PROQRAMI ON ACTUAL PROBLEM OF MATHEMATICS AND MECHANICS...
Transcript of PROQRAMI ON ACTUAL PROBLEM OF MATHEMATICS AND MECHANICS...
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RYAZYYAT V MEXANKANIN AKTUAL PROBLEMLR
Riyaziyyat v Mexanika nstitutunun 55 illiyin
hsr olunmu Beynlxalq konfransn
PROQRAMI
ON ACTUAL PROBLEM OF MATHEMATICS AND MECHANICS
PROGRAM
of the International conference devoted to the 55th
anniversary of the
Institute of Mathematics and Mechanics
, 55-
15-16 may 2014
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Azrbaycan Milli Elmlr Akademiyas Riyaziyyat v Mexanika nstitutunun Elmi
uras 15-16 may 2014-c il tarixlrind nstitutun 55 illiyin hsr olunmu
Riyaziyyat v mexanikann aktual prolemlri Beynlxalq konfransnn keirilmsi
haqda qrar qbul etmidir (15 yanvar 2014-c il, protokol 1).
BA REDAKTOR:
Akif Hacyev
MSUL REDAKTOR:
Misir Mrdanov
MSUL REDAKTORUN
MAVN:
Soltan liyev
MSUL KATB: Vqar smaylov
REDAKSYA HEYTNN
ZVLR:
Rauf Hseynov, Hmidulla Aslanov,
Vaqif Hacyev, Cfr Aalarov,
Qabil liyev, kbr liyev, Ltif
Talbl, Nizamddin sgndrov,
Vaqif Quliyev, Bilal Bilalov, Tamilla
Hsnova, Qeylani Pnahov, li
Babayev, Fariz mranov
TEXNK REDAKTORLAR:
msiyy Muradova
Aygn Orucova
Arzu Paalova
______________________________________________________________________
National Academy of Sciences of Azerbaijan, Institute of Mathematics and Mechanics, V.Bahabzade st.,
9, Azerbaijan Republic, AZ1141
Tel.: (99412) 539 39 24
Fax.: (99412) 539 01 02
e-mail: [email protected]; web: www.imm.science.az
mailto:[email protected]://www.imm.science.az/
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Riyaziyyat v Mexanika nstitutu 55 ild
Azrbaycanda riyaziyyat v mexanika elmlrinin mbdi hesab olunan
Riyaziyyat v Mexanika nstitutu 1959-cu ild Azrbaycan SSR Nazirlr Sovetinin 27
aprel 319 nmrli v Azrbaycan SSR EA-nn Ryast Heytinin 06 may tarixli
qrarlar il Azrbaycan Elmlr Akademiyasnn Fizika v Riyaziyyat nstitutunun
bazasnda yaradlmdr. Fizika v Riyaziyyat nstitutu mstqil qurumlara ayrld
zaman Riyaziyyat v Mexanika nstitutunda 121 mkda -101 elmi ii, bir akademik
(Zahid Xlilov), bir mxbir zv (brahim brahimov), drd elmlr doktoru (Zahid
Xlilov, brahim brahimov, Yusif mnzad, Yaroslav Lapatinskiy) v on iki elmlr
namizdi (amil Vkilov, li Cfrov, Him Aayev, Krim Krimov, Sid
lsgrov,Mais Cavadov, Sasun Yakubov, Mbud smaylov, Boris Ponayoti, Rid
Mmmdov, Framz Maqsudov, Yhya Mmmdov) alrd. Yarand vaxt
nstitutda 6 b: funksional analiz (Zahid Xlilov), funksiyalar nzriyysi (brahim
brahimov), diferensial tnliklr (Him Aayev), inteqral tnliklr (amil Vkilov),
tqribi analiz (li Cfrov), elastikiyyt nzriyysi (Yusif mnzad) v 2
laboratoriya: dinamik mhkmlik (Krim Krimov), hesablamamrkzi (Sid
lsgrov) faliyyt gstrirdi.
55 illik faliyyti rzind Akademiyann Riyaziyyat v Mexanika nstitutu rfli
bir yol kemi, lkmizd riyaziyyat v mexanikann inkiafnda uurlu nticlrin
qazanlmasnda byk naliyytlr ld etmidir. nstitutun elmi kadrlarla tminatnda
v glck inkiafnda Bak Dvlt Universitetinin Mexanika-riyaziyyat, Pedaqoji
Universitetin Riyaziyyat, BDU-nun daha sonra yaradlm Ttbiqi riyaziyyat
fakltlrinin byk rolu olmudur.
Qeyd etmk lazmdr ki, lkmizd riyaziyyat v mexanika elminin inkiafnda,
mhur Sovet alimlri akademiklr Mstislav Keld, Andrey Kolmoqorov, Nikolay
Boqolyubov, Mixail Lavrentyev, Nikolay Musxelivili, van Petrovski, Sergey
Sobolev, Lev Pontryagin, zrail Gelfand, Aleksandr Gelfond, Sergey Bernteyn, Sergey
Nikolskiy, Andrey Tixonov, Lazer Lsternik, Yaroslav Lopatinskiy, Anatoliy Maltsev,
Georgiy ilov, Yuriy Mitropolskiy, Yuriy Proxorov, Valentin Maslov, Xlil
Raxmatulin, Aleksey lyuin,Yuri Robotnov, Pyotr Oqibalov, David erman, Quri
Savin, Viktor Moskvitin byk rol oynamlar.
He bhsiz, Azrbaycanda riyaziyyat v mexanika sahsinin inkiafnda
akademiklr Zahid Xlilov, brahim brahimov, rf Hseynov v akademiyann
mxbir zvlri Maqsud Cavadov, Yusif mnzadnin byk rolu olmudur.
nstitutun ilk direktoru akademik Zahid Xlilov olmudur. O, akademiyann
Fizika-Riyaziyyat v Texnika Elmlri Blmsin akademik-katib seildikdn sonra,
institututa 1959-1963-c illrd akademik brahim brahimov,1963-1967-ci illrd
professor Ham Aayev, 1967-ci ildn mrnn sonuna-1973-c il qdr akademik
Zahid Xlilov, 1974-dn 2000-ci il qdr akademik Framz Maqsudov, 2000-2003-
c illrd akademiyann mxbir zv lham Mmmdov, 2004-c ildn 2013-c il
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qdr akademik Akif Hacyev rhbtlik etmidir. 2013-c ilin mayndan nstitutun
direktoru professor Misir Mrdanovdur.
Respublikamzda riyaziyyatn n inkiaf etmi sahlrindn biri olan, funksional
analiz mktbinin sas akademik Zahid Xlilov trfindn qoyulmudur. O, kemi
Sovetlr birliyind funksional analiz zr ilk Funksional analizin saslar (1949)
kitabnn mllifi olmu, normallam halqalarda v Banax fzalarnda xtti sinqulyar
inteqral tnliklrin abstrakt nzriyysini yaratm, tamam ksilmz operator daxil
olmayan xtti tnliklr nzriyysini inkiaf etdirmi, mcrrd Nter nzriyysini
qurmu v requlyarizatorlarn mumi nzriyysini vermidir. Zahid Xlilov Banax
fzalarnda diferensial tnliklri v kvazixtti diferensial tnliklrin dayanql
mslsini tdqiq edn ilk riyaziyyatlardan biri olmudur. O, hl XX srin 30-cu
illrinin sonlarndan balayaraq riyazi elastiklik nzriyysi sahsind ilmi v qaln
elastiki lvhnin grginlik vziyyti, uzununa dvr qvvlrin tsiri altnda elliptik
lvhnin dayanql, sxlan lvhlrin rqsi v knarlar ixtiyari hamar yri olan btv
lvhnin intensivliyi, koordinatlarn ixtiyari ksilmz funksiyas olan normal qvvnin
tsiri altnda yilmnin mumi mslsini hll etmidi.
Azrbaycan funksiyalar nzriyysi mktbinin banisi v rhbri akademik
brahim brahimovun n yax yaxnlama, interpolyasiya nzriyysi, tam funksiyalar
nzriyysi, funksiyalar sistemlrinin taml, brabrsizliklr v s. kimi sahlrd ld
etdiyi mhm nticlrl bal bir ox problemlr sonradan onun tlblri trfindn
tdqiq edilmi, mumildirilmi v geni istifad olunmudur. Onun funksiyalar
nzriyysi v harmonik analiz sahsind ald nticlr dflrl SSR EA-nn
hesabatlarna daxil olaraq, mhm nticlr kimi qeyd edilmidir. Dnyann tannm
alimlrinin elmi mqallrind istifad olunan bu nticlrin xaricd ap olunmu
monoqrafiyalara daxil edildiyini d qeyd etmk yerin drdi. Onun srlrind hqiqi
v kompleks dyinli funksiyalarn n yax yaxnlamas mslsin, triqonometrik,
cbri polinomlar, tam funksiyalar v onlarn trmlrinin mxtlif normalar arasnda
brabrsizliklrin tdqiqin geni yer verilmidir. Akademik brahim brahimov
funksiyalarn xtti msbt operatorlar ardcll il yaxnlamas msllrin aid
mhm nticlr ld etmi, yaxnlaan operatorlar ardcllnn qurulmasna aid
mumi metod vermi, bir v oxdyinli funksiyalarn kili fzalarnda Korovkin
tipli teoremlr isbat tmi, msbt nvli inteqral operatorlar ardcll il yaxnlama,
yaxnlama trtibi, onun asimptotik qiymti v bunlarla laqli bir ox msllri hll
etmidir.
