Атомна динаміка одновимірних коливальних систем, що мають точний розв’язок, з дефектами: Автореф. дис… канд. фіз.-мат. наук / М.А. Мамалуй, НАН Укра

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

O?CEEI-OAOI?*IEE ?INOEOOO IECUeEEO OAIIA?AOO? ?i. A.?.A??E?IA

Ia i?aaao ?oeiieno

Iaiaeoe Ia??y Aiae???aia.

OAeE 539.2

Aoiiia aeeiai?ea iaeiiaei??ieo eieeaaeueieo nenoai, ui iathoue oi/iee
?ica’ycie, c aeaoaeoaie

01.04.02 — oai?aoe/ia o?ceea

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a — 1998 ?.

Aeena?oaoe?y ? ?oeiienii.

?iaioa aeeiiaia o O?ceei-oaoi?/iiio ?inoeooo? iecueeeo oaiia?aoo? ?i.
A.?. A??e?ia IAI Oe?a?ie.

Iaoeiaee ea?iaiee — Ne?e?i ?aaai Nieiiiiiae/, aeieoi?
oiceei-iaoaiaoe/ieo iaoe, i?ia?aeiee iaoeiaee ni?a?ia?oiee OO?IO IAI
Oe?a?ie.

Io?oe?ei? iiiiaioe:

?aaiia Ieoaeei Ieaen?eiae/, ae. o.-i. i. i?ioani?, caa?aeoth/ee
a?aeae?eii ?inoeoooo iaoaeio?ceee ?i. A.A.Eo?aethiiaa IAI Oe?a?ie;

Caya?i Aiae??e Aiaoieue?ae/, ae. o.-i. i., noa?oee iaoeiaee
ni?a?ia?oiee, i?ia?aeiee iaoeiaee ni?a?ia?oiee OO?IO ?i. A.?.A??e?ia IAI
Oe?a?ie

I?iaiaeia onoaiiaa: Oa?e?anueeee aea?aeaaiee oi?aa?neoao, eaoaae?a
oai?aoe/ii? o?ceee.

Caoeno a?aeaoaeaoueny 16 aa?aciy 1999 ?. i 15 aiaeei? ia can?aeaii?
Niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.175.02 ii caoenoo aeieoi?nueeeo
aeena?oaoe?e i?e O?ceei-oaoi?/iiio ?inoeooo? iecueeeo oaiia?aoo? ?i.
A.?. A??e?ia IAI Oe?a?ie ca aae?anith: 310164, i.Oa?e?a, i?.Eai?ia, 47.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? OO?IO ?i. A.?.
A??e?ia IAI Oe?a?ie (i.Oa?e?a, i?.Eai?ia, 47).

Aaoi?aoa?ao ?ic?neaii 16 ethoiai 1999 ?.

A/aiee nae?aoa? Niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.175.02

Aeieoi? o?ceei-iaoaiaoe/ieo iaoe Eiaaeueia I.N.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeueiinoue oaie. Eeiaoe/ii, oa?iiaeeiaii/ii, ?aciiainii oa iioi
aeanoeainoi e?enoaeia, ui iinoyoue ?iciiiaiioii aeaoaeoe, aeeeeeathoue
o?eaeee iioa?an ye o aaeoci oai?aoe/iiai aiaeico, oae i a aaeoci
aenia?eiaioaeueieo aeineiaeaeaiue[1]-[3]. Oeae iioa?an coiiaeaiee ia
oieueee i/aaeaeiei oaeoii, ui ?aaeueii e?enoaee oi?th aai iioith ii?ith
iaiaeaaeueii, aea e aaaeeeainoth noai?aiiy e?enoaei/ieo no?oeoo?, yei
iathoue cacaeaeaaiaeue caaeaii aeanoeainoi, aeey no/anieo ae?iaieoeoa,
caniiaaieo ia aenieeo oaoiieiaiyo. Cia/ii oniioe a neioaci i?aeoe/ii
iaeiiaeii?ieo no?oeoo?, yei iathoue oe?ieee niaeo? oaoii/ieo
canoinoaaiiue, ?iaeyoue aeineiaeaeaiiy iaeiiaeii?ieo i
eaaciiaeiiaeii?ieo iiaeaeae aeooaeueiith i ia?niaeoeaiith caaea/ath.
Ca?ac iioaineaii aea/athoueny aeaeo?iiii, oiiiiii, ieaciiiii oa iioi
eaaci/anoeieiai caoaeaeaiiy a iaeiiaeii?ieo nenoaiao. Iaiaoiaeii i?e
oeueiio aiaecia/eoe, ui eaaciiaeiiaeii?ia iiaaaeiiea eaaci/anoeieiaeo
caoaeaeaiue ? oa?aeoa?iith ia oieueee aeey eaaciiaeiiaeii?ieo nenoai.
Aiia i?eoaiaiia ie?aiei iecueei/anoioiei iiaeai, yei aiaeuaieththoueny a
niaeo?i oa?oaaoeo e?enoaeia. Oae, a ?iaioao [4,5] ?acoeueoaoe
aenia?eiaioaeueieo aeineiaeaeaiue iecueei/anoioii? aeeiaiiee neeaaeieo
aaaaoioa?oaaoeo e?enoaeia KDy(MoO4)2 oa CsDy(MoO4)2 oniioii
iioa?i?aooaaeeny ca aeiiiiiaith oiiiiiiai niaeo?o eiiieiiai eaioethaeea
c aeaioaoiiiith aeaiaioa?iith eiii?eith. Oaei iiaee eaaciiaeiiaeii?iiai
oa?aeoa?o iathoue iinoea iaaioue a o?eaeii?ieo e?enoaei/ieo no?oeoo?ao,
yei aeaeaei aiae iecueeiaeii?iinoi ca nai?ie iae?ineiii/ieie
aeanoeainoyie oa iciaeith yeeo ? iineaaeaiiy aeaeueiueiai ii?yaeeo
e?enoaei/ii? ?aaoey?iinoi ?icoaooaaiiy aoiiia i cia/ia eieaeueia
aiicio?iiiy iiaeaoiiii? aca?iiaei?. I?eeeaaeii oaei? no?oeoo?e
?AOII-nenoaia oeio 1-2-3, ui iinoeoue iaeiiaeii?ii no?oeoo?ii aeaiaioe,
yei cia/iith ii?ith aecia/athoue ?? aeanoeainoi. C oi/ee ci?o
aeineiaeaeaiiy ?aaeueieo eaaciiecueeiaeii?ieo iniaeeainoae, ui
niinoa?iaathoueny a iiaaaeiioei eaaci/anoeieiaeo niaeo?ia aeooaeueiei ?
aea/aiiy eieeaaeueieo aeanoeainoae ie?aieo aoiiia a?aoee,
iniaeeai—iiaeeco aeaoaeoia, aea aee?eaeaiiy ia?iiaee/iinoi e?enoaeo ?
iaeneiaeueii. Iiaia iioi?iaoeiy i?i oaei aeanoeainoi, a oiio /enei i a
nenoaiao, aea aiaenooiy o?aineyoeieia iiaa?iaioiinoue, iinoeoueny a
eieaeueiie ooieoei? A?iia i eieaeueiie aonoeii noaiia [6]. Ca
aeiiiiiaith oeeo ooieoeie, cie?aia, iiaeia aea/aoe eieaeueii i
eaacieieaeueii eieeaaiiy, oiaoi ca’ycaii noaie ye ana?aaeeii oae i iica
nooeieueiei niaeo?ii, a oaeiae aecia/aoe nooiiiue eieaeicaoei? eieeaaiue
ia aeaiie /anoioi iiaeeco aeaoaeoieo aoiiia. O?aaa, iaeiae, a?aooaaoe,
ui eiaeiee eiie?aoiee iie?ineiii/iee ?ic?aooiie aeey iiaeaeae, yei
aeecueei aei ?aaeueiinoi, noi?iaiaeaeo?oueny, ye i?aaeei, ia/eneaiiyie
oa neiaieieith, yei ?aeoaea a?iiicaeeeie, ui ?iaeoue ?o aaaeeeie aeey
iiaeaeueoiai aeei?enoaiiy. ?icaeyae ni?iuaieo iiaeaeae, ia ia?oee
iiaeyae aeaeaeeo aiae ?aaeueii? neooaoei?, aeicaiey? io?eiaoe
?acoeueoaoe a aiaeioe/iiio aeaeyaei, ui aea? iiaeeeainoue i?aaenoaaeoe
?o a caaaeueiie oa ni?eeiyoiie oi?ii, a oaeiae ioeiieoe nooiiiue
iaaeeaeaiiy ia/enethaaeueieo ?ic?aooieia, ui aeei?enoiaothoueny i?e
?icaeyaei aieueo neeaaeieo iiaeaeae. Iioeie neiaaie, aeey iiaiiai iieno
oa?aeoa?ieo iniaeeainoae iiaaaeiiee eieaeueieo aeaoaeoia oa ?iueiai
ioi/aiiy a ?iciiiaiioieo e?enoaei/ieo no?oeoo?ao, iaiaoiaeia ii?aeiaiiy
aeaio iiaeoiaeia: aea/aiiy iiaeaeae, yei aeecueei aei ?aaeueii?
neooaoei?, i i?inoeo iiaeaeae, ui aeicaieythoue io?eiaoe oi/ii
aiaeioe/ii ?acoeueoaoe. Iaeaieueoi iiaeeeainoi aeey io?eiaiiy
?acoeueoaoia uiaei ?iciiiaiioieo eaaci/anoeieiaeo niaeo?ia a
aiaeioe/iiio aeaeyaei aea? ?icaeyae iaeiiaeii?ieo nenoai [7,8], yei ?
a?aie/iith neooaoei?th i aaciaith iiaeaeeth aeey aeineiaeaeaiiy
eaaciiaeiiaeii?ieo no?oeoo?. Eiei iiaeaeae eieeaaeueieo nenoai, ui
aeicaieythoue ciaeoe oi/iee ?ica’ycie cae/aeieie iaoiaeaie, (iaoiae
ieineeo oaeeue, iai?eeeaae), iaeiae, i aeini ? aeiaiei aocueeei [2]. Ani
?acoeueoaoe, iaaaaeaii a aeena?oaoei?, aoee io?eiaii iaoiaeii yeiaieiaeo
(J-) iao?eoeue (?aeo?neaiei iaoiaeii) [9,10]. Oeae iaoiae aeicaiey? aac
ciaoiaeaeaiiy aeenia?nieieo niiaaiaeiioaiue a aa?iiii/iiio iaaeeaeaiii
iaea?aeoaaoe ?iciiiaiioii aeeiaii/ii i oa?iiaeeiaii/ii oa?aeoa?enoeee
e?enoaeia aoaeue-yeee aeii?iinoi, a oiio /enei neeueii aiicio?iiieo i
oeo, ui iinoyoue aeaoaeoe. Aeei?enoaiiy iaoiaeo J-iao?eoeue a aaaaoueio
aeiaaeeao ni?iuo? ye ?ic?aooiie oae i, aieiaiei /eiii, iioa?i?aoaoeith
iaea?aeoaaieo oa?aeoa?enoee, ineieueee aeaiee iaoiae aea? iiaeeeainoue
?icaeyaeaoe eieeaaeueii oa?aeoa?enoeee ie?aieo aoiiia nenoaie. Aieueo
oiai, aeey iaeiiaeii?ieo eaioethaeeia c aeaoaeoaie, a oaeiae, aeey
ie?aieo oeiia cao?aiue a o?eaeii?ieo nenoaiao, canoinoaaiiy aeaii?
oaoiiee aea? iiaeeeainoue inoioii iioe?eoe eiei iiaeaeae, ui
?ica’ycothoueny oi/ii.

