SaqarTvelos teqnikuri universiteti mecnierebis departamenti
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TEMPUS-1-2013-1-DE-TEMPUS -JPCR,
MathGeAr , (d.natroSvili, S.zazaSvili)
publikaciebi (sul - 3 saxelmZRvanelo, 1 monografia, 109 statia): saqarTveloSi: a) 3 saxelmZRvanelo; b) 20 statia; ucxoeTSi: a) 1 monografia. b) 38 statia (maT Soris impaqt-faqtorian JurnalebSi* -16 statia)
samecniero forumebis muSaobaSi monawileoba: a) saqarTveloSi - (wakiTxul iqna 49 moxseneba) ; b) ucxoeTSi - (wakiTxul iqna 18 moxseneba).
saerTaSoriso kavSirebi: 713
maTematikis departamentis TanamSromlebs samecniero urTierToba aqvT Semdegi qveynebis samecniero centrebTan: aSS, didi britaneTi, germania, safrangeTi, portugalia, italia, poloneTi, avstria, israeli, saberZneTi, ukraina, CexeTi, bulgareTi, sasomxeTi, pakistani.
sagranto dafinansebiT damuSavebuli samecniero-kvleviTi proeqtebi N# 1
# proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 1
drekadi struqturebis dinamikis maTematikuri modelebis gamokvleva srulad
SeuRlebuli Termo-meqanikuri da eleqtro-magnituri velebis gaTvaliswi- nebiT
№ FR/286/5-101/13 (31 marti, 2014 – 31 marti, 2017 ww) SoTa
rusTavelis erovnuli samecniero fondi
daviT natroSvili daviT natroSvili oTar Wkadua Tengiz buCukuri marex ivaniZe diana ivaniZe a) Termo-eleqtro-magnituri drekadobis Teoriis ganzogadebuli modelis farglebSi Camoyalibda maTematikuri sasazRvro, sakontaqto da Siga da zedapiruli bzarebis pirobebi. Camoyalibda amave amocanebis Sesabamisi klasikuri dinamikuri diferencial- uri gantolebisTvis dasmuli sawyis-sasazRvro amocanebi. ganxorcielda dasmuli dinamikuri amocanebis laplasis gardaqmna da moxda maTi dayvana kompleqsur parametrze damokidebul elifsur amocanebebze sixSirul areSi. gamoyvanilia Sesa- bamisi grinis forulebi. damtkicebulia erTaderTobis Teoremebi dinamikuri da elif- suri fsevdorxevis amocanebisTvis. b) grin-nagdis ganzogadebuli Termopiezoeleqtrobis modelisaTvis dadgenilia Sesabamisi amocanebis variaciuli formulireba sobolevis sivrceebSi da gaanalizebu- lia Sesabamisi sesqvilinearuli formebis Tvisebebi. kerZod, dadgenilia gordingis 714
tipis utolobebi.
N# 2 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 2
Kkrebadobis SeTanxmebuli Sefasebebi maRali rigis sxvaobebiT dazustebis meTodSi
xelSekrulebis nomeri FR/406/5-106/12
(15 aprili, 2013 – 15 aprili, 2016 ) SoTa
rusTavelis erovnuli samecniero fondi
givi berikelaSvili givi
berikelaSvili biZina
midodaSvili a) cvlad koeficientebiani elifsuri gantolebisaTvis dasmuli dirixles amocanis amosaxsnelad dafuZnebulia or safexuriani sasrul sxvaobiani meTodi. pirvel safexurze, 2 (
O h sizustis sxvaobian sqemis amonaxsniT vaxdenT am sqemis marjvena mxaris garkveul koreqcias. damtkicebulia koreqtirebuli sqemis amonaxsnis krebadoba ( ),
m O h m ∈ rigiT, Tu diferencialuri amocanis amonaxsni miekuTvneba m - maCveneblian sobolevis sivrces. b) ganxilulia konveqcia-difuziis samganzomilebiani amocana cvladi koeficiente- biT konveqciur wevrebTan. 7-wertilian Sablonze gansazRvrulia Sesabamisi or safexuriani sxvaobiani meTodi. damtkicebulia miaxloebiTi amonaxsnis
rigiT (2< 4
≤ ) krebadoba, Tu zusti amonaxsni miekuTvneba sobolevis m -maCveneblian sivrces.
g) puasonis gantolebisaTvis ganxilulia Sereuli sasazRvro amocana mesame gvaris da dirixles pirobebiT sazRvris sxvadasxva nawilze. miaxloebiTi amonaxsnis misaRebad SemoTavazebulia sasrul-sxvaobiani koreqciis meTodi. damtkicebulia miaxloebiTi amonaxsnis maRali rigiT krebadoba.