Akademik rf Hseynov qeyri xtti sinqulyar inteqral tnliklr nzriyysinin
yaradclarndan biridir. O, hmin nzriyynin inkiaf mqsdi il yeni funksional
fza daxil etmidir ki, hal-hazrda hmin fza onun ad il baldr. Azrbaycan Dvlt
Universitetind (Bak Dvlt Universiteti) akademik rf Hseynovun yaratd v
uzun illr rhbrlik etdiyi sinqulyar inteqral tnliklr mktbi lk riyaziyyatnn
tarixind nmli yer tutmudur. Sonralar bu mktbin davamlar trfindn birll
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sinqulyar inteqrallarn Holder tipli fzalarda v onlarn mumilmlrind yrnilmsi
ld ediln mhm nticlrdndir.
Akademiyann mxbir zv Maqsud Cavadov cbrlr zrind hndsi fzalar
tdqiq etmi, elmi tdqiqatlarn cbrlr zrind afin v proyektiv fzalara hsr etmi,
qeyri-Evklid fzalar nzriyysini yaratmdr. O, 30-dan ox elmi mqalnin,
azrbaycan dilind 7 drsliyin mllifi olmu, lkmizd riyazi terminologiyann
yaradlmasnda yaxndan itirak etmidir.
Akademiyann mxbir zv Yusif mnzad hiss-hiss bircins elastiki
cisimlrin grginlik-deformasiya vziyyti v elastiklik nzriyysinin kontakt
msllrinin analitik v ddi hlli sullarn ilyib hazrlam, Nikolay Musxelivili
v David erman trfindn baxlan msllrin hlli prosesind alnan sonsuz cbri
tnliklr sisteminin kvazirequlyar olmasn isbat etmi, yalnz bir kompleks burulma
funksiyas sasnda mrkkb iibo milin yilm mrkzinin koordinatlar dsturunu
xarm, mhdud elastiki mhitd at mslsinin analitik hllini alm v layl
mxtlifcinsli elastiki cisimlr n mslnin hlli sulunu vermidir.
lkmizd riyaziyyat v mexanikann sonrak inkiaf Azrbaycan Elmlr
Akademiyasnn hqiqi zvlri: Mcid Rsulov, Azad Mirzcanzad, Framz
Maqsudov, Clal Allahverdiyev, Mirabbas Qasmov, Akif Hacyev, akademiyann
mxbir zvlri: Qoqar hmdov, Arif Babayev, Mais Cavadov, Yhya Mmmdov,
fizika-riyaziyyat elmlri doktorlar: mir Hbibzad, Rid Mmmdov, Him
Aayev, li Novruzov v Sasun Yakubovun ad il baldr. Burada Azrbaycann ilk
riyaziyyatlar olan Mmmd by fndiyev, Rid Yusifzad, Mikayl Xdr-zad,
Bylr Aayevi xatrlamaq yerin drdi.
55 il rzind institut il-bil inkiaf etmi, nsillr bir-birini vz etmi, lkmiz
riyaziyyat v mexanika sahsind dnyann aparc elmi mrkzlrind daha yax
tannm, bu sahlrd blgnin aparc elmi tdqiqat mssisllrindn birin
evrilmidir.
Bu uurlarn qazanlmasnda Azrbaycann nc nsil alimlri olan: Bala
skndrov, Rauf Hseynov, Yusif Mmmdov, Mhmmd Mehdiyev, Asf Hacyev,
Htm Quliyev, amil Vkilov, Mlik-Bax Babayev, Hseyn ndirov, Tofiq
Bektai, Arif smaylov, Qmbr Namazov, Nazim Abbasov, li Cfrov, Karlen
Xudaverdiyev, Nadir Sleymanov, lddin Mahmudov, Krim Krimov, Cfr
Aalarov, Mmmd Bayramolu, Frunze miyev, Kazm Hsnov, Allahvern
Cbraylov, Yuriy Domlaq, Mlikmmmd Cbraylov, Mmmd Yaqubov, Niyaz
Mmmdov, Camali Mmmdxanov, Asf skndrov, Valeriy Salayev, Tamilla
Nsirova, lddin amilov, Binli Musayev, Sadiq Abdullayev, Nazim Musayev,
Qardaxan Orucov, Yaar Slimov, Rafiq mnzad, msddin Mtllimov, Siyavir
Bxtiyarov, Yusif Salmanov, Rafiq Feyzullayev, Rafiq liyev, Rxnd Cabbarzad,
Nihan liyev, Tofiq Krimov, li hmdov, Arif Cfrov, li Mhrrmov, Qabil
liyev, Vaqif Hacyev, sak Mmmdov, Misir Mrdanov, Seyidli Axyev, Vaqif
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brahimov, hmd Vliyev, Sadq Vliyev, Ramiz Aslanov, Qaraxan Mirzyev, Musa
lyasov, Ruslan Sadrxanov, Kamal Sultanov, Kamil Aydazad, Mhmmd Axundov,
Hseyn Hseynov, Turab hmdov, dalt Axundov, Vli ahmurov, Akif
brahimov, Oqtay Vliyev, Varqa Klntrov, Telman Mlikov, Kamil Mnsimov, Arif
Slimov, Hamlet Quliyev, Tofiq Slimov, Konstantin Leonov, kbr liyev,
Hmdulla Aslanov, Sabir Mirzyev, Hidayt Hseynov, Hmzaa Orucov, Rizvan
Paayev, Misrddin Sadqov, Vaqif Pirmmmdov, Frhad Hseynov, Abbas zimov,
Ltif Talbl, Barat Nuriyev, lham Mrdanov, lham Pirmmmdov, Fuad Ltifov,
Nazil Rsulova, Mhmmd Quliyev, lmdar Hsnov, Qabil Yaqubov, Arif
mirov, Valeh Quliyevin xidmtlri xsusi qeyd olunmaldr.
Tbii ki, bel naliyytlrin ld olunmasnda tannm Sovet alimlri Aleksandr
Samarski, Lev Kudryavsev, Mark Krasnoselski, Andrey Bitsadze, Vladimir Tixomirov,
Adm Naxuov, Stanislav Poxajayev, Anatoli Kostyuenko, Mixayl Fedoryuk, Olqa
Oleynik, Olqa Ladjenskaya, Vladimir lyin, Marat Yevqrafov, Eyvgeniy Landis,
Muxtarbay Otelbayev, Oleq Besov, Vladimir Mazya, Revaz Qamkrilidze, Yuliy
Dubinskiy, Yevgeniy Mienko, Vladimir Boltyanskiy, Miroslav Qarbauk, Boris
Levitan, Pyotr Lizorkin, Vladimir Marenko, Anatoliy Perov, Sergey Novikov, Leonid
Nijnik, Yuriy Berezanskiy, Promaz Tamrazov, Vladimir Kondratyev, Selim Kreyn,
Mark Kreyn, Mixayl Mixaylov, Fyodor Rofe-Boketov, Anatoliy Skoroxod, Vitaut
Tamuj, Aleksey Svenikov, Boris Qnedenko, Fyodr Vasilyev, Faina Kirilova, Rafael
Qabasov, zizaa axverdiyev, Sabir Hseynzad v b. il birg almalar, qarlql
laqlr byk rol oynamdr.
Sevindirici haldr ki, mstqillik ld etdikdn sonra yaranm siyasi v iqtisadi
tinliklr baxmayaraq, lkmizd riyaziyyat v mexanika sahlri inkiaf etmi,
alimlrimiz lk daxilind v dnyann bir ox lklrind mvffqiyytl elmi
tdqiqat ilri apararaq, Azrbaycann adn daha yksk sviyyd tmsil edn yeni
riyaziyyat v mexaniklr nsli yetimidir: Fikrt liyev, lham Mmmdov, Soltan
liyev, Nazim Krimov, Qalina Mehdiyeva, Bilal Bilalov, Bilndr Allahverdiyev,
Vli Qurbanov, Vaqif Quliyev, Tahir Hacyev, brahim Nbiyev, Aqil Xanmmmdov,
Uur Abdullayev, Qeylani Pnahov, Nizamddin sgndrov, Rhim Rzayev, Asf
Zamanov, , Araz liyev, Rauf mirov, Mbariz Tapdq olu Qarayev, Mbariz Zfr
olu Qarayev, Fxrddin Abdullayev, Heybtqulu Mustafayev, Daniyal srafilov,
lham A. liyev, lham V. liyev, Anar Dosiyev, Nigar Aslanova, Bhram liyev,
Frman Mmmdov, Rvn Hmbtliyev, Elar Orucov, Rstm Seyfullayev,
Vladimir Vasilyev, Natiq hmdov.
55 illik faliyyti dvrnd AMEA-nn Riyaziyyat v Mexanika nstitutu
lkmizd riyaziyyat v mexanika elm sahlrinin mrkzin evrilmidir. Bu illr
rzind riyaziyyat v mexanika sahsind institutda aparlan elmi-tdqiqat ilri
aadak sadalanan istiqamtlr zr uyun blrin mkdalar trfindn hyata
keirilmidir:
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Riyaziyyat sahsind
1. Operatorlarn spektral nzriyysi v operator cbrlri; a) Funksional analiz; b) Qeyri harmonik analiz.
2. Funksional fzalar v funksiyalar nzriyysi; a) Riyazi analiz; b) Funksiyalar nzriyysi.
3. Diferensial tnliklr v riyazi fizikann problemlri; a) Diferensial tnliklr; b) Riyazi fizika tnliklri.
4. Harmonik analiz v approksimasiya nzriyysinin problemlri; a) Riyazi analiz; b) Funksiyalar nzriyysi; c) Qeyri harmonik analiz.
