5

OA?EIANUeEEE AeA?AEAAIEE OIIAA?NEOAO

ai?iaa Iaoaeiy Iaaeiaia

OAeE 537.874

?ICNIssIIss OAEEUeIAEO IO*EIA OA IIIOEUeNIA

IEINEEIE IIAA?OIssIE

01.04.03 — ?aaeiioiceea

AAOI?AOA?AO

aeena?oaoei ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oiceei-iaoaiaoe/ieo iaoe

Oa?eia — 1999

Aeena?oaoeith ?oeiien.

?iaioa aeeiiaia a Oa?eianueeiio aea?aeaaiiio oiiaa?neoaoi

Iiiinoa?noaa inaioe Oe?aie.

Iaoeiaee ea?iaiee aeieoi? oiceei-iaoaiaoe/ieo iaoe, noa?oee
iaoeiaee niia?iaioiee EIE*EAII Ieeiea Ieeieaeiae/, Oa?eianueeee
aea?aeaaiee oiiaa?neoao, i?iaiaeiee niia?iaioiee eaoaae?e oai?aoe/ii
?aaeiioiceee

Ioioeieii iiiiaioe: aeieoi? oiceei-iaoaiaoe/ieo iaoe, i?ioani?

I?INAI?III Na?aie
Eaiiiaeiae/,

?aaeiiano?iiiii/iee iinoeooo
IAI Oe?aie,

caaiaeoaa/ aiaeaeieii
ia/enethaaeueii iaoaiaoeee;

aeieoi? oiceei-iaoaiaoe/ieo
iaoe, i?ioani?

IANAEIA Na?aie
Ieaenaiae?iae/,

Iinoeooo ?aaeiioiceee oa
aeaeo?iiiee IAI Oe?aie,

caaiaeoaa/ aiaeaeieii
iio?ineiii.

I?iaiaeia onoaiiaa: Oa?eianueeee oaoii/iee oiiaa?neoao
?aaeiiaeaeo?iiiee,

eaoaae?a ?aaeiioaoiiee, Iiiinoa?noai inaioe Oe?aie.

Caoeno aiaeaoaeaoueny “_12_” “_aa?aciy_______” 1999 ?. i 14_ aiaeeii
ia caniaeaiii niaoeiaeiciaaii a/aii ?aaee Ae 64.051.02 Oa?eianueeiai
aea?aeaaiiai oiiaa?neoaoo ca aae?anith: 310077, i. Oa?eia, ie. Naiaiaee,
4, aoae. _3-9_

C aeena?oaoeith iiaeia iciaeiieoenue o Oeaio?aeueiie iaoeiaie
aiaeiioaoei OAeO ca aae?anith: 310077, i.Oa?eia, ie.Naiaiaee, 4.

Aaoi?aoa?ao ?icineaiee “_8_” __ethoiai___ 1999 ?.

A/aiee nae?aoa?

niaoeiaeiciaaii a/aii ?aaee
Eyoianueeee A.O.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeueiinoue oaie

O ca’yceo c inaiiiyi iieiiao?iaiai oa noaiieiiao?iaiai aeiaiaciiia
oaeeue oa ?icaeoeii oaoiiee ia?aaea/i neaiaeia iniaeeao oeiiiinoue
iaaoaa iioi?iaoeiy i?i aieea ?icieo oaeoi?ia (aeenia?ni, aeeneiaoei,
eoneiai — iaeii?iaeieo iaae, iayaiinoue iiaenoaeyth/i iiaa?oii oa iio.)
ia aiieiooaeii oa oaciai oa?aeoa?enoeee ?iciianthaeaeaiiy
aeaeo?iiaaiioieo iieia. E?ii oiai, oaeee aiaeic aeioeieueii i?iaiaeeoe c
o?aooaaiiyi aeanoeainoae no?oeoo?e ?aaeueiiai oaeeueiaiai iiey, yea a
aieueoinoi i?aeoe/ieo aeiaaeeia aiae?iciyoueny aiae ieinei oaeei i
cia?aaeo niaith o eiioiiooi. Aei /enea oaeeo neeaaeieo oaeeueiaeo
ooai?aiue aiaeiinyoueny iiey ?iciiiaiioieo aioai, eaaciiioe/ieo
?aciiaoi?ia, aieieiiieo oa aaaaoiiiaeiaeo oaeeaaiaeia. Iayaiinoue
iiaenoaeyth/i iiaa?oii (aeenia?nia na?aaeiaeua c iiaeeiaiiyi) ia o?ani
?iciianthaeaeaiiy oaeeueiaiai io/ea iiaea i?ecaiaeeoe aei niioai?aiiy ia
eeoa no?oeoo?e ii/aoeiaiai iiey, aea i iiey?ecaoei. Oiio aea/aiiy
aieeao iiaenoaeyth/i iiaa?oii ia aeanoeainoi ?iciianthaeaeaiiy
oaeeueiaiai io/ea ia iaio aeooaeueiei. O aeiaaeeo, eiee ia?iaiinoi
cae/aeii iiaa?oii cia/ii aieueoi aeiaaeeie oaeei oaeeueiaiai io/ea,
yeee ?iciianthaeaeooueny, oi ia?iaia iiaa?oiy iiaea aooe cia?aaeaia o
aeaeyaei noie eaaciieineeo iioa?aaeia iiaa?oii. Ii/aoeiaa iiea
?icnithoueny oeeie aeieyieaie iiae eooaie, yei ciaoiaeyoueny a oe?ieiio
iioa?aaei, aeeth/ath/e eooe iiaiiai aioo?ioiueiai aiaeaeooy oa eooe,
aeecei aei eooa eiacaiiy. C oei i?e/eie aaaaeaoueny aaaeeeaei c iaoeiai
oa i?eeeaaeii oi/ie ci?o aea/aiiy aeanoeainoae ?icniyiiy oaeeueiaeo
io/eia, yei iaaeathoue ia iiaa?oith ?icaeieo iiae eooaie aeecueeeie aei
eooia eiacaiiy oa eooia iiaiiai aioo?ioiueiai aiaeaeooy. Aieueo oiai,
naia oi?ia ii/aoeiaiai iiey ( i?inoi?iaa aiieiooaeia oa oaciaa
iaeiath/a) aiina nai ei?aeoeae a oa?aeoa?enoeee ?icniyiiai neaiaeo.

I?iaaaeaii oai?aoe/ii aeineiaeaeaiiy ?iciianthaeaeaiiy oa ?icniyiiy
iaiaaeaieo a i?inoi?i oa a /ani aeaeo?iiaaiioieo oaeeue aeicaieythoue
caeienieoe ?ic?iaee a oaeeo aeooaeueieo i?aeoe/ieo canoinoaaiiyo, ye
iaoiaeeea aeii?thaaiiy oa?aeoa?enoee ?icniyiiai iiey ?iciiiaiioieie
ia?aoeiaeaie, aea/aiiy aeanoeainoae na?aaeiaeua ca ia?aiao?aie
aiaeaeoiai iiey (ia?oeiiaiee eiio?ieue) oa iio.

Na?aae oai?aoe/ieo iiaeaeae, yei iienothoue acaiiaeith iiey oaeeueiaiai
io/ea c iaoa?iaeueiei na?aaeiaeuai iaeaieueo ?iciianthaeaeaiith
aeyaeeanue iiaeaeue iioaa?aeueiiai cia?aaeaiiy iiey oaeeueiaiai io/ea o
aeaeyaei eiioiiooia ieineeo oaeeue c iiaeaeueoei aeei?enoaiiyi
?ica’yceo e?aeiai caaea/i aeey

eiaeii ia?oeiaeueii oaeei ianeii/aiiiai niaeo?o.

