Методи та засоби перетворення однократних часових інтервалів в системах вимірювання та керування: Автореф. дис… канд. техн. наук / О.Й. Кадацька, Ха

OA?UeE?ANUeEEE AeA?AEAAIEE OAOI?*IEE OI?AA?NEOAO ?AAe?IAEAEO?II?EE

Eaaeaoeueea Ieueaa Einei?aia

OAeE 681.325.023: 621.317.725.2

IAOIAeE OA CANIAE IA?AOAI?AIIss IAeIIE?AOIEO *ANIAEO ?IOA?AAE?A A
NENOAIAO AEI??THAAIIss OA EA?OAAIIss

Niaoe?aeuei?noue 05.13.05 – aeaiaioe oa i?eno?i? ia/enethaaeueii?

oaoi?ee oa nenoai ea?oaaiiy

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaith

eaiaeeaeaoa oaoi?/ieo iaoe

Oa?e?a 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia o Oa?e?anueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoao?
?aae?iaeaeo?ii?ee I?i?noa?noaa ina?oe Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?, ?oaeaiei
Ieaa A?eai?iae/,

Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?aae?iaeaeo?iieee,

caa?aeoaa/ eaoaae?e aeaeo?iiieo
ia/enethaaeueieo iaoei

Io?oe?ei? iiiiaioe: aeieoi? oaoi?/ieo iaoe, n.i.n., Aeieo???iei
Aaea??e Aeieo?iae/,

Oa?e?anueeee aea?aeaaiee iie?oaoi?/iee oi?aa?neoao, i?ioani?

eaoaae?e ia/enethaaeueii? oaoi?ee ? i?ia?aioaaiiy

aeieoi? oaoi?/ieo iaoe, i?ioani?, Ai?enaiei Ieaen?e Aiae??eiae/,

Noinueeee aea?aeaaiee oi?aa?neoao, caa?aeoaa/ eaoaae?e aoiiaoeee

? i?iieneiai? aeaeo?ii?ee

I?ia?aeia onoaiiaa: iaoeiai-ae?iaie/a ia’?aeiaiiy «Oa?o?ii»
I?i?noa?noaa i?iieneiai? iie?oeee Oe?a?ie, i. Oa?e?a.

Caoeno a?aeaoaeaoueny 7 aeiaoiy 1999 ?. i 14.30 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.050.07 o Oa?e?anueeiio aea?aeaaiiio
iie?oaoi?/iiio oi?aa?neoao?, ca aae?anith: 310002, i. Oa?e?a-2, aoe.
O?oica, 21.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? Oa?e?anueeiai
aea?aeaaiiai iie?oaoi?/iiai oi?aa?neoaoo.

Aaoi?aoa?ao ?ic?neaiee «30» na?iiy1999 ?.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeinyaiaiiy no/anii? ia/enethaaeueii? oaoi?ee
a?aee?eaathoue iia? iiaeeeaino? eiio?ieth ? ea?oaaiiy a aaaaoueio
aaeocyo ethaenueei? ae?yeueiino?. Ai?iaaaeaeaiiy AII a nenoaie ea?oaaiiy
iaiiaeeeai aac aeei?enoaiiy ia?aoai?thaa/?a aacia?a?aieo aaee/ei naiiai
oe?ieiai eeano. Aeniea oi/i?noue ooieoe?iioaaiiy ia’?eo?a ea?oaaiiy ?
?oiy iaae?ei?noue caaacia/othoueny ca oiiae io?eiaiiy a??ia?aeieo ?
oi/ieo ciaiue ?oi?o iaeaaaeeea?oeo oa?aeoa?enoee, o oiio /ene? ?
/aniaeo.

I?e ??oaii? iaoeiai-oaoi?/ieo i?iaeai, ui aeieeathoue o aaaaoueio
i?e?iaeie/eo ? oaoi?/ieo iaoeao, c’yaeythoueny caaea/? aenieioi/iiai
aei??thaaiiy ?ioa?aae?a /ano c o?aooaaiiyi ?aaeueieo oa?aeoa?enoee
aeine?aeaeoaaieo yaeu, i?ioean?a, ia’?eo?a. Oaeee i?ioean iiaea
oa?aeoa?ecoaaoeny aeieeiaiiyi iaeiie?aoiiai /aniaiai ?ioa?aaeo o ca’yceo
c iaiiaeeea?noth aai aenieith aa?o?noth eiai iiaoi?aiiy.

I?aoeec?eia ia?aoai?aiiy aacia?a?aii? /aniai? ?ioi?iaoe?? a oeeo?iaee
aea?aaeaio aecia/a? iio?aao a ?ic?iaoe? aiaeiai-oeeo?iaeo
ia?aoai?thaa/?a, caniiaaieo ia aenieioi/ieo iaoiaeao aei??o. Aeniea
oi/i?noue ia?aoai?aiiy io?eiaia aeey ia?aoai?thaa/?a ia??iaee/ieo
/aniaeo ?ioa?aae?a o eiae, iiaoaeiaaieo ca iaoiaeii ca?ao. ?icaeoeii
cacia/aiiai iaoiaeo ? iaoiae ca?ao ?iioeuen?a iaeaoaie. I?e aei??thaaii?
aeinoaoiuei i?ioyaeiiai ?ioa?aaeo caa??aa?oueny cia/ei?noue iaoiaeo
i?yiiai i?ae?aooieo ? a iei?oi?e /an, oea iaoiiaeaia ?icaeoeii iiaeo
oaoiieia?e ? iiyaith aeniei/anoioieo na??e aeaiaio?a. Aeey ei?ioeeo
iaeiie?aoieo /aniaeo ?ioa?aae?a canoiniaothoueny ??ciiiai?oi? iaoiaee
ianooaaii–/aniaiai ia?aoai?aiiy, o oiio /ene? iii?oniee, iaoiaee
/an-aiie?ooaeiiai ia?aoai?aiiy, ye? iathoue iaiaaeaiiy ii oi/iino?,
aeeiai?/iiio ae?aiaciio. O ca’yceo c oeei, aeooaeueiith caaea/ath ?
?ic?iaea ? aeine?aeaeaiiy iiaeo iaoiae?a ia?aoai?aiiy iaeiie?aoieo
/aniaeo ?ioa?aae?a o oeeo?iaee aea?aaeaio, ye? iathoue iaeo iioeaeo
ia?aoai?aiiy ? ii?aeiothoue ia?aaaae oeeo?iai? ia?iaee ?ioi?iaoe?? oa
i?inoioo oaoi?/ii? ?aae?caoe??.