5. Cbr, riyazi mntiq v riyaziyyat tarixi; Cbr v riyazi mntiq.
6. Ttbiqi riyaziyyat v multidissiplinar problemlr; a) Hesablama riyaziyyat v informatika; b) Ttbiqi riyaziyyat.
Mexanika sahsind
1. Deformasiya olunan brk cismin mexanikas; a) Elastiklik v plastiklik nzriyysi; b) Srncklik nzriyysi; c) Dala dinamikas.
2. Maye v qaz mexanikasnn nzri problemlri;
a) Maye v qaz mexanikas.
nstitut mkdalarnn grgin elmi faliyyti nticsind sas elmi istiqamtlr
zr bir ox mhm nticlr ld edilmidir. Hmin nticlrin bzilrini qeyd etmk
yerin drdi:
Funksional analiz zr spektral analizin sas msllri mxsusi ddlrin v
mxsusi funksiyalarn asimptotikas, mxsusi funksiyalar zr ayrl, spektrin tdqiqi,
mxsusi ddlrin asimptotik paylanmas, requlyarladrlm izin hesablanmas,
bazislik, tamlq, trs msllrin hlli, operatorun z-zn qoma genilnmsi
yrnilmidir. Spektral parametrdn rasional asl olan bir sinif z-zn qoma
olmayan operatorlarn mxsusi v qoulmu elementlr sisteminin oxqat taml
msllri tdqiq edilmidir. Kompleks potensiall birll redinger operatorunun
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spektrinin diskretliyi, mxsusi v qoulmu funksiyalar sisteminin taml gstrilmi,
spektrin diskretliyi n kriteriya tklif edilmidir. Azalan potensiall redinger
operatorunun msbt mxsusi ddlrinin olmamas haqqnda yeni nticlr
alnm,ksilmz spektr malik geni sinif operator-dstlrinin spektral nzriyysi
ilnib hazrlanmdr. Spektral analizin v spilm nzriyysinin trs msllri
istiqamtind mhm nticlr ld edilmidir. ki spektr gr turm-Liuvill sinqulyar
operatorunun brpas n effektiv sul tklif edilmi, ktl sfr olmayan halda Dirak
tnliklr sistemi n spilm verilnlrin gr trs spilm mslsi tamamil hll
olunmudur. Periodik msall geni sinif adi diferensial operatorlarn spektral analizi
qurulmudur. Birll redinger tnliyinin ksilmz spektrinin uclarnda ksetm
msal tdqiq edilmi, trs spilm mslsi haqqnda Faddeyev teoreminin rtlri
zifldilmidir. Yksktrtibli diferensial operatorlar n trs mslnin hllin
nnvi yanama metodu inkiaf etdirilmidir. Qeyri-stasionar birtrtibli hiperbolik
tnliklr sistemi n yarmoxda v btn oxda dz v trs spilm msllri
yrnilmidir. Operator-diferensial tnliklr n srhd mslsinin hll olunmas
n dqiq rtlr taplm, uyun polinomial operator dstlrinin sasl vektorlarnn
taml haqqnda teoremlr isbat edilmi, operator-diferensial tnliklrin ba hisssin
ksiln msallar daxil olduu halda srhd msllrinin yalnz msallarla ifad olunan
hll olunma rtlri tyin edilmidir. Banax fzalarnda defektli sistemlrin bazislik
xasslri n kriteriya verilmi, nticlr srhd rtlrin spektral parametr daxil olan
diferensial operatorlarn spektral xasslrinin yrnilmsin ttbiq edilmi, drdnc
trtib diferensial operatorlar n qeyri-xtti mxsusi qiymt msllrinin hllrinin
lokal v qlobal bifurkasiyalar tam tdqiq olunmudur. Yarmqruplar nzriyysinin
metodlarnn kmyil Hilbert v Banax fzalarnda xtti v kvazi-xtti tnliklr n
Koi mslsinin hll oluna bilmsi yrnilmidir. Hilbert fzalarnda yksk trtibli
xsusi trmli operator-diferensial tnliklrin birqiymtli, normal v Fredholm
mnada hll oluna bilmsi rtlri tyin edilmidir. Periodik msall oxll
redinger operatorunun mxsusi ddlri n kvazi-periodik srhd rtlri daxilind
paralelipipedd asimptotik dsturlar alnm, spektrin asimptotik tsviri verilmi, Blox
funksiyalari tdqiq edilmi, Bote-Zommerfeld hipotezi hll edilmidir. turm-Liuvil
operatorunun zn qoma genilnmlri tsvir eidlmi, operator msall diferensial
tnliklrin mxsusi ddlrinin asimptotikas hesablanmdr.Berezin simvolu v
Dhamel hasillrinin operatorlar nzzriyysi v Banax cbrlrinin bir ox
msllrin ttbiqlri verilmidir. axlnn tsadfi proseslrin mxtlif siniflri
tdqiq eidlmi, bu proseslrin ylmas haqqnda limit teoremlri isbat olunmu v
limit teoremlri il axlnn proseslrd keid hadislri arasnda qarlql laq
yaradlmdr. Tsadfi proseslr n srhd msllri yrnilmi, srhd
funksionallar n limit teoremlri isbat edilmidir .
Funksiyalar nzriyysi zr f , ,
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, l. K i il . - . dir. , . , , , .
, , .
Mxtlif metrik funksional fzalarda hqiqi v kompleks dyinli funksiyalarn
triqonometrik v tam funksiyalarla yaxnlama msllri yrnilmidir.
ndrey haqqnda nin ksiln funksiyalar sinfind doruluu isbat edilmidir. Mxtlif Banax fzalarnda, xsusil d Morri tipli fzalarda v onlarn mumilmlrind daxilolma teoremlri olunmudur. Diferensial tnliklr zr xsusi trmli diferensial tnliklrin hlli n kontur inteqral v xqlar sulu verilmi v inkiaf etdirilmidir. Hmin sullarn
ttbiqi il srhd rtlrin zamana gr yksk trtib trmlr daxil olan v Zaremba
tipli srhd rtli qarq msllr hll edilmidir. Adi diferensial operatorlarn
rasional dstsi n requlyarlq, sanki requlyarlq v normallq anlaylar verilmi,
bel operatorlarn mxsusi v qoma elementlri zr oxqat ayrl dsturlar
taplmdr.
Yksk trtibli elliptik tnliklr n silindrik oblastlarda alanma prinsiplri
isbat edilmi, limit amplitudu prinsipinin saslandrlmasnda rezonans effekti akar
edilmi, mhdud oblastlarda v qeyri-mhdud silindrik oblastlarda Sobolev tnliklri
v Petrovskiy gr korrekt tnliklr sistemi n Koi mslsi v qarq msllr
tdqiq edilmi v zamann byk qiymtlrind hllrin asimptotikas yrnilmidir.
Sinqulyar msall ikitrtibli mumi xtti qarq tip tnliklr n Trikomi srhd
mslsinin hllinin varl v yeganliyi haqda teoremlri isbat edilmidir.
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Kiik parametrdn asl crlaan xsusi trmli mxtlif tnliklr n srhd
msllrinin hllinin kiik parametr nzrn asimptotikas tdqiq edilmidir.
Qeyri-xtti parabolik v hiperbolik tnliklrdn ibart sistem n qarq
mslnin qlobal hllrinin varl, yeganliyi, hllrin qlobal xarakteri tdqiq
edilmidir. Qeyri-xtti tnliklrin hllrinin sonlu zaman rzind dalmasn myyn
edn yeni metod verilmidir v bu metodun ttbiqi il geni sinif qeyri-xtti
tnlikllrin hllrinin sonlu zaman rzind dalmasn tdqiq etmk mmkn
olmudur.
Lokal v qeyri-lokal, qeyri-xtti ikinci trtib v elc d yksk trtib hiperbolik
tnliklr n qarq mslnin v variasiya brabrsizliklrinin qlobal hll olunmas
n kafi rtlr verilmi, yarmxtti halda is uyun mslnin hllinin asimptotik
xarakteri aradrlaraq hllrin asimptotik sanki dvr olmas gstrilmidir. Oblastn
srhddind dissipasiya, daxilind is antidissipasiya olduqda myyn sinif qeyri-xtti
hiperbolik tnliklr n qoyulmu qarq mslnin hllinin asimptotikas
aradrlm, qlobal minimal attraktorun varl isbat olunmudur.
Myyn dyinlr nzrn yksk trtib trmlrin msallar zaman
dyinin nzrn Lipits rtini dmdikd xtti v qeyri-xtti hiperbolik tnliklrin
hllrinin hamarlnn yalnz hmin dyinlr nzrn itirildiyi myyn edilmi v
uyun korrektlik siniflri seilmidir.
Bir sinif xsusi trmli yarmxtti hiperbolik tnliklr sisteminin qeyri-xtti
hisslrinin artm trtibinin qlobal hllin varlna v ya onun itmsin tsir edn
kriteriyalar myyn edilmidir. Myyn hallarda hmin kriteriyalar mhur Fucita
tipli kriteriyalarn tam analoqunu verir.