Ae?oaee oeyo ?ica’yceo oei caaea/i aiaeioe/iee iaoiae, yeee iieyaa o
aeei?enoaiii ooieoei A?iia e?aeiai caaea/i, ui nai ii niai aea a yaiiio
aeaeyaei ?ica’ycie caaea/i iaiaaeaiiai aeaea?aea i iinoeoue a niai ani
icoioii oice/ii aoaeoe ?icniyiiy iiey ia aeaiie iaaei ?icaeieo. Oeae
iaoiae aeicaieea oieeiooe o?oaeiiuia, ui oa?aeoa?ii aeey eooia iaaeiiiy
aeecueeeo aei eooa iiaiiai aioo?ioiueiai aiaeaeooy oa aei eooa eiacaiiy.
E?ii oeueiai, aiaeioe/iee ?ica’ycie aiae?iciyoueny eiio?ieueiaaiith
oi/iinoth ?ic?aooieia, /ioeinoth noa?e canoinoaaiiy, a oaeiae aieueoith
oaeaeeinoth aeai?eoiia i?e o ?aaeicaoei ia AII. Ana oea aeaco ia
aeooaeueiinoue aea?aii iaoeiai oaiaoeee aeineiaeaeaiue.

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

Aeena?oaoeieio ?iaioo aeeiiaii a ?aieao eeth/iaiai iai?yieo
aeineiaeaeaiiy eaoaae?e oai?aoe/ii ?aaeiioiceee ?aaeiioice/iiai
oaeoeueoaoo Oa?eianueeiai aea?aeaaiiai oiiaa?neoaoo .

?acoeueoaoe aeena?oaoei aaieoee aei iiaeaocianueei i?ia?aie
“Aei?iiiithaaiiy” N 1, 5,2,4, (N Aea?ae. ?ano?aoei 8107462, 1981-1985
?.?. i 0.187.0004411, 1986-1990 ?.?.), eiiieaenii caaaeueiinithcii
oeieueiai i?ia?aie AeEIO N?N? c ?ica’ycaiiy iaoeiai-oaoii/ii i?iaeaie
“Coai?eoe oa inaioe a ae?iaieoeoai eiiieaen i?eeaaeia, caniaia
aaoiiaoecaoei iiaeaeuaii oi/iinoi, iaaeieiinoi, aeiaaiai/iinoi” (
1986-1990 ?.?., oeo? 0.18.01 ), a oaeiae oinii iia’ycaii c i?ii?eoaoieie
iai?yieaie ?icaeoeo iaoee i oaoiiee, i.7- “Ia?niaeoeaii iioi?iaoeieii
oaoiieiai, i?eeaaee eiiieaenii aaoiiaoecaoei nenoai ca’yceo”, a ?aieao
eii?aeeiaoeieieo ieaiia iaoeiai-aeineiaeieo ?iaio Iiiinoa?noaa inaioe
Oe?aie. Aeena?oaoeiy neeaaeiaith /anoeiith aea?aeathaeaeaoieo IAe?, ui
aeeiiothoueny ia eaoaae?i oai?aoe/ii ?aaeiioiceee OAeO (iiia?e
aea?ae?ano?aoei 0194U018557, 0197U015768).

Iaoa oa caaea/i aeena?oaoeieii ?iaioe

Iaoith ?iaioe ?ic?iaea aiaeioe/iiai oa /enaeueiiai iaoiaeia
?ica’ycaiiy caaea/ ?icniyiiy iaiaaeaieo a i?inoi?i oa a /ani iieia
aeiaeaeo?e/ieie na?aaeiaeuaie ia iniiai ooieoeie A?iia e?aeiai caaea/i
noiniaii iiaeaethaaiiy aeii?thaaiiy eiaoioeiioa aiaeaeooy.

Aeey aeinyaiaiiy iinoaaeaii iaoe ?ica’ycaii ianooiii caaea/i:

1. ?icniyiiy aaonianueeiai oaeeueiaiai io/ea ieineith iaaeith ?icaeieo
aeaio aeiaeaeo?e/ieo na?aaeiaeu iaoiaeii ooieoei A?iia.
Ciaoiaeaeaiiy aiaeioe/ieo

ae?acia aeey iieia o aeiaaeeo iaaeiiiy iiae aeiaieueiei eooii. Aeyaeaiiy
oice/ieo aeanoeainoae ?icniyiiy oaeeueiaeo iieia iiaeeco eooia A?thnoa?a
oa eooa iiaiiai aioo?ioiueiai aiaeaeooy.

2. Ocaaaeueiaiiy iaoiaeo ?ica’ycaiiy oa ?ic?iaea ia/enethaaeueiiai
aeai?eoio aeey caaea/i ?icniyiiy io/ea c aeiaieueiith no?oeoo?ith
ii/aoeiaiai iiey aeiaeaeo?e/iei aiaeaeaa/ai i?e iayaiinoi iiaenoaeyth/i
iiaa?oii.

3. Iiaoaeiaa ia iniiai iaea?aeaiiai ?ioaiiy aeaeo?iaeeiaii/ii iiaeaei
aeii?thaaiiy eiaoioeiioa aiaeaeooy iaeiiiiceoeieii oa aeaiiiceoeieii
noai. Anoaiiaeaiiy e?eoa?ia iiaeaeuaiiy oi/iinoi ?acoeueoaoia
aeii?thaaiiy. Aecia/aiiy aeiia aei ia’eoo oa iiaenoaeyth/i iiaa?oii aeey
aeinyaiaiiy iiiiiaeueieo niioai?aiue iiey.

4. ?icaeoie iaoiaeo ooieoei A?iia aeey ?ica’yceo caaea/i ?icniyiiy
iiioeueniiai oaeeueiaiai neaiaeo aeiaeaeo?e/iei iaiiai?inoi?ii.

Iaoeiaa iiaecia

A ?iaioi iaea?aeaii ianooiii ?acoeueoaoe, yei aecia/athoue iaoeiao
iiaecio:

1. ?icaeiooi iaoaiaoe/iee iiaeoiae aei ?ica’yceo e?aeiai caaea/i
?iciianthaeaeaiiy oa ?icniyiiy aaonianueeiai oaeeueiaiai io/ea ia iaaei
?icaeieo aeaio na?aaeiaeu ia iniiai ooieoei A?iia.

2. Iaea?aeaii aiaeioe/ii ae?ace aeey cnoao iaeneioio aiieiooaee iiey
oaeeueiaiai io/ea o ieiueii iaaeiiiy a iai?yieo eiacaiiy oa anoaiiaeaia
caeaaeiinoue aaee/eie oeueiai cnoao aiae ?icieoei iiae eooii iaaeiiiy oa
eooii iiaiiai aioo?ioiueiai aiaeaeooy.

3. Anoaiiaeaii, ui iiaeeco eooa A?thnoa?a niinoa?iaaoueny ?icuaieaiiy
aiaeaeoiai iiey ia aeaa io/ee.

4. ?acoeueoaoe iaea?aeaii i?e aeineiaeaeaiii ?icniyiiy ia iaaei
?icaeieo oaeeueiaeo io/eia c aaeeeith ?icaiaeiinoth.

5. ?ic?iaeaiee iiaeoiae ocaaaeueiaii ia ?icii aeaee ?iciiaeieo
ii/aoeiaiai iiey (eineioniaeaeueia, nooiii/anoa oa iio.) i oeie
?icnithaa/ia.

6. Iaea?aeaii iiai ?acoeueoaoe aeey i?inoi?iai-/aniaeo ?iciiaeieia aeey
?icniyiiy iiioeuenieo oaeeueiaeo io/eia ia aeiaeaeo?e/iiio
iaiiai?inoi?i.

7. Ca ?acoeueoaoaie iaoaiaoe/iiai iiaeaethaaiiy ?ic?iaeaii
?aeiiaiaeaoei noiniaii iieiioaiiy aeii?thaaiiy eiaoioeiioa aiaeaeooy,
ui aeicaieeee i?iaanoe iao?ieiai/io ioeiieo iiaiai i?eeaaeo, iiaecia
yeiai iiaeoaa?aeaeaia aaoi?nueeei naiaeionoaii oa iaoaioii.

