OA?E?ANUeEEe AeA?AEAAIEE OI?AA?NEOAO

I?AeEICIEE Aieiaeeie? A?eoi?iae/

OAeE 537.86

Aeeo?aeoe?y aeaeo?iiaai?oieo oaeeue ia ia??iaee/i?e iine?aeiaiino?
iaoaeiae?aeaeo?e/ieo ?icn?thaa/?a

01.04. 03 — ?aae?io?ceea

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Oa?e?anueeiio aea?aeaaiiio oi?aa?neoao?

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

Iaoeiaee ea??aiee aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?
Eacainueeee Aaaeei Ai?eniae/, Oa?e?anueeee aea?aeaaiee oi?aa?neoao,
i?ioani? eaoaae?e oai?aoe/ii? ?aae?io?ceee.

Io?oe?ei? iiiiaioe: — aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?
I?ina??i?i Na?a?e Eaii?aeiae/, ?aae?iano?iiii?/iee ?inoeooo IAI Oe?a?ie,
caa?aeoaa/ a?aeae?eii ia/enethaaeueii? iaoaiaoeee (i. Oa?e?a);

— aeieoi? oaoi?/ieo iaoe, caneoaeaiee ae?y/ iaoee Oe?a?ie, i?ioani?
Caiyo?i Aaaeei ?aaiiae/, Oa?e?anueeee a?enueeiaee oi?aa?neoao, i?ioani?
eaoaae?e aioaiii-o?aea?ieo i?eno?i?a.

I?ia?aeia onoaiiaa: Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao
?aae?iaeaeo?ii?ee I?i?noa?noaa ina?oe Oe?a?ie, eaoaae?a iniia
?aae?ioaoi?ee.

Caoeno a?aeaoaeaoueny «17» 06 1999 ?. i 1530 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae64.051.02 Oa?e?anueeiai aea?aeaaiiai
oi?aa?neoaoo ca aae?anith: 310077, i. Oa?e?a, ie. Naiaiaee, 4, aoae.
3-9.

C aeena?oaoe??th iiaeia iciaeiieoenue o Oeaio?aeuei?e iaoeia?e
a?ae?ioaoe? Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo ca aae?anith:
310077, i. Oa?e?a, ie. Naiaiaee, 4.

Aaoi?aoa?ao ?ic?neaiee «11» 05 1999 ?ieo

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Eyoianueeee A.O.

4

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

?iaioo i?enay/aii aeine?aeaeaiith aeaeo?iaeeiai?/ieo aeanoeainoae
ia??iaee/ieo a iai?yieo ?iciianthaeaeaiiy oaeeue iine?aeiaiinoae c
aeia?eueiith e?euee?noth iaoaeiae?aeaeo?e/ieo iaiaeii??aeiinoae ?c
neeaaeiei oa?aeoa?ii ?icn?yiiy iie?a. Cai?iiiiiaaia iiaeaeue
ocaaaeueith? /eneaii? ie?ai? iiaoaeiae iaiaaeaieo ia??iaee/ieo no?oeoo?,
ine?eueee a?aoiao? neeaaeio eiiiiceoe?th aeaiaioo, ui iiaoi?th?oueny,
oa?aeoa? ?icn?yiiai iei iiey, aeia?euei? aeanoeaino? ? oei ao?aeieo oa
aeo?aeieo e?i?e ia?aaea/.

Aea?? ia’?eoo aeine?aeaeaiiy iaoiiaeaii, ii-ia?oa, oe?ieei canoinoaaiiyi
ia??iaee/ieo nenoai o ?aae?io?ceoe?, iioeoe?, aeonoeoe?; ii-ae?oaa,
iiaeeea?noth iiaeaethaaiiy i?e?iaeieo na?aaeiaeu, ii-o?ao?; iio?aaith
?ic?iaee ocaaaeueithth/iai aoaeoeaiiai aiae?oe/iiai iaoiaeo aiae?co.

Aeooaeuei?noue oaie. Ia??iaee/i? no?oeoo?e oe?iei aeei?enoiaothoueny ye
aacia? aeiee a aeaeo?iiieo i?eeaaeao, nioaiaeo oa ?aciiainieo o?eueo?ao,
e?i?eieo i?enei?thaa/ao, iieaeoey?ieo i?aeneethaa/ao ? aaia?aoi?ao,
iaa?no?aeueieo e?i?yo ca’yceo, naiio?eueo?oth/eo oaeeaaiaeao, aioaiao
a?aeo/i? oaee? oiui. O ca’yceo c oni?oaie oaoiieia?? ae?iaieoeoaa oiieeo
ie?aie, oaa?aeio?eueieo, iioe/ieo oa aeonoe/ieo a?aoie, ai?iaaaeaeaiiyi
iiaeo iaoa??ae?a (iae?i?eieo i??i- oa i’?ciaeaeo?e/ieo, aeaeo?iiioe/ieo
? o. ?.) a inoaii?e /an ?ioa?an aei aeine?aeaeaiiy ia??iaee/ieo nenoai
ia iniia? neeaaeieo ?icn?thaa/?a ia eeoa a?ae?iaeeany, aea ? a cia/i?e
i??? iineeeany. Oiio e?euee?noue iiaeo i?eeaae?a, a iniia? yeeo eaaeaoue
aeanoeaino? ia??iaee/ieo nenoai, ca?eueoo?oueny ? ia ia? oaiaeaioe?? aei
iane/aiiy.

Aiae?c oiia oa oa?aeoa?o ?iciianthaeaeaiiy oaeeue o iane?i/aiieo
ia??iaee/ieo no?oeoo?ao i?noeoueny o eeane/i?e oai???. Aeey iaiaaeaieo
ia??iaee/ieo no?oeoo? aiia aeecueei iieno? eeoa ?oi? oacia? aeanoeaino?
oei oi/i?oa, /ei a?eueoo e?euee?noue aeaiaio?a aiie iathoue. I?e oeueiio
aaaeeea? aeey i?aeoeee ieoaiiy ocaiaeaeaiiy, aieeao a?aieoeue,
iaiao?aeii? e?eueeino? aeaiaio?a ae??oothoueny iica ?aieaie oe???
oai???. I?e aeine?aeaeaii? no?oeoo? c iaaaeeeith e?euee?noth
aea?aeenoaioii ?icoaoiaaieo iaiaeii??aeiinoae canoiniaothoue iaoiae
iine?aeiaiiai “coeooy” iie?a ia iaeiioeiieo a?aieoeyo. Iiaeaia nenoaiith
aeaaa?a?/ieo ??aiyiue ??oaiiy, iaa?oue iiaeeo?eiaaia oeyoii ?aeo?aioieo
ni?aa?aeiioaiue, ii nai?e noo? i???ioiaaia ia /eneiao ?aae?caoe?th. ?c
c?inoaiiyi e?eueeino? iaiaeii??aeiinoae oaeee i?aeo?ae ? iaei aoaeoeaiei
ye c oi/ee ci?o ianyao ia/eneaiue, oae ? iai/iino? ?acoeueoao?a
?ic?aooieo, o?oaeiiu?a o?ce/iiai aiae?co, oe?eani?yiiaaiiai iiooeo
iioeiaeueieo oiia aenieoaoaoe??, ?ica’ycaiiy caaea/ neioaco.

O. Aaaea (1950 ?.), A.A. ?icaiaa?aii (1958 ?.), A.?. C?eueaa?iaiii,
A.?. Iaea?aiei ?c ni?a?ia?oieeaie (1988 ?.) cai?iiiiiaai? aiae?oe/i?
iaoiaee, ui aeeeth/athoue i?yia ia?aiiiaeaiiy iao?eoe? caeiieaiiy. ?o
oai??y iienoaaea ia??iaee/i? iine?aeiaiino? c i?inoeo ?icn?thaa/?a o
aeaeyae? ae?aeaeo?e/ieo oa??a, ui /a?aothoueny. Oiio aaaaea?oueny ca
aeioe?eueia ?icaeoie aiae?oe/iiai ? aaeineiiaeaiiy /eneiaeo iaoiae?a
aiae?co ia??iaee/ieo no?oeoo? c iaoaeiae?aeaeo?e/ieie
iaiaeii??aeiinoyie, ye? iathoue neeaaeiee oa?aeoa? ?icn?yiiy.

