Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao

Aieeiaa Na?oeaia Aiaoie??aia

OAeE 534.121:519.8

Iiaeaethaaiiy iae?i?eieo nenoai c

?iioeuenieie aieeaaie

01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Aei?i?iiao?ianuee — 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a Oe?a?inueeiio aea?aeaaiiio o?i?ei-oaoiieia?/iiio
oi?aa?neoao?, I?i?noa?noai ina?oe Oe?a?ie

Iaoeiaee ea??aiee:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?,

Ieeei/oe Aaea??e Ieeieaeiae/

Oe?a?inueeee aea?aeaaiee o?i?ei-oaoiieia?/iee oi?aa?neoao,

caa. eao. aeui? iaoaiaoeee.

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?,

I?oe?i TH??e Aieiaeeie?iae/

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

i?ioani? eaoaae?e i?eeeaaeii? iaoaiaoeee.

aeieoi? oaoi?/ieo iaoe, i?ioani?,

Iaiaeai Iaoae?y ?ee?aia

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao,

i?ioani? eaoaae?e ia/enethaaeueii? iaoaiaoeee oa iaoaiaoe/ii?
e?aa?iaoeee.

I?ia?aeia onoaiiaa: Ee?anueeee aea?aeaaiee oi?aa?neoao ?iai? Oa?ana
Oaa/aiea, eaoaae?a iiaeaethaaiiy neeaaeaieo nenoai, oaeoeueoao
e?aa?iaoeee, I?i?noa?noai ina?oe Oe?a?ie, i. Ee?a.

Caoeno a?aeaoaeaoueny «9» aa?aniy 1999 ?. i 930 aiaeeie ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee

E 08.051.09 i?e Aei?i?iiao?ianueeiio aea?aeaaiiio oi?aa?neoao? ca
aae?anith:

320010, i. Aei?i?iiao?ianuee, i?. Ea?ea Ia?ena, 35, ei?i. 3, aoae. 42.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? Aei?i?iiao?ianueeiai
aea?aeaaiiai oi?aa?neoaoo,

320050, i. Aei?i?iiao?ianuee, aoe. Eicaeiaa, 8.

Aaoi?aoa?ao ?ic?neaiee «6» na?iiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ca?aaee
Oo?/eia A. A. CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. I?iaeaia aeine?aeaeaiiy iae?i?eieo nenoai c
?iioeuenieie aieeaaie, caeia? iaeia c oeaio?aeueieo i?noeue o aeeiai?oe?
nenoai. ?? ?ica’ycaiiy aaaeeeaa aeey i?aeoeee a ca’yceo c oe?ieei
aeei?enoaiiyi oaeeo nenoai o oai??? ca’yceo, aaoiiaoeciaaieo nenoaiao
ea?oaaiiy, iaaeeoeei? oa ?i.

I?iaeai? noai?aiiy iiaeaeae oa iaoiae?a ?ic?aooieo nenoai c ?iioeuenieie
aieeaaie i?enay/aii aiaaoi iaoeiaeo i?aoeue. Ua Ioaiea?a aoei
cai?iiiiiaaii iaoiaee iaoaiaoe/iiai iiaeaethaaiiy, o yeeo
aeei?enoiaothoueny i?e?iaei? oa ooo/ii aaaaeai? iae? ia?aiao?e, ui
i?enooi? o oi?ioethaaii? a?aeiia?aeii? caaea/?. Aeae? E?eeia I.I.,
Aiaiethaia I.I. oa Ieo?iiieueneee TH.I. iieacaee i?eaeaoi?noue
aneiioioe/ieo iaoiae?a iae?i?eii? iaoai?ee aeey aeine?aeaeaiiy nenoai c
?iioeuenieie aieeaaie. Ia?oeie ?iaioaie, i?enay/aieie ieoaiith no?eeino?
nenoai c ?iioeuenieie aieeaaie, i/aaeaeii aoee i?aoe? I?eueiaia A.Ae. oa
Ieoe?na A.Ae.

Oe?iei iiaeai? a e?oa?aoo?? iaoiaee iiaeaethaaiiy neeaaeieo nenoai c
?iioeuenieie aieeaaie oeyoii i?yiiai /enaeueiiai aiae?co ( Oaeaiae O.,
Iaiaeai I.?., Aaenea? Ae.) oa iaoiaee aeine?aeaeaiiy no?eeino?
iae?i?eieo nenoai (?iaeei A.O., Oona?iia Ae.ss., Aiaoia I.I.).

Neeaaei?noue iaoaiaoe/iiai oi?ioethaaiiy i?iaeaie aeey aiae?oe/iiai
aeine?aeaeaiiy iaoiiaeaia iaaeaaee?noth a?aeiia?aeieo aeeiai?/ieo
i?ioean?a. Oea i?ecaiaeeoue aei iaiao?aeiino? ?icaeyaeaoe cai?noue
iaei??? nenoaie oe?eo na??th nenoai (o i?ii?aeeao i?ae ?iioeuenaie)
(Naiieeaiei A. I., Ia?anothe I. I., Aoiaoia I.O.). Aeueoa?iaoeaiee
oeyo neeaaea?oueny o aaaaeaii? a ??aiyiiy neiaoey?ieo ooieoe?e, ui
iiaeaeththoue ?iioeuene, ? ?icaeyaeo ??aiyiue ye ?ioaa?aeueieo
oioiaeiinoae o ?aieao oai??? ?iciiae?eo. A oea iio?aao? aeiaeaoeiaeo
iaoaiaoe/ieo iaa?oiooaaiue o iae?i?eiiio aeiaaeeo (Aeaaeeie?ia A.N.,
Ianeia A.I., Iiaeueyiia A. A., ?aaiia A.E.).

Iaeiae, iacaaaeath/e ia aaeee? aeine?aeaeaiiy, i?iaaaeai? a oe?e
iaeano?, caeeoeeeny ia ?icaeyiooeie ?yae aaaeeeaeo i?iaeai. Iaeia c ieo
— oea iiaeaethaaiiy ? ?ic?aooiie iae?i?eieo aeeiai?/ieo nenoai c iaeiei
oa aeaiia nooiaiyie aie? i?e ?iioeuenieo aieeaao, c iaoith iiaeeeaino?
iaea?aeaiiy ?aeeiiai aiae?oe/iiai ?ica’yceo ia anueiio /eneiaiio
?ioa?aae?.

Oaeei /eiii, ye ?c i?aeoe/ii?, oae ? oai?aoe/ii? oi/ie ci?o ?
aeooaeueiith ?ic?iaea iiaeo iiaeaeae, ui a?aoiaothoue oei/aniao
eieae?caoe?th aieea?a ??ciiai oeio oeyoii aeei?enoaiiy iaaeaaeeiai
ia?aoai?aiiy a?aoiaioo, a oaeiae aiae?c oeeo iiaeaeae oa aeine?aeaeaiiy
caeaaeiino? i?ae ia?aiao?aie iiaeae?.

O aeai?e ?iaio? aeey ?ica’yceo iinoaaeaii? caaea/? canoiniao?oueny
iaoiae iaaeaaeeiai ia?aoai?aiiy a?aoiaioo (/ano), ui ?ai?oa c oni?oii
aeei?enoiaoaaany aeey iiaeaethaaiiy aeaaeeeo neeueii iae?i?eieo
eieeaaeueieo i?ioean?a ? i?inoi?iaeo ia??iaee/ieo no?oeoo? (Iaiaae/
E.?., I?oe?i TH.A., Aaeaeen A.O., Naeaiaea? A.Ae., Noa?ooaiei A.A.,
Aiae??aiia ?.A.). A iniia? oeueiai iaoiaeo eaaeeoue niaoe?aeueia
i?aaenoaaeaiiy ?ica’yceo aeeoa?aioe?ei? ??aiyiue, yea aeei?enoiao?
ieeeiiiae?aio ooieoe?th oa a?aoiao? a?oiia? aeanoeaino? neiao???
ia??iaee/ieo i?ioean?a. I?enooi?noue iaaeaaeeiai a?aoiaioo aeyaeeany
oaeiae aeoaea ei?eniith i?e iiaeaethaaii? ?aaeei?a c eieae?ciaaieie
iniaeeainoyie /aniai? oi?ie. Iaoiae iaaeaaeeiai ia?aoai?aiiy a?aoiaioo
noi?ioeueiaaii Ieeei/oeii A.I.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa aeeiiaia
o a?aeiia?aeiino? c ieaiaie aea?aeathaeaeaoieo oai eaoaae?e aeui?
iaoaiaoeee Oe?a?inueeiai aea?aeaaiiai o?i?ei-oaoiieia?/iiai
oi?aa?neoaoo: «?ic?iaea iaoiae?a aeine?aeaeaiiy iae?i?eieo yaeu
o?ceei-iaoaiaoe/ieo oa iaoai?/ieo nenoai » (? 10970390/47),
«Aeine?aeaeaiiy a aeeiai?oe?, e?iaiaoeoe? oa no?eeino? e?i?eieo oa
iae?i?eieo nenoai» (? 47920190).

Iaoa ? caaea/? aeine?aeaeaiiy. Aieiaiith iaoith aeine?aeaeaiiy ?
?ic?iaea e aiae?c iae?i?eieo iaoaiaoe/ieo iiaeaeae aeey nenoai c
?iioeuenieie aieeaaie, noai?aiiy e iaa?oiooaaiiy iaoiae?a aiae?oe/iiai ?
/enaeueiiai aeine?aeaeaiiy iiaiaeaeaiiy cacia/aieo nenoai o caeaaeiino?
a?ae oa?aeoa?o ?iioeueniiai aieeao oa oeio iae?i?eiino?.