Ai?iaiaeiinoue oa iaa?oioiaaiinoue

?acoeueoaoia aeena?oaoei coiiaeaii oi/iinoth ?ica’yceo neeaaeiaeo
caaea/: eeth/iaa

caaea/a ?ica’ycoaaeanue a no?iaie iaoaiaoe/iie iinoaiiaoei; aea?aiee
iaoiae aeicaiey iaea?aeoaaoe ?ica’ycie c ethaith iaia?aae caaeaiith
oi/iinoth; oi/iinoue aiaeioe/ieo ?ica’yceia eiio?iethaaeanue aea?aiei
iaaeeaeaiiyi oa aaaaeaieie iaiaaeaiiyie ia ia?aiao?e caaea/i;
ai?iaiaeiinoue ?acoeueoaoia ia?aai?yeanue ii?iaiyiiyi ic ?acoeueoaoaie,
iaea?aeaieie iioeie aaoi?aie, a oaeiae ii?iaiyiiyi c aenia?eiaioaeueieie
aeaieie.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoaoia iieyaa:

1. A oiiaa?naeueiinoi ?ic?iaeaiiiai iaoiaeo aeey aeineiaeaeaiiy ye
caaaeueiioice/ieo caeiiiii?iinoae, oae i niaoeeoi/ieo iniaeeainoae, ui
iathoue i?eeeaaeia cia/aiiy a aioaiiie oa eaca?iie oaoiioei, nenoaiao
ca’yceo, aeey aiaeico ?iciianthaeaeaiiy oaeeue oa iio.

2. O iayaiinoi aiaeioe/ieo ae?acia iaea?aeaiiai ?ioaiiy aeey iecee
e?aeiio aeiaaeeia, ui aeicaiey i?iaiaeeoe ioeiiee oi/iinoi ?acoeueoaoia,
iaea?aeaieo /enaeueieie iaoiaeaie.

3. O iiaeeeainoi aeei?enoaiiy ?acoeueoaoia a iaa/aeueieo eo?nao aeey
nooaeaioia oice/iiai oa ?aaeiioice/iiai i?ioieth.

4. O ae?iaeaiii ?aeiiaiaeaoeie c aeii?thaaiiy eiaoioeiioa aiaeaeooy.

Ia caoeno aeiinyoueny ianooiii iieiaeaiiy

1. Ia iniiai ooieoei A?iia ?ica’ycaii caaea/i ?icniyiiy aeiaeaeo?e/ieie
na?aaeiaeuaie c aeenia?nith oa iiaeeiaiiyi oaeeueiaeo io/eia c
aiieiooaeiei ?iciiaeieii o aeaeyaei aaoniaia, c?icaiiai aaoniaia, a
oaeiae nooiii/anoei i eineiiniaeaeueiei.

