iiaeauaiey yeaeo?iiii ,
iaoiaeyoeiny a iaeioi?ii ninoiyiee , oioiia /anoiou ( e ii?aaeaeeoue
ninoiyiea, a eioi?ia yeaeo?ii i?e yoii ia?aoiaeeo. Caoai o?aaoaony iaeoe
ooieoeeth ?ani?aaeaeaiey aicaoaeaeaiiuo yeaeo?iiia ii ninoiyieyi. Aeaeaa
neaaeoao ii?aaeaeeoue aeey yeaeo?iiia, aicaoaeaeaiiuo a aeoaeia
iaoaeea,aa?iyoiinoe i?ioiaeaeaiey eie iooe io ianoa aicaoaeaeaiey aei
iiaa?oiinoe, a oaeaea iioa?e yia?aee ia yoii iooe.Caoai iaaei iaeoe
au?aaeaiea aeey iioiea yeaeo?iiia n aeaiiie yia?aeae , iaaeathueo ia
iioaioeeaeueiue ii?ia ia a?aieoea iaoaeea, e ii?aaeaeeoue aa?iyoiinoue
i?ioiaeaeaiey eie /a?ac yoio ii?ia.Iaeiiaoe,iiiiiaeea /enei yeaeo?iiia n
caaeaiiie yia?aeae,iaaeathueo ecioo?e ia 1ni2 iiaa?oiinoe oioieaoiaea ca
1 nae, ia aa?iyoiinoue auoiaea, iiaeii iaeoe aeey aeaiiie /anoiou
oioiyeaeo?iiia n caaeaiiie yia?aeae aia iaoaeea (e?eaoth ?ani?aaeaeaiey
oioiyeaeo?iiia ii yia?aeyi ). A caeeth/aiea,eioaa?e?oy ii anai
yia?aeyi,eiaeii iaeoe iieiue oioioie eae ooieoeeth O e ( (niaeo?aeueiua
oa?aeoa?enoeee aeey ?acee/iuo O ).

?aaioa auoiaea

Iiiyoea ?aaiou auoiaea eae ia?u yia?aee nayce yeaeo?iiia n oaa?aeui
oaeii aicieeei oaea ia ?aiieo noaaeey ?acaeoey yeaeo?iiii oai?ee
iaoaeeia .Aeey iauyniaiey nouanoaiaaiey yeaeo?iiiiai aaca aioo?e iaoaeea
iaiaoiaeeii auei aeiionoeoue iaee/ea o a?aieoe iaoaeea iaeiaai iiey nee
f(x), iai?aaeaiiuo aioo?ue iaoaeea e i?aiyonoaothueo aueaoo naiaiaeiuo
aeaeo?iiia ai aiaoiaa i?ino?ainoai . I?e oaeaeaiey yeaeo?iia ec iaoaeea
niaa?oaaony ?aaioa i?ioea yoeo nee ( ?aaioa auoiaea :

(1)

Oaeei ia?acii , a eeane/aneie oai?ee iaoaeeia ?aaioa auoiaea ?aaiyeinue
nea/eo iioaioeeaeueiie yia?aee yeaeo?iia ia a?aieoea iaoaeea .

A ciiia?oaeueaeianeie iiaeaee iaoaeea iiiyoea ?aaiou
auoiaea ianeieueei oneiaeieeinue . Eioaa?ae au?aaeaiey (1) ii?aaeaeye
oae iacuaaaioth aiaoithth ?aaioo auoiaea Wa , ?aaioth iieiie aeoaeia
iioaioeeaeueiiai yueea iaoaeea . Iaeiaei aeaaea i?e oaiia?aoo?a
yeaeo?iiiiai aaca O=0 ,a ioee/ea io eeanne/aneie oai?ee , n/eoaeinue
/oi ia ana yeaeo?iiu iaeaaeaee eeiaoe/aneie yia?aeae , ?aaiie ioeth , ii
?ani?aaeaeyeenue ii yia?aeyi io ioey aei iaeioi?ie iaeneiaeueiie Wi
?aaiie a?aieoea ?ani?aaeaeaiey Oa?ie . Iiyoiio iaeiaiueoay yia?aey,
eioi?oth iaiaoiaeeii niiaoeoue iaeiiio ec yeaeo?iiia a i?iaiaeeiinoe i?e
O=0 aeey oaeaeaiey aai ec iaoaeea , ieacaeinue ?aaiie