I?iaaaeai? o aeai?e ?iaio? aeine?aeaeaiiy ni?yiiaai? ia ?ic?iaeo iiaeo
oa iie?ioaiiy aenieoaoaoe?eieo oa?aeoa?enoee, ?icoe?aiiy
ooieoe?iiaeueieo iiaeeeainoae a?aeiieo i?eeaae?a ea?oaaiiy o
iaaeaeniei/anoioiiio (IA*) oa i?e?iao?iaiio (II) ae?aiaciiao.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
?iaioa aeeiioaaeany ca?aeii c Eii?aeeiaoe?eiei ieaiii I?iina?oe Oe?a?ie
(i?ia?aia ?4 “Aca?iiae?y aeaeo?iiaai?oiiai aei?ii?ithaaiiy oa iioie?a
ca?yaeaeaieo /anoeiie c ?a/iaeiith”, caoaa?aeaeaia ia 1997-1998 ??.,
iaeac ?6/10-200 a?ae 13.2. 97 ?.). ?? iaoa??aee oa?eoee aei ca?o?a
aea?aeathaeaeaoieo IAe? Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo
“Aaaaoiooieoe?iiaeuei? aeaeo?iaeeiai?/i? nenoaie ia iniia?
eiiiiceoe?eieo iaoa??ae?a” (? 32-14-94-0194 UA01854); “Oai??y
aaaaoioa?iaeo eiiiiceoe?eieo na?aaeiaeu” (? 32-14-97-0197 UA015771).

Iaoa ? caaea/? aeine?aeaeaiiy – aeyaeoe o?ce/i? caeiiii??iino?
aca?iiae?? iie?a c ia??iaee/iith iine?aeiai?noth, ui neeaaea?oueny c
aeia?eueii? e?eueeino? neeaaeiieiiiiceoe?eieo iaoaeiae?aeaeo?e/ieo
?icn?thaa/?a, oa aecia/eoe iia? ooieoe?iiaeuei? iiaeeeaino? i?eeaae?a
ea?oaaiiy ia ?o iniia?. Aeey aeinyaiaiiy oe??? iaoe iaiao?aeii aoei
?ica’ycaoe oae? caaea/?:

1. aeeo?aeoe?y ieinei? aeaeo?iiaai?oii? oaee? oa iaiinaeoiaeiiai
a?aeai?iioeueno ia iine?aeiaiino? ?c N iaai?oiae?aeaeo?e/ieo oa??a c
?acenoeaieie ie?aeaie, aenia?eiaioaeueia aecia/aiiy ?? oa?aeoa?enoee
?icn?yiiy o II ae?aiacii? aeiaaeei oaeeue;

2. aeeo?aeoe?y TM0n– ? TE0n– oaeeue ia N aea?aeenoaioii ?icoaoiaaieo
?aae?aeueieo, e?eueoeaaeo ae?ao?aaiao, ?acenoeaieo ie?aeao c
iaai?oiae?aeaeo?e/ieie oaeaaie o oeee?iae?e/iiio oaeeaaiae?;

3. aeeo?aeoe?y ieinei? H- iiey?eciaaii? oaee? ia ia??iaee/i?e
iine?aeiaiino? a?aoie c ?aeaaeueii i?ia?aeieo a?on?a i?yiieooiiai
iiia?a/iiai ia?a??co;

4. aecia/aiiy noaei? ?iciianthaeaeaiiy aeanii? oaee? o iane?i/aiieo
aiaeiaao no?oeoo?, ui aeine?aeaeothoueny.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. ?ica’ycaii ieceo iiaeo caaea/
aeeo?aeoe?? ia iaiaaeaieo ia??iaee/ieo iine?aeiaiinoyo c
iaiaeii??aeiinoae c? neeaaeiei oa?aeoa?ii ?icn?yiiy oaeeue ye o
a?eueiiio i?inoi??, oae ? o oaeeaaiaeao. ?icaeiooi aoaeoeaiee aeai?eoi
?ic?aooieo oa?aeoa?enoee iie?a ia iniia? oai??? iao?e/ieo ooieoe?e. A
iaeiiiiaeiaiio ?aaeei? eiao?oe??ioe ?icn?yiiy ? aeeneiaoe?? iaaaaeai?
ocaaaeueithth/eie aiae?oe/ieie ae?acaie c aeei?enoaiiyi iie?iii?a Iiaeia
(Mauguin).

Aeyaeai? o?ce/i? oaeoi?e, ui aecia/athoue iieiaeaiiy, oe?eio ? aeeiai?eo
cii eaac?i?ici?ino? oa eaac?caie?aiiy iaiaaeaieo ia??iaee/ieo
iine?aeiaiinoae. Aia?oa iaea?aeaia aneiioioeea eiao?oe??io?a a?aeaeooy
aeeneiaoeaieo iaiaaeaieo ia??iaee/ieo iine?aeiaiinoae i?e c?inoaii? a
ieo e?eueeino? aeaiaio?a oa anoaiiaeaia iaeanoue ia?aiao??a no?oeoo?e,
eiee aiia ca nai?ie aeanoeainoyie aaeaeaaoia iai?aiane?i/aiiei aiaeiaai.

Aeanoeaino? ei?ai?a iie?iii?a Iiaeia neeaee iniiao iiaiai i?aeoiaeo aei
aiae?co ?aciiainieo yaeu. Aeyaeai? iecueeiaeia?ioi?, aenieiaeia?ioi? oa
iaaeaeia?ioi? ?aciiaine o eiaei?e ?c cii eaac?i?ici?ino? ia /anoioieo oa
eooiaeo caeaaeiinoyo eiao?oe??ioo a?aeaeooy iine?aeiaiino? a?aoie c
i?ia?aeieo a?on?a i?yiieooiiai iiia?a/iiai ia?a??co.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?aeeiee i?aeo?ae aei
aiae?co aca?iiae?? oaeeue c iaiaaeaieie ia??iaee/ieie no?oeoo?aie
aeicaieea c?iaeoe ieceo ocaaaeueithth/eo aeniiae?a a?aeiinii /anoioieo,
iiey?ecaoe?eieo ? i?inoi?iaeo oa?aeoa?enoee iie?a ?icn?yiiy, aecia/eoe
?oith aeeiai?eo i?e ci?i? eiiiiceoe??, aaiiao?e/ieo oa iaoa??aeueieo
ia?aiao??a. Aeyaeai? o?ce/i? caeiiii??iino? iathoue i?aeoe/ia cia/aiiy,
ine?eueee ?icaeyioo? iiaeae? iaeneiaeueii a?aoiaothoue iniaeeaino?
iiaoaeiae ?aaeueieo i?eeaae?a, nenoai ? oiiae ?o aenieoaoaoe??. Aiie
oaeiae a?aoiaothoue noaie ?ioaa?aoe??, ao?aoe o iaai?oiae?aeaeo?e/ieo
na?aaeiaeuao, oei caoaeaeoth/eo iie?a ? e?i?e ia?aaea/?. Ana oea
noai?th? oiiae aoaeoeaiiai aeei?enoaiiy iaea?aeaieo ?acoeueoao?a a
nenoaiao aaoiiaoeciaaiiai i?iaeooaaiiy.

Aeyaeai? aeanoeaino? oa?oaaoiai iiaeeiath/iai iie?eooy ae?aio
aeicaieythoue aoaeoeaii ae??ooaaoe caaea/? aeaeo?iiaai?oii? noi?niino?,
caoenoo ethaeae, ye? i?aoeththoue c aeaea?aeaie iiooaeiiai
aei?ii?ithaaiiy. Iaaaaeai? iniaeeaino? oa?aeoa?enoee ?icn?yiiy ?
?aciiainieo yaeu a?aee?eaathoue ia?niaeoeao ?icoe?aiiy ooieoe?iiaeueieo
iiaeeeainoae a?aeiieo i?eeaae?a oa noai?aiiy iaaeaeia?ioieo /anoioieo,
iiaeiaeo oa i?inoi?iaeo o?eueo??a.