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

Aeine?aeaeaiiy ? ?ic?iaee i?iaiaeeeenue a?aeiia?aeii oaiaoe/iiio ieaio
iaoeiai-aeine?aeieo ?ia?o OOO?A ia 1992-1998?., caoaa?aeaeaiiio
I?i?noa?noaii ina?oe Oe?a?ie, o ?aieao aea?aeathaeaeaoieo oai
«Aeine?aeaeaiiy ? ?ic?iaea ia?niaeoeaieo cania?a i?iaeooaaiiy
aeaeo?iiieo nenoai ? ?o canoinoaaiiy a iaa/aeueiiio i?ioean? a
eiii’thoa?i?e ?iaeaia???» (?453-2), «?ic?iaea nenoaie iiaeaethaaiiy
cania?a ia/enethaaeueii? oaoi?ee» (?279-1), «Iia? a?oeoaeoo?i? i?eioeeie
iiaoaeiae nenoai ia?iaee a?aeaicia?aaeaiue a ?aaeueiiio ianooaa? /ano»
(?462-1) oa i?e ?ic?iaoe? oaie «Noai?aiiy iacaiii? eini?/ii? ia?aae?
?aae?ioaeaneii?a aeey aeine?aeaeaiiy ia’?eo?a aeaeueiueiai einiino» ii
aea?aeeiio?aeoo ? 2.2.1-98 «?ioa?oa?iiao?» i?ae Eini?/iei aaainoaii
Oe?a?ie oa ?aae?iano?iiii?/iei ?inoeoooii IAI Oe?a?ie.

Iaoa oa caaea/? aeine?aeaeaiiy. Iaoith ?iaioe ? noai?aiiy iaoiae?a oa
no?oeoo? aiaeiai-oeeo?iaiai ia?aoai?aiiy iaeiie?aoieo /aniaeo ?ioa?aae?a
? o?eaaeino? iaeeii/ieo ?iioeuen?a ?c aeei?enoaiiyi iaoiaeo ca?ao
?iioeuen?a iaeaoaie ? i?ecia/aieo aeey aeei?enoaiiy a nenoaiao
aeeaeiuei? aeaeueiiiao??? oa ?ioeo nenoaiao.

Aeey aeinyaiaiiy iinoaaeaii? iaoe iaiao?aeii ae??oeoe oae? caaea/?:

— i?aeaeuaiiy ?icae?ethaaeueii? ni?iiiaeiino? ? oi/iino?
ia?aoai?thaa/?a iaeiie?aoieo /aniaeo ?ioa?aae?a o oe?ieiio aeeiai?/iiio
ae?aiacii? aeey nenoai ea?oaaiiy ? aei??thaaiiy;

— ?ic?iaea ? aeine?aeaeaiiy iaoiaeo ia?aeaeueiiai ina?aaeiaiiy c
aeei?enoaiiyi ??cieoeaai-ia??iaeiiai eaaioo;

— aeine?aeaeaiiy iiaeeeainoae oaeineiiaeaiiy iii?onieo ia?aoai?thaa/?a;

— ?ic?iaea ? aeine?aeaeaiiy iii?oniiai iaoiaeo c aeei?enoaiiyi iaeaoiiai
ca?ao ?iioeuen?a;

— ?ic?iaea ? aeine?aeaeaiiy iaoiaeo ? oaoi?/ieo cania?a ia?aoai?aiiy
o?eaaeino? iaeeii/iiai ?iioeueno a eiae;

— aecia/aiiy iniiaieo aeanoaa?e?coth/eo /eiiee?a cai?iiiiiaaieo
iaoiae?a ? aeine?aeaeaiiy iioeaie ia?aoai?aiiy, iaoiiaeaieo oeeie
/eiieeaie;

— ?ic?iaea oaoi?/ieo cania?a, ye? ?aae?cothoue cai?iiiiiaai? iaoiaee
ia?aoai?aiiy.

Iaoiaee aeine?aeaeaiiy caniiaai? ia caniaao oai??? eiia??iinoae ?
iaoaiaoe/ii? noaoenoeee, ?ioi?iaoe?eii? oai??? aei???a, niaeo?aeueiiai
aiae?co, oai?aoe/ieo iniia ?ioi?iaoe?eii-aei??thaaeueii? oaoi?ee. Aeey
aeine?aeaeaiiy i?ioeano ooai?aiiy ??cieoeaai-ia??iaeii? i??e
canoiniaoaaeeny iaoiaee oai??? ca?a?a ?iioeuenieo iioie?a.