Banax fzasnda kvazixtti parabolik v hiperbolik tnliklr n Koi
mslsinin lokal v qlobal hll olunmas aradrlm, qeyri-mhdud operator msall
polinomial dstnin mxsusi vektorlarnn oxqat taml isbat edilmi, bu nticlr
elliptik tnliklr n requlyar v qeyri-requlyar srhd msllrinin hllin ttbiq
edilmidir.
Operator msall tnliklr n srhd rtlrind qeyri mhdud operator v
spektral parametr itirak edn srhd msllrinin korrektliyi v fredholmluu
aradrlm, uyun spektral msllr tdqiq edilrk mxsusi ddlrin asimptotikas
myyn edilm, oxqat tamlq v bazislik haqda myyn nticlr ld edilmi, bzi
hallarda requlyarlam iz dsturlar isbat edilmidir.
Dyin operator msall bir trtibli v elcd yksk trtibli mxtlif
evolyusion tnliklr n Koi mslsinin korrektliyi aradrlm, alnm nticlr
zamana gr dyin msall xsusi trmli mxtlif tnliklr n srhd
msllrinin aradrlmasna ttbiq edilmidir.
Qeyri-xtti operator v diferensial operator tnliklrin arasdrlmas n topoloji
v funksional sullar yaradlm, sonlu v sonsuz ll fzalarda kifayt qdr geni
sinif operatorlar n trpnmz nqtnin varl haqqnda teorem isbat edilmidir
-
Qeyri-xtti elliptik v parabolik tnliklrin srhdin xsusi nqtlri trafnda v
qeyri kompakt srhd malik qeyri-mhdud oblastlarda hllrinin zn aparmas
haqda teoremlr isbat edilmidir. Mhdud v qeyri-mhdud oblastlarda ki funksiyas
Makenxoupt rtlrini ,crlaan msallar is, myyn artm rtlrini ddikd,
yksk trtib qeyri-xtti parabolik tnliklr n qoyulmu Dirixle mslsinin
hllrinin keyfiyyt xarakteri tdqiq edilmi v onlar n yeganlik siniflri
taplmdr.
Adi, gecikn arqumentli, neytral tip, bzi paylanm parametrli diferensial
tnliklr v diskret sistemlrl tsvir olunan mhdudiyytli optimal idaretm
msllri aradrlm, birinci v ikinci trtib zruri rtlr, bzi hallarda kafi rtlr,
varlq teoremlri isbat olunmudur. Mxsusi idaredicilrin optimall daha trafl
aradrlm, mxtlif tip yeni zruri rtlr alnmdr.
Riyazi fizika tnliklri zr geni sinif elliptik v parabolik tnliklrin
hllrinin requlyarl, diferensial tnliklrin keyfiyyt nzriyysi, kvazi elliptik
diferensial tnliklrin hllinin asimptotikas v hamarl, kvazi elliptik operatorlarn
normall v mnfi spektri geni tdqiq olunmudur. Bu msllrin tdqiqi yolunda
anizotrop Sobolev fzalarnda Hardi v Puankare tipli brabrsizliklrin mxtlif
modifikasiyalar isbat v ttbiq edilmidir. Yarmxtti hiperbolik v psevdohiperbolik
tnliklr n Koi mslsinin qlobal hll olunmas kriteriyalar alnmdr. kinci
trtib elliptik v parabolik tip tnliklr n mxtlif nv srhd msllrin baxlm,
klassik v mxtlif mnalarda mumilmi hllrin uyun klassik v Sobolev tip
fzalarda hllinin varl v birqiymtli hllolunanl gstrilmi, hllrin oblastn
daxilind v srhdind keyfiyyt xasslri tdqiq edilmidir. Dyin msall ikinci
trtib parabolik tnliklr n tutum v potensial terminlrind birinci srhd
mslsinin srhd nqtsinin requlyarlnn Viner v Petrovskiy tip kriterilri
taplmdr. kinci trtib xtti v kvazi xtti elliptik v parabolik tnliklr n hllrin
Hlder sinfind aprior qiymtlndirilmsi alnm v Fraqmen-Linndelyof tipli
teoremlr isbat edilmidir. Ksiln msall, qeyri-divergent strukturlu elliptik v
parabolik tnliklr n Kordes rtlri daxilind gcl birqiymtli hllolunanlq v
koorsetiv qiymtlndirm gstrilmidir. mumi killi, divergent formal, xtti,
yarmxtti gcl, reaksiya-diffuziya tipli parabolik tnliklr sistemlrind
namlum msallarn v sa trflrin taplmas n qoyulmu trs msllrin
korrektliyi isbat edilmi, tqribi hll n tklif olunan alqoritm saslandrlmdr
Riyazi analiz zr oxll Kalderon-Ziqmund sinqulyar inteqralnn
simvolunun diferensial xasslri, sferik harmonikalar zr Furye sralarnn
multiplikatorlar; daxiolma teoremlri, oxll Evklid, bircins v qeyri bircins tipli
fzalarda, habel myyn hiperqruplarda inteqral operatorlarn mhdudluq teoremlri,
hqiqi analizin inteqral operatorlarnn, o cmldn, maksimal, ksr-maksimal
operatorlarn, potensial tipli inteqral operatorlarn, sinqulyar inteqral operatorlar n
lokal xarakteristikalar terminlrind Ziqmund tipli qiymtlndirmlr alnmdr.
-
Dyin drcli Lebeq v Morri tipli fzalarn mxtlif xasslri yrnilmi,Hardi
tipli inteqral operatorlarn, oxll hndsi orta operatorun, maksimal, ksr-
maksimal operatorlarn, potensial tipli inteqral operatorlarn v sinqulyar inteqral
operatorlarn dyin drcli Lebeq v Morri fzalarnda mhdudluu aradrlmdr.
Lokal v qlobal Morri tipli fzalar n yeni daxilolma teoremlri v inteqral
operatorlarn hmin fzalarda mhdud tsir etmsi haqqnda teoremlr isbat edilmidir.
Lokal Morri tipli fzalarda hqiqi analizin inteqral operatorlarnn mhdudluu n
parametrlr zrin zruri v kafi rtlr taplmdr. Periodik funksiyalarn
brnmsinin hamarlq modulunun n yax yaxnlama terminlrind
qiymtlndirilmsi alnm,mumilmi Morri v Kompanato-Morri fzalar n
daxilolma teoremlri v inteqral operatorlarn hmin fzalarda mhdud tsir etmsi
haqqnda teoremlr isbat edilmidir.
Qeyri harmonik analiz zr o , bazis haqqnda klassik Peli-Viner v Bari teoremlrinin elementlr sistemlri v ya altfzalar sistemlri n mxtlif mumilmlri, m , pL ( 2p )
m, m b b - . Sonsuz defektli sistemlrin Banax fzasnn myyn altfzalarnda bazis olmalar n mhm nticlr alnm, k - B , mhur Stoun-Veyertrass teoreminin mhm kompleks analoqlar alnm v bu nticlr hiss-hiss ksilmz funksiyalar fzas halna rlm, xtti fazaya malik triqonometrik sistemlrin dyin drcli Lebeq fzalarnda bazislik xasslri yrnilmidir. Diferensial operatorlarn mxsusi v qoma sistemlrinin bazislik, birgylma, mntzm v mtlq ylma msllri yrnilmidir. v , . Bir trfd spilmy malik Yakobi operatorlar n spektral analizin dz v trs msllri yrnilmidir. Adi diferensial v ksiln diferensial operatorlarn spektral nzriyysinin bzi msllri tdqiq olunmu v mhm nticlr alnmdr. oxhdli tipli hycanlanmaya malik eksponent,
kosinus, sinus sistemlrinin pL fzalarnda bazis olmalar n zruri v kafi
rtlr taplmdr. Ksiln v ksilmz funsiyalar cbrlrinin qapanmas tsvir olunmu, triqonometrik v eksponent tipli sistemlrin ksiln funksiyalarn Banax fzalarnda tamlq, minimallq v bazislik msllri tdqiq olunmudur. Riman srhd mslsinin bir abstrakt analoquna baxlm, onun nterliyi yrnilmi v alnan nticlr bazislik msllrin ttbiq edilmidir. Qeyri-xtti Kleyn-Gordon
-
sistemi n qarq mslnin hllinin xasslri v bzi crlaan qeyri-xtti tnliklr n keyfiyyt msllri yrnilmidir. myyn ksiln adi diferensial operatorlarn mxsusi v qoma elementlrinin Lebeq fzalarnda bazisliyi
yrnilmi, b -freym anlay verilmi v ona aid mhm nticlr alnm; 4
1
Kadets teoreminin myyn eksponent, kosinus v sinis sistemlri n p -
analoqlar alnmdr. Cbr v riyazi mntiq zr ksimy ayrlmayan yarmqfslr oxobrazllar
haqqnda Evans problemi, kateqoriyalar nzriyysinin Mak-Leynin koherentlik
problemi hll edilmidir. Evans probleminin hlli: ksimy ayrlmayan yarmqrup
oxobrazllarn sintaktik tsviri taplmdr. Cbri sistemlrin aksiomladrlm
siniflrind nv qeyri-standart altdekart tsvirlri n altdekart ayrllara aid
klassik Birkqof teoreminin analoqu isbat edilmidir. Konqruens-sxemlrin say qeyd
olunmu v n-transferabel sas konqruenslri mlum olan oxobrazllar siniflrinin
xarakter lamtlri taplmdr. oxobrazllarn interpretasiya tiplri qfsinin sas
nqtlri n rtklrin mvcudluu akar olunmudur. Topoloji fzalarn xsusi
sinfind homeomorfizm yarmqruplar terminlrind bu fzalarn llrinin ifadsi
alnmdr. Ensiklopedik alim Nsirddin Tusinin riyazi v mntiqi irsi tdqiq edilmy
balanm v bu gn d hmin i davam etdirilir.