Iaea?aeai? ?acoeueoaoe iiaeooue aeei?enoiaoaaoeny ye ?aia?i? aeey
iiaeaethaaiiy o?ce/ieo i?ioean?a o i?e?iaeieo aai ooo/ieo ia??iaee/ieo
ooai?aiiyo, iai?eeeaae, i?e aiae?c? aeaieo ?o aeenoaioe?eiiai
ciiaeoaaiiy, ia?oei?aiiio ?aae?ioaeeaaiio eiio?ie? eiiiiceoe?eieo
iaoa??ae?a oiui.

Iniaenoee aianie caeiaoaa/a. A ?iaioao, ui iioae?eiaai? o ni?aaaoi?noa?,
iniaenoi caeiaoaa/ai ?ica’ycai? caaea/? aeeo?aeoe?? oaeeue ia
ia??iaee/ieo no?oeoo?ao, ?icaeiooi oa ?aae?ciaaii aoaeoeaiee aeai?eoi
?ic?aooieo iie?a ? ?ic?iaeaii eiai i?ia?aiia caaacia/aiiy, i?iaaaeaii
o?ce/iee aiae?c oaeeueiaeo i?ioean?a. Iei cai?iaaaeaeai? ocaaaeueithth/?
ia?aiao?e, ui iienothoue ?aeeiei /eiii iao?eoeth ia?aaea/? ??ciiiai?oieo
?icn?thaa/?a. Aaoi?ii ?ic?aoiaaia oa aeaioiaeaia oa?oaaoa iiaeeiath/a
no?oeoo?a, iinoaaeaii ? aeeiiaii aenia?eiaio c aecia/aiiy ??
oa?aeoa?enoee ?icn?yiiy.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe ?iaioe
iaaiai?thaaeeny ia iaoeiai-oaoi?/ieo eiioa?aioe?yo ?aae?io?ce/iiai
oaeoeueoaoo Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo, oaiaoe/iiio
nai?ia?? “Canoinoaaiiy ?ioaa?aeueieo ??aiyiue o iae?ineii?/i?e
aeaeo?iaeeiai?oe?” o Oa?e?anueeiio oaoi?/iiio oi?aa?neoao?
?aae?iaeaeo?ii?e?, ia i?aeia?iaei?e eiioa?aioe?? “International
Conference on Mathematical Methods in Electromagnetic Theory” (2-5 June,
1998, Kharkov, Ukraine), aoee i?aaenoaaeai? ia i?aeia?iaeiiio neiiic?oi?
“International Symposium on Electromagnetic Theory” (25-28 May 1998,
Thessaloniki, Greece).

Ioae?eaoe??. Ca ?acoeueoaoaie ?iaioe iioae?eiaaii 7 noaoae a iaoeiaeo
aeo?iaeao: “Electromagnetics” (USA), “Aeiiia?ae? IAI Oe?a?ie”,
“?aaeeioaoieea e yeaeo?iieea” (?in?y), “Yeaeo?iiaaieoiua aieiu e
yeaeo?iiiua nenoaiu” (?in?y), “Aanoiee Oa?ueeianeiai oieaa?neoaoa“, 1
aeaiiiiaaiee ?oeiien o AeIOA Oe?a?ie, 3 aeiiia?ae? o iaoa??aeao
eiioa?aioe?e.

No?oeoo?a ? ianya aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c anooio,
/ioe?ueio ?icae?e?a, aeniiae?a, nieneo aeei?enoaieo aeaea?ae. Caaaeueiee
ianya neeaaea? 137 noi??iie. ?iaioa i?noeoue 32 ?ethno?aoe?? (23 ie?ai?
noi??iee), 2 oaaeeoe? (1 noi??iea), nienie aeei?enoaieo e?oa?aoo?ieo
aeaea?ae ia?aoiao? 114 iaeiaioaaiue (12 noi??iie).

Iniiaiee ci?no ?iaioe

O Anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe??, noi?ioeueiaai?
?? iaoa, iaoeiaa iiaecia, i?aeoe/ia cia/aiiy, noenei aeeeaaeaii ci?no,
a?aeiiino? i?i ai?iaaoe?th aeena?oaoe??.

?icae?e 1 “Caaea/? ? iaoiaee aeine?aeaeaiiy aaaaoiaeaiaioieo
ia??iaee/ieo no?oeoo?” iineoue eiioeaiooaeueiee oa?aeoa?. A?aecia/ai?
oi?eaeuei? aeanoeaino? iane?i/aiii? ia??iaee/ii? iine?aeiaiino?
?icn?thaa/?a, caaaeyee yeei ?oi? iaiaaeai? aiaeiae ciaeoee oe?iea
canoinoaaiiy ia eeoa a iioe/ieo oa aeonoe/ieo nenoaiao, aea ? a
aaaaoueio ?aae?io?ce/ieo i?eeaaeao (aeeo?aeoe?ei?, eaaioia?
i?aeneethaa/? oa aaia?aoi?e, aioaie a?aeo/i? oaee?, aaaaoieieia?
/anoioi? oa iiaeia? o?eueo?e, i?enei?thaa/?, ae?ao?aaiiaai? oaeeaaiaee
oiui).

I?e aiae?c? iaiaaeaieo ia??iaee/ieo iine?aeiaiinoae iniaeeaa cia/aiiy
iaaoaa?, c iaeiiai aieo, iaa?oiooaaiiy canoinoaaiiy eeane/ii? oai???
?iciianthaeaeaiiy oaeeue, a c ae?oaiai, — ?icaeoie oai??? aeeo?aeoe??,
ui a?aoiao? ?ici??e no?oeoo?e. Cacia/aii, ui eiioeaioe?y aeanieo oaeeue
c iaaieie i?eiouaiiyie aeicaiey? iienoaaoe nenoaie eeoa c aeoaea
aaeeeith e?euee?noth aeaiaio?a. Iaa?oiooaaiiy ?? canoinoaaiiy iiaeeeai
aai aenia?eiaioaeueii, aai oeyoii c?noaaeaiiy c aeaieie oai???
aeeo?aeoe??. Iaeiae, aiane?aeie i?eioeeiiai? ??cieoe? i?ae iaiaaeaiith
oa iane?i/aiiith nenoaiaie caeeoa?oueny iaiaeiicia/iei aea?? e?eoa??th
?o ii??aiyiiy.

No/ani? iaoaiaoe/i? iaoiaee aeicaieythoue iiaoaeoaaoe no?iao oai??th
ia??iaee/ieo iine?aeiaiinoae. I?e a?aeiiiio ??oaii? caaea/? aeeo?aeoe??
oaeeue ia aaciaiio aeaiaio? aecia/aiiy iiey ?icn?yiiy ?o eaioethaiaiai
niieo/aiiy ia ia? i?eioeeiiaeo o?oaeiiu?a. Aeey neeaaeiieiiiiceoe?eieo
?icn?thaa/?a c oi/ee ci?o iai/iino? oa ?noioiiai nei?i/aiiy ianyao
ia/enethaaeueieo ?ia?o ? iaoiae, cai?iiiiiaaiee aeaaeai?eii E.I.
Eeoaeiaiei ?c ni?a?ia?oieeaie aeey aeine?aeaeaiiy iai?aiane?i/aiieo
iine?aeiaiinoae. Iaeiae, caneoaiao? oaaao ? ?icaeoie iaoiae?a oai???
iao?e/ieo ooieoe?e, ye? aoee canoiniaai? caaaeaieie ?ai?oa aaoi?aie aeey
aiae?co i?inoi? ia??iaee/ii? iine?aeiaiino? ?c ae?aeaeo?e/ieo oa??a.

O ?icae?e? 2 “Aeine?aeaeaiiy ia??iaee/ii? iine?aeiaiino? ?icn?thaa/?a
iaoiaeii iao?e/ieo ooieoe?e” ?icaeyaea?oueny ocaaaeueithth/a iiaeaeue
aaaaoiaeaiaioii? iine?aeiaiino? iaeiioeiieo aeaiaio?a. Noi?ioeueiaaii
eiioeaioe?th eiiieaeniiai aeine?aeaeaiiy iaiaaeaieo ia??iaee/ieo nenoai
oeyoii aaaaeaiiy ocaaaeueiaii? iao?eoe? ia?aaea/? ? aeei?enoaiiy
iaoiae?a oai??? e?e oa iao?e/ieo ooieoe?e.