Iaoeiaa iiaecia aeena?oaoe?eii? ?iaioe iieyaa? a ianooiiiio:

— i?iaaaeaii aiae?c i?eaeaoiino? iaoiaeo ca?ao ?aaoey?ieo ?iioeuenieo
iioie?a ? iaa?oioiaaia aeioe?euei?noue canoinoaaiiy iaoiaeo ca?ao
?iioeuen?a iaeaoaie aeey aei??thaaiiy iaeiie?aoieo /aniaeo ?ioa?aae?a a
i?aoeec?eieo aei??ieeao, ye? iiaeooue aooe aeei?enoai? a nenoaiao
aeeaeiuei? aeaeueiiiao??? aeey ea?oaaiiy i?inoi?iaei iieiaeaiiyi
ia`?eo?a;

— ?ic?iaeaii iaoiae ia?aeaeueiiai ina?aaeiaiiy aeey aei??o /aniaiai
?ioa?aaeo c aeei?enoaiiyi ??cieoeaai-ia??iaeiiai eaaioo, io?eiaia
iaoaiaoe/ia iiaeaeue iaoiaeo ? aeai?eoi eiai ?aae?caoe??;

— ?ic?iaeaii iii?oniee iaoiae ia?aoai?aiiy /aniaeo ?ioa?aae?a ia iniia?
iaeaoiiai ca?ao ?iioeuen?a, io?eiaia a?aeiia?aeia ??aiyiiy ia?aoai?aiiy;

— cai?iiiiiaaii niin?a aei??thaaiiy o?eaaeino? iaeeii/iiai ?iioeueno,
io?eiaii aiae?oe/iee ae?ac, ui iieno? i?ioean ia?aoai?aiiy, iieacaii
aeei?enoaiiy oaeeo ia?aoai?thaa/?a a nenoaiao aei??thaaiiy eii?aeeiao
ia(?eo?a. Iiaecia niiniao i?aeoaa?aeaeaia iaoaioii ?in?enueei?
Oaaea?aoe??;

— ?ic?iaeaii oaoi?/i? caniae, ye? ?aae?cothoue cai?iiiiiaai? iaoiaee
ia?aoai?aiiy /aniaeo ?ioa?aae?a, iiaecia oaoi?/ieo ??oaiue
i?aeoaa?aeaeaia aaoi?nueeeie na?aeioeoaaie ia aeiao?ae.

I?aeoe/ia oe?ii?noue ?iaioe iieyaa? a oiio, ui cai?iiiiiaai? iaoiaee
aeicaieythoue cae?enithaaoe ia?aoai?aiiy iaeiie?aoieo /aniaeo ?ioa?aae?a
c aenieith oi/i?noth, ui aeinyaa? aaee/ei ii?yaeeo iaeeieoeue
i?einaeoiae. ?ic?iaeaii noaie i?eno?i?a, ye? ?aae?cothoue aeai? iaoiaee,
aeey canoinoaaiiy a i?aoeec?eieo aei??ieeao /aniaeo eioa?aae?a oa ?o
aeei?enoaiiy i?e noai?aii? nenoai aaoiiaoe/iiai ea?oaaiiy i?inoi?iaei
i?noeaciaoiaeaeaiiyi ia(?eo?a. Niin?a ? oaoi?/i? ??oaiiy, ?aae?ciaai? o
ia?aoai?thaa/? o?eaaeino? iaeeii/ieo ?iioeuen?a, aoee aeei?enoai? i?e
noai?aii? iacaiii? eini?/ii? ia?aae? aeey aei??thaaiiy eii?aeeiao
eini?/ieo ooo/ieo o?e o ?aae?iano?iiii?/iiio ?inoeooo? IAI Oe?a?ie.
Iaoeia? iieiaeaiiy, aeniiaee ? ?aeiiaiaeaoe??, aeeeaaeai? a
aeena?oaoe??, aoee aeei?enoai? i?e i?aeaioiaoe? eo?n?a “Ia?eoa??ei?
i?eno?i? AII, ia?aae ? nenoai”, ”Nenoaie oeeo?iai? ia?iaee ?ioi?iaoe??”
ia eaoaae?? AII Oa?e?anueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo
?aae?iaeaeo?ii?ee.

iaoiaeo ia?aoai?thaaiiy /aniaeo ?ioa?aae?a. ?iaioe [2-4] iaienai?
iniaenoi aaoi?ii. A ?iaio? [5] aaoi?ii cai?iiiiiaaii niin?a ia?aoai?aiiy
o?eaaeino? iaeeii/iiai ?iioeueno a oeeo?iaee aea?aaeaio, ??aiyiiy
ia?aoai?aiiy, ?ic?iaea i?ioeano ia?aoai?aiiy. A ?iaioao [6,7] aaoi?ii
?ic?iaeaii noaii? ?aae?caoe?? ia?aeaeueiiai ina?aaeiaiiy. A ?iaio? [8]
aaoi?ii io?eiaii ??aiyiiy ia?aoai?aiiy iii?oniiai iaoiaeo, oa eiai
noaiia ?aae?caoe?y. O ?iaioao [9,10] aaoi?ii ?ic?iaeaii iaoiae
ia?aeaeueiiai ina?aaeiaiiy c aeei?enoaiiyi ??cieoeaai-ia??iaeii? i??e,
cai?iiiiiaaii ??aiyiiy ia?aoai?aiiy, noaiia ?aae?caoe?y iaoiaeo. ?iaioa
[11] iaienaia iniaenoi aaoi?ii. O ?iaio? [12] aaoi? ioe?iea iiaeeeaino?
oi/iiai aei??thaaiiy /aniaeo ?ioa?aae?a cai?iiiiiaaiei iaoiaeii.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
aeiiia?aeaeenue ? i?ieoee iaaiai?aiiy ia ?anioae?eainuee?e
iaoeiai-oaoi?/i?e eiioa?aioe?? “No?oeoo?i? iaoiaee i?aeaeuaiiy oi/iino?,
/ooeeaino? ? oaeaeeiae?? aei??thaaeueieo i?eeaae?a ? nenoai” (AEeoiie?,
1985?.), ia III Ananithci?e iaoeiai-oaoi?/i?e eiioa?aioe?? “Iao?ieia?y a
aeaeueiiiao???” ( Oa?e?a, 1988?.), 2-?e oa 3-?e I?aeia?iaeieo
eiioa?aioe?yo “Oai??y oa oaoi?ea ia?aaea/?, i?eeiio oa ia?iaee
?ioi?iaoe??” (Ooaina, 1996?., 1997?.).