Iinoaaeaia iaoa aecia/eea oae? caaea/? aeine?aeaeaiiy:

?ic?iaeo iaoiaeeee iiaeaethaaiiy iae?i?eieo nenoai i?e ?iioeuenieo
aieeaao c eieae?ciaaieie iniaeeainoyie ??ciiai oeio;

noai?aiiy iiaeo iaoaiaoe/ieo iiaeaeae iae?i?eieo aeeiai?/ieo nenoai, ui
aaeaeaaoii iienothoue ?oi? iiaiaeaeaiiy i?e ?iioeueniiio aieea?;

noai?aiiy /enaeueiiai oa aiae?oe/iiai iaoiaeo ?ica’ycaiiy caaea/, ui
aeieeee a ?acoeueoao? iiaoaeiae iiaeaeae ye? iienothoue ia??iaee/iee,
eaac?ia??iaee/iee oa oaioe/iee ?oo;

aiae?c ia?aiao??a caaaeueii? iae?i?eii? iiaeae? aeeiai?/ii? nenoaie i?e
?iioeueniiio aieea? c iaoith iiaoaeiae eieaeueieo iiaeaeae, ui
oa?aeoa?ecothoue iiaaae?ieo aeine?aeaeoaaieo nenoai;

aaeaioaoe?th aneiioioe/ieo i?ioeaaeo? iaoiae?a Ioaiea?a e ina?aaeiaiiy
aeey aeine?aeaeaiiy iae?i?eieo iaoaiaoe/ieo iiaeaeae nenoai i?e
?iioeuenieo aieeaao.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a iieyaa?:

o noai?ai? iaoiaeeee iiaeaethaaiiy aeeiai?/ieo iae?i?eieo nenoai c
iaei??th oa aeaiia nooiaiyie aie? i?e ?iioeuenieo aieeaao.
Cai?iiiiiaaiee i?aeo?ae aeicaiey? iiaeaethaaoe ye aea?aeenoaioi?, oae ?
iaaea?aeenoaioi? ?iioeuene;

o iiaoaeia? iaoaiaoe/ieo iiaeaeae o aeaeyae? e?aeiaeo caaea/, ye? ia
i?noyoue ooieoe?e Ae??aea, ui aea? iiaeeea?noue aiae?oe/iei iaoiaeii
aea/eoe aeeiai?eo nenoaie ia anueiio oei/aniaiio ?ioa?aae?. Iiaoaeiaa
iiaeaeae a?oioo?oueny ia iaoiae? iaaeaaeeiai ia?aoai?aiiy a?aoiaioo;

o aeyaeaii? iiaeeeaeo aeeiai?/ieo ?aaeei?a oa iiaoaeoaaii? eieaeueieo
iiaeaeae cai?iiiiiaaiei /enaeueii-aiae?oe/iei caniaii;

o iiaoaeia? eieaeueieo iiaeaeae, ui iienothoue ye?nii ??ci? oeie
iiaiaeaeaiiy nenoai oa aecia/aii? ?oi?o aeeiai?/ieo oa?aeoa?enoee;

o aiae?c? iaoaiaoe/ieo iiaeaeae nenoai c ?iioeuenieie aieeaaie
iaoiaeii Ioaiea?a oa ina?aaeiaiiy. Iaa?oioiaaia iiaeeea?noue ?o
canoinoaaiiy.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Io?eiai? a ?iaio?
?acoeueoaoe iiaeooue aeei?enoiaoaaoenue i?e iiaeaethaaii? iae?i?eieo
nenoai c eieae?ciaaieie /aniaeie iniaeeainoyie ??ciiai ?iaeo, i?e
?ica’ycaii? caaea/ aeeiai?/ii? no?eeino? oa aiae?co eieeaaeueieo
?aaeei?a iae?i?eieo iaoai?/ieo nenoai c iaei??th oa aeaiia nooiaiyie
aie? i?ae ae??th ?iioeueniiai iaaaioaaeaiiy. Cai?iiiiiaai? ?ica’ycee
iiaeooue aooe ei?enieie i?e aeine?aeaeaii? iiaeeeaeo aeeiai?/ieo aoaeo?a
o /anoeiai caiiaiaieo ??aeeiith no?oeoo?ao, ui ?ooathoueny, a oaeiae
?ic?aooieo aeaiaio?a i?oaeieo eiino?oeoe?e, iiaeaethaaii?
iae?iaeeiai?/ieo i?ioean?a oa aeaeo?iiieo nenoai.

Iniaenoee aianie caeiaoaa/a. I?ae ea??aieoeoaii aeieoi?a o?ceei —
iaoaiaoe/ieo iaoe, i?ioani?a Ieeei/oea A.I. ? i?e iniaeno?e o/ano?
aeena?oaioa io?eiaii iniiai? oai?aoe/i? ?acoeueoaoe oa i?iaaaeaii
/enaeueiee ?ic?aooiie iiaeeeaeo oei?a ?ica’yce?a iae?i?eieo nenoai c
ia??iaee/ieie ?iioeuenieie aieeaaie. A i?aoeyo [1], [2], [4], [5]
aeena?oaioia? iaeaaeeoue iiaoaeiaa eieaeueieo iiaeaeae; a i?aoeyo [6] —
[8] — /enaeueiee aiae?c nenoaie.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe ?iaioe
aeiiia?aeaeenue oa iaaiai?thaaeeny ia iaoeiaeo nai?ia?ao eaoaae?e aeui?
iaoaiaoeee Oe?a?inueeiai aea?aeaaiiai o?i?ei — oaoiieia?/iiai
oi?aa?neoaoo (i. Aei?i?iiao?ianuee, 1995-1999 ?.), ia i?aeia?iaei?e
eiioa?aioe?? ICBM’96 » No?ieoaeueiua iaoa?eaeu e no?ieoaeueiua
eiino?oeoeee» (i. Aei?i?iiao?ianuee, 1996 ?.), i?aeia?iaeiiio neiiic?oi?
«Geomechanica» (i. Ono?iiue, Iieuenueea ?anioae?ea, 1997), ia
i?aeia?iaeiiio neiiic?oi? «Modelowanie w mechanice» (i. A?nea,
Iieuenueea ?anioae?ea, 1998 ?.), ia i?aeia?iaeiiio neiiic?oi?
«Theoretical foundation of civil engineering» (i. Aa?oaaa, Iieuenueea
?anioae?ea, 1998 ?.), ia iaoeiaiio nai?ia?? eaoaae?e i?eeeaaeii?
iaoaiaoeee Oa?e?anueeiai aea?aeaaiiai iie?oaoi?/iiai oi?aa?neoaoo (i.
Oa?e?a, 1998 ?.), ia iaoeiaiio nai?ia?? Aei?i?iiao?ianueeiai
aea?aeaaiiai oi?aa?neoaoo (i. Aei?i?iiao?ianuee, 1999 ?.), ia
?icoe?aiiio iaoeiaiio nai?ia?? oaeoeueoaoo e?aa?iaoeee Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea (i. Ee?a, 1999 ?.).

Ioae?eaoe??. Ca ?acoeueoaoaie aeeiiaieo aeine?aeaeaiue iioae?eiaaii 8
iaoeiaeo i?aoeue. C ieo: 3 noaoo? a iaoeiaeo aeo?iaeao, caoaa?aeaeaieo
AAE; 2 noaoo? iioae?eiaai? a iaoa??aeao eiioa?aioe?e; 1 aeaiiiiaaia
noaooy oa 2 oace.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny c
anooio, i’youeio ?icae?e?a, aeniiae?a oa nieneo aeei?enoaieo aeaea?ae.
Caaaeueiee ianya ?iaioe neeaaea? 145 noi??iie. Nienie aeei?enoaieo
e?oa?aoo?ieo aeaea?ae i?noeoue 215 iaeiaioaaiue. Oaeno aeena?oaoe??
i?noeoue 20 ?enoie?a.

INIIAIEE CI?NO AeENA?OAOe?EII? ?IAIOE

O anooi? iaa?oioiaaia aeooaeuei?noue oaie aeine?aeaeaiiy, noi?ioeueiaai?
iaoa, iniiai? caaea/? ?iaioe, iaoeiaa iiaecia io?eiaieo ?acoeueoao?a ?
?oiy i?aeoe/ia oe?ii?noue. Aeaia caaaeueia oa?aeoa?enoeea ?iaioe.

Ia?oee ?icae?e i?enay/aii aiae?co ?nioth/eo iaoiae?a aeine?aeaeaiiy
iiaiaeaeaiiy nenoai c ?iioeuenieie aieeaaie oa ?oiuei? no?eeino?.

Iieacaii, ui iiaeaethaaiiy nenoai c ?iioeuenieie aieeaaie i?iaiaeeoueny
a aeaio aniaeoao. A?aeiia?aeii aei ia?oiai, ?iioeueni? aieeae
iiaeaeththoueny oae, ui eii?aeeiaoe aai oaeaeeino? caaeiaieueiythoue
aeiaeaoeiaei oiiaai a ieieao oi/ie eieae?caoe?? ?iioeuen?a, iai?eeeaae,
caaeaiiyi no?eae?a oaeaeeinoae o iiiaio ae?? ?iioeuen?a.

Ae?oaee iai?yiie a?oioo?oueny ia oai??? ocaaaeueiaieo ooieoe?e. Ooo
?iioeueni? aieeae iiaeaeththoueny ca aeiiiiiaith aaaaeaiiy o ??aiyiiy
neiaoey?ieo /eai?a oeio SYMBOL 100 \f «Symbol» \s 12 d — ooieoe?e
Ae??aea.

Iniiaia ia?aaaaa ia?oiai caniao iiaeaethaaiiy iieyaa? a oiio, ui
aeeoa?aioe?ei? ??aiyiiy, ye? iienothoue nenoaio, oae? ae, ye ? i?e
a?aenooiino? ?iioeuen?a. I?ioa oe? ??aiyiiy iaiao?aeii ?icaeyaeaoe
ie?aii ia eiaeiiio c ?ioa?aae?a i?ae ?iioeuenaie, ? oaeei /eiii cai?noue
iaei??? nenoaie aiae?co?oueny oe?ea iine?aeiai?noue nenoai. Ae?oaee
niin?a iiaeaethaaiiy aea? ?aeeio nenoaio ??aiyiue ia onueiio /aniaiio
?ioa?aae? aac aaaaeaiiy caaaeaieo aeua oiia ia ci?ii?, aea a?aeiia?aeiee
aiae?c iiaeiai aooe ei?aeoiei a ?aieao oai??? ocaaaeueiaieo ooieoe?e. A
oea iio?aao? o iae?i?eieo aeiaaeeao aeiaeaoeiaiai iaoaiaoe/iiai
iaa?oiooaaiiy.