(=Wa(Wi (2)

Anee yia?aeth iieiyuaainy yeaeo?iiia aia iaoaeea iieiaeeoue ?aaiie ioeth
, oi

(3)

o.a. ?aaioa auoiaea ?aaia acyoie n ia?aoiui ciaeii iieiie yia?aee
aa?oiaai yeaeo?iiiiai o?iaiy E max a iaoaeea, caiyoiai yeaeo?iiii i?e
oaiia?aoo?a yeaeo?iiiiai aaca O=0 ; a naith i/a?aaeue o?iaaiue E max
?aaai o?iaith yeaeo?ioeie/aneiai iioaioeeaea Eo yeaeo?iiiiai aaca .
Iaeiaei e yoi ii?aaeaeaia ?aaiou auoiaea ia aiieia oaeiaeaoai?eoaeueii.
?aaeueiue iaoaee ia i?aaenoaaeyao niaie iioaioeeaeueiiai yueea n
aeaaeeei aeiii, o.a.U(const= -Wa , ii aioo?e iaoaeea iioaioeeae iiey,a
eioi?ii iaoiaeeony eaaeaeue yeaeo?ii,anoue ia?eiaee/aneay ooieoeey
eii?aeeiao, ii?aaeaeyiay no?oeoo?ie ?aoaoee, a oaeaea ninoiyieai anao
inoaeueiuo yeaeo?iiia. Iiaeii aeaoue neaaeothuaa ii?aaeaeaiea yia?aee
nayce yeaeo?iia a oaa?aeii oaea, a /anoiinoe, a iaoaeea, ia caaenyuaa io
eiie?aoiie iiaeaee yoiai oaea. Nai oaeo noaoeeiia?iiai nouanoaiaaiey
yeaeo?iiia aioo?e iaai naeaeaoeuenoaoao, /oi nenoaia ec N p eiiia e N
e=N p yeaeo?iiia aioo?e iaoaeea, iaoiaeyueony a ?aaiiaanee i?e
oaiia?aoo?a O=0 , iaeaaeaao iaiueoae yia?aeae,/ai oa aea N p eiiia n
Ne’= N e – n yeaeo?iiaie i?e oie aea oaiia?aoo?a oaeaea a ninoiyiee
?aaiiaaney.Iaicia/ay yia?aeth ia?aie nenoaiu /a?ac E(Np,Ne) , a
aoi?ie-/a?ac E (Np , Ne), iiaeii caienaoue eciaiaiea yia?aee i?e
oaeaeaiee iaeiiai yeae?iia, o.a. ?aaioo auoiaea i?e O=0 , a neaaeothuai
aeaea :

. (4)

Yoi ii?aaeaeaiea ?aaiou auoiaea aiaeiae/ii ii?aaeaeaieth ?aaiou
eiiecaoeee iaeo?aeueiiai ia aicaoaeaeaiiiai aoiia. I?e T>0 ii?aaeaeaiea
(4) aeaeaaony iaiaeiicia/iui.

?ani?aaeaeaiea yeaeo?iiia ii yia?aeyi a oaa?aeii

oaea(iaoaeeu).

oa?aeoa?ecothuay yoi ?ani?aaeaeaiea, ii?aaeaeyaony, ai-ia?auo,
aa?iyoiinoueth ((E) caiieiaiey eaaioiaiai ninoiyiey n yia?aeae A
yeaeo?iiii:

(1)