Ioae?eaoe??. Iniiai? iieiaeaiiy aeena?oaoe?eii? ?iaioe iioae?eiaaii a 12
ae?oeiaaieo ?iaioao, ?c ieo o 4 noaooyo, 1 iaoaio?, 4 aaoi?nueeeo
na?aeioeoaao, 2 aeaiiiiaaieo iaoeiaeo i?aoeyo, 1 o i?aoeyo Ananithcii?
iaoeiai-oaoi?/ii? eiioa?aioe??.

No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny c anooio, i(yoe
?icae?e?a ? aeniiaeo, aeeth/a? a?ae?ia?ao?th c 104 iaeiaioaaiue, 4
aeiaeaoe?a. Caaaeueiee ianya aeena?oaoe?? neeaaea? 184 noi??iee, a oiio
/ene? 119 noi??iie oaenoo, 25 iaethie?a.

CIINO ?IAIOE

O anooii iaa?oioiao?oueny aeooaeueiinoue oaie, oi?ioeth?oueny iaoa
?iaioe, iaaiaeeoueny ?? iaoeiaa iiaecia oa i?aeoe/ia oe?ii?noue.

O ia?oiio ?icaeiei ?icaeyiooi aaeoc? aeei?enoaiiy ia?aoai?thaa/ia
iaeiie?aoieo /aniaeo iioa?aaeia, io iniaeeainoi, oa i?iaaaeaii aiae?c
?nioth/eo iaoiaeia ia?aoai?aiiy. Aei aaeocae aeei?enoaiiy
ia?aoai?thaa/?a iaeiie?aoieo /aniaeo ?ioa?aae?a iiaeooue aooe a?aeianai?
nenoaie ea?oaaiiy i?inoi?iaei i?noeaciaoiaeaeaiiyi ia’?eo?a,
aei??thaaiiy e?i?eieo ia?ai?uaiue a nenoaiao ea?oaaiiy, aaiaeac?y,
?aae?i- ? iioe/ia eieaoe?y, aei??thaaiiy aeaeo?e/ieo ? ia?aoai?aieo a
aeaeo?e/i? aaee/ei, aeaeo?iii? iaoiaee aei??o a yaea?i?e o?ceoe?.

Aeaia ?iaioa ? ?icaeoeii oai?aoe/ieo oa i?aeoe/ieo ?acoeueoaoia
aeineiaeaeaiue ii noai?aiith AOeI aaee/ei /anoioii-/aniaii a?oie,
i?eioeei ?iaioe yeeo caniiaaiee ia iaoiaei caiao iiioeuenia. ?icaeyiooi
eean iaoiaeia aiaeiai-oeeo?iaiai ia?aoai?aiiy iaeiie?aoieo iioa?aaeia
/ano, io ia?aaaae i iaaeieiee. Iieacaii, ui iaeaieueo aenieo oi/iinoue
ia? iaoiae iaeaoiiai caiao iiioeuenia. Caeieniaii iinoaiiaeo caaea/?
aeineiaeaeaiiy, iaa?oioiaaii iaoo aeineiaeaeaiiy.

Ae?oaee ?icae?e i?enay/aiee ?ic?iaoe? iaoiaeo ia?aeaeueiiai ina?aaeiaiiy
c aeei?enoaiiyi ??cieoeaai-ia??iaeii? i??e.

Aeei?enoiaoth/e ni?aa?aeiioaiiy oai??? ?iia??iino? iieacaii, ui
i?ioyaeiee iaeiie?aoiee /aniaee ?ioa?aae iiaea i?aeeyaaoe noaoenoe/iiio
ina?aaeiaiith i?e ia?aeaeueiiio eiai ia?aoai?aii? a n eaiaeao. A
eiaeiiio c eaiae?a io?eiaii cia/aiiy iaa?aeiii? aaee/eie tx /aniaiai
?ioa?aaeo, ui aei??aiththoue tx1, …, txn. Ina?aaeiaia cia/aiiy
/aniaiai ?ioa?aaeo tx, ui aei??th?oueny, iaoeia aeaeyae:

, (1)

aea Nxi — oeeo?iaee aea?aaeaio i-oeo ?ioa?aae?a /ano;

n1 – /enei aeiaeaoeiaeo eaiae?a ia?aoai?aiiy;

n – caaaeueia /enei aeiaeaoeiaeo eaiae?a ia?aoai?aiiy, n=n1+n2;

T0 – ia??iae iiaoi?aiiy eaaiooth/eo ?iioeuen?a.

