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

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: rmi@lan.ab.az; web: www.imm.science.az

mailto:rmi@lan.ab.azhttp://www.imm.science.az/

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

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

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

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:

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

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 , ,

, 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.

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

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

19

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00,u0t

(7); ,0),(t

u

ttQfx

(8);

0,0u

0

tx x

(9)

)t(Q -

.

. .

file:///C:/Users/Admin/Desktop/aelhan@mail.ru,%20nurlana_az@rambler.ru

20

(.2).

.1 .2

, [2,4]

n

m

n

m

.m

mcos

mcos

T

tmcos

Q

m

T

tmcos

QQ

)t(Q1

2

0

1220

0

2

3

4

3

2232

33

2 (10)

[8]

(2)

(6), (7), (8) (9),

(10), u .

(1)

[3,4]

dr

)t(xexpP

dr

)t(xexp)(P

rx

r

rxU

r

RxA)t,r(P

c

t

k

c

t

ccc

k

2

2

0

2

2

02

2

1 (11)

(2) (3), (4) (7),(8) (9)

u .

:

c

c

rr

crr r

PkbrQ

2 (12)

:

t

ufQ

x

0 (13)

,

, :

0

xrrQQ

c

(14)

(13) )t(P

.

)t(P

(11)

)(tP .

21

1. .., .., .. .

- . 2008. . 81, 2. .358-364.

2. .., A .. . - . 2012. 85.,

6. C.1189-1195

3. .. 2 . .: , 1995.

4. . . .: , 1965.

____________________________________________________________________

1 ..

,

2 .. ,

3..

1 ,

2,

3,

,

.

.

.

.

, .

P1(t), ,

P2(t). q0.

:

s

sqq

qdt

dm

qqqdt

dm

2

1

.

:

21

2

0PPq

q ;

21

22

1PPPq

atmq ;

2,1 mPmiii

;

t,c

22

qs:

22

2

1PPaq

dt

dqs

s .

,

,

.

:

gir

q

or

or

or

qq

aQsP

P

a

sP

q

1

12

2

1

.

32121221

2

222

(

)(

ororororor

oror

gir

q

q

PS

PPS

P

a

Pa

SP

SP

a

q

qPW .

.

____________________________________________________________________

..

aytekinabdullayeva@yahoo.com

Rf ,0: xSm

...2,1,010

mb

x

b

xC

b

nxkxS

kn

n

k

n

kn

mn

k nm

0,0 limlim n

bbbx n

nn

nn

Lemma:

...2,1,010

mb

x

b

xC

b

nxkxS

kn

n

k

n

kn

mn

k nm

c

xS

b

mnxS

b

x

b

xbxS m

n

m

nn

nm 11 1

mailto:aytekinabdullayeva@yahoo.com

23

: xSm

i

n

m

iimm n

b

xAxS

2

0,

n

imb

xA , ,

nb

x constb

xAb

n

imn

,.

1. Kirov G.H. A generalization of the Bernstein polynomials. Mathematica Balkanika.

Vol.6, 1992.

____________________________________________________________________

..

H

),0(),()()()()(

21

2

2

2

TttftuAdt

duAtuAt

dt

tud (1)

,)(,)0( 10 Tuu (2)

)(),(,, 10 tftuH H ,

, :

1) A H ; 2) )(t , ),,0( T

.(t)0

3) jjj AAB .2,1, jH

. )(,):),0(()( 23

102 ADHTLtf

- )(tu , , ),:),0(()( 2 HTLtu

HTLtuA :),0()( 22 (1) ),,0( T

(2)

.10:),(:),(

2

:),(

23

23

222

AAfconstuAuHToLHToLHToL

.

,

(1), (2), .

.

. 1) -3)

.11

2

121 BB

(1), (2) .

24

, )(t ),0( T

.

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//.