715
# 3 # proeqtis dasa- xeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 3
zogierTi arawrfivi arastacionaruli modelis
gamokvleva da ricxviTi amoxsna SoTa rusTavelis erovnuli samecniero fondis granti
# FR /30/5 – 101/12 (# 31/32 sagranto xelSekruleba, 2013–2016)
s. xaribegaSvili s. xaribegaSvili o. joxaZe, T. jangvelaZe, z. kiRuraZe
dasrulebuli proeqtis (etapis) Sedegebi (anotacia) kuTxovan areSi uwyvet funqciaTa klasSi talRis gantolebisaTvis xarisxovani arawrfivobiT Seswavlilia erTi sasazvro amocana dirixles da neimanis pirobebiT aramaxasiaTebel mzidebze. dadgenilia pirobebi amocanis monacemebze, romlebic uzrunvelyofen globaluri amonaxsnis arsebobas da erdaTerTobas. ganxilulia agreTve lokaluri da feTqebadi amonaxsnis arsebobis sakiTxebi. erTi paraboluri tipis arawrfivi integro–diferencialuri gantolebisaTvis Seswavlilia sawyis – sasazRvro amocanis amonaxsnis arsebobis, erTaderTobisa da asimptoturi yofaqcevis sakiTxebi. agebulia Sesabamisi sxvaobiani sqemebi da Catarebulia ricxviTi eqsperimentebi.
FF N# 4
# proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 4
integraluri opera- torebi da sasazRvro amocanebi axal funqciursivrceebSi; furies analizisa da veivletebis Teoriis axali aspeqtebi
xelSekrulebis nomeri D/13-23
(20 dekemberi, 2012 – SoTa rusTavelis erovnuli samecniero fondi r. gewaZe da v. kokilaSvili a.mesxi
l.efremiZe S.tetunaSvili T. tetunaSvili T. TevzaZe i. nanobaSvili
716
20dekemberi, 2015) a)dadgenilia aucilebeli da sakmarisi pirobebi wonaze, romlisTvisac woniani dadebiTguliani integraluri operatori SemosazRvrulia/ kompaqturia cvladmaCveneblian lebegis
sivrceebSi. miRebulia aRniSnuli operatoris arakompaqturobis zomis ormxrivi Sefasebebi. napovnia aucilebeli da sakmarisi pirobebi wonebze romlebic uzrunvelyofs guliani operatoris SemosazRvriulobasa da kompaqturobas wonian amalgam sivrceebSi cvladi maCveneblebiT. aRniSnuli sivrceebi moicavs e.w. vineris amalgamebs. miRebuli Sedegebi axalia mudmivmaCvenebliani amalgam sivrceebisaTvisac. amoxsnilia kvalis amocana potencialebisaTvis amalgam sivrceebSi cvladi maCveneblebiT. srulad aRwerilia erTwoniani utoloba hardi-litlvudisa da wiladuri maqsimaluri operatorebisaTvis aRniSnul sivrceebSi. b)amoxsnilia kvalis amocana mravladwrfivi risis potencialebisa da Sesabamisi wiladuri maqsimaluri operatorebisaTvis. dadgenili piroba wonaze gamWvirvalea da d. adamsis tipisaa. g) miRebulia orwoniani Sefasebebi naxevradwrfivi integraluri operatorebisaTvis cvladmaCveneblian lebegis sivrceebSi. aRniSnuli Sedegebi moicavs kalderon-zigmundis singularul integralebs, oscilatorul singularul integralebs, hardi-litlvudisa da wiladur maqsimalur operatorebs, risis potencialebs da a.S, aRniSnuli tipis utolobebis miReba mniSvnelovania gamoyenebebis kuTxiTac.