O aeai?e ?iaio? aeey iiaeaethaaiiy ?iioeuenieo i?ioean?a
aeei?enoiao?oueny iaoiae, noi?ioeueiaaiee Ieeei/oeii A.I. oa caniiaaiee
ia iaaeaaeeiio ia?aoai?aii? /ano. Oaeee i?aeo?ae aeicaiey?, c iaeiiai
aieo, iiaoaeoaaoe iaoaiaoe/io iiaeaeue, ui ia i?noeoue SYMBOL 100 \f
«Symbol» \s 12 d — ooieoe?e Ae??aea, a c ?ioiai — iaea?aeaoe ??
?ica’ycie o aeaeyae? ?aeeiiai aiae?oe/iiai ae?aco ia onueiio /aniaiio
?ioa?aae?.

Ne?ae cacia/eoe, ui aeiyoie «aioo??oi?o» oaea??a ca aeiiiiiaith
iaaeaaeeeo ia?aoai?aiue i?inoi?iaeo eii?aeeiao canoiniaoaaa AEo?aaeueia
A.O. Iaeiae oeae iaoiae, nei??oa ca ana, aaciina?aaeiuei
aeei?enoiao?oueny o?eueee aei a?a?ioaea?ieo nenoai oa nenoai c
iaeiia?/ieie ia oo?eioth/eie ca’yceaie. I?e oeueiio ia?aoai?aiith
i?aeaea?oueny i?inoi?iaa eii?aeeiaoa, a ia /an. O aeei?enoiaoaaiiio ooo
iaoiae? iniiaiee ia’?eo ia?aoai?aiiy — /an, a ia ooeaia ooieoe?y.

A ae?oaiio ?icae?e? noaaeoueny caaaeueia caaea/a iiaeaethaaiiy
iae?i?eieo nenoai c eieae?ciaaieie /aniaeie iniaeeainoyie,
aeeeaaeathoueny i?eioeeie ?aae?caoe?? oaeeo iiaeaeae, a oaeiae
i?iaiaeeoueny iiaoaeiaa iaoaiaoe/ieo iiaeaeae aac neiaoey?iinoae.

Iiaeaethaaiiy nenoai c eieae?ciaaieie /aniaeie iniaeeainoyie caniiaaii
ia ia?aoai?aii? /ano, o ?acoeueoao? /iai i?inoi?iaa eii?aeeiaoa iaaoaa?
no?oeoo?o aeaaa?e aac ?iciiae?eo

, (symbol 116 \f «Arial» \s 12tsymbol 174 \f «Symbol»
\s 12®symbol 116 \f «Symbol» \s 12t symbol 125 \f «Arial» \s 12,
(1)

— eoneiai-e?i?eia ia??iaee/ia ii t, c ia??iaeii T=4 ieeeiiiae?aia
ooieoe?y

— ?? ia?oa iio?aeia. Ia?aiao? SYMBOL 81 \f «Symbol» \s 12 Q ,
oa?aeoa?eco? oei ?iioeueniiai aieeao. I?e SYMBOL 81 \f «Symbol» \s 12 Q
SYMBOL 185 \f «Symbol» \s 12 ? 0 ooieoe?y SYMBOL 116 \f «Symbol» \s 12
t (t; SYMBOL 81 \f «Symbol» \s 12 Q ) ? einineiao?e/iith, ?iioeuene
ae?thoue ia?aie. I?e SYMBOL 81 \f «Symbol» \s 12 Q = 0 ooieoe?y
SYMBOL 116 \f «Symbol» \s 12 t (t; SYMBOL 81 \f «Symbol» \s 12 Q ) —
neiao?e/ia, ?iioeuene ae?thoue /a?ac ??ai? i?ii?aeee /ano.

Iaiao?aeia ni?aa?aeiioaiiy

io?eiaii oi?iaeueiei aeeoa?aioe?thaaiiyi iaio /anoei ??aiino? (1).

Iieacaii, ui iaaeaaeea ia?aoai?aiiy /ano {t SYMBOL 174 \f «Symbol» \s 12
® SYMBOL 116 \f «Symbol» \s 12 t } ? aoaeoeaiei caniaii iiaeaethaaiiy
nenoai c ?iioeuenieie aieeaaie, yea aeicaiey? iiaoaeoaaoe caaaeueio
iiaeaeue o aeaeyae? e?aeiai? caaea/? ia noaiaea?oiiio ?ioa?aae? (-1
SYMBOL 163 \f «Symbol» \s 12 F SYMBOL 116 \f «Symbol» \s 12 t SYMBOL
163 \f «Symbol» \s 12 F 1) aac SYMBOL 100 \f «Symbol» \s 12 d —
ooieoe?e. Aacoth/enue ia ia??iaee/iino? ooieoe?? SYMBOL 116 \f «Symbol»
\s 12 t (t; SYMBOL 81 \f «Symbol» \s 12 Q ) ?ica’ycie, io?eiaiee ia
i?aia??iae?, iiaeia i?iaeiaaeeoe ia anth /eneiao a?nue.

Ae?y ?iioeuenieo ii?ooaiue ia iiaeaeue iieno?oueny ca aeiiiiiaith
ae?oai? ocaaaeueiaii? iio?aeii? ooieoe?? SYMBOL 116 \f «Symbol» \s 12
t (t; SYMBOL 81 \f «Symbol» \s 12 Q ).

O aeiaaeeo iaia?a?aiiai ?ica’yceo x(t) a?i aoaea aeeeth/aiee ca ?aooiie
oiiae Y SYMBOL 189 \f «Symbol» \s 12 1/2 SYMBOL 116 \f «Symbol» \s 12
t = SYMBOL 177 \f «Symbol» \s 12 ± 1=0.

o ae?ac? aeey ae?oai? iio?aeii? aeicaiey? aeeeth/eoe neiaoey?i? /eaie
c aeo?aeiiai aeeoa?aioe?eiiai ??aiyiiy, yea iieno? iiaeaeue, ui
?icaeyaea?oueny.

Iieacaii iiaeeea?noue iiaeaethaaiiy ?iioeuenieo aieea?a ??ciiai oeio,
oiaoi iiaeaethaaiiy ia o?eueee aea?aeenoaioieo, aea e
iaaea?aeenoaioieo ?iioeuenieo aieea?a, ui cia/ii ?icoe?th? eiei
?ica’ycaieo caaea/.

Iniiai? aoaie iiaeaethaaiiy ?ethno?othoueny ia o?ueio oeiiaeo nenoaiao.

, ui ia?aaea?oueny /a?ac aaniethoii aei?noeo iaaaioaaeoaaeueio aaeeo.
Iiaiaeaeaiiy ieanoeie iieno?oueny ??aiyiiyi

aea SYMBOL 68 \f «Symbol» \s 12 D — aeeoa?aioe?aeueiee iia?aoi?;

D — oeee?iae?e/ia aei?noe?noue;

m — iana ieanoeie, a?aeianaia aei iaeeieoe? ieiu?;

Ny, Nz, Nyz — coneeey a na?aaeeii?e iiaa?oi?.

c ianooiiei canoinoaaiiyi iaoiaeo Aaeuei?e?ia i?ecaiaeeoue aei
iae?i?eii? iiaeae? o aeaeyae? aeeoa?aioe?eiiai ??aiyiiy ae?oaiai
ii?yaeeo oeio Aeoo?iaa c ia??iaee/ieie ?iioeuenieie aieeaaie

(2)

, p ? q — ia?aiao?e;

SYMBOL 101 \f «Symbol» \s 12 e — ia?aiao? iae?i?eiino?.

Aei aiaeia?/iiai aeaeyaeo iiaeooue aooe caaaeai? ? caaea/? aeeiai?ee
?iioeuenieo no?eeeo nenoai.

Iaaeaaeea ia?aoai?aiiy /ano (1) aeicaieeei ?ic?iaeoe caaaeueio iiaeaeue
o aeaeyae? nenoaie aeeoa?aioe?eieo ??aiyiue

(1- SYMBOL 81 \f «Symbol» \s 12 Q 2)X SYMBOL 178 \f «Symbol» \s 12 ? —
2 SYMBOL 81 \f «Symbol» \s 12 Q Y SYMBOL 178 \f «Symbol» \s 12 ? +(1-
SYMBOL 81 \f «Symbol» \s 12 Q 2)2pX = — SYMBOL 101 \f «Symbol» \s 12 e
(1- SYMBOL 81 \f «Symbol» \s 12 Q 2)2Rf ,
(3)

(1+3 SYMBOL 81 \f «Symbol» \s 12 Q 2)Y SYMBOL 178 \f «Symbol» \s 12 ? —
2 SYMBOL 81 \f «Symbol» \s 12 Q (1- SYMBOL 81 \f «Symbol» \s 12 Q 2)X
SYMBOL 178 \f «Symbol» \s 12 ? +(1- SYMBOL 81 \f «Symbol» \s 12 Q 2)2pY
= — SYMBOL 101 \f «Symbol» \s 12 e (1- SYMBOL 81 \f «Symbol» \s 12 Q
2)2If,

c e?aeiaeie oiiaaie

(X’+qX) SYMBOL 189 \f «Symbol» \s 12 1/2 SYMBOL 116 \f «Symbol» \s 12
t = SYMBOL 177 \f «Symbol» \s 12 ± 1= [2 SYMBOL 81 \f «Symbol» \s 12 Q
Y’+ SYMBOL 81 \f «Symbol» \s 12 Q 2(X’+qX)] SYMBOL 189 \f «Symbol» \s 12
1/2 SYMBOL 116 \f «Symbol» \s 12 t = SYMBOL 177 \f «Symbol» \s 12 ± 1,

Y SYMBOL 189 \f «Symbol» \s 12 1/2 SYMBOL 116 \f «Symbol» \s 12 t =
SYMBOL 177 \f «Symbol» \s 12 ± 1=0.
(4)

Iacaaaeath/e ia oi?iaeueii a?eueo neeaaeiee aeaeyae, io?eiaia iiaeaeue
(3)-(4) ia i?noeoue neiaoey?ieo /eai?a. O oeueiio ?? iniiaia ia?aaaaa.
Ae?y ?iioeueniiai aieeao aeyaey?oueny a e?aeiaeo oiiaao c ia?aiao?ii q.
I?e q=0 ?iioeueni? aieeae ia nenoaio ia ae?thoue.