1.1 Iaea?aeaii aiaeioe/ii ae?ace aeey aiieiooaeiiai ?iciiaeieo
?icniyiiai iiey oa cnoao eiai iaeneioio aeey aiaeiiniiai iieacieea
caeiieaiiy n>1 oa n<1 a aeiaaeeo eooa iaaeiiiy aaonianueeiai io/ea aeecueeiai aei eooa iiaiiai aioo?ioiueiai aiaeaeooy. 1.2 C’yniaaii oice/ii iniaeeainoi oi?ioaaiiy ?icniyiiiai iiey oa aeeaae a iueiai ai/ieo oaeeue. 1.3 ?ic?iaeaii aeai?eoi oa ?aaeiciaaia i?ia?aia aeey /enaeueiiai ?ica’yceo aaeoi?ii caaea/i ?icniyiiy ca iayaiinoth iiaenoaeyth/i iiaa?oii. Iieacaii, ui iaeiaioa niioai?aiiy a aiieiooaeiiio ?iciiaeiei aiaeaeoiai iiey niinoa?iaaoueny aeey aaonianueeeo io/eia. 2. Cai?iiiiiaaii iaoaiaoe/ia iiaeaethaaiiy aeey iaeiiiiceoeieii oa aeaiiiceoeieii noai aeii?thaaiiy eiaoioeiioo aiaeaeooy. Ciaeaeaia caeaaeiinoue oi/iinoi aeii?thaaiiy aiae ia?aiao?ia aeii?thaa/a eiaoioeiioo aiaeaeooy. Aecia/aii i?aeoe/ii ?aeiiaiaeaoei c aeai?o oeio aiieiooaeiiai ?iciiaeieo iiey ia aia?oo?i oa acaiiiio ?icoaooaaiith aioaie, ia’eoo oa iiaenoaeyth/i iiaa?oii. 3. Io?eiaii ?ica’ycie caaea/i ?icniyiiy iiioeueniiai oaeeueiaiai io/ea, iaiaaeaiiai a i?inoi?i oa o /ani, aeiaeaeo?e/iei iaiiai?inoi?ii ia iniiai ooieoei A?iia e?aeiai caaea/i. ?ic?iaeaii aeai?eoi oa ?aaeiciaaia i?ia?aia aeey /enaeueiiai ?ic?aooieo i?inoi?iai-/aniaiai ?iciiaeieo ?icniyiiai iiey. Iniaenoee aianie caeiaoaa/a O aeineiaeaeaiiyo, aeeiiaieo o niiaaaoi?noai, aaoi?o iaeaaeeoue: [1]- o/anoue o iinoaiiaoei caaea/i, ?ica’ycie oa aiaeic ?acoeueoaoia; [4,5] - ?ic?iaea iaoaiaoe/ii iiaeaei, /enaeueiiai aeai?eoio oa i?iaaaeaiiy iaoaiaoe/iiai iiaeaethaaiiy aeey iaa?oioiaaiiy aeiia aei ia?aiao?ia aeii?thaaeueii onoaiiaee; [6,7] - i?iaaaeaiiy iaoaiaoe/iiai iiaeaethaaiiy, ?ic?iaea ia/enethaaeueii i?ia?aie oa aiaeic ?acoeueoaoia; [9] - iinoaiiaea caaea/i, ?ica’ycie, aiaeic ?acoeueoaoia. Ai?iaaoeiy ?iaioe ?acoeueoaoe aeena?oaoeieii ?iaioe i?ieoee ai?iaaoeith ia oaeeo eiioa?aioeiyo: Ananithciay eiioa?aioeey “Iao?ieiae/aneia iaania/aiea aioaiiuo ecia?aiee”, AEAE - 4, A?aaai, 1987a.; 5-th International Conference on Mathematical Methods in Electromagnetic Theory (Kharkov, 1994) 7-th International Conference on Mathematical Methods in Electromagnetic Theory (Kharkov, 1998). Ioaeieaoei Iaoa?iaee aeena?oaoeieii ?iaioe aeeeaaeaii a 10 iaoeiaeo ioaeieaoeiyo. C ieo 3 noaooi o iaoeiaeo aeo?iaeao, aaoi?nueea naiaeioeoai -1, iaoaio -1, aeaiiiiaaii ?oeiiene -2 , aeiiiaiaei a iaoa?iaeao eiioa?aioeie - 3. No?oeoo?a oa ia’i aeena?oaoei Aeena?oaoeiy neeaaeaoueny ic anooio, /ioe?ueio ?icaeieia, aeniiaeo, nieneo eioa?aoo?e c 117 iaeiaioaaiue. Ianya ?iaioe - 184 noi?., c ieo 128 noi?iiieiniiaiiai oaenoo, 57 iaethieia ia 40 noi?iieao, 13 noi?iiie eioa?aoo?e, ui oeeoooueny. CIINO ?IAIOE O anooii noenei oa?aeoa?ecooueny eiei iaoeiaeo caaea/, yei aoaeooue ?icaeyiooi a aeena?oaoei, iaii?eiaooueny aeooaeueiinoue oa oi?ioethoueny iaoa ?iaioe. Iaa?oioiaaii aea?aiee iaoiae aeineiaeaeaiiy, i?eaaaeaia no?oeoo?a oa ei?ioeee ciino ?iaioe, aeeeaaeaii iniiaii ?acoeueoaoe oa iaoeiai iieiaeaiiy, yei aeiinyoueny ia caoeno. A ia?oiio ?icaeiei i?iaaaeaii iaeyae eioa?aoo?e ca oaiaoeeith ?iaioe. I?iaiaeeoueny ii?iaiyiiy aeaio iniiaieo iiaeoiaeia aei ?ica’yceo iinoaaeaii a aeena?oaoei caaea/i. Iiae /an aiaeico ?iaio iioeo aaoi?ia aeacooueny ia o?oaeiiui, ui aeieeathoue i?e ae?ioaiii i?iaeai, yei ?icaeyaeathoueny, oa iieacothoueny iiaeeeai oeyoe o ?ica’yceo. I?eaiaeeoueny caaaeueia oa?aeoa?enoeea aea?aiiai iaoiaeo aeineiaeaeaiiy oa aeacooueny ia eiai ia?aaaao. A ae?oaiio ?icaeiei i?iaaaeaii yeiniee i eieueeiniee aiaeic iniaeeainoae ?icniyiiy oaeeueiaeo io/eia. Aeacaia oice/ia i?e/eia o iioiaeaeaiiy. Canoiniaoth/e iiaeoiae, caniiaaiee ia aeei?enoaiii ooieoei A?iia e?aeiai caaea/i, ?icaeyiooa aeeo?aeoeiy oaeeueiaiai io/ea ia ieineie iaaei ?icaeieo aeaio aeiaeaeo?eeia. ?ica’ycie caaea/i caiaeeoueny aei ia/eneaiiy ?icniyiiai iiey u(y,z) ca oai?aiith A?iia wmetafile8? ??U??????????? ???????????yyy????.????1?????? ??????? A????&??yyyy?????Ay?y@r ???&? ?MathType??????u?th?????? Aeey ciaoiaeaeaiiy ia?aeiiiai iiey c caaeaiei ?iciiaeieii aeaea?ae f(y’) aeei?enoiaooueny ooieoeiy A?iia aieueiiai i?inoi?o G(y,z;y’), a aeey ?icniyiiai iiey - ooieoeiy A?iia e?aeiai caaea/i. A aeiaaeeo aaonianueeiai ?iciiaeieo ia?aeiiiai iiey io?eiaii aiaeioe/ia cia?aaeaiiy aeey iiey oaeeueiaiai io/ea, ui ?icniyia iaaeith ?icaeieo aeaio na?aaeiaeu c iieacieeii caeiieaiiy n>1 oa n<1. Iniaeeaa oaaaa i?eaeieaia aiaeico ?ica’yceo aeey iioa?aaeia eooia niinoa?aaeaiiy, aeecueeeo aei eooa iiaiiai aioo?ioiueiai aiaeaeooy (n<1). Aeey c?o/iinoi i?iaaaeaiiy aiaeico a ?ica’yceo aeaeieaia /anoeia iiey, ?icniyiiai caiaeii c caeiiaie aaiiao?e/ii iioeee oa ei?aeooth/ee aeiaeaoie, iaoiiaeaiee iaeiiieiinoth eiaoioeiioa aiaeaeooy i iaiaeii?iaeiinoth aiieiooaeiiai oa oaciaiai ?iciiaeieo aeoiaeiiai iiey. Iaea?aeaii aiaeioe/iee ae?ac aeey aaee/eie cnoao iaeneioio a ?iciiaeiei ?icniyiiai iiey (cnoa Aiina-Oaioaia) aeey eooia iaaeiiiy aeecueeeo aei eooa iiaiiai aioo?ioiueiai aiaeaeooy. Anoaiiaeaia caeaaeiinoue ciaeaeaii aaee/eie cnoao aiae eooa iaaeiiiy, ia?aiao?ia aeoiaeiiai iiey, ?aaeiona e?eaecie oaciaiai o?iioo, iiey?ecaoei, aeanoeainoae ?icnith/i iiaa?oii oa aiaenoaii aei ia. Iiaee?anethoueny, ui aaee/eia cnoao ia noaeith, a caeaaeeoue aiae eooiaiai aiaeoeeo aini aiaeaeoiai io/ea. Aecia/aia caeaaeiinoue iiae eiiieiei oa eooiaei cnoaii iaeneioio aiieiooaeiiai ?iciiaeieo iiey oaeeueiaiai io/ea. A oeueiio ae ?icaeiei ?icaeyiooi ae?oaee aaaeeeaee aeiaaeie, aeiaaath/ee niaoeiaeueiiai ?icaeyaeo, eiee eoo iaaeiiiy aeecueeee aei eooa eiacaiiy. Iioaa?ae a niaeo?aeueiiio cia?aaeaiii ooieoei A?iia, ia/enethoueny iaoiaeii ia?aaaeo c o?aooaaiiyi oi/ie ?icaaeoaeaiiy, yei aecia/athoueny eooii eiacaiiy oa eooii iiaiiai aioo?ioiueiai aiaeaeooy. Iaea?aeaia ooieoeiy A?iia aeey iioa?aaeo eooia niinoa?aaeaiiy aeecueeeo aei ioey a?aoiao iniaeeainoi iiaaaeiiee oace eiaoioeiioa aiaeaeooy aeey oeueiai iioa?aaeo eooia. Iieacaii,ui iiea ai/ii oaeei aiineoue noooaee aianie a aiaeaeoa iiea, eiee iieacieee caeiieaiiy n cia/ii iaioi ca iaeeieoeth, a oaeiae eiee ?icoei iiae oi/eaie ?icaaeoaeaiiy, ui coiiaeaii ?aaeeeaeaie eiaoioeiioo aiaeaeooy, aoaea aeineoue aaeeeei. A iioeo aeiaaeeao iiea ai/ii oaeei iiaeia ia a?aoiaoaaoe. Aeey aaonianueeiai ?iciiaeieo iiey oaeeueiaiai io/ea iaea?aeaii aiaeioe/ia cia?aaeaiiy ?icniyiiai iiey aeey eooia iaaeiiiy aeecueeeo aei eooia eiacaiiy a aeaeyaei ?yaeia ca ooieoeiyie Eoiia?a. A o?aoueiio ?icaeiei iniaeeaa oaaaa i?eaeieaia aiaeico iniaeeainoae ?icniyiiy oaeeueiaeo io/eia iiaeeco eooia A?thnoa?a oa iiaiiai aioo?ioiueiai aiaeaeooy. Aeey iiey?eciaaieo a ieiueii iaaeiiiy aaonianueeeo oaeeueiaeo io/eia, ainue yeeo ni?yiiaaia iiae eooii i aei ?icnith/i iiaa?oii, yeee eaaeeoue a iioa?aaei (br )< i <(br ), aea =arctg(W/z) - eoo aeeo?aeoeieii ?icaiaeiinoi (W - oe?eia oaeeueiaiai io/ea), niinoa?iaaoueny ?icuiieaiiy ia aeaa io/ee. Aiaeicooueny iiaaaeiiea iaeneioiia a aiieiooaeiiio ?iciiaeiei eiaeiiai c aeaio io/eia a caeaaeiinoi aiae eooa iaaeiiiy, oe?eie io/ea, aeiaeaeo?e/ii i?iieeiinoi, oa aiaenoaii aei ?icnith/i iiaa?oii. O aeiaaeeo aieueo neeaaeii eiioiao?aoei ia?aeiiiai iiey (nooiii/anoa, eineioniaeaeueia), eiee eoo iaaeiiiy aeecueeee aei eooa A?thnoa?a, ?icaeyaeaoueny aaee/eia niioai?aiue, ui aiinyoueny a ?icniyia iiea. Aeey ae?oaiai iniaeeaiai aeiaaeeo ?icniyiiy oaeeueiaiai io/ea iiaeeco eooa iiaiiai aioo?ioiueiai aiaeaeooy i?iaiaeeoueny aiaeic oiceee yaeu, iia’ycaieo c aeieeiaiiyi iiey ai/ii oaeei oa aieeao inoaiiuei ia i?inoi?iao no?oeoo?o iiey. Aeineiaeaeooueny caeaaeiinoue eiiieiiai oa eooiaiai cnoaia iaeneioio oaeeueiaiai io/ea aiae ia?aiao?ia caaea/i. A oeueiio ae ?icaeiei i?iaiaeeoueny ii?iaiyiiy aeaio iiaeoiaeia aei ?ica’yceo caaea/ ?iciianthaeaeaiiy oa aeeo?aeoei oaeeueiaiai io/ea ia ieineie iaaei. A ae?oaiio ?icaeiei aoei iaea?aeaii ?ica’ycie caaea/i ?icniyiiy oaeeueiaiai io/ea ye ?acoeueoao iioaa?oaaiiy ?iaiyiue Iaenaaea c caaeaieie noi?iiiiie aeaea?aeaie oa aeacaii iaaeeaeaiiy, yei aeicaieythoue iaea?aeaoe cia?aaeaiiy ye aeey ia?aeiiiai, oae i aeey aiaeaeoiai iieia a aiaeioe/iiio aeaeyaei. Oei iaiaaeaiiy oi?eathoueny niiaaiaeiioaiiy ?icii?o aeaea?aea oa aiaenoaii, ia yeie ni?aaaaeeeaee iaea?aeaiee ?ica’ycie, - ?icii?e aeaea?aea cia/ii iaioi aiaenoaii, ia yeie ?icaeyaeaoueny iiea io/ea. Aeey ii?iaiyiiy i?iaiaeeoueny ?ica’ycaiiy caaea/i ?icniyiiy ye ?acoeueoao iioaa?oaaiiy ?iaiyiue Iaenaaea c caaeaiei noi?iiiii iieai. Iaiaaeaiiy, yei aeicaieythoue iaea?aeaoe aiaeioe/iee ?ica’ycie, a aeaiiio aeiaaeeo noinothoueny iaeanoi cia/aiue iiia?a/ieo oaeeueiaeo /enae. ?iaeoueny aeniiaie, ui ?ica’ycie, iaea?aeaiee c aeei?enoaiiyi ooieoei A?iia, aeicaiey iienaoe iiey oaeeueiaeo io/eia c noooaith ?icaiaeiinoth. Iaea?aeaia c aeei?enoaiiyi aia?aoo iioaa?aea Oo?’ cia?aaeaiiy aeey iiey c aieueoith oi/iinoueth iieno oaeeueiai io/ee c iaeith ?icaiaeiinoth oa cia/iith oe?eiith io/ea, ii?iaiyii c aeiaaeeiith oaeei (kW0 >>1).