______________________________________________________________________

,

-

.. , .. , ..

nR - ,1nn

,0,...,0:...,,,,..., 111, kmmkmmmkkm xxxxxxxR

0 0

21111

21 ,...,cos2,... mmmmmv

s ssxxsxucxuT

kmmkmvmvkmkmkmkmkm ddssxx kmm ...sin...sincos2 11211222 1 ,

- [1]: ,2

1 12

2

2

2

m

i

km

mi ii

i

ii

Bxx

v

xx

,0,...,0,,,,...,,,,...,, 111 kmmmkmmkmm vvRsxssssxxxx vc ,

....,,...,,11 11 kmmkmms vvvvvvT

,1 p

,,...,1,

;,...,1,,

21 kmmidxx

midxxdxdxd

i

v

i

i

i

km

i

ii

0, tt , ,

,:: .,

1

df

,

df

,,

,

p

R

p

vpkkmvp

kkm

xdxxuLuuRL .1 ,, vpvp LL

qp1 . A -

qpK v , [2], vqvp LLA ,,:

kkmvp RLu ,, sdxuTscxAukkmR

s

,

ux supp ,

vkm 2 . ppKA , . 0ia iiami 2,,...,1 kmmi ,...,1 , ivpivp xAxA ,,

25

kmi ,1 , p

kmm v kmv

m xx

22

1 ...1 ikkmikkm xRxxRx :: ,,

0 . ivp xAu , ivp xA ,

,,

1

:

,

,

p

xR

p

ip

ikkm

xdxuu

kmixdx

p

xR

p

ikkm

ip

,1,0,,

1

:,

,

,

0,),(:)()(1

0

,,,

dtttxAuxJp

a

ipipip

i

,

0,),(:)()(1

1

0

,*

,*

,*

dtttxAuxJp

a

ipipip

i

.

1. qp1 , qpKA v , , ))(()( ,*, ipip xJuxJu .

kkmRx , xAux

,,,0

11

,

1

,

dtttucu pa

ip

p

a

iq

ii

0,,,1

1

,

1

,

dtttcq

a

ip

q

a

iq

ii

kmi ,1 , c u .

1. .. .

. , .6, 1951, 2 .102-143.

2. .., .., ..

, - , 2010, 2, c.25-34. _____________________________________________________________________

..

alievakbar@gmail.com

.

50-

.

:

-

;

26

- , ;

- (

);

-

;

- .

,

, ,

. ______________________________________________________________________

-

.. , .. ,

alovsat_qaraca@mail.ru, depart8@iit.ab.az

,

() - , . , , [1,2]. . . , , . . : , (), ; , , . . , , . . ,

mailto:alovsat_qaraca@mail.rumailto:depart8@iit.ab.az

27

[3]. -

, . , . , . , , . , .. , . . .

[4] (.. ), :

min)( XF , 0)( XG , maxmin XXX , ))(),...(),(()( 21 XgXgXgXG m

- , . , ,

KkfXff kkk ,1,)(maxmin .

. SX 0

, - F() . , . , .

, : , ; ; ; , - . , , , . :

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.

_______________________________________________________________________________________

http://www.econindustry.org/SiteDocs/Cover-monitor.jpghttp://www.econindustry.org/SiteDocs/Cover-monitor.jpghttp://www.econindustry.org/SiteDocs/Cover-monitor.jpg

29

.

-1

.. , ..

, , ,

( ) AA . - .

,

.

: [ , , ] [],

[] . [

, ] []

.

, .

,

. , -

, ,

,

- . ,

, ,

, ,

: , ,

( , ), . ,

. , :

, , , -

, , .

. xA - , xB - ,

xAxBxAx

xAxBx

tBtBtA

&

. :

[] ,

[], - .. ,

, . [ ]

1

EIF-2011-1(3)-82/19/1

30

. [] :

,

- .

.. , .

____________________________________________________________________

-

.. , ..

-

,

[1-4].

H

)1,0(),()()( 2 xxuxAuxu , (1)

,0)0(

,0)1()1('

u

uu (2)

- , A - , -

- H , 1A H .

(1), (2).

[5] , (1),

(2) ,

.

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.

____________________________________________________________________

. . , .. e

033

2 xtxt guuDuuDLu (1)

)()0,(),()0,( 10 xuxuxuxu t . (2)

, (1), (2)

:

,1

1

1

)(1)(0

)(1)(0

)(1)(0

1

)(

22

2

22

22

22

22

22

RLRL

RWRW

RLRLRL

mm

m

m

uutc

uutc

uutcu

(3)

21 m . ,

)(xhuuLup

, (3),

.

____________________________________________________________________

32

-

..

gabil_aliyev@yahoo.com

,

- . -

-

, , ,

- .

:

-

- , :

)~~3](

)(

)(

3

21)[(3),(

~)()(2)(

0

0

0

000

a

Ga

Ga

ij

ijijijij

(1)

)( , )( )( :

max

min

0 12

1)

~(1

E

G,

)21)(1(

1)

~(1

maxmax

maxmin

0

E

a,

max

maxmin

0

max21

1)

~(

E (2)

- -

-

, :

max)()(0

10.