Ttbiqi riyaziyyat zr struktur elementlri arasnda daxili qarlql tsirin
mexaniki effekti nzr alnmaqla kompozit materiallar mexanikasnn nzriyysi, lifli
struktura malik evik qeyri-metal borularn layihlndirilmsi nzriyysinin saslar
yaradlm,alnm fundamental tcrbi-nzri nticlr sasnda kompleks elmi-texniki
problem qoyulmu v hll olunmudur. Fiziki-kimyvi xasslrinin dyiilmsi nzr
alnmaqla polimer v kompozit materiallar mexanikasnn nzriyysi polimer v
kompozit materiallarn fiziki-kimyvi chtdn dyimsi nzr alnmaqla
mumildirilml Huk qanununun tyin edilmsinin tcrbi-nzri metodu tklif
olunmudur. Elektromaqnit sahlrinin v maye mhitin kimyvi dyimsinin
qarlql tsiri,maye mhitin kimyvi dyimsinin bu mhitlrd elektromaqnit
dalalarnn yaylmasna tsiri mexanizmi tdqiq olunmu, elektromaqnit dalalarnn
kimyvi dyikn mhitlrd yaylmasnn mumildirilmi Maksvell tnliyi tklif
olunmudur. rtk v lvhlrin mumi riyazi nzriyysi ilnmi, bu mnasibtlr
sasnda rtk v lvhlrin klassik nzriyylrinin ttbiq olunma oblast tyin
edilmidir.
Hesablama riyaziyyat v informatika zr dniz v okeanlarda (Xzr, Qara,
Aralq, Mrmr v Oxot dnizlrind, Meksika krfzind, Atlantik okeannda v s.)
klklrin tsiri altnda axnlarn formalamas prosesi, dayaz su nzriyysi sasnda,
Koriolis qvvsinin vertikal tsiri nzr alnmaqla riyazi modelldirilmi, ddi hll
edilmi, alnan hllin stasionar hll yld isbat edilmi, axnlarn istiqamtinin v
srbst sthin sviyysinin dyimsi dinamik sxemlr klind on-line
-
vizualladrlmdr. Reaktor-regenerator tipli dinamik sistemlrd ii rejimlrin istilik
dinamikasnda srayl relaksasiyalarn v dayanqsz trayektoriyalarn yaranma
sbblri saslandrlm, stasionar vziyytlrin oxsayll v bunlara mvafiq faza
portretlrin topoloji mxtlifliyi gstrilmi, ll faza portretlrinin tam qalereyas
vizualladrlmdr. nsan orqanizminin biopolimelrl v dm qazndan zhrlnmsi
proseslrinin tibbi diaqnostikasnda zhrlnm drcsini, malic alqoritmini
qiymtlndirmy v dqiqldirmy imkan vern riyazi-statistik model,
vizualladrc qrarqbuletm bloklu informasiya sistemi yaradlmdr.
Elastiklik v plastiklik nzriyysi zr elastiki cisimlrin grginlik-
deformasiya vziyyti v elastiklik nzriyysinin kontakt msllrinin analitik v
ddi hll sullar, mrkkb iibo milin yilm mrkzinin koordinatlar dsturu, at
mslsinin analitik hlli, elastiklik nzriyysinin ll msllrindn ikill
msllrin limit keidi sulu. lvh v rtklrin dqiqldirilmi nzriyysi,
mstvi iplr, ortotrop dairvi membranlar deformasiyalarnn qeyri-xtti dz v trs
msllri, balanc grginlikli elastiki-plastik konstruksiya elementlrinin v xarici
mhitin mqavimti nzr alnmaqla bircins, anizotrop konstuksiya elementlrinin
dayanqlq v rqs msllri tdqiq edilmidir. Sferik v silindirik rtklrin ba
istiqamtd xarici mhitin mqavimti nzr alnmaqla dayanql v rqsi
hrkrlri, hminin qeyri bircins borularn elastik, zl mhitin reaksiyas nzr
alnmaqla dayanql, mhkmliyi v rqsi hrktlrinin tdqiqi n hll metodikas
qurulmudur.
Dala dinamikas zr zrby mruz qalan elastiki-plastiki materiallarn
dinamik xasslrini tyin edn orijinal v effektli metod. saplar v saplar sistemin
cisimlrl zrb mslsinin hlli v aerofiniyor nzriyysi yaradlm, qeyri-xtti
zl-elastik materialdan olan iplr zrb zaman dalalarn yaylmas, kt cisimlrl
ip v membranlara zrb msllri tdqiq edilmi, torun hrkt tnliklri xarlaraq
onun dinamikasna aid msllr hll olunmudur. Mxtlif istiqamtlr zr dinamik
dalma hadissi radial atlarn yaylmas nmunsind hm tcrbi, hm d nzri
olaraq tdqiq edilmi v dqiq analitik hll alnmdr. Dzbucaql paralelepipedd
qeyri-stasionar dalalarn yaylmas msllrinin dqiq analitik hllri alnmdr.
Akustik v brk elastiki mhitl qarlql laqd olan v trkibind elastiki
brkidilmi ktl saxlayan dairvi daxiletmnin hrkti,maye v elastiki mhitl
doldurulmu silindrik v sferik rtklrin btv mhitd srbst rqslri tdqiq edilmi,
srbst rqslrinin mxsusi tezliklri tyin olunmudur.
Srncklik nzriyysi zr zlelastik cisimlrin deformasiya v dalma
proseslrini nzr alan yeni mhkmlik nzriyysi hazrlanm, korroziyadan
dalma vaxtn v yerini tyin etmy imkan vern sul, korroziyann mxtlif
parametrlrinin tcrb il uyunlaan qiymtlrini tapmaa imkan vern nzriyy
ilnmidir. xtiyari yklm zaman irsi elastiki, irsi elastiki-plastik cisimlrin
deformasiya v dalmasnn riyazi nzriyysi ilnib hazrlanm,atn uclarnda
-
plastik deformasiyann xsusiyytlri, plastikliyin atn inkiaf dinamikasna tsiri,
atn artma srtinin azaldlmas msllri tdqiq olunmu, ikill elastiki-plastiki
msllrin hll sullar inkiaf etdirilmidir.
Maye v qaz mexanikas zr dispers sistemlrd yaranan qeyri
mntzmliklrin qaz daxili il tnzimlnmsi prosesi, reoloji mrkkb, qeyri-
mntzm sistemlrin boru v msamli mhitd hidrodinamikas tdqiq olunmu,
tnzimlnn yeni zl-elastiki kompozit sistemlr yaradlm v texnoloji proseslrd
mayelrin zl-elastik-plastik xsusiyytlrinin tyin edilmsi n diaqnostik
msallar ld olunmudur.Msamli lay mhitlrind yksk keiricilikli kanallarda
sdd yaradaraq szlmd hat dairsinin genilndirilmsi mqsdi il laydaxili
kvaziperiodik kpk yaratmasnn nzri v praktiki saslar ilnib hazrlanm, fraktal
strukturun inkiafnda, srhdd yaranan fluktuasiyann lokal tzyiq vasitsi il
tnzimlnmsinin mmknly gstrilmi v bunun n hllr alnm, msamli
mhitlrd sxdrmada geyri tarazlq v ya eynifazal haln tnzimlnmsi n
fazadyimsinin mmknly saslandrlmdr. Laydan neftin su il sxdrlmas
prosesinin effektivliyinin artrlmas mqsdi il kapilyar tzyiq mqavimtini df
etmy imkan vern periodik dyin hidrodinamik tzyiqin yaradlmasnn vacibliyi
elmi saslandrlm, neftveriminin texnoloji proseslrind fraktal strukturlarnn
yaranmasn tyin edn diaqnostik sullar ilnib hazrlanmdr. Neft yataqlarnn
ilnmsinin effektliliyini artrmaq n bir sra snaye texnologiyalar yaradlmdr.
Azrbaycan Nazirlr Sovetinin 23 iyun 1978-ci il Srncam v Elmlr
Akademiyasnn 6 iyun 1978-ci il tarixli 211 sayl qrarna sasn Riyaziyyat v
Mexanika nstitutunun nzdind Xsusi Konstruktor Brosu (XKB) yaradlmdr.
XKB-nin sas mqsdi elmi v tcrbi-konstruktor tdqiqat ilrinin nticlrinin
istismar raitin n yaxn olmaq rti il xalq tsrrfatna ttbiqini ilyib
hazrlamaqdan ibart olmudur. 1983-c ild XKB-n;n mmkdalar (Framz
Maqsudov, Vaqif Mirslimov, Valeh Quliyev, Fuad skndrzad) Kompleks elmi
tdqiqat, layih-konstruktor v texnaloji ilrin xalq tsrrfatnn v onun sahlrinin
mhm istiqamtlrinin inkiafna ttbiq edilmsi iin gr SSR Nazirlr Sovetinin
Mkafatn almlar.