?ica’yceii e?aeiai? caaea/? aeey aaciaiai aeaiaioo ? ?aaeooeueiaaia
ocaaaeueiaia iao?eoey ia?aaea/? T (?en.1-3). Aiia ca’yco?
aaeoi?e-noiaioe? iaaeath/iai oa a?aeaeoiai iie?a ia aoiae? (z=mL) oa
aeoiae? (z=(m+1)L) aea?aaeaioiiai 2n-iiethnieea. Iiey ?icn?yiiy oaee?
p-ai oeio an??th no?oeoo?ith ciaoiaeyoueny c iia?aoi?iiai ??aiyiiy

wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
A`???&??yyyy?????Ayyy?yyy ??s?? ???&?
?MathType??@???uath??????

aea T0 oa T3 – iao?eoe? ia?aaea/? (II) ao?aeii? oa aeo?aeii? noai
ca’yceo nenoaie c noi?aeieie iai?ai?inoi?aie.

C iaoith nei?i/aiiy ianyao ia/enethaaeueieo ?ia?o i?e caaaeaii? II aei
nooiaiy N oa iaea?aeaiiy aoaeoeaiiai aeai?eoio ?ic?aooieo, a oiio /ene?
? aiae?oe/iiai ??oaiiy, a ?iaio? aeei?enoiao?oueny ?ioa?iieyoe?eia
oi?ioea Eaa?aiaea oa oai?aia Eae?-Aaieeueoiia oai??? iao?e/ieo
iie?iii?a. A iaeiioaeeaaiio ?aaeei?, eiee aaciaee aeaiaio iieno?oueny
aea?aaeaioiei /ioe?eiiethnieeii, nooi?iue eiai iao?eoe? ia?aaea/?

wmetafile8? ??/???????????
???????????yyy????.????1?????? ???????
A ???&??yyyy?????AyyyYyyy`??e?? ???&?
?MathType??????u?th??????caeaaeeoue a?ae iie?iii?a Iiaeia (Mauguin)

wmetafile8? ??Q???????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????Ayyy?yyy ??H?? ???&?
?MathType??`????uthY?????Ooo wmetafile8? ??“???????????
???????????yyy????.????1?????? ??????? Aa
???&??yyyy?????Ayyy?yyy  ??x?? ???&? ?MathType??P?
???u?????????»????-?????Ca aeiiiiiaith oi?ioe (1) ? (2) eaaei
io?eiaoe eiao?oe??ioe a?aeaeooy (R=B0/A0) oa i?ioiaeaeaiiy (=AN+1/A0)
N-aeaiaioii? no?oeoo?e:

wmetafile8? ??Q???????????
???????????yyy????.????1?????? ??????? ?
.???&??yyyy?????Ayyy®yyya-??.?? ???&?
?MathType??p???uoyY?????aea wmetafile8? ??O???????????
???????????yyy????.????1?????? ???????
@????&??yyyy?????Ayyy¦yyyA??ae?? ???&?
?MathType??`????uthY?????Eiee oaeeueia? i?ia?aeiino? ?aaoey?ii?
ae?eyiee aaciaiai aeaiaioo ? i?aea?aeieo eaiae?a, ni?aiaaeathoue
(T0=T3=I), oi?ioee aeey eiao?oe??io?a ?icn?yiiy ni?iuothoueny. A oeueiio
aeiaaeeo iiaia i?ici??noue nenoaie ia? i?noea i?e aeeiiaii? iaei??? c
aeaio iacaeaaeieo oiia:

wmetafile8? ??—???????????
???????????yyy????.????1?????? ???????
@`???&??yyyy?????Ayyy¦yyy ??ae?? ???&?
?MathType??`????uthY?????Ia?oa iieno? iecueeiaeia?ioi? ?aciiaine ?
caeaaeeoue eeoa a?ae ia?aiao??a aaciaiai aeaiaioo, a ae?oaa –a?aoiao? ?o
e?euee?noue oa oa?aeoa? ca’yceo i?ae ieie. Ei?ai? iie?iii?a Iiaeia X
aecia/athoue ?aciiaini? yaeua o iaaeeneiaoeaieo nenoaiao, o oiio
?aooieo, ia?aiao?e nenoaie, i?e yeeo iathoue i?noea aenieiaeia?ioi?
?aciiaini? eieeaaiiy. ?icaeiooa oai??y aeicaiey? ciaeoe aeani?
eiiieaeni? /anoioe aai oaeeueia? /enea c (1) i?e Ap0=0. Iai?eeeaae, aeey
iaeiioaeeaaiai ?aaeeio a?aeiia?aeia ??aiyiiy ia? aeaeyae

wmetafile8? ??th???????????
???????????yyy????.????1?????? ???????
@????&??yyyy?????Ayyy¦yyyA??ae?? ???&?
?MathType??`????uthY?????Iaaaaeai? ??oaiiy oa aeai?eoi eiai
?aae?caoe?? ?iaa??aioi? aei aeanoeainoae ?icn?thaa/?a, ui
iiaoi?ththoueny, oa ?oiuei? e?eueeino?. ?iaeea?aeoaeuei?
aeaeo?iaeeiai?/i? iniaeeaino? iaiaaeaii? iine?aeiaiino? i?iyaeythoueny
eeoa o iao?eoe? ia?aaea/? aaciaiai aeaiaioo. ?? eiiiiiaioe aecia/athoue
noaeo ?iciianthaeaeaiiy aeanii? oaee? iane?i/aiiiai oa eiao?oe??io
a?aeaeooy iai?aiane?i/aiiiai aiaeia?a no?oeoo?e, ui aeine?aeaeo?oueny.
?icaeiooee i?aeo?ae caaacia/o? iiaoaeiao caieiaii? oai??? iaiaaeaieo
ia??iaee/ieo no?oeoo?, ui aeei?enoiaothoueny o ?aaeueieo i?eeaaeao oa
nenoaiao aeaiaioii? aace IA* oa II ae?aiacii?a.

?icae?e 3 “Ia??iaee/ia iine?aeiai?noue oa??a c ieaia?ieie
?icn?th-aa/aie” i?enay/aii aiae?co aeaeo?iaeeiai?/ieo aeanoeainoae
iaiaaeaieo ia??iaee/ieo iine?aeiaiinoae c ia?aciiainieo
iaiaeii??aeiinoae a ioi/aii? ?aaoey?ieo ae?eyiie oaeeaaiaeieo eaiae?a c
??cieie oaeeueiaeie oa?ae-oa?enoeeaie. Cai?iiiiiaai? ocaaaeueithth/?
iiaeae? iiaeeiath/iai iie?eooy (i?ae?icae?e 3.1) ? oaeeaaiaeiiai
iiaeiaiai naeaeoi?a (i?ae?icae?e 3.2) (?en.2).

Iao?eoeth ia?aaea/? aaciaiai aeaiaioo iiaeeiath/iai iie?eooy aeey oaeeue
i?oiaiiaeueieo iiey?ecaoe?e ciaeaeaii /a?ac aea?aaeaioi? a?aie/i? oiiae
ia ?acenoeai?e ie?aoe?. Iaaaaeaii, ui a?aei?iia iniaeea?noue iaiaaeaieo
ia??iaee/ieo iine?aeiaiinoae ?icn?thaa/?a — aeniei/anoioi? inoeeeyoe??
eiao?oe??ioa a?aeaeooy o ciiao eaac?i?ici?ino? no?oeoo? (?en.4).

I?iaaaeaii ii??aiyeueiee aiae?c no?oeoo?e, ui aeine?aeaeo?oueny, oa ??
iai?aiane?i/aiiiai aiaeiao, aeyaeaii oa?aeoa? aieeao ia ?oi? aeanoeaino?
aeanieo ?aaeei?a ?o iane?i/aiiiai i?ioioeio. Aeeneiaoe?y aia?a?? ?
aeiaeaoeiaei oaeoi?ii, ui i?ecaiaeeoue aei ua a?eueoiai “?icieooy”
a?aieoeue i?ae iaeanoyie c aenieei oa iaeei ??aiai a?aeaeooy oaeeue ia
/anoioieo oa eooiaeo caeaaeiinoyo.