Iaoa ?iaioe. Aeey ?icoiiiiy i?ioeania, ui aiaeaoaathoueny ye o aeania
iecueeiaeii?ieo ?a/iaeiao, oae i a oeo, ui iathoue iniaeeainoi
iecueeiaeii?iiai oa?aeoa?o, oa eiio?iethaaiiy oeeo i?ioeania, iaiaoiaeii
i?iaiaeeoe yeiiiaa aieueo iiaiee aiaeic iiaaaeiiee oiiiiieo niaeo?ia
iaeiiaeii?ieo eaioethaeeiaeo no?oeoo?, ui iinoyoue aeaoaeoe
?iciiiaiioiiai oeio (iiiaeeiei aeiiioee caiiuaiiy, ai?iaaaeaeaiiy,
aeaoaeoii eeanoa?e ic aioo?ioiueith no?oeoo?ith-iai?eeeaae, aeiiioeiai
iieaeoee; iayaiinoue iaae, oiui). A caaea/i aeaii? ?iaioe aoiaeeoue: 1)
c’ynoaaoe caaaeueii e?eoa?i? oi/ii? ae?iooaaeueiinoi iiaeaeae
iaeiiaeii?ieo nenoai c eieaeueieie aeaoaeoaie oa ?ic?iaeoe iaoiae
ciaoiaeaeaiiy aiieiooaeii-/anoioieo oa?aeoa?enoee aeey aoaeue-yeiai
aoiio oaei? nenoaie; 2) aeey eiie?aoieo iaeiiaeii?ieo nenoai, ui
iaeaaeaoueaeiaecia/aiiaieeana iiaeaeae, yei iathoue oi/iee ?ica’ycie,
io?eiaoe oi/ii aiaeioe/ii niiaaiaeiioaiiy,uiyeiiiaaaieueo iiaiei /eiii
c’yniaothoue aieea eieaeueieo aeaoaeoia ia oiiiiiee niaeo? aeaieo
no?oeoo?. Iniaeeai, a aiaeioe/iiio aeaeyaei io?eiaoe oiiae eieaeicaoei?
oa oa?aeoa?enoeee eieaeiciaaieo eieeaaiue ia /anoioao ye a iaeanoi
nooeieueiiai niaeo?o, oae i ca ?? iaaeaie. A oeie ?iaioi aeey ?yaeo
o?eaeii?ieo nenoai iieacaia eaaciiaeiiaeii?ia iiaaaeiiea oa?aeoa?enoee
eieaeiciaaieo eieeaaiue i iiaeeeainoue canoinoaaiiy aeey ?oiueiai
iaaeeaeaiiai iieno ?acoeueoaoia, yei io?eiaii ye oi/ii ?ioaiiy a ?aieao
iaeiiaeii?ieo iiaeaeae. Oea oaeiae neeaaeaei iaeio c caaea/ aeaiiai
aeineiaeaeaiiy.

Iaoeiaa iiaecia. A aeena?oaoei? aia?oa noi?ioeueiaaii e?eoa?ie oi/ii?
ae?iooaaeueiinoi iaeiiaeii?ii? niaeo?aeueii? caaea/i iaoiaeii yeiaieiaeo
iao?eoeue. Ciaeaeaiee ?ica’ycie a oi/iinoi aei?iaith? nai?e aiaeioe/iie
ai?ieneiaoei?. A oi/iie aiaeioe/iie oi?ii io?eiaii eieeaaeueii
oa?aeoa?enoeee aeey eiie?aoieo iaeiiaeii?ieo iiaeaeae, ui
caaeiaieueiythoue e?eoa?ith, yeee noi?ioeueiaaii (iaiaiaaeaii oa
iaiiaiaiaaeaii, a oaeiae, aaeni?aiaaii eaioethaeee aoiiia c iaeii- i
aeaioaoiiieie aeaiaioa?ieie eiii?eaie, ui iinoyoue eieaeueii aeaoaeoe).
A ?iaioi iieacaii, ui iaaioue o aeiaaeeo a?aie/ii aaeeeiai ?aiao
cao?aiiy, iiaea aeyaeoeny iiaeeeaei io?eiaoe iioi?iaoeith i?i ii?iaiai
cia/aiiy ia?aiao?ia aeaoaeoo a oi/iie aiaeioe/iie oi?ii. ?icaeyiooi
iiaeaei iaeiiaeii?iiai eaioethaeea, ui iinoeoue ?iciiiaiioii eieaeueii
aeaoaeoe, a ciaiioiueiio ia?iiaee/iiio iiei oa iieacaii, ui oaea
iiaeaeue aeicaiey? iienoaaoe eieaeicaoeith eieeaaiue iiaeeco ieineiai
aeaoaeoo a o?eaeii?iiio e?enoaei. Io?eiaii niiaaiaeiioaiiy a oi/iinoi
aiaeiiaiaeathoue aeiaaeeo e?enoaeo c i?inoith eoai/iith a?aoeith, ui
iinoeoue ieinei aeaoaeoe, yei aiaeiai/ii ca nai?th no?oeoo?ith
iaeiiaeii?iei aeaoaeoai, ui aoei aeineiaeaeaii.