I?iaiaeeoueny ii?iaiyeueiee aiaeic iniaeeainoae ?icniyiiy aeaio aeaeia
oaeeueiaeo io/eia aiey eooa A?thnoa?a oa eooa iiaiiai aioo?ioiueiai
aiaeaeooy.

Ia iniiai aeai?eoio ?ica’yceo caaea/i aeeo?aeoei oaeeueiaiai io/ea ia
iiaa?oii aeiaeaeo?eea aoei i?iaaaeaii iaoaiaoe/ia iiaeaethaaiiy
aeii?thaaiiy eiaoioeiioa aiaeaeooy. I?iaiaeeeanue ioeiiea aieeao
ia?aiao?ia ?aaeueii onoaiiaee ia oi/iinoue aeii?thaaiiy c o?aooaaiiyi
oi?ie aeiaa?aie iai?yieaiinoi aei?iiiithaa/a oa ?iciiaeieo
ia?aaiaeaeoiai iiey.

Iniiaii ?acoeueoaoe iiaeaethaaiiy ii?iaithaaeenue c aenia?eiaioii.
Niinoa?iaaany aeinoaoiuei aeia?ee yeiniee caia ?ic?aoiaaiiai oa
aenia?eiaioaeueii iaea?aeaiiai ?iciiaeieo aiaeaeoiai iiey, ui aeaco ia
i?aaiii?iinoue iiaeaethaaiiy c aeei?enoaiiyi ?ic?iaeaiiai aeai?eoio.

Ia iniiai ?acoeueoaoia iaoaiaoe/iiai iiaeaethaaiiy i ii?iaiyiiy
iaeiiiiceoeieii oa aeaiiiceoeieii noai aeii?thaaiiy ?ic?iaeaii
i?iiiceoei, yei ni?yiiaaii ia iiaeaeuaiiy oi/iinoi aeii?thaaiiy oa
oaeaeeiaei i?eeaaeo.

A /aoaa?oiio ?icaeiei ?icaeiooa oai?iy aiaeaeooy iaiaaeaieo a i?inoi?i
oaeeueiaeo iieia (aaonianueeeo oaeeueiaeo io/eia, eineioniaeaeueiiai oa
nooiii/anoiai ?iciiaeieaiue) aiae aeiaeaeo?e/iiai c?aceo ca iayaiinoi
iiaenoaeyth/i iiaa?oii, i?iioiaaii ia?aeaeueii aini iiey. Aeei?enoaiee
i?e ?ica’yceo caaea/i iaoiae ooieoei A?eia aeicaiey i?iaanoe
iiaoaiiee ?ica’ycie, iia’ycaiee c aaaaoi?aciaei ia?aaiaeaeooyi
iieia, yei aeineiaeaeoaaeenue, c o?aooaaiiyi ciiie iiey?ecaoei.
?ic?iaeaii /enaeueiee aeai?eoi ?ica’yceo, yeee aeicaiey ciaoiaeeoe
i?inoi?iaee ?iciiaeie iiey a ?icieo ieiueiao. O aeiaaeeo aaonianueeiai
oaeeueiaiai io/ea iaea?aeaii ?iciiaeieaiiy aiieiooaee oa oace a ieiueiao
aeineiaeaeoaaiiai c?aceo, iiaenoaeyth/i iiaa?oii oa i?eeia/a. I?iaaaeaii
ii?iaiyiiy ?iciiaeieaiue iiaeoey aiieiooaee oa oace a ieiueii i?eeia/a c
o?aooaaiiyi iiaeaieiiai ia?aaiaeaeooy iiaenoaeyth/i iiaa?oii (i?e
i?yiiio oa cai?ioiiio ?iciianthaeaeaiii) c aiaeiai/ieie caeaaeiinoyie,
yei iaea?aeaii aac o?aooaaiiy oeueiai aieeao.

Iaeiei ic aoaiia aeineiaeaeaiiy aiaeaeoiai aiae c?aceo iiey ?aaeueieo
aia?oo? aiaeic aieeao iiaenoaeyth/i iiaa?oii ia i?inoi?iaee ?iciiaeie
aiieiooaee oa oace iiey. I?inoi?iaee ?iciiaeie aiieiooaee oa oace aeey
o?ueio oeiia oaeeueiaeo io/eia iai/ii aeaiiino?o ciiie, yei aiineoue
iiaenoaeyth/a iiaa?oiy. Nooiiiue niioai?aiue a cia/iie ii?i caeaaeeoue
aiae no?oeoo?e iniiaiiai iiey, eiai iiey?ecaoei oa ia?aiao?ia
iiaenoaeyth/i iiaa?oii.