Aeiaaeeiaee ?iceeae ia?aiao??a e?i?e cao?eiee, ia yeeo io?eiai? tx1,
…, txn ?ioa?aae?a, caaacia/o? aeiaaeeiaee oa?aeoa? iiyae noa?oiaeo ?
noiiiaeo ?iioeuen?a a ?ioa?aae? T0, ui ? ia??iaeii iiaoi?aiiy
?iioeuenii? iine?aeiaiino?. I?e oeueiio /an ia?aoai?aiiy ca?eueoeoueny
ia iaea?eueoee /an cao?eiee a?aeiia?aeii? e?i?? cao?eiee ( ec max.
Iieacaii, ui e?ioeaaa o?eaae?noue ?iioeuen?a iine?aeiaiinoae,
?icaeyiooeo a oaeiio ia?aoai?aii?, i?ecaiaeeoue aei iiyae /aniai?
iaaecia/aiino?, aeeeeeaii? ca?aaie noa?oiaeo ? noiiiaeo ?iioeuen?a c
eaaiooth/eie.

Ia iniia? aeine?aeaeaiiy iaoaiaoe/ii? iiaeae? i?ioeano ca?ao ?aaoey?ieo
?iioeuenieo iine?aeiaiinoae aeae?eai? ?aaeeie ca?ao, ui a?ae??ciythoueny
??ciith aaee/eiith iiaeoey ??cieoe? (t=|T1-T0| ia??iae?a iiaoi?aiiy T1 ?
T0 ca?aeieo iioie?a:

— o?eaaeino? ?iioeuen?a iaio iine?aeiaiinoae o ??ai? aaee/ei? (t, oiaoi

( = (t;

— o?eaaeino? ?iioeuen?a iaio iine?aeiaiinoae a?eueoa aaee/eie iiaeoey
??cieoe? ia??iae?a, oiaoi o>(t aai o>>(t.

. Ooo f0 ? f1 – aeecuee? /anoioe i?ioiaeaeaiiy ca?aeieo iioie?a ?c
ia??iaeaie iiaoi?aiiy O0 ? O1. A?aeiii, ui i?aeaeuaiiy ?icae?ethaaeueii?
caeaoiino? ? oi/iino? ia?aoai?aiiy iiaea aooe aeinyaiooa i?e
aeei?enoaii? ca?ao ?iioeuen?a iaeaoaie.

O ?iaio? aeey onoiaiiy /aniai? iaaecia/aiino?, aeeeeeaii? ca?aaie
noa?oiaeo ? noiiiaeo ?iioeuen?a ?c eaaiooth/eie i?e ia?aoai?aii? c
ia?aeaeueiei ina?aaeiaiiyi, aoaeaii aeei?enoiaoaaoe ??cieoeaai-ia??iaeio
i??o (?II):

. (2)

Ne?ae cacia/eoe, ui a oeueiio ?aaeei? ca?a?a a?aeaoaa?oueny
ianooaaii-/aniaa ia?aoai?aiiy /aniaeo ?ioa?aae?a, iaoiiaeaieo
ia?aiao?aie ao?aeieo ?aaoey?ieo ?iioeuenieo iioie?a. Iaeia ?c ca?aeieo
?iioeuenieo iine?aeiaiinoae ia? ia??iae iiaoi?aiiy 2O0, ?ioa —
iine?aeiai?noue cao?eiaieo ia e?i?yo cao?eiee noa?oiaiai ? noiiiaiai
?iioeuen?a o a?aeiia?aeieo eaiaeao ia?aoai?aiiy. Iaea?eueo i?eeiyoiith
ioe?ieith o?eaaeino? aeine?aeaeoaaieo ?ioa?aae?a ? o?enaoe?y ia /ania?e
a?n? oeaio??a iaeao?a ca?ao. ??aiyiiy ia?aoai?aiiy, iaoiiaeaia iaoiaeii
ia?aeaeueiiai ina?aaeiaiiy, ia? aeaeyae:

tx = (noe2 + N n/2 — noe2′)(t, (3)

aea noe2, n’oe2 – iiia? oeaio?aeueiiai ?iioeueno iaeaoa ca?a?a a
noa?oiaeo ? noiiiaeo eaiaeao a?aeiia?aeii;

N – oeeo?iaee aea?aaeaio ?ioa?aaeo /ano, a?aeiia?aeiee iiaiiio
/eneo ia??iae?a eaaiooth/i? /anoioe i?ae noa?oiaei ? noiiiaei
?iioeuenaie.

Iiia?e oeaio?aeueieo ?iioeuen?a iaeao?a ca?ao a noa?oiaeo ? noiiiaeo
eaiaeao, ui aoiaeyoue a (3), aecia/athoueny ye:

noe2=N0+N1/2,
(4)

n’oe2=N’0+ N’1 /2,
(5)

aea N0, N’0 – /enei iiceoe?e, ui a?aeiia?aeathoue noa?oiaiio aai
noiiiaiio iioieai, ui ia ni?aiaee c ae?oaei ?iioeuenii iioieo c
ia??iaeii iiaoi?aiiy O0 ? (aai) ?iioeuenai cacia/aieo iioie?a, ui
ni?aiaee, c aiie?ooaeith, iaaeinoaoiueith aeey i?aeeth/aiiy aeaiaio?a
noaie;

N1, N’1 – /enei iaeeieoeue, a?aeiia?aeieo ?iioeuenai noa?oiaiai aai
noiiiaiai iioie?a, ui ni?aiaee c iioieii, yeee ia? ia??iae iiaoi?aiiy
2O0.

Eaaioii a aeaiiio iaoiae? ? aaee/eia ??cieoeaai-ia??iaeii? i??e (t.

O ?iaio? iieacaii, ui aeey ooai?aiiy a noa?oiaiio ? noiiiaii eaiaeao ii
iaeiiio iaeaoo ca?a?a icia/aieo ca?aeieo iioie?a, iaiao?aeii aeeiiaiiy
oiiae (t=2T0/n.