XKB-y 1978-1981-ci illrd akademik Framz Maqsudov, 1981-1997-ci
illrd t.e.n Fuad skndrzad, 1997-2001-ci illrd is prof. Turab hmdov
rhbrlik etmilr.
55 il rzind institut mkdalar 93 monoqrafiya v 10000-dn ox elmi mqal
ap etdirmilr. Bu mqallrin 1500-dn oxu nfuzlu xarici jurnallarda nr
edilmidir.
Vaxtil Riyaziyyat v Mexanika nstitutunda ilmi alimlrin 67 nfri hal-
hazrda xarici lklrin (Trkiy, Rusiya, Ukrayna, Qazaxstan, Almaniya, Meksika,
AB, Avstraliya, Byk Britaniya, Belarus v s.) aparc elm v thsil mssislrind
alrlar. Onlarn 29 nfri elmlr doktoru, digrlri is flsf doktorudurlar.
-
Hazrda institutda 242 nfr alr, onlardan 1-i akademik (Akif Hacyev), 4-
akademiyann mxbir zv (Rauf Hseynov, Mhmmd Mehdiyev, Htm Quliyev,
Surxay kbrov), 42-si elmlr doktoru, 84- flsf doktorudur. Onlarn siyahsn
oxucularn diqqtin tqdim edirm:
Elmlr doktorlar
1. Misir Mrdanov 2. Soltan liyev 3. Mmmd Bayramolu 4. Qabil liyev 5. Vaqif Hacyev 6. Cfr Aalarov 7. Vaqif Mirslimov 8. Nadir Sleymanov 9. Camali Mmmdxanov 10. Sadiq Abdullayev 11. Nihan liyev 12. Musa lyasov 13. kbr liyev 14. Telman Mlikov 15. Hmdulla Aslanov 16. Sabir Mirzyev 17. Hidayt Hseynov 18. Bilal Bilalov 19. Vli Qurbanov 20. Vaqif Quliyev 21. Ltif Talbl
22. Yuriy Turovskiy 23. lham liyev V. 24. Nizamddin sgndrov 25. Tahir Hacyev 26. brahim Nbiyev 27. Aqil Xanmmmdov 28. Fda Rhimov 29. Frman Mmmdov 30. Araz liyev 31. Rhim Rzayev 32. dalt Axundov 33. Turab hmdov 34. Asf Zamanov 35. Qeylani Pnahov 36. Nazil Rsulova 37. Alik Ncfov 38. Rvn Hmbtliyev 39. Ziyatxan liyev 40. Bhram liyev 41. Vqar smaylov 42. Nigar Aslanova
Flsf doktorlar
1. Rais Kazmova 2. Nriman Sbziyev 3. Tamilla Zeynalova 4. Xasay Musayev 5. Tamilla Hsnova 6. Mehdi Balayev 7. Vladimir Yusufov 8. Aydn ahbazov 9. li Babayev
10. Eldar Abbasov 11. bdrrhim Quliyev 12. Murad Muxtarov 13. Fariz mranov 14. Vidadi Mirzyev 15. Telman Qasmov 16. Mfiq liyev 17. Aft Cbraylova 18. Fxrddin Muxtarov
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19. Mtant Mrslova 20. brahim Mhrov 21. Rvn Bndliyev 22. Zaman Sfrov 23. Cavanir Hsnov 24. Mbariz Hacbyov 25. Aydn Hseynov 26. Niyazi lyasov 27. irmayl Barov 28. lizad Seyfullayev 29. Rakib fndiyev 30. Hsamddin Qasmov 31. Namiq Hmidov 32. Rft fndiyev 33. Rahim Quliyev 34. Fuad Xudaverdiyev 35. Mbariz Rsulov 36. Leyla eyxzamanova 37. Mahir Mehdiyev 38. Mhsti Rstmova 39. Mehriban Mmmdova 40. Nazim Cfrov 41. Gldst Mmmdova 42. lqar liyev 43. Vqar Xlilov 44. Valid Salmanov 45. kbr Hsnov 46. Sarvan Hseynov 47. Torul Muradov 48. Minavr Mir-Slim-Zad 49. Namiq Quliyev 50. Vfa Mmmdova 51. Shrab Bayramov
52. Nigar krova 53. Kmal Mmmdzad 54. Fuad Hseynov 55. Vqar Sadov 56. Sbin Sadqova 57. li Hseynli 58. Miqdad smaylov 59. Zaur Qasmov 60. Qabil liyev 61. Gln Aayeva 62. Famil Seyfullayev 63. Elmddin ahbndyev 64. Knl Mmmdova 65. hla krova 66. Arzu liyeva 67. Aft Yzbayeva 68. Elin Mmmdov 69. Skin smaylova 70. Tran Kngrli 71. Mahir Calalov 72. Arzu Babayev 73. rad badova 74. Elad Hmidov 75. Seymur liyev 76. Sevinc Quliyeva 77. msr Mmmdov 78. Kamilla limrdanova 79. Aydn krov 80. Rft Mmmdzad 81. Aygn Ltifova 82. Rafiq Teymurov 83. Sevinc Rsulova 84. msiyy Murado
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n
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21
1. .., .., .. .
- . 2008. . 81, 2. .358-364.
2. .., A .. . - . 2012. 85.,
6. C.1189-1195
3. .. 2 . .: , 1995.
4. . . .: , 1965.
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-
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: xSm
i
n
m
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b
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2
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n
imb
xA , ,
nb
x constb
xAb
n
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1. Kirov G.H. A generalization of the Bernstein polynomials. Mathematica Balkanika.
Vol.6, 1992.
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24
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.
1. S.S.Mirzoev, G.A.Agaeva, On correct Solvability of one Boundary value problems for the differential equations of the second order in Hilbert space //
Applied Mathematical Sciensec, v. 7.2013, N:79, 3935-3945//.
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-
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, - , 2010, 2, c.25-34. _____________________________________________________________________
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-
27
[3]. -
, . , . , . , , . , .. , . . .
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min)( XF , 0)( XG , maxmin XXX , ))(),...(),(()( 21 XgXgXgXG m
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-
28
1) F(X) G(X) , . . [5]; 2) . [5]. : 1) ; 2) , . -. .
, , [6]. . , -, . . .
1. : . . / . ..
. .: . 2010. . 7. 161 . 2. .., ... -
. . 1(27) 2005.
3. .., ... . . 2012. 10 (101). .33-38.
4. ... .. . :
. , 4. 2013. .19-35. 5. ... : .: ,
2003. 392 . 6. .., ...
. : . 5, 2013. .1-7.
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-
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u
uu (2)
- , A - , -
- H , 1A H .
(1), (2).
[5] , (1),
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.
1. .. .. -
. . , 1981,
.3-16.
2. .. -.
. . . 1980, .32, 2, .248-252.
3. .. -
-
31
. . . . 2010, 62,
1, .3-14.
4. ., .. -. . . .-
2010, 62, 7, . 867-877.
5. .., .. -
. , 90-
.
, 2013, . 119-120.
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-
33
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:
-
34
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,
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1. ..
- . . .
,
ISBN 978-9952-13-3, ., 2012 ., 288 .
2. Gabil G. Aliyev, Faik B. Naqiyev. Engineering Mechanics of Polymeric Materials
(Theories, Properties and Applications). Monoqrafiya. USA, CPC Press, Taylor and
Frencis Group. ISBN hard: 978-1-926895-55-0. Cat # 10868, 402 p.p., 2013.
3. Gabil G. Aliyev. Experimental-Theoretical Metod for Defining Physical-
Mechanical Properties of Polymer Materials with Regard to Change of Their
Phisical-Chemical Properties. USA, International Journal of Chemoinformatics and
Chemical Engineering (IJCCE), 2(1), January-June, 12-24, 2012.
_____________________________________________________________________
..
ryyqyp )()( ,0),,,,,,( lxyyyyxF (1)
0,=sin)(cos)(0,=sin(0)cos(0)
0,=sin)()(cos)(0,=sin(0))(cos(0)
lTylyTyy
lyplyypy
(2)
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,][0,l ,],0[],,0[],,0[ lCrlACqlACp ],2
,0[,,,
F ,gfF 5],0[, RlCgf :
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;,1|||,||,|,10],,0[|,||),,,,,(| RwvsulxuMwvsuxf (3)
|)||||||(|0),,,,,( wvsuwvsuxg (4)
-
35
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.R .
,,0),()())()(())()(( lxxyxrxyxqxyxp (5) (2). (5), (2)
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-
36
),,0( lx (iv) ,0)0()0( yy (v) 0)0( y ,0)0()0( yy (vi)
,0)0()0( yy ),2()( x ),0( lx .
.kkk
SSS ,
,
kS ,k , E .
,k
Sy )(xy
),0( l [3].
ER
(1), (2). )(
kkSR , ,
kkk ., k
, )0,( (1),
(2) ,, kSRk ,
.k
1. (1),(2) , ,
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SR
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I .)(min,],[],0[
000xrrrMrMI
lxkkk
Nk ,
kC
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kI)0,(
(1), (2) .k
SR
1. Nk ,
kC
- ,})0{( kk
I },0{kI )(
kSR
})0{( k
I ER .