Anoaiiaeaii, ui eiao?oe??io a?aeaeooy – neeaaeia aaaaoiia?aiao?e/ia
ooieoe?y c aeno?aiaeueieie cia/aiiyie. Oea aeicaiey? iioei?coaaoe

aenieoaoaoe?ei? oa?aeoa?enoeee ? i?iaeooaaoe aenieiye?ni? iiaeeiath/?
(i?ina?oeyth/?) iie?eooy ia a?aeaeaath/iio ae?ai?. Aeey aeeneiaoeaieo
nenoai iaea?aeaia aneiioioeea eiao?oe??ioa a?aeaeooy o aeiaaeeo aaeeei?
e?eueeino? aeaiaio?a. Aecia/aia iaeanoue ia?aiao??a iaiaaeaii?
ia??iaee/ii? iine?aeiaiino?, eiee ?? ?icn?thaaeuei? ? aeeneiaoeai?
aeanoeaino? ye?nii ni?aiaaeathoue, aai aeecuee? aei ??
iai?aiane?i/aiiiai aiaeiaa.

A i?ae?icae?e? 3.2 cai?iiiiiaaii iiaeaeue oaeeaaiaeieo oacioi?ioth/eo
i?eeaae?a, /anoioieo ? iiaeiaeo naeaeoi??a, oe?ieinioaiaeo aoaithaoi??a,
aoaeiiieo a?aeaeca?eaethaa/?a, ocaiaeaeoth/eo iaaaioaaeaiue. Aiia yaey?
niaith ia??iaee/io iine?aeiai?noue c N ieaia?ieo neiao?e/ieo a?aeiinii
a?n? ?aaeoeaieo ae?ao?aai aai ?acenoeaieo ie?aie i?ae
iaai?oiae?aeaeo?e/ieie oaeaaie o oeee?iae?e/iiio oaeeaaiae? (?en.2).
Iao?eoey ia?aaea/? aaciaiai aeaiaioo ciaeaeaia c ??oaiiy caaea/?
aeeo?aeoe?? neiao?e/ieo TM0n- ? TE0n- oaeeue a aeiaaioaeeueiaiio
iaaeeaeaii? iaoiaeii aeainoi?iii?o aea?aaeaioieo a?aie/ieo oiia oeio
Aaeiooaeia-Neaiaa.

*anoioia caeaaei?noue a?aeaeoeiai? ni?iiiaeiino? ae?ao?aaie aecia/a?
aiie?ooaeo aeniei/anoioieo inoeeeyoe?e o ciiao eaac?i?ici?ino? oa
aeia?ioi?noue ?aciiainieo eieeaaiue, ui ca?eueoo?oueny ?c c?inoaiiyi
e?eueeino? aeaiaio?a nenoaie. Iieacaii, ui ciae ?aaeoeaiino? aieeaa? ia
iieiaeaiiy, a ?? aaee/eia – ia oe?eio cii eaac?caie?aiiy
(eaac?i?ici?ino?). Iiey?ecaoe?eia ai?cio?ii?y (?en.5) i?iyaey?oueny a
aeueoa?iaoeaiiio iieiaeaii? cii eaac?i?ici?ino? ? eaac?caie?aiiy aeey
i?oiaiiaeueieo oei?a oaeeue ia aeenia?n?eieo caeaaeiinoyo. Aeniea
a?aeaeoeiaa ni?iiiaei?noue ae?ao?aai i?ecaiaeeoue aei aaeueie aocueei?
ciie eaac?i?ici?ino?, ui ciaioo?oueny c? ca?eueoaiiyi /anoioe.

O ?icae?e? 4 “Aenieiaeia?ioiee /anoioiee oa eooiaee aeene?ei?iaoi? ?c
?aciiainieo ?icn?thaa/?a” cai?iiiiiaaii ? aeine?aeaeaii iiaeaeue
o?eueo?o c aenieei nooiaiai naeaeoe?? a oe?ieiio oa iaaeaocueeiio
ae?aiacii? aa??aoe?? /anoioe oa eooa iaae?iiy oaee?. A?i ooai?aiee c N
ia?aeaeueieo aea?aeenoaioii ?icoaoiaaieo o a?eueiiio i?inoi?? a?aoie c
i?ia?aeieo a?on?a i?yiieooiiai iiia?a/iiai ia?a??co (?en.3).

Ia iniia? a?aeiieo oi/iiai ? iaaeeaeaiiai ??oaiue caaea/? aeeo?aeoe??
ieinei? H-iiey?eciaaii? oaee? ia aaciaiio aeaiaio? i?aaenoaaeaii eiai
iao?eoeth ia?aaea/? a aaaaoioaeeaaiio oa aeiaaioaeeueiaiio ?aaeeiao.
?ica’ycaii caaea/o aeeo?aeoe?? oaeeue ia ia??iaee/i?e iine?aeiaiino?
a?aoie. Ooo oaeiae niinoa??aathoueny ciie eaac?i?ici?ino? oa
eaac?caie?aiiy ia /anoioieo oa eooiaeo caeaaeiinoyo eiao?oe??io?a
?icn?yiiy nenoaie. A aeiaaioaeeueiaiio ae?aiacii? aiae?oe/ii aecia/ai?
?aciiaini? aeene?aoi? iaai?e aaiiao?e/ieo ? iieueiaeo ia?aiao??a nenoaie
(wmetafile8? ??ae???????????
???????????yyy????.????1?????? ??????? 
`???&??yyyy?????Ayyy¦yyy ??AE?? ???&? ?MathType??P?
???u?????????»????-?????Z?A???UH???Z?E ???UO
???Z?1/2???UB???uthY?????wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
@ ‘???&??yyyy?????Ayyy¦yyy`’??ae?? ???&? ?MathType??`?
???u?????????»????-?????Z?e???Um???uthY?????Aeey
iine?aeiaiino? a?aoie ?c oiieeo a?on?a (?<<1) aiie iathoue aeaeyae: wmetafile8? ??U??????????? ???????????yyy????.????1?????? ???????  `-???&??yyyy?????Ayyy¦yyy -??AE?? ???&? ?MathType??P? ???u?????????"????-?????Z?&???U«???uthY?????Aecia/aii, oaeiae aeeiai?eo oe?eie oa iieiaeaiiy cii c? c?inoaiiyi /anoioe, e?eueeino? aaciaeo aeaiaio?a oa aa??aoe?? ia?aiao??a a?aoee. Iai?eeeaae, aeey aecia/aii? iine?aeiaiino? ??cieoey i?ae iaeneiaeueiei ? i?i?iaeueiei cia/aiiyi neeaaea?: wmetafile8? ??u??????????? ???????????yyy????.????1?????? ??????? ?`$???&??yyyy?????Ayyy?yyy $????? ???&? ?MathType??0???uthY?????aea n – iiia? ciie. Ca?aene aeieeaa? ciaioaiiy ciie eaac?i?ici?ino? ?c ca?eueoaiiyi /anoioe, aenioe ? oe?eie a?on?a, oa iacaeaaei?noue a?ae e?eueeino? ia??iae?a aeey aaaaoieieiaeo nenoai (N>10). A caaaeueiiio aeiaaeeo oey oaiaeaioe?y caa??aa?oueny
(?en.6).

A?aei?oia iniaeea?noue ia??iaee/ieo iine?aeiaiinoae c ?aciiainieo
?icn?thaa/?a iieyaa? a oiio, ui aeaeo?iaeeiai?/iee ca’ycie i?ae
?aaoey?ieie ae?eyieaie non?aei?o ia??iae?a ? ?aciiainiith ooieoe??th
/anoioe oa eooo iaae?iiy. Oea aaaea aei aenieiaeia?ioieo ?
iaaeaeia?ioieo eieeaaiue, oe?ieeo eooiaeo oa /anoioieo cii
eaac?caie?aiiy (?aaeaeoi?iee nioaiaee o?eueo?), c?inoaiith aiie?ooae
inoeeeyoe?e a aaeueie aocuee?e cii? eaac?i?ici?ino? (iaaeaeia?ioiee
o?eueo?).