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoaoia. Eaaciiaeiiaeii?ii nenoaie
ca?ac iathoue oe?ieee niaeo? canoinoaaiiue a iie?iaeaeo?iiioei
(iai?eeeaae, ye iaeei c aeaiaioia iaaeiiiiaoth?ieo iaiiai?iaiaeieeiaeo
i?eeaaeia [11]), aiioaoiieiaiyo, oiui. Iaeii?th c iiaeeeaeo noa?
i?aeoe/iiai canoinoaaiiy iioi?iaoei? i?i iieiaeaiiy eieaeueii?
eieeaaeueii? iiaee aaeni?aiaaiiai eaioethaeea aoiiia iiaea neoaeeoe
i?ioean eaca?ii? i/enoee iiaa?oiiue ca aeiiiiiaith eiio?ieueiaaii?
iecueeioaiia?aoo?ii? aeani?aoei? [12]. I?e oeueiio aia?aiy
aei?iiiithaaiiy aeo?a/a?oueny ia «?icia?ia» eeoa i?eiiaa?oiaai?
eieaeueii? iiaee aei iiiaioo iiaiiai ia?eaaiiy ca’yceo. A oie aea /an,
iiyaa iaca’ycaieo iieaeoe ca iaaii? /anoioe eaca?a aeacoue iiaeeeainoue
aecia/aoe i?oaeio noaeo ca’yceo aaeni?aiaaii? iieaeoee c iiaa?oiath.
Iioaineaii ?icaeaathoueny oaoiieiai?, ui caniiaaii ia aeei?enoaiii
oiieeo ieiaie oa iioa?eaeueiaaieo e?enoaeia, ia aeanoeainoi yeeo
cia/iith ii?ith aieeaa? iayaiinoue aeaoaeoia (ye i?e?iaeieo oae i oeo,
yeeo aaaaeaii aeey io?eiaiiy ?a/iaeie ic cacaeaeaaiaeue caaeaieie
oa?aeoa?enoeeaie). Oae, ia no?oeoo?o oa oaeaeeinoue c?inoaiiy oiieeo
ieiaie iiaeia aieeaaoe ca aeiiiiiaith iaianaiiy noaiiiioa?iaeo iie?eoue
c aaeni?aiaaieo aoiiia ?iciiiaiioieo aacia [13]. Aeey ?icoiiiiy,
i?iaiicoaaiiy oa eiio?iethaaiiy i?ioeania, ui aiaeaoaathoueny a oaeeo
nenoaiao, ae?ae aaaeeeai iaoe oi/iee aiaeioe/iee iien aieeao aee?eaeaiue
ia?iiaee/ii? no?oeoo?e a?aoee ia oiiiiiee niaeo? e?enoaeo. Io?eiaiith i
aiaeico oeueiai iieno aeey eiie?aoieo eieeaaeueieo nenoai, ui
aiaeaeaathoue, na?aae iioiai, e caaaeueii caeiiiii?iinoi iiaaaeiiee
a?aoie c eieaeueieie aeaoaeoaie, i?enay/aia ?iaioa, ui i?iiiio?oueny.

Ai?iaaoeiy ?acoeueoaoia aeena?oaoei?. Aeeeaaeaii a ?iaioi ?acoeueoaoe
aoee i?aaenoaaeaii ia iaoeiiiaeueieo i iiaeia?iaeieo eiioa?aioeiyo:

1.XXI International Conference on Low Temperature Physics, Prague, 1996.
A.M.Kosevich, O.Yu.Batin, S.B.Feodosyev, I.A.Gospodarev, M.A.Mamalui,
E.S.Syrkin //Quasi-low-dimensional effects in vibrational
characteristics of 3D-cristals.

2.Oai?ey eiiaeaine?iaaiiiai ninoiyiey, Oa?ueeia, 1994. I.A.Iaiaeoe,
A.N.Nu?eei, N.A.Oaiaeinueaa //Oi/ii ?aoaaiua caaea/e aeeiaieee
iaeiiia?iie oeaii/ee n ?aciiai ?iaea aeaoaeoaie.

3.16th general conference on the condenced matter division, Leuven
(Belgium), 1997., A.M.Kosevich, S.B.Feodosyev, I.A.Gospodarev,
M.A.Mamalui, E.S.Syrkin //Calculations of partial density of vibrational
states as effective method of investigation of layered crystals.

4.The International Conference Dedicated to the 80-th Anniversary of
Academician I.M.Lifshitz, Moskow, 1997. M.A.Mamalui, E.S.Syrkin,
S.B.Feodosyev //Dynamics of the Linear Symmetrical Chain Containing
Defects.

5.III Iaaeaeoia?iaeiay Eiioa?aioeey Oece/aneea yaeaiey a oaa?aeuooaeao,
Oa?ueeia, 1997. I.A.Iaiaeoe, A.N.Nu?eei, N.A.Oaiaeinueaa, //Aeeiaieea
neiiao?e/iuo eeiaeiuo oeaii/ae n aeaoaeoaie.

6.Hidden Symmetry of Physical Structures. Layered Crystals, Rzesz’ow
(Poland), 1998. S.B.Feodosyev, I.A.Gospodarev, V.I.Grishaev,
M.A.Mamalui, E.S.Syrkin //Quasi-one-dimensional behaviour of
oscillations in semi-infinite layered crystals with complex lattice.

7.IV Ukrainian-Polish Meeting on Phase transitions and Ferroelectric
Physics, Dnepropetrovsk, 1998. M.A.Mamalui, E.S.Syrkin, S.B.Feodosyev
//Effect of local defects on low temperature dynamics of one-dimensional
structures.

Iniiaii ?acoeueoaoe aeena?oaoei? iinoyoueny a oaeeo noaooyo:

I.A.Iaiaeoe, A.N.Nu?eei, N.A.Oaiaeinueaa. Aeeyiea i?eiiaa?oiinoiuo
eneaaeaiee ia eieaaaoaeueiue niaeo? eeiaeiie oeaii/ee.// OOO.-1996.-
38,-c.3683-3691.

I.A.Iaiaeoe, A.N.Nu?eei, N.A.Oaiaeinueaa. Eieaeecaoeey eieaaaiee ia
aeaoaeoao a iaeiiia?iuo no?oeoo?ao ni neiaeiie yeaiaioa?iie y/aeeie. //
OIO.-1998.- 24,-c.773-783.

Sergei B. Feodosyev, Igor A. Gospodarev, Maria A. Mamalui and Eugenii S.
Syrkin. Lattice dynamics of FCC-cryocrystals with many-parametric
impurities. // Jornal of Low Temperature Physics .-1998.-
111,-c.441-447.

I.A.Iaiaeoe, A.N.Nu?eei, N.A.Oaiaeinueaa. Aeeyiea eieaeueiuo aeaoaeoia
ia eieaaaoaeueiua oa?aeoa?enoeee iieoaaneiia/iuo e aaneiia/iuo
iaeiiia?iuo no?oeoo? a ia?eiaee/aneii aiaoiai iiea. // OIO.-1999.-
25,-c.32-40.

Iniaenoee aianie aaoi?a. Noaooi aaoi?a ii oaii aeena?oaoei? iaienaii a
niiaaaoi?noai, i?e oeueiio aecia/aeueia /anoeia ia/eneaiue i?iaaaeaia
aaoi?ii iniaenoi. Aaoi? a?aea aaciina?aaeith o/anoue a aeineiaeaeaiii ia
anio eiai noaaeiyo aeeth/ath/e ?ic?iaeo iiaeoiaeia i caniaia ?ioaiiy
caaea/, iaienaiiy iaoeiaeo noaoae oa iiaeaioiaoei aeiiiaiaeae ia
eiioa?aioei?.

No?oeoo?a i ianya aeena?oaoei?. ?iaioa neeaaea?oueny c anooio, /ioe?ueio
?icaeieia, aeniiaeia oa nieneo oeeoiaaii? eioa?aoo?e c 102 iaeiaioaaiue.
Caaaeueiee ianya aeena?oaoei•-ae?oeiaaieo 103 eenoa. ?iaioa iinoeoue 14
iaethieia.

Iniiaii iieiaeaiiy, ui aeiinyoueny ia caoeno:

1.Noi?ioeueiaaii e?eoa?ie iiaeeeainoi iaea?aeaiiy oi/iiai ?ica’yceo
niaeo?aeueii? caaea/i. Caiaeii oeueiai e?eoa?iy, ca aeiiiiiaith iaoiaea
J-iao?eoeue niaeo?aeueii aonoeie eieeaaiue aoaeue-yeiai aoiia eiiieiiai
eaioethaeeo c ia?iiaee/iei ?icoaooaaiiyi aoiiia, yeee iinoeoue aeaoaeoii
eeanoa?e, iiaeooue aooe iaea?aeaii a oi/iie aiaeioe/iie oi?ii. Aeaiee
eaioethaeie iiaeiiee aooe aai a) iaiaiaaeaiee neiao?e/iee; aai a)
iaiiaiaiaaeaiee; aai a)iaiaaeaiee.

2. Aeey eiie?aoieo iaeiiaeii?ieo nenoai c eieaeueieie aeaoaeoaie, yei
aiaeiiaiaeathoue aecia/aiiio eeano iiaeaeae, ui iathoue oi/iee
?ica’ycie, aea/aii oiiae eieaeicaoei? oa oa?aeoa?enoeee eieaeiciaaieo
eieeaaiue c /anoioaie ye a ciii iaia?a?aiiai niaeo?a oae i ca ??
iaaeaie.

3. Aeey ?yaeo o?eaeii?ieo nenoai iieacaia eaaciiaeiiaeii?ia iiaaaeiiea
oa?aeoa?enoee eieaeiciaaieo eieeaaiue oa iaa?oioiaaii iiaeeeainoue
canoinoaaiiy aeey ?oiueiai iaaeeaeaiiai iieno oi/ieo ?acoeueoaoia, yeeo
iaea?aeaii a ?aieao iaeiiaeii?ieo iiaeaeae.

Ca’ycie ?aaioe c ieaiaie, i?ia?aiaie, oaiaie. ?iaioa aeeiiaia ca?aeii c
oaiith “Aaceaaeaey o e??ie?enoaeao”, iiia? aea?ae. ?a?no?aoe??
0196U0002950 oa o iaaeao i?iaeo?a “No?oi”(N4.2/88), “Aea?eiee”
(N2.3/624) oa “USKO”(2.4/165), ye? i?aeo?eiai? oiiaeii ooiaeaiaioaeueieo
aeine?aeaeaiue AeEIO Oe?a?ie o a?aeae?e? eaaioiaeo aeanoeainoae oa
iae?i?eieo yaeu a iae?ineii?/ieo nenoaiao O?ceei-oaoi?/iiai ?inoeoooo
iecueeeo oaiia?aoo? ?i.A.?.A??e?ia IAI Oe?a?ie.