I?e aecia/aii? oi/iino? ia?aoai?aiiy iaoiaeo ia?aeaeueiiai ina?aaeiaiiy
c canoinoaaiiyi ??cieoeaai-ia??iaeii? i??e anoaiiaeai? iniiai?
aeanoaa?e?coth/? /eiieee, ui ? i?e/eiaie aeieeiaiiy ?ino?oiaioaeueii? ?
iaoiaee/ii? iioeaie. Iieacaii, ui iaoiaee/iith iioeaeith ia?aoai?aiiy ?
aaee/eia ??cieoeaai-ia??iaeii? i??e (t. ?acoeueoaoe aiae?co i?ioeano
ia?aoai?aiiy na?ae/aoue i?i oa, ui aeey ?aaeeio ca?ao ?iioeuen?a
iaeaoaie oa?aeoa?ia iayai?noue iioeaie /a?ac ei?ioei/anio
ianoaa?euei?noue ( /anoio canoiniaoaaieo aaia?aoi??a ?iioeuen?a, a
oaeiae aeiaaeeiaeo aeaeo?e/ieo oeoeooaoe?e, ui ae?thoue o aoceao
ia?aoai?thaa/a. Ci?ia /enea ?iioeuen?a iaeaoo ca?ao, ui aeeeeea?oueny
ei?ioei/aniith ianoaa?euei?noth /anoioe, aei??aith?

. (6)

Iaaecia/ai?noue /enea ?iioeuen?a iaeaoa ca?ao, ui aecia/a?oueny ae?th/ei
cia/aiiyi oaieiaiai ooio Uo, ia? aeaeyae:

, (7)

aea Eu – eiao?oe??io e?ooecie o?iioo ?iioeuen?a ca?ao.

Cia/aiiy aaee/eie Uo aecia/a?oueny ??aiyiiyi Iaeea?noa.

Aeei?enoaiiy i?eioeeio ae??aithaaiiy /anoeiieo iioeaie
?ino?oiaioaeueiiai oa?aeoa?o aeey iaoiaeo ia?aeaeueiiai ina?aaeiaiiy c
aeei?enoaiiyi ??cieoeaai-ia??iaeii? i??e aeicaieeei ciaeoe iioeiaeueia
cia/aiiy ??cieoeaai? /anoioe fp, i?e yeiio ??ai? iioeaee /a?ac oaieia?
ooie (7) ? ianoaa?euei?noue /anoio (6). Cieaeaiiy iioeaee ia?aoai?aiiy
iiaea aooe aeinyaiooi oeyoii ciaioaiiy aaee/eie ??cieoeaai? /anoioe, aea
i?e oeueiio aaee/eia ?ino?oiaioaeueii? iioeaee c?inoa?. Oea i?ecaiaeeoue
aei iaiao?aeiino? canoinoaaiiy eaa?oeaaeo aaia?aoi??a c iaeith
ianoaa?euei?noth /anoioe 10-10 n oa iaioa. Iioeaea ia?aoai?aiiy aeey
?ioa?aae?a o?eaaeino? 500 in neeaaea? aaee/eio 0,4 in.

O o?aoueiio ?icae?e? ia iniia? aeine?aeaeaiiy iniiaieo neeaaeiaeo
iioeaee iii?oniiai iaoiaeo ia?aoai?aiiy iieacaii, ui ?nio? iioeaea, ui
aeeeeea?oueny e?ioeaaith o?eaae?noth ?iioeuen?a iioie?a aaia?aoi?a
iniiaii? ? iii?onii? /anoioe. Oea i?ecaiaeeoue aei ca?ao ?iioeuen?a
?icaeyaeoaaieo iioie?a iaeaoaie ? ? ia?aoeiaeith a iiaeaeueoiio
aaeineiiaeaii? iii?onieo aei??iee?a /aniaeo ?ioa?aae?a.

I?e ?ic?iaoe? iii?oniiai iaoiaeo ia?aoai?aiiy c aeei?enoaiiyi ?II,
i?iiiio?oueny canoinoaaiiy icia/aiiai iaaeie?eo aeey i?aeaeuaiiy
oi/iino? ia?aoai?aiiy. A?aecia/a?oueny, ui a ?aaeei? ca?a?a iaeaoaie
a?aeaoaa?oueny ianooaaii-/aniaa ia?aoai?aiiy iniiaii? ? iii?onii?
iine?aeiaiinoae. Aeey ooi/iaiiy iioeaie eaaiooaaiiy ii/aoeo ? e?ioey
?ioa?aaeo /ano, ui aei??th?oueny, canoiniaaii i?eioeei
aeaioeaiaeueiino?. *ania? ?ioa?aaee t1 ? t2, ui ? iioeaeaie eaaiooaaiiy
ii/aoeo ? e?ioey a ?aaeueiiio ianooaa? /ano, o?ainoi?iothoueny a
o?eaaeino? iaeao?a ca?a?a o noa?oiaiio ? noiiiaiio eaiaeao a?aeiia?aeii.
??cieoeaaa /anoioa fp i?ioiaeaeaiiy iaeao?a ? i?e oeueiio iecueeith
/anoioith. Ia??iae i?ioiaeaeaiiy O0 iniiaii? /anoioe, ia ye?e ooai?ai?
/ania? cnoae t1 ? t2, ia?aoai?th?oueny a ia??iaee i?ioiaeaeaiiy iaeao?a
O?1 ? O?2 o noa?oiaiio ? noiiiaiio eaiaeao a?aeiia?aeii.