(oa?ieiiu ), a /anoiinoe aeey yeaeo?iiia , ec yoiai i?eioeeia auoaeaao
i?eioeei Iaoee. I?e oaiia?aoo?a O=0 ?aaiiaaniui ?ani?aaeaeaieai ethauo
/anoeoe ?ani?aaeaeaiea, niioaaonoaothuaa ieieioio iieiie yia?aee. Aeey
oa?ieiiia yoi oneiaea aoaeao auiieiaii, anee eie aoaeoo caiyou eaaioiaua
ninoiyiey, niioaaonoaothuea naiui iecei yia?aaoe/aneei o?iaiyi; /enei
yoeo ninoiyiee Z , i/aaeaeii , ?aaii N . I?e T >0 ?aaiiaaniia ninoiyiea
niioaaonoaoao ieieioio naiaiaeiie yia?aee.Aeey nenoaiu oa?ieiia yoi
oneiaea oaeiaeaoai?yaony, anee aa?iyoiinoue ((E) ?aaia

, (2)

aaea E0 ( oae iacuaaaiue yeaeo?ioeie/aneee iioaioeeae nenoaiu (/anoi aai
iacuaatho oaeaea o?iaiai yeaeo?ioeie/aneiai iioaioeeaea eee o?iaiai
Oa?ie). Baee/eia E0 aeey nenoaiu yeaeo?iiia a iaeioi?ii oaea, acyoay n
ia?aoiii ciaeii , iacuaaaony oaeaea ?aaioie auoiaea yoiai oaea e
iaicia/aaony /a?ac ( eee e(, o. a. (E0=(=e(. Oi?ioeo (2) i?eiyoi
iacuaaoue oi?ioeo Oa?ie. Ec (1) , o/eouaay (2) , iieo/ei

(3)

Yeaeo?ioeie/aneiai iioaioeeaea E0 au/eneyaony ec oneiaey ii?ie?iaee:

aaea N( iieiia /enei yeaeo?iiia nenoaiu .

Naeaeoeaiue oioiyooaeo

(.

.Yoa caaeneiinoue oioiyooaeoa iacuaaaony iiey?ecaoeeiiiie
naeaeoeaiinoueth eee aaeoi?eaeueiui yooaeoii.

Ia ?en. iieacaiu

Caaeneiinoue oioiyooaeoa io aeeeiu aieiu yeaeo?e/aneiai aaeoi?a

eieaaeauaainy a ieineinoe iaaeaiey

Caaeneiinoue oioiyooaeoa io aeeeiu yeaeo?e/aneiai aaeoi?a

eieaaeauaainy a ieineinoe ia?aeeaeueiie ieineinoe iaaeaiey

?en

a yoii neia(a ia iioieo,iaaeaauaio iaiiaa?oiinoue).Anoanoaaiii
iiyoiio, /oi eeoue naaoiaia iiea a yoii oiieii iiaa?oiinoiii neia e
ii?aaeaeyao neeo oioioiea.

eaaioiiaoaie/aneay oai?ey oioiyooaeoa

Iniiau eaaioiiaoaie/aneie oai?ee oioiaeaeo?iiiie yiennee iaoaeeia auee
nicaeaiu E. A. Oaiiii e N. I. Ooaeiui e aiineaaenoaee ooi/iaiu e
aeiiieiaiu Ieo/aeii e ae?oaeie enneaaeiaaoaeyie . Ia enoiaeiuo
iieiaeaieyo oai?ee Oaiia-Ooaeia-Ieo/aea e aa ?acoeueoaoao iu caeanue
neaaeai oieueei i/aiue iaiiiai .

I?e iino?iaiee oai?ee i?aaeaea anaai iaaei auei auynieoue , eaeei
ia?acii naiaiaeiua yeaeo?iiu iaoaeea iiaoo iiaeauaoue oioiiu. Aeaei a
oii , /oi niaa?oaiii ia naycaiiue yeaeo?ii ia iiaeao oeaeeeii
iiaeioeoue oioii , oae eae i?e yoii iaeuecy iaeiia?aiaiii
oaeiaeaoai?eoue caeiiai nio?aiaiey yia?aee e nio?aiaiey eiioeuena .

Iai?eia? , aeey iaeaieaa i?inoiai no/ay iiaeiuaiey oioiia iieiyueiny
yeaeo?iiii yoe aeaa caeiia iiaeii caienaoue oae

aaea v ( nei?inoue yeaeo?iia iinea aeoa iiaeauaiey. Ii yoe aeaa
o?aaiaiey ianiaianoeiu i?e ethauo v

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