INIIAIEE CIINO ?IAIOE

O anooii aei aeena?oaoei? iaa?oioiaaii aeooaeueiinoue oaie aeaii?
?iaioe, iiaecia oa i?aeoe/ia oeiiiinoue io?eiaieo ?acoeueoaoia, a oaeiae
iaaaaeaii ia?aeie noaoae i aeiiiaiaeae ca o/anoth caeiaoaa/a ii oaii
aeena?oaoei?.

Ia?oee ?icaeie aeena?oaoei? i?enay/aiee iaeyaeo eioa?aoo?e i iaoiaeo
aeineiaeaeaiue. Aiaeicothoueny ?acoeueoaoe aea/aiiy oiiiiiiai niaeo?o
iaeiiaeii?ieo nenoai c eieaeueieie aeaoaeoaie, iniaeeai — iiaeeeainoi
io?eiaiiy eieeaaeueieo oa?aeoa?enoee oaeeo nenoai a oi/iie aiaeioe/iie
oi?ii. Noenei aeeeaaeaii iniiaii iiiaioe ?icaeoeo aeineiaeaeaiue
eieeaaiue iaiaeaaeueieo e?enoaeia c iie?ineiii/ii? oi/ee ci?o oa
iaa?oioiaaiee aeai? iaoiaeo J-iao?eoeue ye oaeiai, ui aeicaiey? cia/ii
iioe?eoe eean iiaeaeae iaiaeaaeueieo iaeiiaeii?ieo nenoai, ui iathoue
oi/iee ?ica’ycie. Iaaaaeaii aecia/aeueii iieiaeaiiy iaoiaeo J-iao?eoeue,
i ia ?oiie iniiai noi?ioeueiaaii e?eoa?ie iiaeeeainoi ciaoiaeaeaiiy
oi/iiai ?ica’yceo iaeiiaeii?ii? niaeo?aeueii? caaea/i. Io?eiaii ae?ace,
ui aeicaieythoue ciaoiaeeoe aiieiooaeii-/anoioii oa?aeoa?enoeee
aoaeue-yeiai aoiio nenoaie. Caiaeii iaoiaeo yeiaieiaeo iao?eoeue,
i?inoi? ciiuaiue aoiiia eaioethaeea H ca aeiiiiiaith aiaeiiaiaeiiai
aeai?o oae caaieo ii?iaeaeoth/eo aaeoi?ia h0(i), ?ai?acaioo?oueny o
aeaeyaei i?yii? noie i?oiaiiaeueieo (oae caaieo oeeeei/ieo)
iiaei?inoi?ia H(i), yei ? iiaa?iaioieie aiaeiinii iia?aoi?a
L(r,r’)=(r,r’)/(m(r)m(r’))1/2, ui iieno? eieeaaiiy eaioethaeea
((r,r’)-iao?eoey neeiaeo noaeeo e?enoaeo). Oei iiaei?icoi?e ? eiiieieie
iaieiieaie, ui iaoyaiooi ia iineiaeiaiinoue eiiieii iacaeaaeieo aaeoi?ia
Lnh0(i)n=0. I?oiii?iaeicoaaaoe aeaio iineiaeiaiinoue ie io?eia?ii
i?oiaiiaeueiee aacen hn(i)n=0, a yeiio iia?aoi? L(i), ui eiaeoeiaaiee
iia?aoi?ii L a iiaei?inoi? H(i), i?aaenoaaeaiee o aeaeyaei
o?eaeiaaiiaeueii? yeiaieiai? iao?eoei (J-iao?eoei). *anoioii ?iciiaeiee
eieeaaiue aoiiia nenoaie ? ooieoeiyie iao?e/ieo aeaiaioia a?iiianueeiai
iia?aoi?a G=(I-L)-1 (-eaaae?ao /anoioe-aeania cia/aiiy iia?aoi?a L).
sseui aea?aoe aaeoi? h0=ruH—ciiuaiiy u aoiio c ?aaeion-aaeoi?ii r ye
ii?iaeaeoth/ee, oiaei iao?e/iee aeaiaio G00()(h0,Gh0) aoaea iinoeoe
iiaio iioi?iaoeith i?i /anoioii oa?aeoa?enoeee oaeeo eieeaaiue nenoaie,
a yeeo aeaiee aoii ?ooa?oueny acaeiaae u. Oiiae iayaiinoi o G00() oyaii?
/anoeie aecia/athoue iaaei nioa nooeieueiiai niaeo?o eieeaaiue, a naia
oyaia /anoeia aoaea oa?aeoa?ecoaaoe /anoioiee ?iciiaeie eieeaaiue
aeaiiai aoiio ana?aaeeii oeeo nioa. Ii?iiaaia ia iaeeieoeth niaeo?aeueia
aonoeia aei?iaith? (ImG00(). Ooieoeiy ?iciiaeieo eaaae?aoia /anoio g() ?
na?aaeiii a?eoiaoe/iei niaeo?aeueieo aonoei, ui aiaeiiaiaeathoue eiiieii
iacaeaaeiei ii?iaeaeoth/ei aaeoi?ai h0(i). Ooieoeiy G00() iiaea iaoe
iiethne eeoa iica nooeieueiei niaeo?ii, oiaoi a oie iaeanoi, aea aiia ?
aeieniith ooieoei?th. Oei iiethne d aecia/athoue eaaae?aoe aeene?aoieo
/anoio eieeaaiue (eieaeueieo aai uieeiieo). Ae/aoe a aeaieo iiethnao
d,0resdG00() aoaeooue iioaineaiinoyie aeaieo eieeaaiue. Ona?aaeiaiee ii
/ano eaaae?ao aiieiooaee eieeaaiue aoiio c ?aaeion-aaeoi?ii r ye
ooieoeiy eaaae?aoo /anoioe oa oaiia?aoo?e ? i?yii i?iii?oeieiee ( — aeey
eieeaaiue c /anoioith, ui eaaeeoue a nioci nooeieueiiai niaeo?o, i d,0 —
aeey eieeaaiue c aeene?aoiith /anoioith. sse ii?iaeaeoth/ee aaeoi? h0
iiaeia aea?aoe i iaeii/ania ciiuaiiy aeaeieueeio aoiiia. sseui iaeanoue
iaia?a?aiiai niaeo?o iaeiica’ycia i ia ia? «etheia», iao?e/ii aeaiaioe
J-iao?eoei ic c?inoaiiyi iiia?a i?aaiooue aei iaaieo a?aie/ieo aaee/ei,
ui caeaaeaoue aiae cia/aiue aa?oiuei? i ieaeiuei? iaae nioae
iaia?a?aiiai niaeo?o [9]. I?e?iaiyaoe oeei a?aie/iei cia/aiiyi ani
ai-aeiaaiiaeueii i bi-iaaeiaaiiaeueii iao?e/ii aeaiaioe J-iao?eoei i?e
in aeey ooieoei? A?iia io?eia?ii:[10]
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 (1)

aea K( ? ooieoei?th a?aie/ieo cia/aiue iao?e/ieo aeaiaioia;
Pm(x)-iieiiiie, ui aecia/athoueny ?aeo?aioiei niiaaiaeiioaiiyi: bm
Pm+1(x)=(x — am) Pm(x) — bm-1Pm-1(x) ca ii/aoeiaeo oiia: P-1(x)=0;
P0(x)=1. Qm(x) aecia/athoueny oei aea ?aeo?aioiei niiaaiaeiioaiiyi, aea
ca ii/aoeiaeo oiia: Q0(x)=0; Q1(x)=1/b0. sseui iaeanoue iaia?a?aiiai
niaeo?o ? aaaaoica’yceiaa, aneiioioe/ia iiaaaeiiea iao?e/ieo aeaiaioia
J-iao?eoei (yea, acaaaei, iiaea aooe aeoaea neeaaeiith) i?e ?icaeyaei
iiaeaeae eiiieieo eaioethaeeia c aaaaoiaoiiieie aeaiaioa?ieie eiii?eaie
/anoi aeyaey?oueny ia?iiaee/iith: limmai+mk=i, lim mbi+mk=i, ui
aeicaiey? io?eiaoe K( ye ooieoeith Pm() i Q m(), iiaoaeiaaieo ca
aeiiiiiaith aeaiaioia i,i iao?eoei iia?aoi?a L. Aeey niaeo?aeueii?
aonoeie 0( c (1) ia?ii:
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 (2)