1. D.O. Banks, G.J. Kurowski. A Prufer transformation for the equation of the vibrating beam // Trans. Amer. Math. Soc., 1974, V.199, p. 203-222.
2. D.O. Banks, G.J. Kurowski. // A Prufer transformation for the equation of a vibrating beam subject to axial forces, J. Diff. Equat., 1977, V. 24, p. 57-74.
3. Z.S. Aliyev, Bifurcation from zero or infinity of some fourth order nonlinear problems with spectral parameter in the boundary condition, Transactions NAS
Azerb., ser. phys.-tech. math. sci.,math. mech., 2008, V.28, 4, p.17-26.
____________________________________________________________________
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-
-
37
( ) ,
[1],
,
. [2]
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),1,0(),()()21( xxyxyxxy (1) ),021()021(,0)0( yyy (2)
,)21()021()021( yyy (3)
).1()1( yay (4)
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L (1)-(4).
(1)
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,210,)sin(),(
xxx
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(1)-(3), 0)1( y -
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...,...21
k
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; ii) ,2 (1)-(4)
, 1
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(1)-(4) , 1
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3,...,2,=k
, (1)-(4)
,
-
38
1 , ,
k 3,...,2,=k
; iv) ,4
(1)-(4) , 1
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, ) , ,k
3,...,2,=k
, 1
,
2
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, 1
, ,k
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.
3. r . ) 0a 0a ,1)(
k ,k
rkkk
xy,1
)}({ (1)-(4)
;)1,0(2
L ) 0a ,2)( m . ,
1
mm
rkkkxy
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1) mri )0(,)
mmccmrii
,)1,0(2
L mriii ) )0(
mmcc
,)1,0(2
L
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1)0(
mLmmmmmyayyyaayc
1)]),1(( m
y ),)),1((||||( 221 2
kLm
yay ,),(
=)(1
m
m
xyxy
m -
.m
1. .., .. // . . 1961. .197. 7. .1011-1014.
2. Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H. Solvable Models in
Quantum Mechanics. AMS Chelsea Publ., Providence, RI, 2005.
3. .. p
L
// . . 2011. .46. 6. . 764-775.
____________________________________________________________________
,
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-
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,
-
39
,0 ,)()(=)()())()(())()(())(( lxxyxxyxrxyxqxyxpxyr
(1)
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,][0,lx ],,0[,],,0[],,0[ lCrlACqlACp ,,, -
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),( xy
.
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-
40
,0)0( Ty (2), (2) ].2,0(
)(01
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,
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nn ),(
)( xyn
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2n 1n
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, ),(0
),,0( l (. (3)).
1. Banks D.O., Kurowski G.J. A Prufer transformation for the equation of the vibrating beam // Trans. Amer. Math. Soc., 1974, v. 199, p. 203-222.
2. Banks D.O. and Kurowski G.J. A Prufer transformation for the equation of a vibrating beam subject to axial forces // J. Diff. Equat., 1977, v. 24, p. 57-74.
3. Kerimov N.B, Aliyev Z.S. On oscillation properties of the eigenfunctions of a fourth order differential operator // Trans. NAS Azerb., ser. phys.-tech. math. sci.,
math. mech., 2005, v. 25, 4, p. 63-76.
4. Amara J.Ben. Sturm theory for the equation of vibrating beam // J. Math. Anal. Appl., 2009, v. 349, 1, p. 1-9.
5. .. , .. , .. . // . , 2012, .
444, 3, . 250-252.
____________________________________________________________________
-
41
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1. (1)-(3)
.
2. R (1)-(3) ,)(1
AG'
.)(=1
2
1
2
11caA
.
3. ,,,2121 R (1)-(3)
.)(11
AG' .)(12
AG'
1. :
)(i (1)-(3) , 0
T
( , )
, n
T 2,...,1,=, n ;
)(ii (1)-(3) , 0
T
,
S , S
T ( ,
, )
, n
T
2,...,1,=n ,Sn ;
)(iii (1)-(3)
, 0
T ,
n
T 2,...,1,=, n .
-
43
1. Binding P.A., Browne P.J., Seddici K. Sturm-Liouville problems with eigenparameter dependent boundary conditions // Proc. Edinburgh Math. Soc.
1993, v.37, p. 57-72.
2. .., .. -
// . , 2012, .442, 1, .583-586.
3. .. p
L
// . , 2011, .46, 6, . 764-775.
___________________________________________________________________
.. , .. ,
),1,0(),(=)()()( xxyxyxqxy (1)
,)0()()0()(0000
ydcyba (2)
,)1()()1()(1111
ydcyba (3)
, ),];1,0([)( RCxq ,1,0,,,, idcbaiiii -
, .0=,0=1111100000 cbdacbda
(1)-(3) 0,010
[1], 0,010
[2].
(1)-(3) .0,010
(1)-(3) .
)( , 0Im 2
, 0=Im .
1. .0,010 (1)-
(3) 2)(1=
kn
k
,,1=
nn
kk
.
. 00 .0
1 (1)-(3)
,
;
-
44
;
, .
1. .., .. -
// . , 2012, .442, 1, .583-586.
2. .. .. - //
. , 2013, .451, 5, .487-491.
____________________________________________________________________
-
-
..
.. ([1], 2.1, . 57)
-
RxxfxuAxuDAxuDuDL nnn ,)(...)()()( 11 .
-
RxxfxuAAaxuDAAaxuDuDL nnnnn ,)(...)()()( 111 .
- [2]
xfxuAxuAaxuLun
j
jn
j
jnjn
j
j
n
)()()(11
1,0,1,0,)()1(1
1 1
qq
k
j
n
q
j
jq
mmxxfxuuuuL
,
jq - , 0 , -
, njAj 1, .1,0 HLp
(. 2.6, . 77)
0 .,...,,: 0100 uLuLuLu n
),()()()()()()( xuxuxCxuxBxuxAxu (1) xC ,xB ,xA Rx .
-
45
ERLp 1 ,
ERL ,2 -. I . xB
Rx xA Rx ,
xADuuxAuxADxBD ,xBu , C x . 1. :
1. xA Rx ;
2. yxCyIyx 1-]AyA-x[A , ,
3. RK Iyx
yxkCeyAxA 1 ,
4. ,arg , )(1
)(1
xq
MxA
1xq
)(xqLimx
;
5. xA 1 ; 6. 1 xB xC x
xA 21
.xA (1) pERLp 1,, , ..
, ,
.
, 1 , 4
, xq , ..
ax
xxdttq )(lim 0a
2. . HRL ,2 (1).
2. :
1. xA H Rx , ..
xAD 0AD , ,0 arg
11 )1()( CIxA ;
2. yxCyyx 1-]AyA-x[A ,1 . HRLf ,2
-
46
)()()()()( xfxuIxAxuxuIL (2) arg
),(
1
),( 22||
HRLHRLfCu
3. :
1. xA H Rx , ..
xAD 0AD , ,0 arg
11 )1()( CIxA ;
2. yxCyyx 1-]AyA-x[A ,1 ;
3. HxA p1
, 0p
4. ,arg ,)(1
)(1
xq
CIxA
xxq
arg , L
-,
)),((),( 2 HRLLR q pq
2
2
4. :
1. xA H x
;arg,1
,2
2
,0,,,
1
1
x
CIxA
pHxARx p
2. ;,1 1 yxCyAyAxAyx
3. xB ,H
xADxBD 21
0 ,
,, 21
2
1
xADuuCuxAuxB
xC xADxCDH , 0 . xADuuCuxAuxC , .
(1) a -
-
47
(1) .,2 HRL
1. .. - . , , 1985, 220 .
2. Yakubov S., Yakubov Ya. Differential-Operator Equations. Ordinary and Partial Differential Equations, Chopman and Hall/CRC, Boca Raton, 2000, 542p.
____________________________________________________________________
N
..
1: zCzT , .
Tz
d
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2
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T
k
k di
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1
2
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T
k
k di
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1
2
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. (., ., [1, .5, C, 3 ]) ,
: dttftd TLLf log , , , Zkak ,
Nkbk ,
T
k
k dFi
a
1
2
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T
k
k dFi
b
1
2
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F F
zF zF Tz . , ,
F F T (1) .
N -
(1) .
Rba , h ( )[ ] ( )xhxh n = nxh xhnxh n sgn nxh .
mailto:[email protected]
-
48
1[2].
b
a
nn
dxxhlim ,
h Q - ba, , baQh , ,
Q - b
a
dxxhQ .
, Q -
,
. Q -
ba, h 1:, oxhbaxm , , (2)
m , Q - .
, , 2 - ,
, R ,
xfxm :,lim . (. [3])
tfq
ctgtxqfPn
22;;;
1
11 ,, nnnn qxqxqxqxt , Zn , ,
txqfPxxtmxfPq
;;;:,limlim;1
1 , (3)
txqfPxxtmxfPq
;;;:,limlim;1
2 , (4)
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xf
xfxfPxfPxfxr f
, (3)
(4) 2,0x . fiff ImRe , 2,0 ,
xirxrxr fff Im,Re,, , , xr fRe, xr fIm,
2,0x . 2. CSM ;2,0
2,0 f , xr f,
2,0x ,
dttr f,0
limlim
2,0, ~f (2), ~
, ,
dttr f,0
limlim2
,
2,0, . 3. f CSM ;2,0 Q -
2,0 , N -
2,0 . ( ) ( ) ( )2
0+
2
02
+
dxxrlimi
dxxfQ f, N - ,
f
10 q
f
-
49
2
0
,
2
0
lim2
dxxri
dxxfQf
N -
2,0
2
0
dxxfN
2
0
dxxfN .
f T .
itit efeitf * , 2,0t . 4. *f N -
2,0 , f N - T , N - N - f T
2
0
* dttfNdxxfNT
,
2
0
* dttfNdxxfNT
.