, )0( max (3)

0. )0( 0. )0(

- , ..

0 ; 1max. )( - -

, .. max . ,

)(.

, max0 ,

(3).

-

, :

)(12

)()()(

2

22

hEkp (4)

)(

mailto:gabil_aliyev@yahoo.com

33

)( kp , .

),( )(h )(E

, (4)

.

, ,

, . ,

.

.

, ,

.

,

.

. -

)(kp f

h

max0 , :

max

1

32

hkp (5)

- :

;

,

:

0)1()( QQ (6)

)(Q :

0)()( QQR 0 (7)

(7) ,

. 0 0)( QR

.

:

0)( QR (8)

-

. a

n - )1( n -

:

34

1

1

nn

n

nq

q (9)

nq 1nq -

n t n - )1( n - .

-

,

.

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)

C , ,)( yqypTy ,0,0 qp 0r

,][0,l ,],0[],,0[],,0[ lCrlACqlACp ],2

,0[,,,

F ,gfF 5],0[, RlCgf :

,0M ,

;,1|||,||,|,10],,0[|,||),,,,,(| RwvsulxuMwvsuxf (3)

|)||||||(|0),,,,,( wvsuwvsuxg (4)

35

)0,0,0,0(),,,( wvsu ],0[ lx

.R .

,,0),()())()(())()(( lxxyxrxyxqxyxp (5) (2). (5), (2)

[1,

2], ,

- ;......021

k

),(xyk

,k

1k ).,0( l

E .,.],0[3 lC

,||||3

0

0

)(

3

i

iyy ..

(2), 0

|||| sup- ].,0[ lC

{S |Ey ),,0(,0)()( lxxy i |{}3,0 Eyi y 0 y ),,0( l 0)()( Tyy ; )(y 0)( Ty ),,0( l

}.0)()( yy

,Sy sincos][ 3ryJ

).(sin)(sin)(=)(),(sin)(cos)(=)(

),(cos)(cos)(=)()(),(cos)(sin)(=)(

xxxrxTyxxxrxy

xxxrxpyxxxrxy

(5)

).,0( lx

,

kS ,Nk , ,Sy

: 1) )(xy 1k

),0( l ; 2) ;1)(sgnlim0

xyx 3)

,)2,0()( x ;),2()( x 4)

, (5)

: ,20 ;2)( kl ,=(0) ,,=)( knl

k 0 ,/2=(0) 0 ,/2=)( l

knk 1k ),/2,0((0) 1

1n kn

k 1k , },1{\k

(0) ),,/2[ (0)(0) ctgw -

,sin)0(sin)0()0() yywa

,cos)0(sin)0)(()0() yypwc

,cos)0(cos)0)(()0() Tyypwb

;sin)0(cos)0()0() Tyywd 5) )(x ),(x ),,0( lx ,2)12( m

m , m ...,,2,1,0m , ; 6) (i)

,0)0()0( yy (ii) ,0)0( y (iii) 0)0( y ,0)0()0( yy )2,0()( x

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) , ,

)0,( ,k

SR

,k

I .)(min,],[],0[

000xrrrMrMI

lxkkk

Nk ,

kC

,kC ,

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.

____________________________________________________________________

-

.. , .. ,

-

37

( ) ,

[1],

,

. [2]

- . ,

- , -,

.

),1,0(),()()21( xxyxyxxy (1) ),021()021(,0)0( yyy (2)

,)21()021()021( yyy (3)

).1()1( yay (4)

, , Ra , ,0 .0a

)1,0(2

L (1)-(4).

(1)

),021()021(,0)0( yyy ,)21()021(021 yyy

.121),21)(2(sin)()sin(

,210,)sin(),(

xxx

xxxy

(1)-(3), 0)1( y -

, -

......21

k

, ,0k

,...,3,2k ).4sgn(sgn1

: ,),,(1

kkkk

.0

1. 0a (1)-(4)

...,...21

k

0k

,2k ).2sgn(sgn1

0a i) ,2

(1)-(4) , 1

, ,k

2,3,...,=k

; ii) ,2 (1)-(4)

, 1

( ,

) , ,k

3,...,2,=k

; iii) ,42

(1)-(4) , 1

(

, ) , ,k

3,...,2,=k

, (1)-(4)

,

38

1 , ,

k 3,...,2,=k

; iv) ,4

(1)-(4) , 1

(

, ) , ,k

3,...,2,=k

, 1

,

2

( ,

) , ,k

4,...,3,=k

, (1)-(4)

, 1

, ,k

3,...,2,=k

.