Ooieoeiy (2) ? aiaeioe/iith ai?ieneiaoee?th niaeo?aeueii? aonoeie. sseui
ae?ac (2) aeey iaaii? nenoaie ? oi/iei, inoeiia niaeo?aeueia aonoeia ?
aiaeioe/iith ooieoei?th eaaae?aoo /anoioe, ui i?eoaiaiii eeoa
iaeiiaeii?iei no?oeoo?ai. A a?aoeao aieueoi? aeii?iinoi iiaia oiiiiia
aonoeia caaaeaee ia? oae caaii iniaeeainoi Aai Oiaa. Aeey oaeeo no?oeoo?
(2) ? iaaeeaeaiiyi niaeo?aeueii? aonoeie, ui oi/ii aiaeaeaa? iiaaaeiieo
?? 2n-1 ia?oeo iiiaioia. Ae?ace (1), (2) aeey ooieoei? A?iia i
niaeo?aeueii? aonoeie aoaeooue oi/ieie, yeui, ii/eiath/e c iaaiiai
iiia?a n, aeaiaioe J-iao?eoei aei?iaiththoue nai?i a?aie/iei cia/aiiyi.
Oaea iiaaaeiiea iao?e/ieo aeaiaioia icia/a? ia?iiaee/io iiaoi?thaaiinoue
aoiiieo ciiuaiue a aacenieo aaeoi?ao hn(i)n=0 i ia?iiaee/io caeaaeiinoue
aiae iiia?a n iiaeoeae aeaieo aaeoi?ia. Oea iiaeeeai, yeui /enei
cao?aieo aoiiia a ieo ia cacia? iaiaiaaeaiiai c?inoaiiy i?e c?inoaiii n,
a oaeiae ? ia?iiaee/iith ooieoei?th iiia?a, ui iiaeia o?aeooaaoe ye
aeoiae eieeaaiue a oaeeueiao ciio. Aeey eiiieieo eaioethaeeia ic
aca?iiaei?th iaeaeeae/eo noniaeia aacenii aaeoi?e aoaeooue iiaiaeeoeny
aiaeiiaiaeiei ia?acii, yeui:

a) eaioethaeie iaiiaiaiaaeaiee-a oeueiio aeiaaeeo o?aaa, ye
ii?iaeaeoth/ee aaeoi?, aea?aoe ciiuaiiy eiioeaaiai aoiio;

a) eaioethaeie iaiaiaaeaiee a iaeaeai noi?iie, aea ia? oeaio? neiao?i?.

?icoaoo?ii a oeaio?i neiao?i? ii/aoie eii?aeeiao oa caioia?o?ii aoiie c
aiaeaeaeaiiyi aiae oeueiai oeaio?o a iaeaeai noi?iie ye nn=0 .Iiaeeeai
aeaa aeiaaeee: 1) a oeaio?i neiao?i? ciaoiaeeoueny aoii, oiaei H=H(0)
H(1), aea aacen hn(0)n=0 ooai?aiee ciiuaiiyi aeaiiai aoiio (n=0) oa
neioacieie (aioeneiao?e/ieie) ciiuaiiyie aoiiia c iiia?aie n, a aacen
hn(1)n=0 -i?ioeoacieie (neiao?e/ieie) ciiuaiiyie aoiiia c iiia?aie (n+1)
(aoii n=0 a oeueiio iiaei?inoi?i ? iaii?ooiee).

2) a oeaio?i neiao?i? aoiio iaia? (oiaoi aeiaeai c aoiiia ia ia? iiia?o
n=0), oiaei H=H(+) H(-), aea aacene hn(+)n=0 i hn(-)n=0 ooai?aii
aiaeiiaiaeii neioacieie i i?ioeoacieie ciiuaiiyie aoiiia c iiia?aie
(n+1). Aaeoi?e i?oiii?iiaaiiai aacena hn(i)n=0 ca’ycaii
niiaaiaeiioaiiyi: hn=Pn(L)h0, ui aeeiio?oueny aeey eiaeiiai c /ioe?ueio
?icaeyiooeo aacenia, oiaoi eiaeiee c iiaei?inoi?ia ? oeeeei/iei. Aeaia
niiaaiaeiioaiiy aeicaiey? io?eiaoe oi/ii aiaeioe/ii ae?ace niaeo?aeueieo
aonoei eieeaaiue ia /anoioao iaia?a?aiiai niaeo?o i iioaineaiinoae
aeene?aoieo eieeaaiue aeey aoaeue-yeiai (n-oiai aiae aeaoaeoo) aoiio
nenoaie:

nn(ImGnn()=P2n(0( (3)

d,nresdGnn()=P2n(dd,0
(4)

Ineieueee ciiuaiiy aoiio c iiia?ii n aei?iaith? na?aaeiueiio
a?eoiaoe/iiio aaeoi?ia, ui iaeaaeaoue aca?iii i?oiaiiaeueiei
iiaei?inoi?ai, (a ia?oiio aeiaaeeo: hn(0)n=0 ? hn(1)n=0; a ae?oaiio
aeiaaeeo: hn(+)n=0 i hn(-)n=0), ooieoeiy A?iia eieeaaiue oeueiai aoiio
aoaea na?aaeiii a?eoiaoe/iei aiaeiiaiaeieo aeiaaiiaeueieo aeaiaioia
a?iiianueeiai iia?aoi?a nenoaie G, ui caienaiee a cai?iiiiiaaieo
aacenao. C (3,4), cie?aia, aeoiea?, ui i?e aoaeue-yeiio n iaeanoi
inioaaiiy oyaieo /anoei ooieoeie Gnn() (oiaoi nioae iaia?a?aiiai
niaeo?o) ? iaeiaeiaeie, iiethne ooieoeie Gnn(), yei aecia/athoue
eaaae?aoe /anoio aeene?aoieo eieeaaiue (eieaeueieo aai uieeiieo) d,
oaeiae niiaiaaeathoue aeey anio n. Oi?ioea (4) aeicaiey? ciaeoe nooiiiue
eieaeicaoei? oa oa?aeoa? caoooaiey oaeeo eieeaaiue.

A ae?oaiio ?icaeiei aeey eieeaaeueiiai niaeo?o iaiaiaaeaiiai eiiieiiai
eaioethaeea, ui iinoeoue eieaeueii aeiiioee caiiuaiiy aai ai?iaaaeaeaiiy
(a caaaeueiiio aeiaaeeo-o?ueioaoiiiee aeaoaeoiee eeanoa?) i
iaiiaiaiaaeaiiai eaioethaeea c aeiiioeith, ui caiiua? eiai «iiaa?oiaaee»
aoii, i?iaiaeiciaaii aaiethoeith eieaeueieo aonoei aoiiia aeaii? nenoaie
a caeaaeiinoi aiae ia?aiao?ia aeaoaeoo (=(m-m)/m — aeaoaeo iane oa
=() — aeaoaeo neeiai? aca?iiaei?, aea m’ i aiaeiiaiaeii ? iana i
eiinoaioa neeiai? aca?iiaei? aeiiioeiaiai aoiio c aoiiaie iao?eoei, a m
i oa?aeoa?ecothoue iano i eiinoaioo neeiai? aca?iiaei? iiae aoiiaie
iao?eoei), a oaeiae aiae aiaenoaii aei aeaoaeoo. Aecia/aii caeaaeiinoue
aiae ia?aiao?ia aeaoaeoo oiia aeieeiaiiy oa /anoio eieaeueieo eieeaaiue,
a oaeiae aiieiooae eieeaaiue c aeaieie /anoioaie ?icieo aoiiia nenoaie
(oiaoi oa?aeoa? ?oiueiai caoooaiiy). Oae, a iaiaiaaeaiiio eaioethaeeo,
aeene?aoii eieeaaiiy c eaaae?aoaie /anoio

aiaeuaieththoueny ca oiia: >l(0)/(2+) oa >l(1)1, aea eieaeueia eieeaaiiy
l(0) ii?iaeaeo?oueny ciiuaiiyie naii? aeiiioee, a l(1) — ciiuaiiyie ??
iaeaeeae/eo noniaeia. Oaeei /eiii, i?e >1, iacaeaaeii aiae iane
aeiiioee, a nenoaii, ui ?icaeyaeaeany, aeieeathoue aeaa aca?iii
i?oiaiiaeueieo eieaeueieo eieeaaiiy. Io?eiaii i i?iaiaeiciaaii oi/ii
aiaeioe/ii ae?ace, ui aecia/athoue ii?iaiai cia/aiiy ia?aiao?ia aeaoaeoo
ye ooieoeith aiaenoaii aiae aeiiioeiaiai aei iiaa?oiaaiai aoiio
eaioethaeea.

Ia ?en.1 i?aaenoaaeaia aaiethoeiy ii?iaiaeo cia/aiue ia?aiao?o aeaoaeoo
ca’yceo a caeaaeiinoi aiae /enea k aoiiia iiae aeiiioeith oa
«iiaa?oiath» i ia?aiao?o iane aeiiioeiaiai aoiio . Aeaeii, ui i?e k100
ii?iaiai e?eai aneiioioe/ii niiaiaaeathoue c ii?iaiaeie caeaaeiinoyie,
ui ? oa?aeoa?ieie aeey aeiiioee a iaiaiaaeaiiio eaioethaeeo, a k=0
(aeiiioea a ?iei iiaa?oiaaiai aoiio) — ?aeeiee aeiaaeie inioaaiiy eeoa
iaeiiai aeene?aoiiai noaio.