I?ney iiaeaethaaiiy iaaea?aeenoaioii? nenoaie i?iaaaeaii iiaeaethaaiiy
aea?aeenoaioiiai ( SYMBOL 81 \f «Symbol» \s 12 Q =0) i?ioeano. Iiaa eaea
i?i ?ic?iaeo iaoaiaoe/ii? iiaeae? aeey aeiaaeeo ??aiia?aeaeaeaieo
?iioeuen?a. I?e oeueiio ?iioeuene iiaeaeththoueny ca aeiiiiiaith
neiao?e/ii? ieeeiiiae?aii? ooieoe?? SYMBOL 116 \f «Symbol» \s 12 t
(t). No?iai eaaeo/e, oaea caaea/a ? ie?aiei aeiaaeeii
iaaea?aeenoaioiiai i?ioeano. I?ioa caaea/a ? oe?eaaith, ine?eueee
?aae?caoe?y iaoaiaoe/ii? iiaeae? aac ooieoe?e Ae??aea iiaeeeaa ca
aeiiiiiaith ia?aoai?aiiy, ui i?noeoue o?eueee X — eiiiiiaioo (Y=0).
?acoeueoaoii iaaeaaeeiai ia?aoai?aiiy ? iaoaiaoe/ia iiaeaeue o aeaeyae?
e?aeiai? caaea/?, ui i?eionea? oi/iee ?ica’ycie ??oaiiy a ae?ioe/ieo
ooieoe?yo.

2. Iae?i?eia iiaeaeue nenoaie c aeaiia nooiaiyie aie? oeio ??aeeia —
aaniethoii oaa?aea o?ei. I?iaaaeaii aeine?aeaeaiiy iiaeae?,
iiaoaeiaaii? Ieeei/oeii A.I. oa ?a?aa?iii ?.A., ui iieno? aca?iiae?th
??aeeie c aeeiai?/iith no?oeoo?ith.