N# 5 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 5
harmoniulianalizis, aproqsimaciisTeoriisa daintegraluropera- torTaTeoriisTaname- droveproblemebiaxal funqciursivrceebSi; gamoyenebebisasazRvro amocanebSi
xelSekrulebis nomeri 31/47
SoTa rusTavelis erovnuli samecniero fondi
l. efremiZe
v.kokilaSvili, a.mesxi S. tetunaSvili, v. paataSvili, c. canava, n. danelia
717
(15 aprili 2013 – 15 aprili 2016) a)dadgenilia modificirebuli maqsimaluri funqciebis, kalderon-zigmundis singularuli integralebisa wiladuri integraluri operatorebis SemosazRvruloba grand moris sivrceebSi. amocana Seswavlilia rogorc kvazimetrikul zomian sivrceebSi zomaze gaormagebis pirobiT, aseve e.w. araerTgvarovan sivrceebSi, sadac zomaze gaormagebis piroba SeiZleba ar sruldebodes. miRebuli Sedegebi gamoyenebulia zogierTi elifsuri kerZowarmoebulebiani diferencialuri gantolebis amonaxsnis regularobis Sesaswavlad. dadgenilia agreTve kvalis utolobis kriteriumebi wiladuri integralbisaTvis grand lebegis sivrceebSi. b)miRebulia dazusebuli erTwoniani Sefasebebi camxrivi integraluri operatorebisaTvis makenhaupris maxasiaTeblis terminebSi. Seswavlili operatorebi moicavs calmxriv hardi-litlvudisa da wiladuri maqsimalur funqciebs, aseve calmxriv riman-liuvilisa da veilis gardaqmnebs. analogiuri amocana Seswavlilia iseTi jeradi integraluri operatorebisaTvis, rogoricaa Zlieri maqsimaluri funqciebi, hilbertisa da risis gardaqmnebi namravliani gulebiT, namravlianguliani wiladuri integralebi da sxv.
N# 6 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 6
dinamikur sistemaTa Teoriis zogierTi sakiTxi granti 31-24. saangariSo periodi (15.04.2013---15.04.2014) SoTa rusTavelis erovnuli samecniero fondi givi giorgaZe givi giorgaZe, aleqsi kirTaZe, gogi fanculaia
718
1). naCvenebia, rom namravli topologiiTa da iamasaki-xaraziSvilis zomiT aRWurvili namdvil ricxvTa mimdevrobebis R ∞ sivrcisaTvis zomis Semnaxavi wrfivi izomorfizmebis jgufi aris sakmaod mdidari. xaraziSvilis midgomis saSualebiT, damtkicebulia rom yoveli usasrulo-ganzomilebiani polonuri wrfivi sivrceze SesaZlebelia ganisazRvros yvelgan-mkvrivi qvejgufis mimarT invariantuli borelis sigma-sasruli zoma. es Sedegi aZlierebs Sauderis bazisiT aRWurvili banaxis sivrceebisaTvis gillis( Gill), fanculaiasa da zaxaris( Zachary) mier adre miRebul Sedegs. naCvenebia, rom usasrulo-ganzomilebian polonur wrfiv sivrceze gansazRvruli arcerTi sigma- sasruli borelis zoma romelic Rebulobs erTis tol mniSvnelobas fiqsirebul kompaqtur simravleze da aris invariantuli yvelgan-mkvrivi qvejgufis mimarT, ar flobs erTaderTobis Tvisebas.absoluturad krebadi markuSeviCis bazisiani banaxis sivrceebze gansazRvruli konkretuli sigma-sasruli borelis zomis gasrulebisaTvis msgavsi amocana gadawyvetilia dadebiTad. erTaderTobis amocana absoluturad krebadi markuSeviCis bazisian banaxis X sivrceze gansazRvruli ara-sigma-sasrulo Zvrebis mimarT invariantuli borelis zomisaTvis romelic Rebulobs erTis tol mniSvnelobas standartul paralelepipedze wydeba uaryofiTad. damatebiT, agebulia magaliTi iseTi 0