*ania? ?ioa?aaee t1 ? t2, ui i?aeeyaathoue ia?aoai?aiith a noa?oiaiio ?
noiiiaiio eaiaeao, aecia/athoueny oaeei /eiii:

t1=n10 (T1 – T0),
(8)

t2=n02 (T0 – T2),
(9)

aea O1 ? O2 – ia??iaee iiaoi?aiiy iii?onieo iioie?a a noa?oiaiio ?
noiiiaiio eaiaeao a?aeiia?aeii;

n10 – /enei ?iioeuen?a ia??iaeo iiaoi?aiiy O1 a?ae noa?oiaiai
?iioeueno aei na?aaeeie iaeaoo ca?ao a noa?oiaiio eaiae?;

n02 – /enei ?iioeuen?a ia??iaeo iiaoi?aiiy O2 a?ae noa?oiaiai
?iioeueno aei na?aaeeie iaeaoo ca?ao a noiiiaiio eaiae?.

??cieoey ia??iae?a iiaoi?aiiy O1 ? O0 ?iioeuen?a iniiaii? ? iii?onii?
/anoioe a noa?oiaiio eaiae? ? ia??iae?a iiaoi?aiiy O0 ? O2 ?iioeuen?a
iniiaii? ? iii?onii? /anoioe a noiiiaiio eaiae?, ui aecia/athoueny ye
?II (2) (t10 ? (t02 noa?oiaiai ? noiiiaiai eaiae?a, ciaoiaeyoueny
ne?aeoth/ei /eiii:

, (11)

aea fp1, fp2 – ??cieoeaaa /anoioa a noa?oiaiio ? noiiiaiio eaiaeao
a?aeiia?aeii.

Aaee/eie n10 ? n02, ui aoiaeyoue o ae?ace (8) ? (9), aecia/ai? ye

+N’1, (12)

+N’2, (13)

aea N11, N12, N21, N22 – /enei ?iioeuen?a a ia?oiio ? ae?oaiio iaeaoao
ca?a?a a noa?oiaiio ? noiiiaii eaiaeao a?aeiia?aeii;

N’1 – /enei ?iioeuen?a /anoioe f1, i?ae?aoiaaia ca /aniaee ?ioa?aae
a?ae noa?oiaiai ?iioeueno aei ?iioeueno ii/aoeo iaeaoo ca?ao;

N’2 – /enei ?iioeuen?a ia??iae?a iiaoi?aiiy O2, ye? i?ieoee a?ae
noiiiaiai ?iioeueno aei ?iioeueno ii/aoeo iaeaoo ca?ao.

Aiae?c ae?ac?a (8), (9) iieacaa, ui aeii?ioth/eie iioeaeaie ? a oeueiio
aeiaaeeo ? iioeaee a?ae ianoaa?eueiino? /anoioe f1 ? f2, yeui ceii
aei??thaaeueii? ?ioi?iaoe?? cae?enithaaoe o?aaeeoe?eii. Iiaeaeueoiai
i?aeaeuaiiy ?icae?ethaaeueii? ni?iiiaeiino? ? oi/iino? iiaeia
aeiiiaoeny, cae?enithth/e i?ioean ia?aoai?aiiy o aeaeyae?

, (14)

, (15)

aea N1 ? N2 — /enei ?iioeuen?a iioie?a c ia??iaeaie iiaoi?aiiy O1 ? O2
a?ae iiiaioo ioneo a?aeiia?aeieo aaia?aoi??a aei e?ioey ia?oiai iaeaoo
ca?a?a a noa?oiaiio ? noiiiaiio eaiaeao.

A?aecia/a?oueny, ui eiao?oe??io ianooaaii-/aniaiai ia?aoai?aiiy
aecia/a?oueny ye Ei=O??/O0, i?e ?=1,2. I?e iino?eiiio eiao?oe??io?
o?ainoi?iaoe?? i?ioyaii oeeeeo ia?aoai?aiiy aiae?oe/i? ae?ace aeey
?ioa?aae?a t1 ? t2 aecia/ai? ye

, (16)

, (17)

aea Np1, Np2 – /enei ?iioeuen?a, a?aeiia?aeia ia??iaeai ??cieoeaaeo
/anoio a noa?oiaiio ? noiiiaiio eaiaeao a?aeiia?aeii. Cia/aiiy t1 ? t2,
ciaeaeai? oaeei /eiii, ?iaa??aioi? uiaei cia/aiue /anoio f1 ? f2, a
ioaea ? ?o ianoaa?eueiinoae.

?icaeyiooi iaoai?cie aeieeiaiiy caaaeueii? iioeaee ca?ao iii?oniiai
iaoiaeo ia?aoai?aiiy c aeei?enoaiiyi ?II, ui neeaaea?oueny c iaoiaee/ii?
? ?ino?oiaioaeueieo iioeaie.

Iaeneiaeueia cia/aiiy iaoiaee/ii? iioeaee a ?aaeueiiio ianooaa? /ano i?e
f0(f1(f2=f neeaaea? aaee/eio

.

Oaea ae cia/aiiy iaoiaee/ii? iioeaee ia ??cieoeaa?e /anoio?, ae?aaeaia
/a?ac /enei ia??iae?a iiaoi?aiiy O0, ia? aeaeyae:

, (18)

aea (O? – aea?aaeaio ??cieoeaai-ia??iaeii? i??e (t;

O? =fp-1 – ia??iae ??cieoeaai? /anoioe.

Cia/aiiy (NM aei??aith? iaeiiio ia??iaeo iiaoi?aiiy ?iioeuenii?
iine?aeiaiino?, ia ye?e aeine?aeaeo?oueny ?ioa?aae /ano, ui
ia?aoai?th?oueny.