Ia?aaeaa/a?oueny, ui iaieiiea ? aaniethoii aei?noeith. Iiaeaeeth
??aeeie, ui a?eueii eieeaa?oueny , ? iayoiee aeiaaeeie L. Iayoiee
aeinyaa? no?iee iaieiiee, eiee eoo c aa?oeeaeueiith neeaaeiaith
aei??aith? SYMBOL 113 \f «Symbol» \s 12 q = SYMBOL 177 \f «Symbol» \s
12 ± SYMBOL 113 \f «Symbol» \s 12 q 0. Oaea?e iayoieea ia no?iee o?ea
iienai? oaiiiaiieia?/ii iioaioe?eiei iieai, neaaeei a iaeano? SYMBOL
231 \f «Symbol» \s 12 c SYMBOL 113 \f «Symbol» \s 12 q SYMBOL 231 \f
«Symbol» \s 12 c SYMBOL 60 \f «Symbol» \s 12 < SYMBOL 113 \f "Symbol" \s 12 q 0 ? oaeaeei c?inoath/ei a ieie? oi/ie SYMBOL 113 \f "Symbol" \s 12 q = SYMBOL 177 \f "Symbol" \s 12 ± SYMBOL 113 \f "Symbol" \s 12 q 0. I?e oeueiio, neea aca?iiae?? aecia/a?oueny noaoa/iith ooieoe??th eooa SYMBOL 113 \f "Symbol" \s 12 q c aenieei iieacieeii. O ?acoeueoao? aca?iiae?? iayoieea c o?eii a?aeaoaa?oueny ?icn?thaaiiy aia?a??. Ia?aaeaa/a?oueny, ui ai?eciioaeueia eiiiiiaioa aieeao aei??aith? ioeth, a aa?oeeaeueia ? ia??iaee/iith na???th ?iioeuen?a. Ca ia??iae ia nenoaio ae?thoue aeaa iiceoeaieo ?iioeuene. Iaoaiaoe/iith iiaeaeeth nenoaie no?oeoo?a-??aeeia ? aeeoa?aioe?eia ??aiyiiy ae?oaiai ii?yaeeo a iao?e/i?e oi?i? , (5) aea ?iioeueni? iaaaioaaeaiiy ae?aaeaii /a?ac ae?oao ocaaaeueiaio iio?aeio ieeei SYMBOL 47 \f "Symbol" \s 12 / a); 2a - a?aenoaiue i?ae aeaiia non?aei?ie ?iioeuenaie; 2p ?oiy aiie?ooaea. ), N(x) - caaeai? iao?eoe?, ui oa?aeoa?ecothoue a?aeiia?aeii ?ia?oe?ei?, i?oaei? aeanoeaino? iiaeae?, a oaeiae ciai?oi? aieeae ? o?ce/io iae?i?ei?noue; SYMBOL 98 \f "Symbol" \s 12 b - iino?eiee ?ici??; x - iao?eoey-noiai/ee aac?ici??ieo eoo?a (o /anoeao SYMBOL 113 \f "Symbol" \s 12 q 0). O ?acoeueoao? iaaeaaeeiai ia?aoai?aiiy /ano aeo?aeia nenoaia ?iciaaea?oueny ia aea? iaca'ycai? i?ae niaith caaea/? ia aeani? cia/aiiy. (6) Io?eiaia iiaeaeue (6) ia i?noeoue SYMBOL 100 \f "Symbol" \s 12 d - ooieoe?e. Ae?y ?iioeuenieo aieea?a ia iiaeaeue aeyaey?oueny a e?aeiaeo oiiaao c ia?aiao?ii ?. Nenoaia oeio Aai-aea?-Iiey i?ae ae??th ia??iaee/iiai ?iioeueniiai iaaaioaaeaiiy. Oe?eaao a i?aeoe/iiio oa oai?aoe/iiio ieai? caaea/o yaey? niaith aeine?aeaeaiiy oa?oaaoiai na?aaeiaeua c o?aooaaiiyi iiaa?oiaaeo ca?yae?a ia iaaeao iiae?eo i?ioa?e?a a aeaeo?iaeeiai?oe?, ??aiyiiy yei? ia? aeaeyae , (7) aea a - /aa?oue ia??iaeo ciai?oiueiai aieeao; SYMBOL 101 \f "Symbol" \s 12 e - iaeee ia?aiao?; ia?aiao? SYMBOL 120 \f "Symbol" \s 12 x oa?aeoa?eco? ?iceaae i?ae aeaniith /anoioith eieeaaiue ? /anoi oith ciai?oiueiai iaaaioaaeaiiy; p - iino?eiee ia?aiao?. Aaaaea?ii, ui /anoioa iniiaiiai oiio ciai?oiueiai aieeao aei??aith? iaeeieoe?, oiaoi a= SYMBOL 112 \f "Symbol" \s 12 p SYMBOL 164 \f "Symbol" \s 12 ¤ 2. ?aae?caoe?y iiaeae? aac SYMBOL 100 \f "Symbol" \s 12 d - ooieoe?e aeey aaoieieeaaeueii? nenoaie (7) caniiaaia ia canoinoaaii? eiiieaeniiai i?aeoiaeo, ui aeeth/a? iaoiae iaaeaaeeeo ia?aoai?aiue a?aoiaioo oa iaoiae aeaioianooaaieo ?iceeaaeaiue. Aaaaeaii aea? /ania? ci?ii?: ?ieue oaeaeeiai /ano a?a? ci?iia SYMBOL 116 \f "Symbol" \s 12 t , iia?eueiee /an aaaaeaii cae/aeiei /eiii: t0 = SYMBOL 101 \f "Symbol" \s 12 e t. ?ic?iaeaii iiaeaeue, ui iieno?oueny nenoaiith ??aiyiue o /anoeiieo iio?aeieo , (8) c e?aeiaeie oiiaaie Ca ?aooiie e?aeiaeo oiia aeeeth/ai? neiaoey?i? /eaie a ia?aoai?ai?e nenoai?. ?ica’ycie io?eiaii? caaea/? iiaeia ciaeoe iaoiaeii ina?aaeiaiiy. O o?aoueiio ?icae?e? i?iaaaeaii /enaeueiee aiae?c iiaeeeaeo oei?a ?ica’yce?a, o caeaaeiino? a?ae ia?aiao??a SYMBOL 101 \f "Symbol" \s 12 e , SYMBOL 81 \f "Symbol" \s 12 Q oa p iiaeae? oeio Aeoo?iaa (2) c ?iioeuenieie aieeaaie, c iaoith aeae?eaiiy eieaeueieo iiaeaeae. Aeey oeueiai iiia?aaeiuei i?iaaaeaii aiae?oe/ia ia?aoai?aiiy i?ae ?iioeuenaie. Oaeee i?aeo?ae aea? iai/i?noue, ciaioo? e?euee?noue noaiaea?oieo ia/eneaiue ? caiuaaeaeo? iaoeiiee /an. i?eioneathoue aiae?oe/ia ?ioaa?oaaiiy. Ci?iia ae?? I i?ae ?iioeuenaie caeeoa?oueny iino?eiith, o oie /an ye ci?ie eoo SYMBOL 106 \f "Symbol" \s 12 j ci?ith?oueny. Iaoae {I, SYMBOL 106 \f "Symbol" \s 12 j } ? {I, SYMBOL 106 \f "Symbol" \s 12 j } - ci?ii? ae?y-eoo, ui ia/eneythoueny a?aeiia?aeii i?ney ae?? iiceoeaiiai ? iaaaoeaiiai ?iioeueno. Oiiae ia?aoiaeo ?ica’yce?a /a?ac iaaaoeaiee oa iiceoeaiee ?iioeuen iathoue aeaeyae Ooo (2 SYMBOL 177 \f "Symbol" \s 12 ± 2 SYMBOL 113 \f "Symbol" \s 12 q ) - a?aenoaiue i?ae aeaiia non?aei?ie ?iioeuenai, SYMBOL 68 \f "Symbol" \s 12 D SYMBOL 177 \f "Symbol" \s 12 ± I, SYMBOL 68 \f "Symbol" \s 12 D SYMBOL 177 \f "Symbol" \s 12 ± SYMBOL 106 \f "Symbol" \s 12 j - ?ici?? no?eaea i?e ia?aoiae? ?ica’ycea /a?ac ?iioeuen. Ia iniia? /enaeueiiai aiae?co iiaoaeiaaii a?oo?eaoe?ei? ae?aa?aie, ui aeaiiino?othoue ??ci? aeeiai?/i? ?aaeeie (ia??iaee/i?, ?aaoey?i? eaac?ia??iaee/i? oa ia?aaoey?i? noioanoe/i?). I?iaaaeaii aiae?c oei?a ?ica’yce?a o caeaaeiino? a?ae ia?aiao?a iiaeae? SYMBOL 81 \f "Symbol" \s 12 Q aeey ??cieo cia/aiue iae?i?eiino? ( SYMBOL 101 \f "Symbol" \s 12 e = 0.5, SYMBOL 101 \f "Symbol" \s 12 e = 1.5). Iieacaii, ui aeey aeiaaeeo iaaaee/ei? iae?i?eiino? ( SYMBOL 101 \f "Symbol" \s 12 e = 0.5) ?niothoue ia??iaee/i? ( SYMBOL 81 \f "Symbol" \s 12 Q =0.01; SYMBOL 81 \f "Symbol" \s 12 Q =0.5; SYMBOL 81 \f "Symbol" \s 12 Q =1.0), eaac?ia??iaee/i? (0.01 < SYMBOL 81 \f "Symbol" \s 12 Q < 0.5) oa neeaaei? (0.5 < SYMBOL 81 \f "Symbol" \s 12 Q < 1.0) ?aaeeie. I?ney eeaneo?eaoe?? eieaeueieo iiaeaeae i?iaaaeaii aiae?oe/ia aeine?aeaeaiiy iiaeae? o aeiaaeeo ia??iaee/ieo ?ica’yce?a. ?icaeyiooi aeiaaeie iaei? iae?i?eiino? SYMBOL 101 \f "Symbol" \s 12 e ? iaei? aea?aeenoaioiino? ?iioeuen?a ( SYMBOL 81 \f "Symbol" \s 12 Q SYMBOL 32 \f "Symbol" \s 12 SYMBOL 126 \f "Symbol" \s 12 ~ SYMBOL 101 \f "Symbol" \s 12 e ). Iayai?noue iaeiai ia?aiao?a SYMBOL 101 \f "Symbol" \s 12 e aeicaieeea nei?enoaoeny noaiith Ioaiea?a. Oaeee i?aeo?ae i?eca?a aei ?iciaaeo aeo?aeii? caaea/? ia iine?aeiai?noue e?aeiaeo caaea/ ia i?ii?aeeo (-1 SYMBOL 163 \f "Symbol" \s 12 F SYMBOL 116 \f "Symbol" \s 12 t SYMBOL 163 \f "Symbol" \s 12 F 1). Ii?iaeaeoth/ith ? e?i?eia ( SYMBOL 101 \f "Symbol" \s 12 e = 0) iaca'ycaia uiaei X, Y - eiiiiiaio e?aeiaa caaea/a ia aeani? cia/aiiy X0 SYMBOL 178 \f "Symbol" \s 12 ? + SYMBOL 108 \f "Symbol" \s 12 l 2 X0 =0, (X0 SYMBOL 162 \f "Symbol" \s 12 c + qX0) SYMBOL 189 \f "Symbol" \s 12 1/2 SYMBOL 116 \f "Symbol" \s 12 t = SYMBOL 177 \f "Symbol" \s 12 ± 1 = 0, Y0 SYMBOL 178 \f "Symbol" \s 12 ? + SYMBOL 108 \f "Symbol" \s 12 l 2 Y0 =0, Y0 SYMBOL 189 \f "Symbol" \s 12 1/2 SYMBOL 116 \f "Symbol" \s 12 t = SYMBOL 177 \f "Symbol" \s 12 ± 1 = 0. O caeaaeiino? a?ae cia/aiue SYMBOL 108 \f "Symbol" \s 12 l ?niothoue aeaa ??cieo oeie aeanieo oi?i eieeaaiue. O ia?oiio iaaeeaeaii? io?eiaia iae?i?eia iia'ycaia uiaei X, Y - eiiiiiaio e?aeiaa caaea/a. Anoaiiaeaii ni?aa?aeiioaiiy i?ae ia?aiao?aie iiaeae?, ui caaacia/othoue no?ee?noue ia??iaee/ieo ?ica’yce?a , (9) aea A - aiie?ooaea eieeaaiue; SYMBOL 108 \f "Symbol" \s 12 l 2j - aeani? cia/aiiy. . O aeiaaeeo iiaeaethaaiiy iaaea?aeenoaioieo ( SYMBOL 81 \f "Symbol" \s 12 Q SYMBOL 185 \f "Symbol" \s 12 ? 