µ zomisa X sivrceze, romelic flobs arsebiTi erTaderTobis Tvisebas amave zomis gansazRvris areze gansazRvruli Zvrebis mimarT invariantuli iseTi zomebis klasSi, romelTa mniSvnelobebi aragadagvarebul paralelepipedebze emTxvevian maT moculobebs. aseve agebulia usasrulo-ganzomilebiani standartuli da ordinaluri lebegis zomis analogebi absoluturad krebadi markuSeviCis bazisian banaxis X sivrceze. 2) . ganxilulia [A.L.Dawidowicz, A. Poskrobko, On chaotic and stable behaviour of the von Foerster- Lasota equation in some Orlicz spaces, Proc. Est. Acad. Sci., 57(2) (2008), 61–69] naSromSi ganxiluli foester-lasotas diferencialuri gantolebis erTi usasrulo-rigis ganzogadeba da miRebulia am gantolebis amonaxsenis warmodgena cxadi saxiT. mocemulia namravli topologiiT aRWurvil namdvil ricxvTa mimdevrobebis R ∞ sivrceSi Sesabamisi moZraobebis yofaqcevis aRwera ordinaluri da standartuli ”lebegis zomebis” terminebSi. 3) naCvenebia, rom TavisTavze mkvriv araTvlad aralokalurad kompaqtur polonur jgufze gansazRvruli yoveli Zvrebis mimarT invariantuli kvazi-finituri difuziuri borelis µ zomisaTvis ar arsebobs iseTi dadebiTi konstanta c romelic uzrunvelyofs
-ze meti µ -zomis mqone simravleSi iseTi sami wertilis arsebobas, romelTa mier gansazRvruli samkuTxedis farTobi 1-is tolia. es Sedegi uaryofiTad pasuxobs p.erdoSis mier [P. ErdЁos, Set-theoretic, measure-theoretic, combinatorial, and numbertheoretic problems concerning point sets in Euclidean space, Real Anal.Exchange, 4(2), (1978/79), 113–138] naSromSi dasmuli amocanis erT modifikacias. 719
4) ∞ R sivrceze gansazRvruli furies diferencirebadobis operatoris saSualebiT aRwerilia arsebiTad gansxvavebuli midgoma r. qarmiqaelis mier 1936 wels dasmuli Zveli funqcionaluri amocanis gadasaWrelad. ufro zustad, garkveul bunebriv SezRudvebSi, Cven vaxerxebT wrfivi araerTgvarovani usasrulo rigis mudmivkoeficientebiani diferencialuri gantolebis amonaxsenis cxadi saxiT Caweras. damatebiT, Cven vagebT Sesabamisi diferencialuri gantolebisaTvis invariantul zomas. amasTan Cven aRvwerT erT midgomas specialuri saxis araerTgvarovani usasrulo rigis mudmivkoeficientebiani diferencialuri gantolebis amosaxsnelad da aRvwerT am gantolebiT gansazRvruli moZraobis yofaqcevis daxasiaTebas lebegis zomis kerZo analogebis terminebSi. 5) ganxilulia liuvilis tipis Teoremebi, romlebic aRweren sxvadasxva fazuri moZraobebis yofaqcevas ∞
sivrceze gansazRvruli ordinaluri da standartuli “lebegis zomis” terminebSi. am mimarTulebiT ganxilulia Semdegi sami amocana: A) sxvadasxva funqcionalur sivrceSi lebegis zomis kerZo analogebis arsebobisa da erTaderTobis sakiTxi; B) sxvadasaxva funqcionalur sivrceSi diferencialuri gantolebebiT gansazRvruli dinamikuri sistemebis ageba; C) funqcionalur sivrceebze gansazRvruli sxvadasxva dinamikuri sistemisaTvis liuvilis tipis Teoremebis marTebulobis dadgena lebegis zomis kerZo analogebis terminebSi.