Ci?ia e?eueeino? ?iioeuen?a iaeao?a a noa?oiaiio ? noiiiaiio eaiaeao ca
?aooiie oaieiaeo ooi?a aecia/a?oueny ae?acii

. (19)

Iioeaea ia?aoai?aiiy, iaoiiaeaia ianoaa?euei?noth /anoioe, yea ae?aaeaia
a ci?i? e?eueeino? ?iioeuen?a iaeao?a, aei??aith?

. (20)

Aaiiao?e/ia neeaaeaiiy icia/aieo iioeaie (18,19,20) aea? ioe?ieo
iaeneiaeueiiai cia/aiiy iioeaee eiae?a a?ae ci?ie e?eueeino? ?iioeuen?a
iaeaoo

. (21)

Iaeneiaeueia cia/aiiy iioeaee ia?aoai?aiiy iii?oniiai iaoiaeo c
aeei?enoaiiyi ?II oa a?aooaaiiyi (21) aecia/a?oueny ae?acii:

, (22)

aea i=1, 2.

Cia/aiiy NEI neeaaea? aaee/eio 5,6in ca ?acoeueoaoaie 30 a?i??thaaiue
?ioa?aaeo /ano o?eaae?noth 400in.

*aoaa?oee ?icae?e i?enay/aiee ?ic?iaoe? niiniao ia?aoai?aiiy o?eaaeino?
iaeeii/iiai ?iioeueno a oeeo?iaee aea?aaeaio.

Ianooaaii-/aniaa ia?aoai?aiiy ao?aeiiai neaiaeo cae?eniaii ca
aeiiiiiaith iaeaoiiai ca?ao ?iioeuen?a aeaio ?aaoey?ieo ?iioeuenieo
iine?aeiaiinoae. ?iioeuen o?eaaeino? tx, ui ia?aoai?th?oueny,
aaaaoi?aciai iiaoi?th?oueny ia aeaio (n–1)-?ic?yaeieo e?i?yo cao?eiee, o
?acoeueoao? /iai ooai?ththoueny aea? iine?aeiaiino? ?iioeuen?a ?c
ia??iaeaie iiaoi?aiiy O1 ? O2 ? ??cieoeaai-ia??iaeiith i??ith (t=O2–O1.
Aeae? oi?io?oueny iaeao ca?ao oeyoii eia?/iiai ia?aiiiaeaiiy ?icaeyiooeo
iine?aeiaiinoae, a iio?i o?eno?oueny /enei ?iioeuen?a iaeaoo, ui
ni?aiaee iiai?noth. ?icaeyae iaeaoo ca?ao a aeaeyae? ?ioaa?aeueiiai
neaiaeo aeicaiey? a?aecia/eoe, ui a aeaiiio aeiaaeeo a?aeaoaa?oueny
o?ainoi?iaoe?y niaeo?o ? /aniaeo ia?aiao??a aeo?aeieo ?iioeuenieo
iioie?a. Aeine?aeaeaiiy i?ioeano ia?aoai?aiiy ao?aeiiai ?iioeueno a
a?eueo i?ioyaeiee, ui ? iaeaath/ith iaeaoo ca?a?a, iieacaee, ui
eiao?oe??io ianooaaii-/aniaiai ia?aoai?aiiy aecia/eoueny ne?aeoth/ei
/eiii:

,

aea O? – ia??iae iiaoi?aiiy iaeao?a ?iioeuen?a;

O1 – ia??iae iiaoi?aiiy ao?aeiiai ?iioeueno;

tx – o?eaae?noue aeine?aeaeoaaiiai ?iioeueno;

(n – o?eaae?noue iaeaoo ca?a?a.

Iieacaii, ui /enei iiceoe?e ?iioeuen?a iaeaoo ca?a?a, a?aeiia?aeieo
?iioeuenai, ui ni?aiaee, c aiie?ooaeith, iaaeinoaoiueith aeey
ia?aeeth/aiiy aoce?a ia?aoai?thaa/a, aecia/a?oueny oeyoii ?iaa?niiai
eaaiooaaiiy ? ooai?aiiy aeiaeaoeiaeo iaeao?a. ?oi? ?icoaooaaiiy a
?acoeueooth/aio iaeao? aecia/a?oueny ianooiiei /eiii:

,

,

aea k – iiia? i?noeaiieiaeaiiy ?iioeueno a aeiaeaoeiaiio iaeao?.

??aiyiiy ia?aoai?aiiy aeaiiai niiniao ia? aeaeyae:

tx=[(N1+1) +2 (N’0-1)](t\={(N1+1) +2[(n-1)- N’1]} (t, (24)

aea N1 – oeeo?iaee aea?aaeaio o?eaaeino? ?iioeueno, yeee iaiaaeaiee
ii?iaii ia?aeeth/aiiy noai ca?ao (i?yia eaaiooaaiiy);

N’1 – oeeo?iaee aea?aaeaio iieiaeie o?eaaeino? ?iioeueno c aiie?ooaeith,
?icoaoiaaiith ieae/a ii?iao ia?aeeth/aiiy noai ca?ao (?iaa?nia
eaaiooaaiiy);

N’0 – /enei ?iioeuen?a aeiaeaoeiaiai iaeaoo ca?ao (ioeueiaee iaeao);

n – /enei aeiaeaoeiaeo eaiae?a aei??o.

Ae?aiacii aei??o o?eaaeino? ?iioeuen?a, ui aei??ththoueny (24),
aecia/aiee ye

(t=tx min

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