A o?aoueiio ?icaeiei aeena?oaoeieii? ?iaioe 1) iieacaii, ui eaaciuieeiii
eieeaaiiy, yei aeieeathoue a oa?oaaoiio e?enoaei ci neeaaeiith
aeaiaioa?iith eiii?eith, iathoue eaaciiaeiiaeii?iee oa?aeoa?, i ?oii
oa?aeoa?enoeee iiaeooue aooe c oi/iinoth aei iaeiai ia?aiao?o
aiaeiioaiiy iiae — oa aioo?ioa?iai? aca?iiaei? iienaii a ?aieao
iaeiiaeii?ii? iiaeaei, ui ia? oi/iee ?ica’ycie. 2) io?eiaii oi/ii
aiaeioe/ii ae?ace aeey ooieoeie A?iia eiiieiiai eaioethaeea c
aeaioaoiiiith aeaiaioa?iith eiii?eith, ui iinoeoue eieaeueii aeaoaeoe
(ecioiie/ia aeiiioea caiiuaiiy, iayaiinoue «aaeni?aoth/iai» ca’yceo c
iaaiith iaii?ooiith iiaa?oiath). Aeineiaeaeaii iiaio ciiio oiiiiiiai
niaeo?o, a oaeiae niaeo?aeueii aonoeie eieeaaiue aoiiia aeaoaeoiiai
eeanoa?a (aeiiioeiaee aai iiaa?oiaaee aaeni?aiaaiee aoii oa eiai
iaeaeeae/i noniaee). I?iaiaeiciaaii oiiae aiaeuaieaiiy oa oa?aeoa?enoeee
eieaeueieo i uieeiieo eieeaaiue. Aeey eiiieiiai eaioethaeea c
aeaioaoiiiith aeaiaioa?iith eiii?eith, eiaeiee c aoiiia yeiai ? oeaio?ii
neiao?i?, nooeieueiee niaeo? eaaae?aoia aeanieo /anoio neeaaea?oueny c
aeaio nioa iaeiaeiai? oe?eie. Niaeo?aeueii aonoeie iaio aoiiia (a ioaea
e ?oii aiieiooaee eieeaaiue) iathoue ei?aiaai iniaeeainoi a ioei oa ia
aa?oiie iaaei niaeo?o. Aiieiooaea eieeaaiue aaaeeiai aoiio ia? ua iaeio
ei?aiaao iniaeeainoue ia aa?oiie iaaei aeonoe/ii? ciie (02) i aei?iaith?
ioeth ia ieaeiie iaaei iioe/ii? (02). Aiieiooaea eieeaaiue eaaeiai
aoiio, iaaiaee, aei?iaith? ioeth i?e =02 i ia? ei?aiaao iniaeeainoue i?e
=02. Iayaiinoue a oaeiio eaioethaeeo eaaei? ecioiii/ii? aeiiioee
caiiuaiiy i?ecaiaeeoue aei aacii?iaiaiai ooai?aiiy eieaeueieo eieeaaiue,
ui aiaeuaieththoueny aiae aa?oiuei? iaaei iioe/ii? ciie, iacaeaaeii aiae
oiai a yeie c iiaea?aoie ?icoaoiaaia aeiiioea. E?ii oiai, yeui eaaea
aeiiioea ?icoaoiaaia o aaaeeie iiaea?aooei, aiae aa?oiuei? iaaei
aeonoe/ii? ciie aiaeuaieth?oueny uieeiia eieeaaiiy, yea eieaeico?oueny,
aieiaiei /eiii, ia iaeaeeae/eo noniaeyo aeiiioee. Aaaeea aeiiioea a
eaaeie iiaea?aooei i?ecaiaeeoue aei ooai?aiiy uieeiiiai eieeaaiiy, ui
aiaeuaieth?oueny aiae ieaeiuei? iaaei iioe/ii? ciie. Aaaeea aeiiioea a
aaaeeie iiaea?aooei ia ooai?th? eieeaaiue c aeene?aoieie /anoioaie, a
iaoiiinoue coiiaeth? «ia?aea/eo» oiiiiia c iioe/ii? ciie a aeonoe/io.
Aieea aieueii? iaeiiaeii?ii? iiaa?oii ia eieeaaeueii oa?aeoa?enoeee ?
iiaiinoth aiaeiai/iee aieeao aaaeeiai ecioiia c m’/m=2. Oa?aeoa?enoeee
eieeaaiue iaiiaiaiaaeaiiai eaioethaeea c icioiii/iith aeiiioeith ia
eiioei iiaeooue aooe io?eiaii c aiaeiiaiaeieo oa?aeoa?enoee
iaiaiaaeaiiai eaioethaeea caiiiith 1+2.

?icaeie /aoaa?oee. Caaaeueiee e?eoa?ie io?eiaiiy oi/ieo ?ioaiue (ia
iniiai iaoiaeo J-iao?eoeue) aeey eieeaaeueieo oa?aeoa?enoee eiiieieo
iaeiiaeii?ieo nenoai c eieaeueieie aeaoaeoaie, ui noi?ioeueiaaii a
ia?oiio ?icaeiei, iiaea aooe oniioii canoiniaaiee aeey aea/aiiy ciii, ui
aiaeaoaathoueny a oiiiiiiio niaeo?i oaeeo nenoai ca iayaiinoi
aeoeaaoei?, aai, a aa?iiii/iiio iaaeeaeaiii, ia?iiaee/iiai ciaiioiueiai
iiey. Ciaiioi? (aeey eaioethaeea) ia?iiaee/ia iiea onoaa? ?icaiaeiinoue
na?aaeiueieaaae?aoe/ieo ciiuaiue, ui aeanoeaa iaeiiaeii?iei a?aoeai
(iaia?a?aiee niaeo? aeanieo cia/aiue aeeiaii/iiai iia?aoi?a L
neeaaeathoue eaaae?aoe /anoio, ui eaaeaoue a iioa?aaei [0,m], aea
(m-0)/4=/m ) i ?icaeyaeoaaia caaea/a, ui ia? oi/iee ?ica’ycie, iiaea
aooe aaciina?aaeiuei canoiniaaia aei ?aaeueieo ia’?eoia. Oaeei /eiii
iiaea aooe aeineiaeaeaia, iai?eeeaae, iiaeaeue eaioethaeea, yeee
aca?iiaei? c iaaiith iiaeeiaeeith. A aeaiiio ?icaeiei, c o?aooaaiiyi
aeoeaaoei?, aea/aii iiaeaei: iaiaiaaeaiiai eiiieiiai eaioethaeea c
iaeiiaoiiiith aeaiaioa?iith eiii?eith, ui iinoeoue eieaeueiee
aeiiioeiaee eeanoa? (aeaioaoiiia aeiiioeiaa iieaeoea), i
iaiiaiaiaaeaiiai eaioethaeea c icioiii/iith aeiiioeith, ui caiiua?
iiaa?oiaaee aoii. Niaeo?aeueii aonoeie eieeaaiue aoiiia aeaioaoiiii?
aeiiioeiai? iieaeoee a iaeiiaoiiiiio eaioethaeeo i?aaenoaaeaii ia ?en.2.

Niaeo?aeueii aonoeie a iiaei?inoi?ao H(+) (e?eai 1-5) i H(-) (e?eai
6-10), ii?iaeaeaieo aiaeiiaiaeii neioacieie i i?ioeoacieie ciiuaiiyie
aeaioaoiiii? aeiiioeiai? iieaeoee a iaeiiaoiiiiio eiiieiiio eaioethaeeo,
ui ciaoiaeeoueny a ciaiioiueiio ia?iiaee/iiio iiei: e?eai 1,6 —
iayaiinoue a nenoaii eieaeueiiai eieeaaiiy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()()d=1-l(); e?eai 2,7 — ii?iaiai cia/aiiy ia?aiao?ia aeaoaeoo,
iaiaoiaeii aeey ooai?aiiy eieaeueieo eieeaaiue (ei?aiaaa iniaeeainoue
i?e =m); e?eai 3,8—niaeo?aeueii aonoeie ()() iaeaaeueiiai eiiieiiai
eaioethaeea (ei?aiaaa iniaeeainoue i?e =0 o (+)() i i?e =m o (-)();
e?eai 4,9—ii?iaiai cia/aiiy aeey ooai?aiiy uieeiieo eieeaaiue (ei?aiaaa
iniaeeainoue i?e =0); e?eai 5,10—iayaiinoue a nenoaii uieeiiiai
eieeaaiiy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()()d=1-g(). Io?eiaii eieeaaeueii oa?aeoa?enoeee iaiiaiaiaaeaiiai
eaioethaeea, yeee aaeni?aiaaii ia iiaa?oii iaii?ooiiai oaa?aeiai oiea.
Aeey eaioethaeea, c o?aooaaiiyi aeoeaaoei•, ciaeaeaii oa i?iaiaeiciaaii
caeaaeiinoi ii?iaiaeo cia/aiue ian aeaio icioiii/ieo aeiiioie aiae
aiaenoaii iiae ieie. ?icaeyiooi iaeiiaeii?ii nenoaie iiaeooue aooe
aaciina?aaeiuei ocaaaeueiaii aeey o?eaeii?iiai aeiaaeeo. sse aiaeiii,
eieeaaiiy, ui eieaeiciaaii iiaeeco ieineeo aeaoaeoia a o?eaeii?ieo
e?enoaeao, iienothoueny iaeiiaeii?ieie ?iaiyiiyie [2,3]. Oi/ii
aiaeioe/ii ae?ace, yeeo io?eiaii a aeaiiio ?icaeiei, a oi/iinoi
aiaeiiaiaeathoue eieeaaiiyi, ui eieaeiciaaii iiaeeco ieineiai aeaoaeoo a
e?enoaei c i?inoith eoai/iith a?aoeith, aoiie aeaio noniaeiio aoiiieo
ieiuei yeiai iathoue iano, aiaeiiiio aiae iane aoiiia iao?eoei;
aca?iiaeiy iiae aeaieie ieiueiaie oaeiae aiae?iciy?oueny aiae aca?iiaei•
iiae aoiiaie iao?eoei. A oaeiio e?enoaei, ?iaiyiiy ?ooo, caienaii aeey
aiieiooae ciiuaiue aoiiia a iai?yieo, ui ia?iaiaeeeoey?iee aeaoaeoiei
ieiueiai c eii?aeeiaoieie iiia?aie n=0, n=1 , iathoue aeaeyae:

(1+)u0=(+2)u0-(+1)u1-u-1+0u0

(1+)u1=(+2)u1-(+1)u0-u2+0u1
(7)

un=(/m)[2un-un-1-un+1]+0un,

aea n=-1, 2, 3,…, ui niiaiaaea? c ?iaiyiiyie ?ooo aoiiia ?icaeyiooiai
eiiieiiai eaioethaeea, yeee iinooue aeaioaoiiio aeiiioeiao iieaeoeo.
Ia?aiao? 0, yeiai aoei aaaaeaii aeey eaioethaeea oi?iaeueiei /eiii, a
eoai/iiio e?enoaei aiaeiiaiaea? ieaeiie iaaei nooeieueiiai niaeo?o oa
aei?iaith?:

0=(2/m)2-coskx-cosky,

aea kx, ky — eiiiiiaioe aeaiaeii?iiai oaeeueiaiai aaeoi?o.

A aeniiaeao iaaaaeaii iniiaii ?acoeueoaoe aeena?oaoei?, ui a nei?i/aiiio
aeaeyaei, iinoyoueny o aeeeaaeaieo ieae/a oacao:

1. Noi?ioeueiaaii caaaeueiee e?eoa?ie iiaeeeainoi ciaoiaeaeaiiy oi/iiai
?ica’yceo niaeo?aeueii? caaea/i iaoiaeii yeiaieiaeo (J-) iao?eoeue,
canoinoaaiiy yeiai ia?aaeaa/a? oi/io ?iaiinoue ciaeaeaiiai ?ioaiiy eiai
aiaeioe/iie ai?ieneiaoei?.

2. Aeey ?yaeo iaeiiaeii?ieo nenoai, ui caaeiaieueiythoue aeaiiio
e?eoa?ith, a aiaeioe/iiio aeaeyaei io?eiaii: ooieoei? A?iia,
niaeo?aeueii aonoeie eieeaaiue aoiiia ye ana?aaeeii oae i iica
aeaoaeoiei eeanoa?ii, /anoioe aeene?aoieo eieeaaiue, oiiae ?oiueiai
aiaeuaieaiiy, caeii caoooaiiy aiieiooae eieeaaiue aoiiia ia
aiaeiiaiaeieo aeene?aoieo /anoioao. Aeineiaeaeaii eieeaaeueii
oa?aeoa?enoeee oaeeo iiaeaeae: iaiaiaaeaii eaioethaeee aoiiia, ui
iinoyoue icieueiaaii aeiiioee ai?iaaaeaeaiiy i caiiuaiiy, c iaeii- oa
aeaioaoiiiith aeaiaioa?iith eiii?eith, aiaeiai/ii iaiiaiaiaaeaii
eaioethaeee c aeiiioeith, ui caiiua? e?aeiie («iiaa?oiaaee») aoii
nenoaie; eiiieii iieaeoee, ui aaeni?aiaaii ia iiaa?oii iaii?ooiiai
oaa?aeiai oiea; eaioethaeee aoiiia, ui iinoyoue eieaeueii aeaoaeoe, ca
iayaiinoth aeoeaaoei? (aeaioaoiiia aeiiioeiaa iieaeoea, icioiii/ia
aeiiioea caiiuaiiy, iayaiinoue «aaeni?aoth/iai» ca’yceo c iaaiith
iiaa?oiath).

3. Iieacaii, ui iaaioue a aeiaaeeo a?aie/ii aaeeeiai ?aiao aeaoaeoo,
iiaea aeyaeoeny iiaeeeaei io?eiaoe a oi/iie aiaeioe/iie oi?ii
iioi?iaoeith i?i oiiae iiyae eieaeiciaaieo noaiia. Ciaeaeaii:

n caeaaeiinoue ii?iaiaeo cia/aiue ia?aiao?ia ca’yceo i iane aeiiioie
caiiuaiiy i ai?iaaaeaeaiiy aiae aiaenoaii iiae aeiiioeiaei i iiaa?oiaaei
aoiiaie nenoaie;

n caeaaeiinoue ii?iaiaeo cia/aiue ian ia?e icioiiia aiae aiaenoaii iiae
ieie.

4.Aeey ?yaeo oa?oaaoeo nenoai iieacaia eaaciiaeiiaeii?ia iiaaaeiiea
oa?aeoa?enoee aeene?aoieo noaiia i iiaeeeainoue canoinoaaiiy aeey
?oiueiai iaaeeaeaiiai iieno ?acoeueoaoia, io?eiaieo ye oi/ii ?ioaiiy a
?aieao iaeiiaeii?ieo iiaeaeae.

5.?icaeyiooa iiaeaeue eaioethaeea, ui iinoeoue eieaeueii aeaoaeoe, ca
iayaiinoth aeoeaaoei?, aeicaiey? io?eiaoe oi/ii aiaeioe/ii ae?ace, ui
iienothoue noaie, yei eieaeiciaaii iiaeeco ieineeo aeaoaeoia a
o?eaeii?iiio e?enoaei c i?inoith eoai/iith a?aoeith.

[1] Lifshits I.M. Some problems of the dynamic theory of the nonideal
crystal lattices Nuovo Cim.Suppl. -1956.- 3, N4.-P.716-734.

[2] Ia?aaeoaeei A.A. Aeaoaeou e eieaaaoaeueiue niaeo? e?enoaeeia.
Oai?aoe/aneea e yenia?eiaioaeueiua aniaeou aeeyiey oi/a/iuo aeaoaeoia e
iaoii?yaei/aiiinoae ia eieaaaiey e?enoaeeia. -I.: Ie?, 1980.-310n.

[3] Einaae/ A.I. Oai?ey e?enoaeee/aneie ?aoaoee. -O.: Aeua oeiea,
1988.-298n.

[4] Eooueei A.E., Oa?/aiei TH.I., Ianoa?aiei I.I., Ao?nean A.A.
Iecei/anoioiua aicaoaeaeaiey a KYDy(MoO4)2 e KErDy(MoO4)2. OIO. -1996.-
22, N2.-N.785-791.

[5] Eooueei A.E. Iecei/anoioiue eieaaaoaeueiue niaeo? CsDy(MoO4)2 OIO.
-1998.- 24, N6.-N.393-399.

[6] Caeiai Aeae. Iiaeaee aanii?yaeea. -I.: Ie?, 1982.-235n.

[7] Aeieeiaaoeeee E.A., O?eoiai A.I., Oioeia A.E. Yia?aaoe/aneee niaeo?
nieiiaie X-Y oeaii/ee n i?eianueth OOAE.-1973.- 18, N5.-N.810-818.

[8] Eeaeia? A.C., Oeoea?iee A.I. Noaoe/aneea iaaieoiua naienoaa nieiiaie
oeaii/ee n i?eianueth OIO.-1980.- 6, N3.-N.332-338.

[9] Ia?anaaea A.E. Oeceea eiiaeaine?iaaiiiai ninoiyiey.-O.: ecae-ai
OOEIO AI ONN?, 1968.-N.172-190.

[10] Haydock R. Recursive solution of Schr»odinger’s equation. Solid
State Physics, 35.- New York: Academic Press, 1980.-?.129-200.

[11] Proceeding of the IInd NATO ASI Conf. «Quantum Dot Materials for
Nonlinear Optic Applications», Sept. 15-26, Bressanone, Italy (1996).

[12] Aeooei A.ss., O?enaiia A.A. Eieaaaoaeueiua iiaeu ia?aie/aiiie
oeaii/ee aoiiia. OIO. -1997.- 23, N12.-N.1215-1223.

[13] Iaeaoiee E.N., Ooen I.ss., Einaae/ A.I. Iaoaieciu ia?aciaaiey e
noano?oeoo?a oiieeo ieaiie.- I: Iaoea, 1982.-210n.

Iaiaeoe I.A. Aoiiia aeeiaiiea iaeiiaeii?ieo eieeaaeueieo nenoai, ui
iathoue oi/iee ?ica’ycie, c aeaoaeoaie. — ?oeiien. Aeena?oaoeiy ia
caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oiceei-iaoaiaoe/ieo iaoe ca
niaoeiaeueiinoth 01.04.02 — oai?aoe/ia oiceea. — Oiceei-oaoii/iee
iinoeooo iecueeeo oaiia?aoo? ii.A.I.A??eiia IAIO, 1998, Oa?eia, Oe?a?ia.