A oeueiio ae ?icaeiei ?icaeyiooi aeiaaeie ?icniyiiy oaeeueiaiai io/ea,
ui iaaea ia iiaa?oith c iiaeeiaiiyi c aaeeeei cia/aiiyi aeiaeaeo?e/ii
i?iieeiinoi iiae iaeeie eooaie. Iaea?aeaii aiaeioe/ia cia?aaeaiiy aeey
/anoeie iniiaiiai iiey, ?icniyiiai iiaenoaeyth/ith iiaa?oiath. I?e
oeueiio aeei?enoiaooueny ooieoeiy A?iia, yea iaea?aeaia aeey eooia
niinoa?aaeaiiy aeecueeeo aei /2 oa aaeeeeo cia/aiue iiaeoey iieacieea
caeiieaiiy. Aaeeea cia/aiiy iiaeoey iieacieea caeiieaiiy aiaeiiaiaea
i?e?iaeiei iie?eooyi caiii iiaa?oii. I?eeiyoa iaeaaeicaoeiy i?ioeano
?icniyiiy iieyaa a oiio, ui ?aaeueia caiia iiaa?oiy caiiiaia ieiueiie c
aiaeiiaiaeiei cia/aiiyi eiiieaenii aeiaeaeo?e/ii i?iieeiinoi. A
?acoeueoaoi anoaiiaeaii cia/iee aieea ia iniiaia iiea ?icaeyiooiai oeio
iiaenoaeyth/i iiaa?oii iacaeaaeii aiae aeaeyaeo ooieoei, yea iieno
aonoeio ?iciiaeieo aeaea?ae iiey.

I?iaaaeaii aeineiaeaeaiiy aieeao iaaei ?icaeieo aeaio aeiaeaeo?eeia ia
iiea iiioeueniiai oaeeueiaiai io/ea i?e neio?iiiiio caoaeaeaiith
nenoaiie

aeaeo?e/ieo (iaaiioieo) aeeiieia. ?icaeyaeaany aieea iiaenoaeyth/i
iiaa?oii ia aiieiooaeo iniiaiiai iiey iacaeaaeii aiae aeaeyaeo ooieoei,
yea iieno aonoeio ?iciiaeieo aeaea?ae iiey. Aeineiaeaeoaaeinue
?iciiaeieaiiy ieooaeo cia/aiue aiieiooaee aiaeaeoiai iiey iaaeith
?icaeieo c iieacieeii caeiieaiiy n>1.

AENIIAEE

1. ?icaeiooi iaoiae ooieoei A?iia e?aeiai caaea/i aeey
eoneiai-iaeii?iaeieo aeiaeaeo?e/ieo no?oeoo? ia aeiaaeie ?icniyiiy
oaeeueiaeo io/eia c aeiaieueiei

aiieiooaeiei oa oaciaei i?inoi?iaei ?iciiaeieii.

2. Iaea?aeaii aiaeioe/iee ?ica’ycie caaea/i ?icniyiiy aaonianueeiai
oaeeueiaiai io/ea ieineith iaaeith ?icaeieo aeaio aeiaeaeo?eeia c
iieacieeii caeiieaiiy n>1 oa n<1, aeeth/ath/e eooe iaaeiiiy, yei aeecueei aei eooa iiaiiai aioo?ioiueiai aiaeaeooy oa eooa eiacaiiy. ?ica’ycie cia?aaeaii a aeaeyaei niaoeiaeueieo ooieoeie Eoiia?a, aeey yeeo ?ic?iaeaii aeai?eoi o ia/eneaiiy. Aiaeic ?ica’yceo aeicaieea ia oieueee anoaiiaeoe iniiaii oice/ii iniaeeainoi ?icniyiiy oaeeueiaeo io/eia, aea e ioeiieoe oi/iinoue /enaeueiiai ?ica’yceo caaea/i. Anoaiiaeaii, ui aocueei aaonianueei io/ee i?e iaaeiiii ia aeiaeaeo?e/iee iaiiai?inoi? o aeiaaeeo n>1 iiae eooaie, aeecueeeie aei
eooa A?thnoa?a (iiey?ecaoeiy a ieiueii iaaeiiiy), ?icuiieythoueny ia
aeaa io/ee. Aecia/aii naeoi? eooia iaaeiiiy, a yeiio aiaeaoaaoueny oaea
?icuiieaiiy.

I?iaiaeiciaaii eieueeinii ciiie aeaio iaeneioiia iiey oa o ca’ycie c
iniiaieie ia?aiao?aie caaea/i.

Iieacaii, ui iai?yiie ?iciianthaeaeaiiy iiey aeey iaeneiaeueieo
aiieiooae ia niiaiaaea c aaiiao?iiioe/ieie caeiiaie ?iciianthaeaeaiiy
oaeeue.

3. Iaea?aeaii aiaeioe/ii ae?ace aeey cnoao iaeneioio aiieiooaee
?icniyiiai iiey (cnoa Aiina-Oaioaia) aiae aini io/ea aeey iaeaieueo
neeaaeiiai a iaoaiaoe/iiio aiaeiioaiii aeiaaeeo — aeey eooia iaaeiiiy
aeecueeeo aei eooa iiaiiai aioo?ioiueiai aiaeaeooy. Anoaiiaeaia
caeaaeiinoue cnoao Aiina-Oaioaia aiae aaee/eie aeiaeaeo?e/ii
i?iieeiinoi, oe?eie io/ea, oieonii aiaenoaii oa iio.

Iieacaii ?icieoeth iiae cnoaii Aiina-Oaioaia aeey oe?ieeo oa aocueeeo
aaonianueeeo io/eia. Anoaiiaeaii, ui aeey aocueeeo io/eia eiai aaee/eia
ia caeeoaoueny iaciiiiith ia ?icieo aiaenoaiyo aiae ?icnith/i iiaa?oii.
Oaea eiai caeaaeiinoue iia’ycaia c ?iciei aianeii ai/ii oaeei a iiaia
iiea.

4. I?iaaaeaii aiaeic aiieiooaeieo oa oaciaeo i?inoi?iaeo ?iciiaeieia
?icniyieo iieia aeey aia?oo?ieo iieia aioai, ui iae/anoioa
aeei?enoiaothoueny ia i?aeoeoei (nooiii/anoiai, c?icaiiai aaoniaia,
eineioniaeaeueiiai oa iio.), i?e o iaaeiiii ia aeiaeaeo?e/ia na?aaeiaeua
i anoaiiaeaii o caaaeueii oa aiaeiiiii iniaeeainoi.

5. I?iaaaeaii ii?iaiyiiy aeaio iiaeoiaeia aei ?ica’yceo caaea/i
?icniyiiy oaeeueiaeo io/eia: niaeo?aeueiiai iaoiaeo oa iaoiaeo,
caniiaaiiai ia aeei?enoaiii ooieoei A?iia e?aeiai caaea/i. Iieacaii, ui
niaeo?aeueiee iaoiae iaeaieueo

i?eaeaoiee aeey oe?ieeo io/eia (W0 1000), a iaoiae ooieoei A?iia oa
iaea?aeaii ia eiai iniiai aiaeioe/ii ?ica’ycee iiaeooue aooe canoiniaaii
ye aeey oe?ieeo, oae i aocueeeo io/eia aae aei W0 5.

6. Aeineiaeaeaii aieea ii?nueei iiaa?oii ia iiea oaeeueiaiai io/ea o
aeiaaeeo eooia iaaeiiiy aeecueeeo aei eooa eiacaiiy oa aaeeeeo cia/aiue
iieacieea caeiieaiiy.

Anoaiiaeaii, ui oaea iiaa?oiy i?eaiaeeoue aei caiioieo niioai?aiue
?icniyiiai iiey iacaeaaeii aiae oi?ie ia?aeiiiai iiey. Iaeiaioa
niioai?aiiy niinoa?iaaoueny aeey aaonianueeiai io/ea.