0) ?iioeuen?a iiaoaeiaai? ia??iaee/i? ?ica’ycee c oi/i?noth aei /eai?a ii?yaeeo SYMBOL 101 \f "Symbol" \s 12 e . Aecia/aiiy ianooiieo /eai?a ?iceeaaeaiiy ia i?noeoue i?eioeeiiaeo o?oaeiiu?a. Aeae? ?icaeyiooi aeiaaeie aea?aeenoaioieo ?iioeuen?a (7). Ine?eueee ?iioeuene ae?thoue /a?ac ??ai? i?ii?aeee /ano, oi iiaeaethaaiiy i?ioeano iiaeeeai ca aeiiiiiaith neiao?e/ii? ( SYMBOL 81 \f "Symbol" \s 12 Q = 0) ooieoe?? SYMBOL 116 \f "Symbol" \s 12 t (t). Iieacaii, ui a oeueiio aeiaaeeo aeo?aeia caaea/a i?eionea? oi/iee ?ica’ycie a ae?ioe/ieo ooieoe?yo. Iaea?aeaii oi/iee ?ica’ycie o ooieoe?yo sseia? aeey aea?aeenoaioii? ( SYMBOL 81 \f "Symbol" \s 12 Q = 0) iae?i?eii? ( SYMBOL 101 \f "Symbol" \s 12 e SYMBOL 185 \f "Symbol" \s 12 ? 0) iiaeae?. I?iaaaeaii ii??aiyiiy ?acoeueoao?a oi/iiai e aneiioioe/iiai oa /enaeueiiai ?ica’yceo. Aeey aiie?ooaee A=1 oi/iee e aneiioioe/iee ?ica’ycie ca?aathoueny, ui aiai?eoue i?i aeinoaoiuei aa?io oi/i?noue cai?iiiiiaaiiai i?aeoiaeo. I?e A=4 ? iaaaee/e? ?ica?aeiino? ( SYMBOL 187 \f "Symbol" \s 12 » 1.1%). O /aoaa?oiio ?icae?e? i?iaaaeaia /enaeueia aeine?aeaeaiiy i?ioeano aca?iiae?? ??aeeie c aeeiai?/iith no?oeoo?ith. Aeey ci?iieo ae?y-eoo {Ij, SYMBOL 106 \f "Symbol" \s 12 j j} iiaoaeiaaia ni?iuaia iiaeaeue, yea oa?aeoa?eco? ??ci? noaie nenoaie c aeaiia nooiaiyie aie? i?e ia?aiao?e/iiio ?iioeueniiio aieea?. Iiaiaeaeaiiy nenoaie iieno?oueny nenoaiith aeaio aeeoa?aioe?eieo ??aiyiue ia?oiai ii?yaeeo uiaei ci?iieo {Ij, SYMBOL 106 \f "Symbol" \s 12 j j} (10) oa oiiaaie ia?aoiaeo ?ica’yce?a /a?ac iiceoeaiee ?iioeuen aea SYMBOL 68 \f "Symbol" \s 12 D Ij, SYMBOL 68 \f "Symbol" \s 12 D SYMBOL 106 \f "Symbol" \s 12 j j no?eaee ci?iieo ae?y - eoo {Ij, SYMBOL 106 \f "Symbol" \s 12 j j} i?e ieoo?aeo aieeaao. SYMBOL 106 \f "Symbol" \s 12 j j o i?eiouaii? a?aenooiino? aioo??oiueiai ?aciiaino. I?ae ?iioeuenaie ci?iia ae?? Ij caeeoa?oueny iino?eiith, a eoo SYMBOL 106 \f "Symbol" \s 12 j j ci?ith?oueny ? caeaaeeoue a?ae a?aenoai? 2a i?ae ?iioeuenaie. Iieacaii, ui oea ??aiyiiy ia ia? oi/iiai ?ica‘yceo. Ia iniia? /enaeueiiai aiae?co iiaoaeiaai? a?oo?eaoe?ei? ae?aa?aie, ui aeaiiino?othoue ??ci? aeeiai?/i? ?aaeeie nenoaie (ia??iaee/i?, ?aaoey?i? eaac?ia??iaee/i? oa ia?aaoey?i? noioanoe/i?). Aeine?aeaeaii aaiethoe?th no?oeoo?e ?ica’yceo i?e ci?i? ia?aiao?a iae?i?eiino? SYMBOL 98 \f "Symbol" \s 12 b a?ae 0.5 aei 2.0. Aea/aii iniiai? oa?aeoa?enoeee iiaaae?iee nenoaie a caeaaeiino? a?ae aiie?ooaee ?iioeueniiai aieeao ?. I?e ioeueiaiio cia/aii? ia?aiao?a ? iiaeae? ia nenoaio ia ae?thoue ?iioeueni? aieeae. Eieeaaiiy nenoaie iinyoue no?eeee ia??iaee/iee oa?aeoa?. C ?inoii p aaee/eia Ij oaeaeei ?inoa, ia??iaee/i? ?aaeeie cieeathoue, iinooiath/enue i?noeai eaac?ia??iaee/iei (0 < p SYMBOL 163 \f "Symbol" \s 12 F 0.4) ? aeae? ua a?eueo neeaaeiei ?aaeeiai (0.4 < p SYMBOL 163 \f "Symbol" \s 12 F 1). Oaeiae aea/aii iniaeeaino? iiaaae?iee a caeaaeiino? a?ae a?aenoai? ? i?ae ?iioeuenaie oa cia/aiiy iae?i?eiino? SYMBOL 98 \f "Symbol" \s 12 b . Ia ae?aa?ai? ia??iaee/iee ?oo a?aeiia?aea? «aoceai», eaac?ia??iaee/iee - nooe?eueiei e?i?yi, oaioe/iee - aacii?yaeeia?e iiiaeei? oi/ie. Oaeei /eiii, ca aeiiiiiaith /enaeueiiai ?ic?aooieo aeine?aeaeaii ia?aiao?e i?ioeano oa ?oi?e aieea ia aeeiai?eo nenoaie, aeae?eai? ia??iaee/i? ?ica’yee, aeey yeeo aiae?oe/iei caniaii iiaoaeiaaii eieaeueio iiaeaeue. Ae??oaii i?iaeaio aeeiai?/ii? no?eeino? ??aiiaaaeiiai iieiaeaiiy aiae?ciaaii? nenoaie. Aiae?c iiaeae? (6) i?e ?=0 aeicaieea iaea?aeaoe ni?aa?aeiioaiiy aeey neioacii? oa aioeoacii? e?i?eii? iiaee. Aiae?c iiaeae? (6) i?e ? SYMBOL 185 \f "Symbol" \s 12 ? 0 i?iaaaeaii o oa?i?iao aieiaieo eii?aeeiao q1, q2. A?aeiinii aieiaieo eii?aeeiao io?eiaia ca'ycia e?aeiaa caaea/a, yea i?noeoue aieiai? eii?aeeiaoe o e?aeiaeo oiiaao. Iiaoaeiaaii ia??iaee/i? ?ica’ycee aeo?aeii? nenoaie e oiiae ?o ?nioaaiiy. Caaaeai? oiiae yaeythoue niaith nenoaio aeaio aeaaa?a?/ieo ??aiyiue, o i?ioean? ?ica’yceo eio?eo io?eiaia caeaaei?noue a=a(p) ia??iaeo eieeaaiue a?ae aaee/eie ?iioeueniiai aieeao, aeeaeie iaiiaiaiiy iaieiiee oa iane ??aeeie. E?ea? a=a(p) ?icaeaathoue ieiueio ia?aiao??a ?-a ia iaeano? no?eeino? oa iano?eeino?. I?e p=0 e?aeia? oiiae (6) noathoue iaeii??aeieie, e?ea? a=a(p) ia?aoai?ththoueny a i?yi?. O i’yoiio ?icae?e? i?iaaaeaii /enaeueiee aiae?c aaoieieeaaeueii? nenoaie (8) oeio Aai-aea?-Iiey, o ?acoeueoao? /iai aeae?eai? eieaeuei? iiaeae?, ui a?aeiia?aeathoue aeeiai?/iiio ?ooo o?ueio oei?a, o caeaaeiino? a?ae ia?aiao??a iiaeae? SYMBOL 120 \f "Symbol" \s 12 x ? SYMBOL 101 \f "Symbol" \s 12 e . Iiia?aaeiuei aeey iieno iiaiaeaeaiiy nenoaie i?ae ?iioeuenaie aoee aaaaeai? ci?ii? Aai-aea?-Iiey , aea aiie?ooaea A(t) oa oaca SYMBOL 106 \f "Symbol" \s 12 j (t) ? ooieoe?yie /ano t. Ca aeiiiiiaith ci?iieo Aai-aea?-Iiey iiaoaeiaaia ni?iuaia iiaeaeue, ui iieno?oueny nenoaiith aeeoa?aioe?eieo ??aiyiue ia?oiai ii?yaeeo (11) Nenoaia (11) cia/ii i?ino?oa aeo?aeii?, ine?eueee a iiaeae? (11) oaeaee? ? iia?euei? i?yioaaiiy ?icae?eai?. I?e/iio ia?oa ??aiyiiy i?eionea? ?ioaa?oaaiiy iacaeaaeii a?ae ae?oaiai ? iieaco?, ui aiie?ooaea A( SYMBOL 116 \f "Arial" \s 12 t ) ci?ith?oueny iia?eueii, oiio ui ?? iio?aeia ia? ii?yaeie SYMBOL 101 \f "Symbol" \s 12 e . ?ieue oaeaeeiai ci?iiiai a?a? oaca SYMBOL 106 \f "Symbol" \s 12 j ( SYMBOL 116 \f "Arial" \s 12 t ). I?e ia?aoiae? /a?ac oi/ee eieae?caoe?? ?iioeuen?a oaca SYMBOL 106 \f "Symbol" \s 12 j ( SYMBOL 116 \f "Arial" \s 12 t ) oa aiie?ooaea A( SYMBOL 116 \f "Arial" \s 12 t ) caciathoue ci?ie. Io?eiaii oiiae ia?aoiaeo nenoaie /a?ac oi/ee eieae?caoe?? ?iioeuen?a. I?iaaaeaii /enaeueiee aiae?c iiaeae? (8), c iaoith aecia/aiiy aieeao ?iioeuenieo iaaaioaaeaiue ia ?icaeoie aeeiai?/iiai i?ioeano i?e aa??thaaii? ia?aiao??a iiaeae? SYMBOL 120 \f "Symbol" \s 12 x ? SYMBOL 101 \f "Symbol" \s 12 e , a oaeiae aeey aeyaeaiiy iniiaieo iniaeeainoae oeueiai ?icaeoeo. Aea/aii oa?aeoa?i? ?ene aeeiai?ee iiaeae? oeio aaoieieeaaeueii? nenoaie Aai-aea?-Iiey c ia??iaee/iei ?iioeueniei iaaaioaaeaiiyi. Iiaoaeiaaii eieaeuei? iiaeae? aeey o?ueio ??cieo oei?a i?yioaaiue, iiaoaeiaai? a?oo?eaoe?ei? ae?aa?aie, ui ?ice?eaathoue oa?aeoa? aeeiai?