3. r . ) 0a 0a ,1)(

k ,k

rkkk

xy,1

)}({ (1)-(4)

;)1,0(2

L ) 0a ,2)( m . ,

1

mm

rkkkxy

,1)}({

1) mri )0(,)

mmccmrii

,)1,0(2

L mriii ) )0(

mmcc

,)1,0(2

L

)1(),[()),1(())1((21

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.

____________________________________________________________________

,

.. , .. ,

-

, .

,

39

,0 ,)()(=)()())()(())()(())(( lxxyxxyxrxyxqxyxpxyr

(1)

0,=sin(0))(cos(0) ypy (2a)

0,=sin(0)cos(0) Tyy (2b)

0,=sin)()(cos)( lyply (2c)

0,=sin)(cos)( lTyly (2d)

C , ,)( yqypTy 0)(,0)(),( xqxxp

,][0,lx ],,0[,],,0[],,0[ lCrlACqlACp ,,, -

, ).,2(],2,0[,,

(1), (2)

]2,0[,0,0 rq [1], ]2,0[,0 r

[2], ),2(,0,0 r [3], ),2(,0 r

[4], ]2,0[ [5].

1. C - ),( xy

(1), (2)-(2). ],0[ lx

),( xy

.

)0(n )2(n n , -

(1), (2) 0 2 ),( ly

,),( lTy . , ),(),()( lylTyFr

-

,)\(1=

RC

n

n

.)0(,)),0(),0((01

nnnn

1. ),,( xy ),,0( l

.

:

.2),0(

),2,0[,2

0

0

Farctg

)(m ),,( xy ),0( l .

2. ).(01

,)],0(),0(( 1 nnn 1)( ns .

3. )(010

0),0( 0 y ,0

0),0( 0 yT ),2,0( 0),0( 0 y 2 .

0> , }{),(000 ),,( xy

),,0( l ),,(0xy

),,0( l .. )()(0 ss }{),(

000 .

4. )(01

)1()2( )()()1()2( ss .

12 , , (1) ,0)0()0()0( yyy (2) ,0 )0(y

40

,0)0( Ty (2), (2) ].2,0(

)(01

(1)

,0)0()0()0( yyy (2) ,0 )0(y

)0(Ty 0 ,(2), (2) 2,0 . )(i ),( xy

- ),0( l 0

.0

)(01

, , ,...,2,1, k

k (1), )0()0( yy

,0)0( y (2) ,0 ,0)0()0( Tyy (2), (2) ],2,0(

,

1.

5.

.)()())(,( 01

k

kis (3)

2. ,,

(1), (2)

.)(1=

nn ),(

)( xyn

),(n

2n 1n

),,0( l )()(

1xy

],2(0

, ),(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

-

.. , .. ,

),1,0(),(=)()()( xxyxyxqxy (1)

,)0()()0()(0000

ydcyba (2)

,)1()()1()(1111

ydcyba (3)

, )(xq

[0,1], 1,0,,,, idcbaiiii

, 01c

.0=,0=1111100000 cbdacbda (4)

0,010 (1)-(3) [1]

[2]. -

.

(1)-(3)

.0)1(),0()()0()(

),1,0(),(=

0000yydcyba

xxyxyxqxy

(5)

C (5) ,

0}{

nn

[1].

),( xy (1)

,)(0,,)(0,0000

baydcy

]1,0[x .

:

,0)1()1(11

ycya (3')

.0)1()1(11

yayc (3'')

(1), (2), (3') (1), (2), (3'') -

, -

1

}{nn

1

}{nn

, ...1100

011ca ...

1100 .0

11ca , ,0

11ca

,)0(11

caF ,00 ,0

11ca ,)0(

11acF ,0

0

,),1(

),1()(

y

yF

,)\(

0=

n

n

KK RC ),,( 1 nnnK },0{n 1 .

:

)(1,)(1,)(11

ycyam ,...,1,0),,(1

nTnnn

42

.1

, ( )

(1)-(3)

0.=)(1,)()(1,)(1111

ydcyba

, ( )

(. [2])

,=)(11

22

cdabcaG

,)(1,)(1,

)(1,)(1,=)(

11

11

ycya

yaycG

n

n

T1=

)\( RCT -

, n

},0{, Nnn

, .