Aeniiaee

Ia iniia? iaoiae?a oai??? e?e ? iao?e/ieo ooieoe?e ?icaeiooi aoaeoeaiee
aeai?eoi aecia/aiiy oa?aeoa?enoee ?icn?yieo iie?a oe?ieiai eeano
aaaaoiaeaiaioieo ia??iaee/ieo nenoai, yeee aeeeth/a? iine?aeiaia
ia?aiiiaeaiiy iao?eoeue ia?aaea/?. A?i ia caeaaeeoue a?ae eiiiiceoe?? ?
ia?aiao??a iaiaeii??aeiinoae, ui iiaoi?ththoueny, ?oiueiai /enea, oeio
caoaeaeoth/i? oaee?, aeanoeainoae o?aea?ieo eaiae?a. ?iaeea?aeoaeuei?
aeanoeaino? no?oeoo? a?aeia?aaea? iao?eoey ia?aaea/? ia??iaeo. Aeey
iaeiiiiaeiaiai ?aaeeio ??oaiiy caaea/ aeeo?aeoe?? iiaeaii i?yieie
aiae?oe/ieie oi?ioeaie c aeei?enoaiiyi iie?iii?a Iiaeia (Mauguin).

Aeiaaaeaii, ui iaeano? ia?aiao??a iaiaaeaieo ia??iaee/ieo
iine?aeiaiinoae c aenieei oa iecueeei ??aiai a?aeaeooy iia’ycai? c
oiiaaie iioe?aiiy aeanieo oaeeue ?oi?o iane?i/aiieo aiaeia?a (ciie
i?ici?ino? oa caie?aiiy). Iieacaii, ui iieiaeaiiy, oe?eia cii, ?o
aeeiai?ea ? na?aaei?e ??aaiue a?aeaeooy caeaaeaoue a?ae aeanoeainoae
neeaaeiee?a ia??iaeo. Caaaeueia aeanoea?noue caeaaeiinoae eiao?oe??io?a
?icn?yiiy iaiaaeaieo ia??iaee/ieo nenoai a?ae /anoioe ? oaeeueiaiai
?ici??o aaciaiai aeaiaioo – iayai?noue ae??aiiianooaaieo inoeeeyoe?e.
sseui ia??iae ia? ao?aoe, ?o aiie?ooaea ciaioo?oueny, ? i?e aaeeei?
e?eueeino? ia??iae?a oa?aeoa?enoeee iie?a ?icn?yiiy iaiaaeaieo oa
iai?aiane?i/aiieo no?oeoo? i?aeoe/ii ni?aiaaeathoue.

Iiaoaeiaaii oai??th ?aciiainieo yaeu a iaiaaeaieo ia??iaee/ieo
iine?aeiaiinoyo. Iieacaii, ui ?o iaeneiaeueia (i?e a?aenooiino? ao?ao —
iiaia) i?ici??noue ia? i?noea i?e aeeiiaii? oi/a a iaei??? c aeaio oiia,
ui iiaeai? o aeaeyae? o?ainoeaiaeaioieo ??aiyiue. Ia?oa iaaaaeaii o
ia?aiao?ao ia??iaeo oa aecia/a? /anoioe iecueeiaeia?ioieo ?aciiain?a.
Ae?oaa caeaaeeoue a?ae aeanoeainoae ei?ai?a iie?iii?a Iiaeia, a naia:
/enea ia??iae?a, aeaeo?iaeeiai?/ii? ca’ycee i?ae non?aei?ie ?aaoey?ieie
ae?eyieaie, oa iieno? aenieiaeia?ioi? oa iaaeaeia?ioi? ?aciiaini?
eieeaaiiy o nenoaiao c ieaia?ieo oa ia’?iieo ?icn?thaa/?a, a?aeiia?aeii.

Aiae?oe/ieie oi?ioeaie iiaeaii aneiioioeeo ??oaiiy o?ainoeaiaeaioieo
??aiyiue. Ciaeaeaii ieceo aaiiao?e/ieo, iaoa??aeueieo ? iieueiaeo
ia?aiao??a, i?e yeeo ia? i?noea aaniethoia i?ici??noue iaaeeneiaoeaieo
no?oeoo?. Aecia/ai? ??aiyiiy aeey aeanieo eiiieaenieo /anoio ?
oaeeueiaeo /enae, noaei? ?iciianthaeaeaiiy ?o iane?i/aiieo aiaeia?a.

Cai?iiiiiaai? ocaaaeueithth/? iiaeae? oa iaaaaeai? ?acoeueoaoe aiae?co
iie?a ?icn?yiiy iiaeeiath/iai (i?ina?oethth/iai) oa?oaaoiai iie?eooy
iaoaeaaiai ae?aio c ?acenoeaieie ie?aeaie, aaaaoieieiaiai /anoioiiai ?
iiaeiaiai oaeeaaiaeiiai o?eueo?o c ieaia?ieo e?eueoeaaeo ? ?aae?aeueieo
ae?ao?aai, aenieiaeia?ioiiai /anoioiiai oa eooiaiai aeene?ei?iaoi?a c
iine?aeiaiino? ia??iaee/ieo a?aoie ?c i?ia?aeieo a?on?a.

Iicia/ai? oeyoe ? aeiaaaeaii (o oiio /ene? aenia?eiaioaeueii)
iiaeeea?noue iioei?caoe?? aenieoaoaoe?eieo oa?aeoa?enoee iiaeeiath/iai
iie?eooy ia a?aeaeaiiio ae?ai?, a naia: aeinyaiaiiy iaeneiaeueiiai
iiaeeiaiiy aia?a?? i?e aenieiio ??ai? ocaiaeaeaiiy o oe?ieiio ae?aiacii?
/anoio ? eoo?a iaae?iiy.

Aaee/eia ? oa?aeoa? ?aaeoeaiino? ieaia?ieo ae?ao?aai o aaaaoieieiaeo
oaeeaaiaeieo o?eueo?ao aecia/a? nooi?iue naeaeoe?? oei?a oaeeue,
aeia?ioi?noue ?aciiainieo eieeaaiue oa aeueoa?iaoeai? oiiae ?icn?yiiy
oaeeue i?oiaiiaeueieo iiey?ecaoe?e ye o aocuee?e, oae ? a oe?ie?e nioc?
/anoio.

A?aei?oia iniaeea?noue ia??iaee/ii? iine?aeiaiino? N a?aoie c a?on?a —
?aciiainiee aeaeo?iaeeiai?/i?e ca’ycie i?ae ?aaoey?ieie ae?eyieaie
non?aei?o ia??iae?a ?, ye iane?aeie, aenieiaeia?ioi? aeani? eieeaaiiy
a?aoee. Iieacaii, ui ?aaeeie c aenieith /anoioiith ? eooiaith
aea??i?noth (iaaeaeia?ioi? ?aciiaine) niinoa??aathoueny aaea i?e iaei?
e?eueeino? a?aoie. Aia?oa aeyaeaii iiaio i?ici??noue ia (N-1) aeecueeeo
cia/aiiyo eooo iaae?iiy o eiaei?e cii? eaac?i?ici?ino? (ocaaaeueiaiiy
aoaeoo A.Ae. Iaethaeeioey).

Iaaaaeaia oai??y oaeeaaeo i?ioean?a o eean? no?oeoo?, ooai?aieo
ia??iaee/iith iine?aeiai?noth c aeia?eueii? e?eueeino? ?icn?thaa/?a,
caaea/?, ye? ?icaeyioo? ia ?? iniia?, ?ic?iaeai? /enaeuei? oa aiae?oe/i?
aeai?eoie aiae?co ? ?ic?aooie?a, io?eiai? iaoeia? ? i?eeeaaei?
?acoeueoaoe i???ioiaai? ia noai?aiiy iiaeo, aaeineiiaeaiiy,
iioei?caoe?th aenieoaoaoe?eieo oa?aeoa?enoee a?aeiieo ooieoe?iiaeueieo
aoce?a aeaiaioii? aace IA* ? II ae?aiacii?a.

nienie IIOAE?EIAAIEO i?aoeue ca oaiith aeena?oaoe??

1. Kazanskiy V.B., Podlozny V.V. Quasiperiodic layered structure with
resistive films // Electromagnetics. Washington.: Taylor & Francis, —
1997. — ? 2. — P.131-145.

2. Eacaineee A.A., Iiaeeiciue A.A. Enneaaeiaaiea ia?eiaee/aneeo
ia?aie/aiiuo no?oeoo? n eniieueciaaieai iieeiiiia Iiaeia // Aeiiia?ae?
IAI Oe?a?ie. — 1998. — ?3. — N.86-91.