/iiai i?ioeano. Aeine?aeaeaia aaiethoe?y no?oeoo?e ?ica’yceo aeey ??cieo cia/aiue iae?i?eiino?. Iieacaii, ui aeey iaaaee/eeo cia/aiue iae?i?eiino? ( SYMBOL 101 \f "Symbol" \s 12 e =0.5) oa ciai?oiueiai iaaaioaaeaiiy (p=0.01) ia??iaee/i? ?aaeeie ?niothoue aeey SYMBOL 120 \f "Symbol" \s 12 x =0.05 oa SYMBOL 120 \f "Symbol" \s 12 x =1.32. Aeae? i?iaaaeaia aiae?oe/ia aeine?aeaeaiiy iiaeae?, ui a?aeiia?aea? ia??iaee/iei i?yioaaiiyi. ?ica’ycie caaea/?, ui aeieeea i?e iiaoaeia? eieaeueii? iiaeae?, ciaeaeaii iaoiaeii ina?aaeiaiiy. Ii?iaeaeoth/ith ? e?i?eia iaeii??aeia e?aeiaa caaea/a, iniaeea?noue ??oaiiy yei? iieyaa? a oiio, ui aiii i?noeoue iaaecia/ai? ooieoe?? iia?eueiiai /ano. Oe? ooieoe?? aecia/athoueny ia ianooiiiio e?ioe? aneiioioe/ii? i?ioeaaeo?e. Caaea/a a ia?oiio iaaeeaeaii? i?noeoue ?aciiaini? /eaie, ui i?ecaiaeeoue aei iiyae naeoey?ieo /eai?a o ?ica’yceo. I?ioa ine?eueee iiaee ia?aiao? SYMBOL 116 \f "Symbol" \s 12 t iaiaaeaiee (-1 SYMBOL 163 \f "Symbol" \s 12 F SYMBOL 116 \f "Symbol" \s 12 t SYMBOL 163 \f "Symbol" \s 12 F 1) ? ? ia??iaee/iith ooieoe??th aeo?aeiiai /ano t, oe? naeoey?i? /eaie caa??aa?ii. Aieth , ui caeeoeeany , i?e aeai?? ooieoe?e iia?eueiiai /ano A0, D0 aeei?enoiaothoue ia aeey aeeeth/aiiy ?aciiainieo /eai?a, a aeey caaeia?eueiaiiy e?aeiaei oiiaai. A ?acoeueoao? io?eiaia nenoaia aeeoa?aioe?eieo ??aiyiue aeey aecia/aiiy ooieoe?e iia?eueiiai /ano. Iieacaii, ui oey ina?aaeiaia nenoaia ia? oi/iee ?ica’ycie. Ni?iuaiiy a ii??aiyii? c aeo?aeiith iiaeaeeth iieyaa? a oiio, ui iiaa nenoaia oi/a ? iae?i?eia, aea ia i?noeoue neiaoey?ieo /eai?a ? iieno? o?eueee iia?eueio neeaaeiao. Iio?i aeey iiaeae?, ui iieno? ia??iaee/i? ?ica’ycee, ?icaeyiooi ?aaeei neio?ii?caoe?? (caoiieaiiy /anoioe). Aecia/aii ia?aiao?e neio?ii?caoe?? oa ?? iaaeo. Ine?eueee a ?aaeei? caoiieaiiy /anoioe ci?ii? A0, D0 iiaeii? caeeoaoeny iino?eieie, ??aiyiiy ?aciiainii? e?eai? ia? aeaeyae . (12) Ni?aa?aeiioaiiy (12) ca'yco? ?iceaae SYMBOL 120 \f "Symbol" \s 12 x , aiie?ooaeo ciai?oiueiai aieeao p oa aiie?ooaeo eieeaaiue ia /anoio? ciai?oiueiai aieeao. Iieacaii, ui i?e aeayeiio aeai?? ?iceaaeo /anoio SYMBOL 120 \f "Symbol" \s 12 x oa aaee/eie ?iioeueniiai iaaaioaaeaiiy ? ?niothoue ia??iaee/i?, eaac?ia??iaee/i? oa ia?aaoey?i? oaioe/i? i?yioaaiiy nenoaie. Ni?aa?aeiioaiiy (12) caaea? caeaaei?noue aiie?ooaee SYMBOL 114 \f "Symbol" \s 12 r eieeaaiue a?ae aiie?ooaee ? ciai?oiueiai aieeao oa «?iceaaeo» SYMBOL 120 \f "Symbol" \s 12 x . a b n ?en. 1. ?acoeueoaoe ia/eneaiue aeey cia/aiue ia?aiao- ??a p=0.8 ? SYMBOL 120 \f "Symbol" \s 12 x =1.5. a) i?iaeoe?y oaciaiai i?inoi?o nenoaie ia ieiueio (x,y); b) a?aeia?aaeaiiy Ioaiea- ?a; c) a?ao?ee x(t) aeey aiae?oe/iiai (oiiea e?i?y) oa /enaeueiiai (oianoa e?i?y) ?ica’yce?a. Ia??iaee/i? ?ica’ycee a?aeiia?aeathoue iiceoeaiei ei?aiyi eoa?/iiai ??aiyiiy (12) a?aeiinii SYMBOL 114 \f "Symbol" \s 12 r . I?e cia/aiiyo ia?aiao??a p ? SYMBOL 120 \f "Symbol" \s 12 x c iaeano? ?nioaaiiy iaeiiai ae?eniiai iiceoeaiiai ei?aiy ( SYMBOL 120 \f "Symbol" \s 12 x =0.2; p=0.8) onoaiiaeth?oueny a?aie/iee oeeee (ia??iaee/iee ?ica’ycie). I?e oeueiio /enaeueiee oa aiae?oe/iee ?ica’ycie ca?aathoueny iaeei c iaeiei, a?aeia?aaeaiiy Ioaiea?a ca?aa?oueny aei oi/ee. sseui ia?aiao?e p ? SYMBOL 120 \f "Symbol" \s 12 x iaeaaeaoue iaeano?, aea ia ?nio? ae?eniiai iiceoeaiiai ei?aiy ??aiyiiy (12), iai?eeeaae, p=0.8 ? SYMBOL 120 \f "Symbol" \s 12 x =1.5, oi a?aie/iee oeeee ia anoaiiaeth?oueny, i?ae aiae?oe/ieie oa /enaeueieie ?ica’yceaie nenoaie ? iii?oi? ?ica?aeiino? i?e aaeeeeo cia/aiiyo t (?en. 1.c), a a?aeia?aaeaiiy Ioaiea?a (?en. 1.b) ia ia? oa?aeoa?ii? a?aie/ii? oi/ee. AENIIAEE Cai?iiiiiaaii iaoiaeeeo iiaeaethaaiiy iae?i?eieo nenoai c eieae?ciaaieie iniaeeainoyie /aniai? oi?ie. Aeine?aeaeaii eean nenoai - iae?i?eieo inoeeeyoi??a c iaei??th oa aeaiia nooiaiyie aie? i?e ?iioeueniiio aieea?. Iieacaii, ui a ?aieao ieeeiiiae?aiiai ia?aoai?aiiy iiaeia ei?aeoii iienaoe ae?th ieoo?aeo iaaaioaaeaiue ia nenoaio ? i?iaanoe aeaoaeueiee aiae?c iiaeeeaeo eieeaaeueieo i?ioean?a. ?ic?iaeaii iaoaiaoe/i? iiaeae? iae?i?eieo nenoai oeio Aeoo?iaa, aaoieieeaaeueii? nenoaie oa nenoaie c aeaiia nooiaiyie aie?, ye? ciaoiaeyoueny i?ae ae??th ?iioeuenieo aieea?a. I?iaaaeaii aiae?c iniaeeainoae iiaeaethaaiiy neeaaeieo nenoai c ?iioeuenieie aieeaaie. A?aecia/aii ia?aaaae oa iaaeie?ee eiaeiiai c cania?a iiaeaethaaiiy ieoo?aeo aieea?a. I?iaaaeaii aaeaioaoe?th iaoiae?a ina?aaeiaiiy oa Ioaiea?a aeey ?ica’yce?a caaea/, ui aeieeee i?e iiaoaeia? aeuaaeacaieo iiaeaeae. Aeey aea/aiiy aeeiai?ee iiaeaeae oa aeyaeaiiy oa?aeoa?ieo iciae ?ooo ia aaeeeeo ?ioa?aaeao /ano canoiniaaii iaoiae oi/eiaeo a?aeia?aaeaiue. Aeae?eaii o?e oeie eieaeueieo iiaeaeae (ia??iaee/i?, eaac?ia??iaee/i? oa oaioe/i?). Iiaoaeiaaii iiaeae? neeueii iae?i?eieo nenoai, i?iaaaeaia eeaneo?eaoe?y a?oo?eaoe?eieo ae?aa?ai. Aeey aeine?aeaeaiiy ia?aaoey?ieo i?ioean?a o nenoai? oeio Aai-aea?-Iiey canoiniaaii iaoiae oi/eiaeo a?aeia?aaeaiue Ioaiea?a, aea/aia i?iaeoe?y ia oaciao ieiueio. Aeey ia??iaee/ieo ?ica’yce?a nenoai oeio Aeoo?iaa, Aai-aea?-Iiey oa nenoaie c aeaiia nooiaiyie aie? aiae?oe/iei caniaii iiaoaeiaai? eieaeuei? iiaeae?, ciaeaeai? caeaaeiino? i?ae ia?aiao?aie iiaeae?, ui caaacia/o? ?nioaaiiy no?eeeo ia??iaee/ieo ?aaeei?a. ?aae?caoe?y iiaeae?, ui ia i?noeoue neiaoey?ieo /eai?a, caniiaaia ia iaaeaaeeiio ia?aoai?aii? /ano. Anoaiiaeaii a?aie/i? cia/aiiy aeieeiaiiy neeaaeieo ?ica’yce?a. Iieacaii, ui i?e aeayeeo cia/aiiyo ia?aiao??a nenoaie iaeano? iano?eeino? ciaioothoueny. Anoaiiaeaii caeaaei?noue oa?aeoa?o ?ooo nenoaie Aeoo?iaa a?ae oeio ?iioeueniiai aieeao. Iieacaia iiaeeea?noue iiaeaethaaiiy iaaea?aeenoaioieo oa aea?aeenoaioieo ?iioeuenieo i?ioean?a. Aea/aii aieea ia?aiao?a aneiao??? ia no?ee?noue nenoaie. I?iaiae?ciaaii aieea aaee/eie iae?i?eiino? oa aaee/eie ?iioeueniiai aieeao ia iiaiaeaeaiiy aeine?aeaeoaaieo nenoai. Iniiai? iieiaeaiiy aeena?oaoei? iioae?eiaai? o oaeeo i?aoeyo: Ieeei/oe A.I., Aieeiaa N.A. Enneaaeiaaiea ia?eiaee/aneeo no?oeoo? n eiioeueniui eciaiaieai ia?aiao?ia // Ainiee Aeiii?iiao?ianueeiai oiiaa?neoaoo. - 1998. - Aei. 4. - N. 107 - 117. Pilipchuk V., Volkova S., Starushenko G. Study of a Non-Linear Oscillator under Parametric impulsive Excitation using a Non-Smooth Temporal transformation // Journal of Sound and Vibration. - 1999. - Vol. 222, No. 2. - P. 307 - 328. Ieeei/oe A.I., Aieeiaa N.A. Iaaeaaeeia i?aia?aciaaiea aeeiaie/aneie nenoaiu n aeaoiy noaiaiyie naiaiaeu iiae aeaenoaeai ia?aiao?e/aneie eiioeueniie iaa?ocee // I?iaeaie ia/enethaaeueii? iaoai?ee ? i?oeiino? eiino?oeoe?e. - 1998. - O. 4. - N. 111 - 121. Ieeei/oe A.I., Aieeiaa N.A. Aiaeec aaoieieaaaoaeueiie nenoaiu n ia?eiaee/aneie eiioeueniie iaa?oceie iin?aaenoaii iaaeaaeeiai i?aia?aciaaiey a?aoiaioa // Polish-Ukrainian seminar «Theoretical foundations of civil engineering». Vol. 6. - Aa?oaaa. - 1998. - P. 529 - 532. Pilipchuk V., Volkova S. An analytical technique for modeling of processes generated by a pulse forcing // XXXVII Sympozjon «Modelowanie w mechanice». - Vol. 7. - Aenea. - 1998. - P. 289-293. In?aaeiaiea nenoaiu Aai-aea?-Iiey n ia?eiaee/aneei eiioeueniui aicaoaeaeaieai i?e iiiiue iaaeaaeeiai i?aia?aciaaiey a?aoiaioa / Ieeei/oe A.I., Aieeiaa N. A. - Eeaa, 1995. - 15 n. - ?on. - Aeai. a AIOA Oe?aeiu 01.12.95, ? 2537. - OE 96. Ieeei/oe A.I., Aieeiaa N.A. Aeeyiea aiaoiae ia?eiaee/aneie eiioeueniie neeu ia naiiaicaoaeeiue inoeeeeyoi? // Oac. IV iaaeaeoia?iaeiie eiioa?aioeee «No?ieoaeueiua iaoa?eaeu e no?ieoaeueiua eiino?oeoeee». - Oii 1. -Aeiai?iiao?iane. - 1995. - n. 51. Ieeei/oe A.I., Aieeiaa N.A. Enneaaeiaaiea iaeeiaeiuo inoeeeeyoi?ia // Oac. IV iaaeaeoia?iaeiie eiioa?aioeee «No?ieoaeueiua iaoa?eaeu e no?ieoaeueiua eiino?oeoeee». - Aeiai?iiao?iane. - 1995. - n. 95. Aieeiaa N.A. Iiaeaethaaiiy iae?i?eieo nenoai c ?iioeuenieie aieeaaie. - ?oeiien. Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa o?ceei - iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.05.02 - iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee. - Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao, Aei?i?iiao?ianuee, 1999 ?. Aeena?oaoe?eia ?iaioa i?enay/aia iiaeaethaaiith oa aiae?co aeeiai?ee iaoai?/ieo oa o?ce/ieo nenoai c ia??iaee/ieie ?iioeuenieie aieeaaie. Aeine?aeaeaiiy a?oioo?oueny ia iaaeaaeeiio ia?aoai?ai? /ano. Ia?aoai?aiiy aeicaiey? aeeeth/eoe neiaoey?i? /eaie c ??aiyiiy ?ooo. Iaoiae aeaiiino?o?oueny ia oaeeo i?aeoe/ii aaaeeeaeo nenoaiao ye nenoaia eieeaaiue ieanoeiee, nenoaia n aeaiia noaiaiyie aie? oa ?i. Iaoiae iiaea aooe aeei?enoaiei aeey aea/aiiy iiaaae?iee iiaeae? aaoieieeaaeueii? nenoaie Aai-aea?-Iiey i?ae ae??th ia??iaee/ii? na??? ?iioeuen?a Ae??aea. A ?acoeueoao? aeine?aeaeaiiy aeeiai?oe? nenoai a aeoaea iae?i?eiiio aeiaaeeo anoaiiaeaii ia??iaee/i?, ?aaoey?i? eaac?ia??iaee/i? oa ia?aaoey?i? noioanoe/i? ?aaeeie. Eeth/aa? neiaa: iiaeaethaaiiy ?iioeuenieo aieea?a, iaaeaaeea ia?aoai?aiiy a?aoiaioo, eieaeuei? iiaeae?. Aieeiaa N.A. Iiaeaee?iaaiea iaeeiaeiuo nenoai n eiioeueniuie aicaoaeaeaieyie. - ?oeiienue. Aeenna?oaoeey ia nieneaiea iao/iie noaiaie eaiaeeaeaoa oeceei - iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.05.02 - iaoaiaoe/aneia iiaeaee?iaaiea e au/eneeoaeueiua iaoiaeu. - Aeiai?iiao?ianeee ainoaea?noaaiiue oieaa?neoao, Aeiai?iiao?iane, 1999 a. A aeenna?oaoeeiiiie ?aaioa ?anniao?eaaaony caaea/a iiaeaee?iaaiey aeeiaieee iaeeiaeiuo iaoaie/aneeo nenoai n ia?eiaee/aneeie eiioeueniuie aicaoaeaeaieyie. Niioaaonoaothuea aeeiaie/anee ?aaeeiu aaaeiu n oi/ee c?aiey eiaeaia?iie i?aeoeee, a oaeaea /anoi ieacuaathony i?aaeiaoii oai?aoe/aneiai ?anniio?aiey a iaoaieea, ?aaeeiyeaeo?iieea, aeeiaieea iae?iiiuo naoae e ae?oaeo iaeanoyo. A aeenna?oaoeeiiiie ?aaioa ?aoaaony i?iaeaia aaeaeaaoiiai auai?a niiniaa iiaeaee?iaaiey eiioeueniuo aicaeaenoaee ia nenoaio a iaeeiaeiii neo/aa. I?e yoii iaeiia?aiaiiue o/ao iaeeiaeiinoe e iaiauaiiuo ooieoeee, iiaeaee?othueo iaiiaaiiua aicaeaenoaey, a ?aieao aaeeiie nenoaiu ia?aaeei i?ioeai?a/ao o?aaeeoeeiiiie o?aeoiaea iaiauaiiuo ooieoeee eae eeiaeiuo iai?a?uaiuo ooieoeeiiaeia e o?aaoao eiaeeaeaeoaeueiiai iaoaiaoe/aneiai iainiiaaiey eaaeaeie oaeie iiaeaee. E?iia oiai, i?enoonoaea neiaoey?iuo ooieoeee cia/eoaeueii ia?aie/eaaao auai? n?aaenoa aiaeeca iieo/aiiuo aeeooa?aioeeaeueiuo o?aaiaiee aeaeaeaiey. A ?aaioa eiioeueniua aicaoaeaeaiey ia nenoaio iiaeaee?othony n iiiiuueth aoi?ie iaiauaiiie i?iecaiaeiie ieeiia?aciie ooieoeee. Aeey ?aoaiey iinoaaeaiiie caaea/e i?eiaiai iaoiae iaaeaaeeiai i?aia?aciaaiey a?aoiaioa, noi?ioee?iaaiiue Ieeei/oeii A.I.. I?e yoii, i?ino?ainoaaiiay eii?aeeiaoa i?eia?aoaao no?oeoo?o aeaaa?u aac aeaeaiey. I?aaenoaaeaiea aeey ia?eiaee/aneiai ?aoaiey niaea?aeeo ieeiia?aciue neion e i?yiioaieueiue eineion. Oaeie iiaeoiae iicaieyao iino?ieoue iaoaiaoe/aneoth iiaeaeue, ia niaea?aeauoth neiaoey?iinoae. Neiaoey?iua /eaiu eneeth/athony ca n/ao e?aaauo oneiaee. Iieacaia aiciiaeiinoue iiaeaee?iaaiey i?ioeannia aeaoo oeiia: iayeaeaeenoaioiuo e yeaeaeenoaioiuo. Iniiaiua yoaiu iiaeaee?iaaiey eeethno?e?othony ia o?ao oeiiauo nenoaia: iaeeiaeiay iiaeaeue eieaaaiee aeaoi?ie?iaaiiiai oaea; iaeeiaeiay iiaeaeue nenoaiu n aeaoiy noaiaiyie naiaiaeu; iaeeiaeiay iiaeaeue oeia aaoieieaaaoaeueiie nenoaiu. Ia i?eia?a iiaeaee oeia Aeoooeiaa iieacaia aiciiaeiinoue ei??aeoiiai iienaiey yeaeaeenoaioiuo e iayeaeaeenoaioiuo eiioeueniuo aicaeaenoaee e enneaaeiaaiu oeiu aiciiaeiuo eieaaaiee a caaeneiinoe io oa?aeoa?a eiioeueniiai aicaeaenoaey e «aaee/eiu» eiioeuena. Aoi?ay iiaeaeue iienuaaao acaeiiaeaenoaea aeeaeeinoe n aeaeaeouaeny iaiei/eie. Iaiei/ea /anoe/ii caiieiaia aeeaeeinoueth. I?iaaaeai aiaeec aeeiaie/aneie eeiaeiie onoie/eainoe nenoaiu. Iieo/aiu i?aeoe/aneea ?aeiiaiaeaoeee ioiineoaeueii onoie/eainoe enneaaeoaiie nenoaiu. Enneaaeiaaiea aaoieieaaaoaeueiie nenoaiu iieacaei, /oi a ?aieao iaaeaaeeiai i?aia?aciaaiey a?aoiaioa aiciiaeii aiaeeoe/aneia eco/aiea ia oieueei ia?eiaee/aneeo eieaaaoaeueiuo ?aaeeiia, ii e aieaa neiaeiuo (e?aceia?eiaee/aneeo) i?ioeannia. I?iaaaeai /eneaiiue aiaeec nenoaiu. Eco/aiu oneiaey aicieeiiaaiey i?aaeaeueiiai oeeeea. Iieo/aiu oneiaey nouanoaiaaiey onoie/eauo ia?eiaee/aneeo ?aoaiee e iino?iaiu caaeneiinoe iaaeaeo ia?aiao?aie iiaeaee, iaania/eaathuea yoo onoie/eainoue aeaeaeaiee. I?iaaaeaii niiinoaaeaiea ?acoeueoaoia /eneaiiiai e aneiioioe/aneiai enneaaeiaaiey. Aeey aiaeeca neiaeiuo eieaaaoaeueiuo ?aaeeiia i?eiaiyaony /eneaiiue ?an/ao n i?aaeaa?eoaeueiuie aiaeeoe/aneeie i?aia?aciaaieyie iaaeaeo eiioeuenaie. Oaeie iiaeoiae aeaao iaaeyaeiinoue e iicaieyao nie?aoeoue eiee/anoai noaiaea?oiuo iia?aoeee. O/eouaaaony, /oi eii?aeeiaoa a oi/eao aeaenoaey eiioeuenia iinoiyiiay, a nei?inoue eiaao nea/ie. Iino?iaiu aeoo?eaoeeiiiua aeeaa?aiiu, aeaiiino?e?othuea ea/anoaaiii ?acee/iua iiaaaeaiey enneaaeoaiuo nenoai. Eeth/aaua neiaa: iiaeaee?iaaiea eiioeueniuo aicaeaenoaee, iaaeaaeeia i?aia?aciaaiea a?aoiaioa, eieaeueiua iiaeaee. Volkova S.A Modeling of non-linear systems with pulse excitations. - Manuscript. Thesis for a scientific degree of the candidate phisic - mathematical sciences on a specialty 01.05.02 - mathematical modeling and computing methods. - Dnepropetrovsk state university, Dnepropetrovsk, 1999. The thesis deals with dynamics of nonlinear mechanical and physical systems under periodic impulse excitation. A preliminary stage of study is based on the special non-smooth (saw-tooth) transformation of the time parameter. The transformation eliminates discontinuous terms from the differential equations of motion and hence significantly improves its structure for both analytical and numerical analysis of the models. The technique is implemented for different practically important systems such as parametrically excited moved of Duff’ing system, a double-pendulum model of the liquid sloshing phenomenon in moving tanks subjected to the periodic impulsive loading, etc. It has been shown that the technique can be applied to study the self-excited oscillation of the Van-der-Paul's model under external series of the Dirac's impulses. The results show that the dynamics related strongly depends on the systems parameters and can perform periodic, quasi-periodic and quite complicated irregular stochastic-like regimes. Key words: Modeling of impulsive excitations, non-smooth transformation of argument, local models. PAGE 3 ) 2 ( ) 1 0 0 2 0 0 2 02 2 2 2 Y t Y t Y X t XY Y t X Y t a Y X a ¶? ¶? -? ¶? ¶? +? ¶? ¶? +? ¶? ¶? +? ¶? ¶? -? +? ¶? ¶? -? e? x? t? -? ¶? ¶? +? ¶? ¶? +? ¶? ¶? +? ¶? ¶? ¶? -? =? +? ¶? ¶? X Y a Y a XY X X a X t a a Y a Y t? t? t? t? e? t? 2 2 0 2 2 2 2 2 1 1 2 1 2 ( z? z? t? z? t? z? z? z? z? z? t? "? +? =? i? i? i? F? F? +? -? F? F? -? =? ), 4 ( ) ( 3 1 ), 2 ( 1 1 , ) ( e Y X t x ) ( ) ( ) ( t? t? +? =?

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