1. -
T . Zkak ,
Tz
d
izF
2
1, Dz
T
k
k dFNi
a
1
2
1, Zk ,
F zF Tz . 2. -
T . Nkbk ,
Tz
d
izF
2
1, Dz
T
k
k dFNi
b
1
2
1, Nk .
F zF Tz .
[1] . , pH , .: , 1984.
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[3] . . ,
, . , 73:1 (2003), 821. ____________________________________________________________________
f
-
50
.. , .. , ..
.
, .
1, nn -
,
P,, .
1,1
nSn
k
kn ,
nfSn ana :1inf
1, nSn tfa , 0t ,
0a . ,
inf . a
([1], [2]).
tftfa nP
E [3] .
[1], [2] tfa
,
a
aaa fS a a .
a a a .
a , nP a a .
, 01 E , 12 D tfa
:
1) a tfa -
0t , tfa a ;
-
51
2) a t
tfa
t ;
3) )(ann a , )(ann )(1
nfn
a
a ,0)( nfa , a ,
4) tfa , ..
)(ann )(amm a , 1m
n
5)
1mf
nf
a
a a ,
, 1) 2) , nnfa
n aa NN . ,
10, attfa 1)-4).
1 2 .
, , 1m
,dttum
1itMetu , ,Rt , 12 i . , mnSn ,
xPn
rnPdr
drnw aaa ,,
SE
rSPrh nSS nn , 1n 0:1inf nSn 8 .
.
tfa 1
,aaa NNann Ra a .
rhn
rnwa
~, a
R ,
.,2
12
2
Rxex
x
1. .. . - .
. 1982, . XXVII, 4, . 643-656.
-
52
2. . . . .
. 1990, . 35, . 373-377.
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____________________________________________________________________
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a
:
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)2(),0()(),0(
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xxxu
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xtuxtuxtuxtuxtFxtuxtu
xxxx
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, (1)-(3)
),( xtu , ],0[],0[ T
, (1),
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sin)(),(n
n nxtuxtu ,
]),0[,...;2,1(sin),(2
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0
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nn dxdenxxun
etu
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22
sin)),((2
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]),0[,...;2,1( Ttn ,
mailto:[email protected]
-
53
,...)2,1(sin)(2
0
nnxdxxn
,
)),(),,(),,(),,(,,()),(( xtuxtuxtuxtuxtFxtu xxxxxx .
,
),0(;],0[ 52 WTC , , .
1. .., ..
.
, .-., 1, 2009, .5-17.
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, , ,
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,
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.
, .
.
, .
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nR n nxxxx ,...,, 21
rx-aRxraB n ::, nR 0rnRa N n ,...,, 21
n
nxxxx 21 21 n ...21 n ,...,, 21
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r
axdt
r
attf
raxfP
k ra
rak
,
.,,
1:
raB , ),( raB k
),0( t 00
1t k
kt
t
-
54
nR
rxkrk dttfPtftxrxf ,,1)(
, :;,
,
nloc RLf 1 , k ,
n
xncx
1
1;: , 0 , ,nc
,
nR
dxx 1 ,
r
xrx nr
)()( nRxr ,0 .
nkkf RxrrxfH ,0 : ;,sup: ,, , 0 . , , , .
,
.
,
.
.
.
,
, .
1. , , , , , .
1. .. -
kBMO ,
kH , . . . -, 1996,
.2, .164-175.
____________________________________________________________________
nloc RLf 0 Nk k
1
0
,
,
, :
t
dt
t
tf
k
fk 1
0 t:sup:
,
,
, t
tf
k
fk
,
,
kHO nloc RLf
,
,
kA
:,,
kHOf
,
,
kA
Z
Odtt
t
10
0 Nk 1k 1 k,min Z
kA,
,
kHO
-
55
.. , .. , ..
,
R
),0[ x ., , ,
E x .
, .
),( txu t -.
[1]
02
t
w
Rx
u, (1)
01
x
p
t
u
(2)
),( txpp , ),( txww
.
-
-h x , . )(xhh . ,
, )(xh )(xE
)()( 10 xghxh )()( 2 xgExE ,
)(1 xg )(2 xg , 0h E -
.
)}(1{)(2 10 xghxh .
)(1 xg )(2 xg
1)(lim)(lim 21 xx
xgxg ,
.
xexg x sin1)(1 , xexg x sin1)(2
, (3)
.
,
[1],
mailto:[email protected]
-
56
.0 pR
N
N
0
0 )(
h
xgh
dzN , R
wxgE )(2 .
)(1)( 1220 xgxgE
R
whp . (4)
,,
E
pp
ER
NN ,,),,( 0
02
02
0
2
0
00 hxxR
hE
c
httt
,,,, 0,0000
0 hhhwhwh
tuu
, ,
(1)-(3)
wxgxgp 221 )()(1 (5)
02
0
w
x
u
x
pu
(6)
(6) ),( txu
,
w
(4),
0)(1)(
122
2
12
2
2
p
xgxgx
p (7)
(7) , -
,
)}(1){(2
12 xgxgc
(8)
, c x
.
, (8) (3),
}sin2){1(2
xeec xx
x )0( x 2~c ,
x )( x , ,
~c , -.
-
57
. , ,
sxg 1)(1 [2]
)(2 xgc
1. . .-.:, 1977.-520.
2. .. , .., .. .
. , 2003,.39, 4, .555-566.
____________________________________________________________________
. .
)( 22 L
),,)((),)()(,(
),)()(,(),)()(,(),(),(),(
2121210
21
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21221
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ttSttbttSttbttttattR
K
1: tCt - ,
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-
58
)(
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k
t
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ikt
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sin, )( 1
)(
1
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2
2 L
,)()(4)(22)(
)2(
11
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1
2
0
0)( 222
2
Lnnn
k
kLnEKEEKbaRR
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inf)(,),,,(max
LTqn
ttqEttKK
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n
nk
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inf)(1 , )4(
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432
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SbSbSbIaR 0)2(
2
)1(
10
0 ,
0210 ,,, bbba - .
2. 0))()()(( 0210021002100210 bbbabbbabbbabbba
.. SbSbSbIaR 0)2(
2
)1(
10
0 )( 22 L .
Nn nnnn SbSbSbIaR 0)2(
2
)1(
10
0 )( 22 L ,
10 nR , ,2,1n
10 R )( 22 Lf
)()2( 1)(1010
22fEcfRfR nLn
c - .
1. ..
. I// .. - .-1970.-.11-.181-196.
2. ..
. II // . . .-1975.- 4, . 3-13.
3. ..
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4. .., ..
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_____________________________________________________________________ ,
.. , ..
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, [1], [2],
,
, . ,
,
. ,
.
,
.
,)1,0(,0),(),(),( 4)2(2)4( xxyxybxay (1)
:
),(),0();(),0( 1)2(
0 yy ),(),1();(),1( 3)4(
2
)1( yy (2)
a b (1) , ,0ab
.
, )(xy ,
4
1
),(),()(m
mm xKxy (3)
(1), )4,1(),( mxKm ,
)1,0(x
, ,
(1) [3],
)4,1()( mm ,
. (3) (2),
)(m )4,1( m
)()()( A , (4)
-
60
)(A , ),( xKm
0x 1x , )( - ,
, )( - .
)3,0()( kk [2],[3]
, )(A , (4)
, , R ,
)()()( 1 A .
1. .. . // , ., 1964
2. .. .// , ., 1975
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____________________________________________________________________
, -
..
mHHH 210 ,...,, , ii HH 1 ,
12,...,2,1,0 mi , . iH
nii RHLH ,2 .
uDxAuDxLm
2
, , nRx
n ..., 21 , n ...21 , n
nxxxD
...21 21. mHxu 2
,
mHuD
2.
, nRx xA , 0
: 02 HH m . xAxA 00 , 0A
00 HH m , 1
0
A
-
61
mn
k ckA21
0
. ...0 21
0A .
l ,
, l , 0
m
H
RH
uELCdxuDn2
22
00
1 EL 00 HH .
.
1. ...
. . , 1993, .4, .172-173.
2. ...
. . , 1993, .53,
.3, .153-155.
____________________________________________________________________
-
.. , ..
HLH ,,021 , H ,
-
yxRyxQyxP nnn 1 00 jy , 1,...,1,0 nj .
xP , xQ xR
......21 n .
N ,
0 , ..
n
N 1.
-
62
sxn ,
xQxRSxPxR n 121 . , k
1 0 0
2,n
k
n sx
dxds
.
1 0 02
12
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1~
1
nk
nnk
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dxds
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dxdsN
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,
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.
.
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u
y
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2
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u,u (2)
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zyxa
t
(3)
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u,u
t
t|
0 (4)
-
63
, t=0, t=, . (3) (4)
, t t,
t=0, t=. :
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14 S
d)t(az),t(ay),t(axgt
),z,y,x(
(4')
., )t,z,y,x(u , :
t
d),z,y,x()t,z,y,x(u0
, (5)
,