.),()(

=)( 2

1

0

2

2

1

2

1 dxxym

ca

d

dG

(6)

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

..

aliyevrashid@hotmail.ru

1: zCzT , .

Tz

d

izF

2

1, 1: zCzDz ,

Tz

d

izF

2

1, 1: zCzDz ,

.

D D zF zF :

0k

k

k zazF , Dz ,

1k

k

k

z

bzF , Dz ,

Zkak , , Nkbk ,

T

k

k di

a

1

2

1, Zk ,

T

k

k di

b

1

2

1, Nk .

. (., ., [1, .5, C, 3 ]) ,

: dttftd TLLf log , , , Zkak ,

Nkbk ,

T

k

k dFi

a

1

2

1, Zk ,

T

k

k dFi

b

1

2

1, Nk , (1)

F F

zF zF Tz . , ,

F F T (1) .

N -

(1) .

Rba , h ( )[ ] ( )xhxh n = nxh xhnxh n sgn nxh .

mailto:aliyevrashid@hotmail.ru

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)

,0

;;sgnsgn 12,

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.

[2] E .C. Titchmarsh, On conjugate functions, Proceedings of the London Math. Soc.,

9 (1929), 4980.

[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.

3. . . .

. . 2005, . 50, . 158-161.

____________________________________________________________________

..

arzu.66@bk.ru

a

:

)3(),0(0),()0,(),()0,(

)2(),0()(),0(

)1(),0,0(

)),(),,(),,(),,(,,(),(),(

Tttutututu

xxxu

xTt

xtuxtuxtuxtuxtFxtuxtu

xxxx

xxxxxxxxxxtxx

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, (1)-(3)

),( xtu , ],0[],0[ T

, (1),

(1)-(3) .

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1

sin)(),(n

n nxtuxtu ,

]),0[,...;2,1(sin),(2

)(

0

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, ,

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22

sin)),((2

)(

]),0[,...;2,1( Ttn ,

mailto:arzu.66@bk.ru

53

,...)2,1(sin)(2

0

nnxdxxn

,

)),(),,(),,(),,(,,()),(( xtuxtuxtuxtuxtFxtu xxxxxx .

,

),0(;],0[ 52 WTC , , .

1. .., ..

.

, .-., 1, 2009, .5-17.

____________________________________________________________________

..

laleliyeva@box.az

- ,

, , ,

, ,

. , .

,

, , -

.

, .

.

, .

,

,

kHO

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

,

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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

.. , .. , ..

mexanika.bsu.az@mail.ru

,

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:mexanika.bsu.az@mail.ru

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.

____________________________________________________________________

. .

1919-bdu@mail.ru

)( 22 L

),,)((),)()(,(

),)()(,(),)()(,(),(),(),(

2121210

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t

k

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58

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sin, )( 1

)(

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)()( .

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2

2 L

,)()(4)(22)(

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11

)2(

1

2

0

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2

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,,21

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1

1

1

1

1, Ctt kkk

n

nk

n

nk

k

kk

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inf)(1 , )4(

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nk

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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 .

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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. ..

// . . 2006, .79, .6, . 803-824.

59

4. .., ..

// . -, .-. , 2012, 1, .78-85.

5. . . .:,.I, 1965, 630.,.II,1965,540 .

_____________________________________________________________________ ,

.. , ..

aahmadf07@rambler.ru, aygun_abbasova@bk.ru

, [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)

mailto:aahmadf07@rambler.rumailto:aygun_abbasova@bk.ru

60

)(A , ),( xKm

0x 1x , )( - ,

, )( - .

)3,0()( kk [2],[3]

, )(A , (4)

, , R ,

)()()( 1 A .

1. .. . // , ., 1964

2. .. .// , ., 1975

3. ..

- .//Elm v thsild KT-

nin ttbiqi Beynlxalq Konfransn Materiallar, Bak, 2004, sh.131

____________________________________________________________________

, -

..

aslanov.50@mail.ru

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.

____________________________________________________________________

-

.. , ..

aslanov.50@mail.ru

HLH ,,021 , H ,

-

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......21 n .

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0 , ..

n

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62

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dxds

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.

____________________________________________________________________

,

..

-

.

.

, .

:

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u

y

u

x

ua

t

u

2

2

2

2

2

2

2

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2

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u,u (2)

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2

2

2

2

22

2

2

zyxa

t

(3)

),z,y,x(gt

u,u

t

t|

0 (4)

63

, t=0, t=, . (3) (4)

, t t,

t=0, t=. :

1

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)

,