7. ?icaeiooi iaoiae ?ica’yceo caaea/i ?icniyiiy oaeeueiaiai io/ea c
?iciith oi?iith aia?oo?iiai iiey ia aeiaeaeo?e/iiio iaiiai?inoi?i ca
iayaiinoi aeiaeaeo?e/ii iiaenoaeyth/i iiaa?oii c o?aooaaiiyi
ia?aoai?aiiy iiey?ecaoeie aiaeaeoiai iiey. I?iaiaeiciaaii aieea
iiaenoaeyth/i iiaa?oii ia i?inoi?iaee ?iciiaeie aiaeaeoiai aeiaeaeo?eeii
iiey c iaoith ei?aeoei iaoiaeeee aeii?thaaiiy eiaoioeiioa aiaeaeooy.
Anoaiiaeaia caeaaeiinoue aaniethoii oa aiaeiinii iioeaee aiae eooa
iaaeiiiy, aiaenoaii aei iiaa?oii, ia?aiao?ia ia’eoo. ?acoeueoaoe oai?i
oa aenia?eiaioo aeia?a ocaiaeaeothoueny.

I?iaaaeaiee /enaeueiee aiaeic iieaco, ui iayaiinoue iaaioue iaeii
aiaeaeaeaii iiaenoaeyth/i iiaa?oii i?eaiaeeoue aei inoioiiai niioai?aiiy
aiieiooaeiiai oa oaciaiai ?iciiaeieo oa ciiie iiey?ecaoei.

Anoaiiaeaii, ui o aeiaaeeo eineioniaeaeueiiai oa nooiii/anoiai
oaeeueiaeo io/eia niioai?aiiy iniiaiiai iiey iiaenoaeyth/ith iiaa?oiath
niinoa?iaaoueny ye ia iaeeo, oae i aaeeeeo aiaenoaiyo aiae aia?oo?e.
Aecia/aii i oaei oa?aeoa?ii aiaenoaii, i?e yeeo niioai?aiiy iiey
iiiiiaeueii. Oea niinoa?iaaoueny aeey oeo eooia, i?e yeeo eiaoioeiio
aiaeaeooy ieinei oaeei aeecueeee aei ioey.

8. ?aeiiaiaeaoei oai?i aoee aeei?enoaii i?e ?ic?iaoei iaeiiiiceoeieii
oa aeaiiiceoeieii noai, iiaeaethth/eo aeii?thaaiiy eiaoioeiioa
aiaeaeooy.

Iiaecia oa i?aeoe/ia cia/aiiy cai?iiiiiaaiiai oaoii/iiai ?ica’yceo
i?iaeaie iiaeaeuaiiy oi/iinoi aeii?thaaiiy eiaoioeiioa aiaeaeooy
iiaeoaa?aeaeaii aaoi?nueeei naiaeioeoaii ia aeiaoiae.

9. ?ic?iaeaii /enaeueiee aeai?eoi ?ica’yceo caaea/i ?icniyiiy
oaeeueiaiai iiioeueniiai io/ea, iaiaaeaiiai ye a i?inoi?i, oae i a /ani,
ia iniiai ooieoei A?iia e?aeiai caaea/i iiioeueniiai aeaea?aea. sse
aeoiaeiee neaiae aea?aia iiea c i?inoi?iaei aaoniacueeei ?iciiaeieii, a
/aniaa caeaaeiinoue cia?aaea niaith aecaiiiiiaeiaio oi?io. Aeey oaeiai
eieaeueiiai iiioeueno iaea?aeaii i?inoi?iaee ?iciiaeie aiaeaeoiai aiae
aeiaeaeo?eea io/ea ye ooieoei /ano. Aeenia?niy na?aaeiaeua i?ecaiaeeoue
aei niioai?aiiy oi?ie i?inoi?iaiai ?iciiaeieo iiey c /anii. Oaeee

iiaeoiae iiaea aooe aeei?enoaiei i?e aiaeici ?iciianthaeaeaiiy
oe?ieinioaiaeo neaiaeia, iaiaaeaieo a i?inoi?i aia?oo?ieo iieia ca
iayaiinoi aiaeaeaath/eo ia’eoia.

NIENIE IIOAEIEIAAIEO AAOI?II I?AOeUe CA OAIITH AeENA?OAOeI

1. Aai?iaa I.I., O?aoueyeia I.A. Enneaaeiaaiea aeeo?aeoeee aieiiauo
io/eia ia iniiaa ooieoeee A?eia e?aaaie caaea/e // ?aaeeioaoieea e
yeaeo?iieea. — 1984. — O.24 — N 2. — N. 207-214.

2. Aai?iaa I.I. Niiinoaaeaiea aeaoo iiaeoiaeia e ?aoaieth caaea/e
aeeo?aeoeee aieiiaiai io/ea ia ieineie a?aieoea // ?aaeeioaoieea e
yeaeo?iieea. — 1989. — O.34. — N 10. — N. 2212-2214.

3. Aai?iaa I.I. Enneaaeiaaiea aeeyiey iiaenoeeathuae iiaa?oiinoe ia
?ani?ino?aiaiea aieiiaiai io/ea // Aanoi. Oa?uee. oi-oa. ?aaeeioeceea e
yeaeo?iieea. — 1998. — N. 405. — N. 75-78.

4. A.N. 1554594 NNN?. Ono?ienoai aeey ecia?aiey eiyooeoeeaioa
io?aaeaiey iauaeoa a naiaiaeiii i?ino?ainoaa. / Aai?iaa I.I., Eie/eaei
I.I., Eaeoaei A.A., Iieiaieeia A.A., O?aoueyeia I.A./ Ca?aaeno?e?iaaii a
Ain. ?aano?a ecia?. NNN? 01.12.89.

5. Iaoaio 1554594 (?inneeneay oaaea?aoeey). Ono?ienoai aeey ecia?aiey
eiyooeoeeaioa io?aaeaiey / Aai?iaa I.I. e ae?./ Ca?aaeno?e?. a Ain.
?aano?a ecia?. 28.06.93.

6. Iniaaiiinoe i?ino?ainoaaiiiai ?ani?aaeaeaiey iiey aieiiaiai io/ea,
ia?aio?aaeaiiiai ieineie a?aieoeae ?acaeaea / Aai?iaa I.I., Eie/eaei
I.I.; Oa?ueeianeee oieaa?neoao. — Oa?ueeia, 1988. — 31n. — ?on.- Aeai. a
Oe?IEEIOE 28.09.88. N 2489 — Oe88.

7. Aai?iaa I.I., Eie/eaei I.I. Iiaeaee?iaaiea ecia?aiey eiyooeoeeaioa
io?aaeaiey a naiaiaeiii i?ino?ainoaa // Eca. aocia. ?aaeeioeceea. —
1989. — O. 33. — N. 1 — N.34 (Aeai.?oe. 13n.)

8. Aai?iaa I.I., Eie/eaei I.I. Enneaaeiaaiea aeeyiey
aiieeooaeii-oaciaiai ?ani?aaeaeaiey iaaeathuaai iiey ia oi/iinoue
ecia?aiey eiyooeoeeaioa

io?aaeaiey // A ei. “Aioaiiua ecia?aiey” Oac. aeiee. Ananithciie eiio.
“Iao?ieiae/aneia iaania/aiea aioaiiuo ecia?aiee”. — A?aaai, AIEE?E,
1987. — N. 124 — 125.

9. Egorova N.P., Kolchigin N.N. Propagation of pulse wave beam in the
vicinity of underlying surface // International Conference on
Mathematical Methods in Electromagnetic Theory. Digest MMET94, Kharkov,
1994.- P.103-107.

10. Egorova N.P. Mathematical modeling of an antenna with corner
reflector // International Conference on Mathematical Methods in
Electromagnetic Theory. Digest MMET98, Kharkov, 1998. — P. 583 — 585.

AIIOAOeI

ai?iaa I.I. ?icniyiiy oaeeueiaeo io/eia oa iiioeuenia ieineeie
iiaa?oiyie.- ?oeiien.