3. Iiaeeiciue A.A. Acaeiiaeaenoaea eiioeuena n iineaaeiaaoaeueiinoueth
iiaeiuathueo yeaiaioia // Aanoiee Oa?ueeianeiai oieaa?neoaoa.
?aaeeioeceea e yeaeo?iieea. — 1998. — ?.405. — N. 83-86.

4. Eacaineee A.A., Iiaeeiciue A.A. Aiaeeoe/aneee iaoiae ?aoaiey caaea/e
?annayiey aiei ia iineaaeiaaoaeueiie niaieoiiinoe iaeiioeiiuo yeaiaioia
// ?aaeeioaoieea e yeaeo?iieea. – 1998. O. 43, ? 12. — N. 1459-1462.

5. Eacaineee A.A., Iiaeeiciue A.A., Oa?aeeeia A.A. Enneaaeiaaiea
oa?aeoa?enoee ?annayiey iineaaeiaaoaeueiinoe iaeiioeiiuo yeaiaioia n
eniieueciaaieai oai?aiu Eyee-Aaieeueoiia // Yeaeo?iiaaieoiua aieiu e
yeaeo?iiiua nenoaiu. — 1999. O. 4, ?3. — N. 19-27.

6. Eaai/aiei Ae.Ae., Iiaeeiciue A.A. Yenia?eiaioaeueiia enneaaeiaaiea
iiaeiuathueo naienoa neienoie ia?eiaee/aneie no?oeoo?u n ?acenoeaiuie
ie?ieaie // A?niee Oa?e?anueeiai oi?aa?neoaoo. ?aae?io?ceea oa
aeaeo?ii?ea. — 1999. — ?427. — N.95-97.

7. Eacaineee, A.A., Iiaeeiciue A.A. Iiiaieaiaeueiue aunieiaeia?ioiue
/anoioiue e i?ino?ainoaaiiue naeaeoi? iiey. // A?niee Oa?e?anueeiai
oi?aa?neoaoo. ?aae?io?ceea oa aeaeo?ii?ea. — 1999. — ?.427 – N.98-101.

8. Eaaceia?eiaee/aneay neienoay no?oeoo?a / Eacaineee A.A.,
Iiaeeiciue A.A. – Eeaa, 1996. – 40 n. – ?on. — Aeai. a AIOA Oe?aeiu
12.06.1996, ?.1398 — Oe96.// Aiio. a ?AE “Aeaiiiiaai? iaoeia? ?iaioe”
1997. ?1, Na/i 434.

9. Kazanskiy V. B., Podlozny V.V. Analytical Investigation of Reflection
and Absorption of Quasiperiodic Structures on the Base of Mauguin
Polynomials // Proc. International Symp. on Electromagnetic Theory. —
Thessaloniki (Greece). – 1998. 25-28 May, — V. 2, — P. 745-747.

10. Kazanskiy V. B., Podlozny V.V., Khardikov V.V. Waveguide section of
sequentially included identical elements // Proc. International Conf. on
Mathematical Methods in Electromagnetic Theory. — Kharkov (Ukraine).
– 1998. — June 2-5, V. l. — P. 396-398.

11. Podlozny V.V., Scattering and Absorption of Videopulse by a Set of
Alternated layers With Resistive Films// Proc. International Conf. on
Mathematical Methods in Electromagnetic Theory. — Kharkov (Ukraine).
– 1998. — June 2-5, V. l. — P. 209-211.

Aiioaoe?y

I?aeeiciee A.A. Aeeo?aeoe?y aeaeo?iiaai?oieo oaeeue ia ia??iaee/i?e
iine?aeiaiino? iaoaeiae?aeaeo?e/ieo ?icn?thaa/?a. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.04.03 — ?aae?io?ceea. —
Oa?e?anueeee aea?aeaaiee oi?aa?neoao, i. Oa?e?a, 1999.

Ia iniia? iaoiaeo oai??? iao?e/ieo ooieoe?e ocaaaeueiaii ? iioei?ciaaii
aeai?eoi ??oaiiy caaea/ aeeo?aeoe?? aeaeo?iiaai?oieo oaeeue ia
ia??iaee/ieo iine?aeiaiinoyo ?c aeia?eueiiai /enea eiiiiceoe?eieo
iaoaeiae?aeaeo?e/ieo iaiaeii??aeiinoae o a?eueiiio i?inoi?? oa
oaeeaaiaeao. A iaeiioaeeaaiio ?aaeei? iaea?aeai? aiae?oe/i? ae?ace aeey
eiao?oe??io?a ?icn?yiiy ? aeeneiaoe??, ??aiyiiy aeey aeanieo eiiieaenieo
/anoio oa oaeeueiaeo /enae, ?icaeiooi oai??th ?aciiainieo yaeu.
?icaeyioo? oa?oaao? iiaeeiath/? iie?eooy iaoaeaaiai ae?aio,
aenieiaeia?ioiee /anoioiee ? eooiaee aeene?ei?iaoi? ia aac?
iine?aeiaiino? a?aoie ?c a?on?a, aaaaoie?eueoeaaee /anoioiee ? iiaeiaee
oaeeaaiaeiee o?eueo? ?c e?eueoeaaeo oa ?aae?aeueieo i?ia?aeieo
ae?ao?aai. Anoaiiaeaii aneiioioeeo eiao?oe??io?a a?aeaeooy aeeneiaoeaieo
nenoai c aeia?eueii? e?eueeino? ia??iae?a oa ?oi? ae?ace aeey
iai?aiane?i/aiieo aiaeia?a. Aeine?aeaeaiiy ni?yiiaai? ia ?ic?iaeo iiaeo
i?eno?i?a ? aaeineiiaeaiiy a?aeiieo i?eeaae?a oa nenoai IA* e II
ae?aiacii?a.

Eeth/ia? neiaa: aeeo?aeoe?y, ia??iaee/i? no?oeoo?e, iao?eoey ia?aaea/?,
iie?iiie Iiaeia, iiaeeiath/a iie?eooy, ae?ao?aaia, aeeo?aeoe?eia a?aoea,
ciia caie?aiiy, o?eueo?.

Summary

Podlozny V.V. Diffraction of electromagnetic waves by a periodic set of
metallodielectric scatterers. – Manuscript.

Thesis for candidate’s degree by speciality 01.04.03 — radiophysics.-
Kharkov State University, Kharkov, 1999.

The algorithm for the solution of the problem of the electromagnetic
wave diffraction by a periodic sequences of arbitrary number of
composite metallodielectric scatterers in free space and in waveguides
is generalized and optimized by using the theory of matrix functions. In
the single-mode regime, analytical formulas for scattering and
dissipation coefficients, equations for complex eigen frequencies and
wave eigenvalues are obtained and the theory of resonance phenomena is
developed. The multilayered absorbing coatings of a metal screen, high
Q-factor frequency and angular discriminator formed by a sequence of
gratings of perfectly electric bars, frequency and mode waveguide
iterated filter formed by ring and radial diaphragms are considered in
the work. The formulas for the asymptotic reflection coefficients of
dissipative systems of arbitrary number of periods and the expressions
for their semi-infinite analogs are obtained. The goal of the
investigations are the development of new instruments and the
improvement of operational characteristics of known devices and systems
of microwave and MM ranges.

Key words: diffraction, periodic structures, transfer matrix, Iauguin
polynomials, absorbing coating, diaphragm, diffraction grating, cutoff
zone, filter.

Aiiioaoeey

Iiaeeiciue A.A. Aeeo?aeoeey yeaeo?iiaaieoiuo aiei ia ia?eiaee/aneie
iineaaeiaaoaeueiinoe iaoaeeiaeeyeaeo?e/aneeo ?annaeaaoaeae. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.03 — ?aaeeioeceea. —
Oa?ueeianeee ainoaea?noaaiiue oieaa?neoao, a. Oa?ueeia, 1999.