A aeena?oaoeieiie ?iaioi aeineiaeaeo?oueny aoiiia aeeiaiiea
iaiaeaaeueieo iaeiiaeii?ieo iiaeaeae, ui iathoue oi/iee ?ica’ycie.
Noi?ioeueiaaii e?eoa?ie iiaeeeainoi iaea?aeaiiy oi/iiai ?ica’yceo
niaeo?aeueii? caaea/i. Caiaeii oeueiai e?eoa?iy, ca aeiiiiiaith iaoiaea
J—iao?eoeue niaeo?aeueii aonoeie eieeaaiue aoaeue—yeiai aoiia
eiiieiiai eaioethaeea c ia?iiaee/iei ?iciiuaiiyi aoiiia, yeee iinoeoue
aeaoaeoii eeanoa?e, iiaeooue aooe iaea?aeaii a oi/iie aiaeioe/iie oi?ii.
Aeey eiie?aoieo iaeiiaeii?ieo nenoai c eieaeueieie aeaoaeoaie, yei
aiaeiiaiaeathoue aecia/aiiio eeano iiaeaeae, ui iathoue oi/iee
?ica’ycie, aea/aii oiiae eieaeicaoei? oa oa?aeoa?enoeee eieaeiciaaieo
eieeaaiue c /anoioaie ye a ciii iaia?a?aiiai niaeo?a oae i ca ??
iaaeaie. Aeey ?yaea o?eaeii?ieo nenoai iieacaii iayaiinoue
eaaciiaeiiaeii?ii? iiaaaeiiee oa?aeoa?enoee eieaeiciaaieo eieeaaiue oa
iaa?oioiaaii iiaeeeainoue canoinoaaiiy aeey ?oiueiai iaaeeaeaiiai iieno
oi/ieo ?acoeueoaoia, yeeo iaea?aeaii a ?aieao iaeiiaeii?ieo iiaeaeae.

Eeth/ia? neiaa: iecueeiaeii?ii e?enoaee, eieaeueii aeaoaeoe, oiiiie,
eieaeueii eieeaaiiy, eaacieieaeueii

eieeaaiiy, ooieoeiy A?iia, niaeo?aeueia aonoeia, oi/iee ?ica’ycie.

Iaiaeoe I.A. Aoiiiay aeeiaieea oi/ii ?aoaaiuo iaeiiia?iuo eieaaaoaeueiuo
nenoai n aeaoaeoaie. — ?oeiienue. Aeenna?oaoeey ia nieneaiea o/aiie
noaiaie eaiaeeaeaoa oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe
01.04.02—oai?aoe/aneay oeceea. – Oeceei-oaoie/aneee einoeooo ieceeo
oaiia?aoo? ei.A.E.Aa?eeia IAIO, 1998, Oa?ueeia, Oe?aeia.

A aeenna?oaoeeiiiie ?aaioa enneaaeoaony aoiiiay aeeiaieea oi/ii
?aoaaiuo iaeaeaaeueiuo iaeiiia?iuo iiaeaeae. Noi?ioee?iaai e?eoa?ee
oi/iie ?aoaaiinoe niaeo?aeueiie caaea/e, niaeanii eioi?iio iaoiaeii
J—iao?eoe niaeo?aeueiua ieioiinoe eieaaaiee ethaiai aoiia eeiaeiie
oeaii/ee n ia?eiaee/aneei ?aniieiaeaieai aoiiia, niaea?aeauae aeaoaeoiua
eeanoa?u, iiaoo auoue iieo/aiu a oi/iii aiaeeoe/aneii aeaea. Aeey
eiie?aoiuo iaeiiia?iuo nenoai n eieaeueiuie aeaoaeoaie, niioaaonoaothueo
auaeaeaiiiio eeanno oi/ii ?aoaaiuo iiaeaeae, enneaaeiaaiu oneiaey
eieaeecaoeee e oa?aeoa?enoeee eieaeeciaaiiuo eieaaaiee ia /anoioao eae a
iaeanoe nieioiiai niaeo?a, oae e ca aa i?aaeaeaie. A aiaeeoe/aneii aeaea
iieo/aiu: ooieoeee A?eia, niaeo?aeueiua ieioiinoe eieaaaiee aoiiia
aioo?e e aia aeaoaeoiiai eeanoa?a, /anoiou aeene?aoiuo eieaaaiee,
oneiaey eo iouaieaiey, caeii caoooaiey aiieeooae eieaaaiee aoiiia ia
niioaaonoaothueo aeene?aoiuo /anoioao. Enneaaeiaaiu eieaaaoaeueiua
oa?aeoa?enoeee neaaeothueo iiaeaeae: aaneiia/iua oeaii/ee aoiiia,
niaea?aeauea eciee?iaaiiua i?eiane caiauaiey e aiaae?aiey, n iaeii—e
aeaooaoiiiie yeaiaioa?iie y/aeeie, aiaeiae/iua iieoaaneiia/iua oeaii/ee
n i?eianueth, caiauathuae e?aeiee (“iiaa?oiinoiue”) aoii nenoaiu;
eeiaeiua iieaeoeu, aaeni?ae?iaaiiua ia iiaa?oiinoe iaiiaeaeaeiiai
oaa?aeiai oaea; oeaii/ee aoiiia, iiiauaiiua ai aiaoiaa ia?eiaee/aneia
iiea e niaea?aeauea eieaeueiua aeaoaeou (aeaooaoiiiay i?eianiay
iieaeoea, ecioiie/aneay i?eianue caiauaiey, iaee/ea “aaeni?ae?othuae”
nayce n iaeioi?ie iiaa?oiinoueth). Iieacaii, /oi aeaaea a neo/aa
i?aaeaeueii aieueoiai ?aiaa aeaoaeoa iiaeao ieacaoueny aiciiaeiui
iieo/eoue eioi?iaoeeth ia oneiaeyo iiyaeaiey eieaeeciaaiiuo ninoiyiee a
oi/iie aiaeeoe/aneie oi?ia. Iaeaeaiu: caaeneiinoue ii?iaiauo cia/aiee
ia?aiao?ia nayce e iannu i?eianae caiauaiey e aiaae?aiey io ?annoiyiey
iaaeaeo i?eianiui e iiaa?oiinoiui aoiiaie nenoaiu; caaeneiinoue
ii?iaiauo cia/aiee iann ia?u ecioiiia io ?annoiyiey iaaeaeo ieie. Aeey
?yaea o?aoia?iuo nenoai iieacaii eaaceiaeiiia?iia iiaaaeaiea
oa?aeoa?enoee eieaeeciaaiiuo eieaaaiee e i?eiaieiinoue aeey eo
i?eaeeaeaiiiai iienaiey ?acoeueoaoia, iieo/aiiuo eae oi/iua ?aoaiey a
?aieao iaeiiia?iuo iiaeaeae. Oae, ?anniio?aiiay iiaeaeue oeaii/ee,
niaea?aeauae eieaeueiua aeaoaeou, ai aiaoiai ia?eiaee/aneii iiea
iicaieyao iieo/eoue oi/iua aiaeeoe/aneea au?aaeaiey, iienuaathuea
ninoiyiey, eieaeeciaaiiua aaeece ieineeo aeaoaeoia a o?aoia?iii
e?enoaeea n i?inoie eoae/aneie ?aoaoeie.

Eeth/aaua neiaa: iecei?acia?iua e?enoaeeu, eieaeueiua aeaoaeou, oiiiiu,
eieaeueiua eieaaaiey, eaaceeieaeueiua eieaaaiey, ooieoeey A?eia,
niaeo?aeueiay ieioiinoue, oi/ii ?aoaaiay iiaeaeue.

Iaria A.Mamalui. Atomic dynamics of exactly solvable one-dimensional
vibrational systems with defects. -Manuscript dissertation is to achieve
the degree of Doctor of Phylosophy in physics and mathematics on the
speciality 01.04.02 — theoretical physics. Kharkov Institute B.I.Verkin
for Low Temperature Physics NAS of Ukraine. Kharkov. Ukraine. 1998.

Atomic dynamics of exactly solvable one-dimensional nonideal vibrational
models is investigated. The criterion of possibility to solve the 1D
spectral problem exactly in linear approximation is formulated. In
agreement with this criterion, spectral densities of vibrations for each
atom of linear chaine having atoms located in a periodic order and
containing defect clusters can be obtained analitically. Conditions for
the localization and characteristics of localized vibrations for the
frequencies located both in the area of continuous spectrum and beyong
this area are analized for the certain 1D systems which containe local
defects and belong to the defined class of exactly solvable models. For
a few types 3D systems quasi-one-dimensional behaviour of the
characteristics of localized vibrations and possibility to use the exact
results obtained in the framework of 1D models for their approximate
description is shown.

Key words: low-dimensional crystals, local defects, phonons, localized
vibrations, quasilocalized vibrations, Green’s function, spectral
density, exactly solvable model.

Добавить комментарий

Ваш e-mail не будет опубликован. Обязательные поля помечены *