Aeena?oaoeiy ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
oiceei-iaoaiaoe/ieo iaoe ca niaoeiaeueiinoth 01.04.03 — ?aaeiioiceea.-
Oa?eianueeee aea?aeaaiee oiiaa?neoao, Oa?eia, 1998.

A aeena?oaoei ?icaeiooi iaoiae ooieoei A?iia e?aeiai caaea/i noiniaii
caaea/ ?icniyiiy iaiaaeaieo a i?inoi?i oa a /ani oaeeueiaeo io/eia
?iciiai aiieiooaeiiai oa oaciaiai ?iciiaeieo ia ieineeo iaaeao ?icaeieo
aeiaeaeo?e/ieo na?aaeiaeu c iaoith aeei?enoaiiy iaea?aeaieo
?acoeueoaoia i?e iiaeaethaaiii aeii?thaaiiy eiaoioeiioa aiaeaeooy.
?icaeyiooi caaea/i ?icniyiiy oaeeueiaeo io/eia ia aeiaeaeo?e/iiio
iaiiai?inoi?i c iiaenoaeyth/ith iiaa?oiath oa aac ia i?e iayaiinoi
iiaeeiaiiy. Iaea?aeaii aiaeioe/ii ?ica’ycee o aeiaaeeao, eiee eooe
iaaeiiiy aeecueei aei eooia iiaiiai aioo?ioiueiai aiaeaeooy oa eooa
eiacaiiy. Aeyaeaii iniiaii iniaeeainoi ?icniyiiy oaeeo io/eia oa
ae?iaeaii ?aeiiaiaeaoei uiaei iaoiaeeee aeii?thaaiiy eiaoioeiioo
aiaeaeooy i?e ?ic?iaoei iaeiiiiceoeieii oa aeaiiiceoeieii noai
aeii?thaaiiy.

Eeth/iai neiaa: ?icniyiiy oaeeue, oaeeueiai io/ee, iiioeuen,
aeii?thaaiiy eiaoioeiioa aiaeaeooy, iiaenoaeyth/a iiaa?oiy, eoo iiaiiai
aioo?ioiueiai aiaeaeooy, eoo eiacaiiy.

Aai?iaa I.I. ?annayiea aieiiauo io/eia e eiioeuenia ieineeie
iiaa?oiinoyie. — ?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, Oa?ueeia, 1998.

A aeenna?oaoeee ?acaeo iaoiae ooieoeee A?eia e?aaaie caaea/e aeey
caaea/

?annayiey ia?aie/aiiuo a i?ino?ainoaa e ai a?aiaie aieiiauo io/eia n
i?iecaieueiui aiieeooaeii-oaciaui ?ani?aaeaeaieai ieineeie a?aieoeaie
?acaeaea aeeyeaeo?e/aneeo n?aae n oeaeueth eniieueciaaiey iieo/aiiuo
?acoeueoaoia i?e iiaeaee?iaaiee ecia?aiee eiyooeoeeaioa io?aaeaiey.
?anniio?aiu caaea/e ?annayiey aieiiauo io/eia ia aeeyeaeo?e/aneii
iieoi?ino?ainoaa n iiaenoeeathuae iiaa?oiinoueth e aac iaa i?e iaee/ee
iiaeiuaiey. Iieo/aiu

aiaeeoe/aneea ?aoaiey a neo/ayo, eiaaea oaie iaaeaiey aeecie e oaeo
iieiiai aioo?aiiaai io?aaeaiey e oaeo neieueaeaiey. Ii?aaeaeaiu iniiaiua
iniaaiiinoe ?annayiey aieiiauo io/eia e au?aaioaiu ?aeiiaiaeaoeee ii
iaoiaeeea ecia?aiey eiyooeoeeaioa io?aaeaiey i?e ?ac?aaioea
iaeiiiiceoeeiiiie e aeaooiiceoeeiiiie noai ecia?aiey.

Eeth/aaua neiaa: ?annayiea aiei, aieiiaua io/ee, eiioeuenu, ecia?aiea
eiyooeoeeaioa io?aaeaiey, iiaenoeeathuay iiaa?oiinoue, oaie iieiiai
aioo?aiiaai io?aaeaiey, oaie neieueaeaiey.

Egorova N.P. Scattering of wave beams and pulses by plane surfaces.

Thesis for a cand. degree of Phys. & Math. Sci by speciality 01.04.03 —
radiophysics. — Kharkov State University, Kharkov, 1998.

The method of Green’s function of boundary problem is developed in the
thesis for the scattering problem of the wave beams limited in space and
time with arbitrary amplitude and phase distribution on the plane
interface of two dielectrics. The thesis object is to employ the
obtained results to model scattering coefficient measurements.

To achieve this aim the solution of the scattering problem of the
Gaussian wave beam by the interface between two semi-infinite
dielectrics, using the Green’s function method has been found. As a
result, the space distribution of the amplitude of the scattered field
and displacement of its maximum have been obtained in the analytical
form for the refraction index n>1 as well as n<1 when the incident angle of Gaussian wave beam is sufficiently close to the critical angle of total reflection and grazing angle. The solution is represented as Cummer's functions for which the numerical algorythm has been developed. The analysis of the solution permits not only to establish the fundamental physical peculiarities of the wave beams scattering, but also to estimate the accuracy of the numerical solution. Comparison between the approaches to solution of the scattering problem the spectral method and the method based on the Green's function of the boundary problem has been carried out. It is shown that the spectral method is more suitable for the wide wave beams (beam width is W0 1000), but the Green's function method and the analytical solutions by it may by used both for wide beams and narrow beams up to W0 5. The analytical expressions in the difficult mathematical case when the incident angle is near the angle of total reflection for the maximum scattered field amplitude's displacement relatively to beam axis (Goos-Hanchen shift) is obtained. The Goos-Hanchen shift dependencies on the dielectrical permittivity value, beam width and the distance to the scattering surface are established. It is shown that narrow Gaussian wave beam at the incidence at dielectric half-space with refraction index n>1 and the incidence angle near the Brewster’s angle (i.e.,
parallel polarization) divides into two beams. The angular sector in
which the division occurs is defined by the far field diffraction angle
of the Gaussian beam.

The quantitative variations of the two field maximums and in regard
with the main problems parameters are established. It is shown that the
direction of the field maximums propagation disagrees with the
geometrical optics laws.

The method of solution is generalized to the problem of the beam with
arbitrary original field scattered by dielectric reflector in the
presence of the underlying surface.

The employed Green’s function method permits a step by step carrying
out of the problem, regarding the multireflections of investigated
fields under polarization variations. The developed numerical algorythm
enables to define the spacial distribution of the field in different
planes.

The analytical expression obtained for the wave beam field scattered
under the angles near the grazing angle at high reflection indexes
permits taking into account the sea surface influence. It is
established, that such surface leads to considerable distortions of the
scattered field independently on the original field shape. However the
smaller distortions are observed for the Gaussian wave beam.

The numerical algorythm using the Green’s function of the boundary
problem is developed for the solution of the scattering problem of the
wave pulse beam limited in space and time. The field with Gaussian space
distribution is chosen as initial signal and the time dependence is
represented by the bell shape. For this local pulse wave beam scattered
by dielectric surface the space distributions has been obtained.

The electromagnetic model for the reflection coefficient measurements
is worked out on the base of the obtained solution. The criteria for the
measurement precision bettering are obtained. Requirements to antennas
location inregard to both a measured object and underling surface in
order to achieve minimum field distortions are specified.

Taking into account the main peculiarities of wave beam scattering,
the recommendations on the method of the reflection coefficient
measurements are proposed concerning the elaboration of one-position and
two-position measurement schemes.

Key words: wave scattering, wave beams, pulses, reflection coefficient
measurement, underlying surface, angle of total internal reflection,
grazing angle.

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