A ?aaioa enneaaeiaaiu yeaeo?iaeeiaie/aneea naienoaa ia?eiaee/aneeo a
iai?aaeaiee ?ani?ino?aiaiey aiei iineaaeiaaoaeueiinoae ec ethaiai /enea
N iaoaeeiaeeyeaeo?e/aneeo iaiaeii?iaeiinoae ni neiaeiui oa?aeoa?ii
?annayiey aiei eae a naiaiaeiii i?ino?ainoaa, oae e a aieiiaiaeao.
?anniao?eaaaiay iiaeaeue iaiauaao iiiaea /anoiua iino?iaiey eiia/iuo
ia?eiaee/aneeo no?oeoo?. Iia i?aaeoniao?eaaao neiaeioth eiiiiceoeeth
ia?eiaea, eiiieaeniue oa?aeoa? yeaeaaeaioiie i?iaiaeeiinoe, ?aciiainioth
e iieiniaoth, /anoioioth e iiey?ecaoeeiiioth naeaeoeeth iieae aai
ninoaaiuie yeaiaioaie, ia caaeneo io oeiia aicaoaeaeathuaai iiey,
aoiaeiuo e auoiaeiuo aieiiaaaeoueo eaiaeia.

Ia iniiaa iaoiaeia oai?ee oeaiae e iao?e/iuo ooieoeee a ?aaioa
?acaeaaaony yooaeoeaiue aeai?eoi ?aaeecaoeee ?aoaiey caaea/ aeeo?aeoeee,
eneeth/athuee ia?aiiiaeaiea ?aaeooee?iaaiiuo iaiauaiiuo iao?eoe
ia?aaea/e aaciaiai yeaiaioa. A iaeiiiiaeiaii ?aaeeia aeey eiyooeoeeaioia
?annayiey ia?aie/aiiuo iineaaeiaaoaeueiinoae iieo/aiu aiaeeoe/aneea
au?aaeaiey /a?ac iieeiiiu Iiaeia (Mauguin), eo aneiioioeea i?e iaee/ee
iioa?ue n ?inoii /enea ia?eiaeia, eiyooeoeeaiou io?aaeaiey io
iieoaaneiia/iuo aiaeiaia, o?aaiaiey ioiineoaeueii iinoiyiiuo
?ani?ino?aiaiey aiei a niioaaonoaothueo aaneiia/iuo nenoaiao.
Eiaeeaeaeoaeueiua iniaaiiinoe enneaaeoaiuo nenoai ii?aaeaeythony
iao?eoeae ia?aaea/e eo ia?eiaea.

Ia iniiaa naienoa ei?iae iieeiiiia Iiaeia iino?iaia oai?ey ?aciiainiuo
yaeaiee. I?aaenoaaeaiu aeaa iacaaeneiuo oneiaey i?ic?a/iinoe
ia?aie/aiiuo ia?eiaee/aneeo iineaaeiaaoaeueiinoae. Iaeii ec ieo caaeneo
io ia?aiao?ia aaciaiai yeaiaioa e iienuaaao ieceiaeia?ioiua ?aciiainiua
eieaaaiey. Aoi?ia – caaeneo io eo /enea e yeaeo?iaeeiaie/aneie nayce
iaaeaeo ieie e ii?aaeaeyao aunieiaeia?ioiua, a oii /enea,
naa?oaeia?ioiua ?aciiainu. Iieo/aiu o?aaiaiey ioiineoaeueii nianoaaiiuo
eiiieaeniuo /anoio e aieiiauo /enae.

I?aaeeiaeaiu iaiauathuea iiaeaee e i?aaenoaaeaiu ?acoeueoaou aiaeeca
iieae ?annayiey iiaeiuathuaai (i?inaaoeythuaai) neienoiai iie?uoey
iaoaeee/aneiai ye?aia, iiiaicaaiiiai /anoioiiai e iiaeiaiai
aieiiaiaeiiai oeeueo?a ec ieaia?iuo eieueoeaauo e ?aaeeaeueiuo
aeeao?aai, niaeaniaaiiie iiaeiuathuae iaa?ocee, aunieiaeia?ioiiai
/anoioiiai e oaeiaiai aeene?eieiaoi?a, ia?aciaaiiiai ia?eiaee/aneie
iineaaeiaaoaeue-iinoueth ?aciiainiuo ?annaeaaoaeae. ?aoaiu caaea/e
?ani?ino?aiaiey aiei a eo aaneiia/iuo aiaeiaao.

Iieacaii, /oi nouanoaoao ei??aeyoeey iaaeaeo /a?aaeothueieny iaeanoyie
ia?aiao?ia iiiaiyeaiaioiie ia?eiaee/aneie iineaaeiaaoaeueiinoe n
ioiineoaeueii ieceei e aunieei eiyooeoeeaioaie io?aaeaiey e ciiaie
i?ic?a/iinoe e caie?aiey aaneiia/iiai aiaeiaa. N?aaeiee o?iaaiue
io?aaeaiey, aiieeooaea iaeeiianooaaiuo inoeeeeyoeee caaeneo io
oa?aeoa?enoee iieae ?annayiey ninoaaiuo /anoae ia?eiaea. Ii?aaeaeaiu
oneiaey, eiaaea naienoaa aeenneiaoeaiuo ia?aie/aiiie e iieoaaneiia/iie
ia?eiaee/aneeo iineaaeiaaoaeueiinoae eaeaioe/iu. Eiyooeoeeaiou
io?aaeaiey nenoai n iioa?yie – iiiaiia?aiao?e/aneay ooieoeey n
yeno?aiaeueiuie cia/aieyie. Oai?aoe/anee e yenia?eiaioaeueii iainiiaaia
aiciiaeiinoue ?ac?aaioee iiaeiuathuaai iie?uoey iaoaeee/aneiai ye?aia,
iaania/eaathuaai iaeneiaeueiia iiaeiuaiea yia?aee n aunieei o?iaiai
niaeaniaaiey a oe?ieie iaeanoe /anoio e oaeia neaie?iaaiey. Onoaiiaeaia
yaiethoeey ai a?aiaie io?aaeaiiiai iiey iaiinaeoiaeiiai aeaeaieiioeuena
io iiaeiuathuaai iie?uoey iaoaeee/aneiai ye?aia.

I?aaenoaaeaiu iaai?u ec N-1 aeene?aoiuo cia/aiee oaeia iaaeaiey, /anoio,
aieiiauo ?acia?ia ia?eiaea e eo /enea, eioi?ua iaania/eaatho iieiia
i?ioiaeaeaiea yia?aee a eaaeaeie ec cii eaacei?ic?a/iinoe. Aeia?ioiinoue
niioaaonoaothueo ?aciiainia caaeneo io io?aaeaoaeueiie niiniaiinoe
iiaoi?ythuaainy ?annaeaaoaey e ?anoao n oaaee/aieai eo /enea. Oa?aeoa?
?aaeoeaiinoe aeeao?aai a iiiaicaaiiuo aieiiaiaeiuo oeeueo?ao ii?aaeaeyao
iieiaeaiea e oe?eio /anoioiuo cii eaacecaie?aiey, a a? aaee/eia —
noaiaiue iiaeiaie naeaeoeee, aeia?ioiinoue ?aciiainia. Aeey N
yeaeaeenoaioii ?aniieiaeaiiuo ?aoaoie ec i?iaiaeyueo a?onueaa
i?yiioaieueiiai iiia?a/iiai na/aiey auyaeaia iiaoi?ythuayny ?aciiainiay
i?ic?a/iinoue ia N-1 aeeceeo cia/aieyo oaea iaaeaiey a eaaeaeie oaeiaie
ciia eaacei?ic?a/iinoe (iaiauaiea yooaeoa A.Ae. Iaethaeeioea).

?acoeueoaou enneaaeiaaiey i?eaioe?iaaiu ia ?ac?aaioeo iiauo e
niaa?oainoaiaaiey ecaanoiuo i?eai?ia e nenoai yeaiaioiie aacu NA* e II
aeeaiaciiia, iiaeaee?iaaiea oece/aneeo i?ioeannia a i?e?iaeiuo
ia?aciaaieyo, ?aoaiey caaea/ yeaeo?iiaaieoiie niaianoeiinoe, caueou
ia?niiaea, ?aaioathuaai a oneiaeyo aunieie ieioiinoe ?aaeeiyeaeo?iiiie
aiia?aoo?u e iaeo/aiey iiauoaiiie iiuiinoe.

Eeth/aaua neiaa: aeeo?aeoeey, ia?eiaee/aneea no?oeoo?u, iao?eoea
ia?aaea/e, iieeiiiu Iiaeia, iiaeiuathuaa iie?uoea, aeeao?aaia,
aeeo?aeoeeiiiay ?aoaoea, ciia caie?aiey, oeeueo?.

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