# 7 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 7
funqciebis zomadobis cnebis zogierTi modifikacia da maTi gamoyenebebi granti 31-25. saangariSo periodi 15.10.2013---15.04.2014 SoTa rusTavelis erovnuli samecniero fondi gogi fanculaia
gogi fanculaia, aleqsandre xaraziSvili, aleqsi kirTaZe, mariam beriaSvili 720
a) namdvil ricxvTa yvela mimdevrobebis sivrceSi agebulia sigma-sasrulo, metrikuli tranzitulobis Tvisebis (ergoduli) mqone, yvelgan mkvrivi qvesivrcis mimarT invariantuli, borelis zomis mimarT masiuri simravleTa ojaxi. aseTi simravleebis xarjze agebulia miTiTebuli zomis araseparabeluri gagrZeleba, romlis gasrulebac flobs erTaderTobis Tvisebas. b) Semotanilia aranulovani sigma-sasrulo borelis difuziuri µ zomiT aRWurvil metrikul sivrceze namdvil-mniSvnelobian funqciaTa zogierTi klasis cneba da Seswavlilia maT Soris urTierTmimarTeba CarTvis TvalsazrisiT. kerZod, naCvenebia, rom roca metrikuli sivrce
warmoadgens polonur sivrces, maSin µ -masiurobis Tviseba V - ze gansazRvruli uwyveti funqciebis traeqtoriebis gaswvriv eqvivalenturia µ - masiurobis Tvisebis V -ze gansazRvruli zomadi funqciebis traeqtoriebis gaswvriv. g) daxasiaTebulia yvela is komutatiuri jgufi, romlisTvisac arsebobs absoluturad arazomadi homomorfizmi namdvil ricxvTa aditiur jgufSi (an erTeulovan torSi). es daxasiaTeba emyareba komutatiuri jgufis perioduli nawilis struqturis aRweras. gamokvleulia araTvladi komutatiuri jgufebis iseTi homomorfizmebi, romlebsac aqvT paTologiuri deskrifciuli struqtura. dadgenilia, rom mTel rig SemTxvevebSi aseTi homomorfizmebis warmoSoba ganpirobebulia absoluturad nulzomadi araTvladi komutatiuri jgufebis arsebobiT. d) ganxilulia zomis Teoriisa da namdvili analizis zogierTi aqtualuri sakiTxi da Ria problema, romlebic uSualod dakavSirebulia zomis gagrZelebis zogad amocanasTan. naCvenebia, rom aRniSnul amocanas aqvs mravali aspeqti, kerZod, wminda simravlur- Teoriuli, algebruli da topologiuri. Seswavlilia dasmuli problemebis kavSirebi Tanamedrove simravleTa Teoriis damatebiT aqsiomebTan (kontinuumis hipoTezasTan, ganzogadebul kontinuumis hipoTezasTan, martinis aqsiomasTan, didi kardinaluri ricxvebis arsebobis aqsiomebTan).
# 8
# proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 8
Ffuries koeficientebi da krebadobis sakiTxebi xelSekrulebis nomeri №FR/223/5-100/13. (31 marti, 2014 – 31 marti, 2016 ww) SoTa
rusTavelis erovnuli samecniero fondi
LlerigogolaZe
LlerigogolaZe vaxtang cagareiSvili omar ZagniZe duglas ugulava 721
2014wels grantis TemasTan dakavSirebiT sCems mier Seswavlilia ori Semdegi sakiTxi: a)LlokaluradkompaqturabelisjgufebzegansazRvrulhaariszomiTintegrebadfunqciaTa furies integralebisspecialurisaSualoebiswertilovanikrebadoba. miRebuli Sedegebi ilustrirebulia magaliTebiT. Sedegebi moxsenebulia i. vekuas gamoyenebiTi maTematikis seminaris gafarToebul sxdomebze. Qqveyndeba statia seminaris moxsenebaTa krebulSi. b) lokalurad kompaqtur abelis jgufebze TiTqmis periodul funqciaTa furies mwkrivebis Sejamebadoba. miRebuli Sedegebi anzogadeben periodul funqciaTaTvis furies mwkrivTa Sejamebadob cnobil klasikur Sedegebs lokalurad kompaqturi abelis jgufebisaTvis. SedegebimoxsenebuliasaqarTvelosmaTematikosTa me-5 saerTaSorisokonferenciaze. GgamzadebuliastatiadasabeWdad.
# 9 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 9 maqsvelisgantolebaTa sistemaze dafuZnebuli zogierTi arawrfivi integro– diferencialuri modelis gamokvleva da ricxviTi amoxsna (CNRS / SRNSF2013, 04/26,2014-2016)
SoTa rusTavelis erovnulisamecnie ro fondi da safrangeTis samecniero kvlevebis erovnuli centri
T.jangvelaZe (saqarTvelosmxr idan)
f.heqti
(safrangeTismxr idan)
saqarTvelos mxridan: T. jangvelaZe z. kiRuraZe
safrangeTis mxridan: f. heqti o .pironau i. danaila dasrulebuli proeqtis (etapis) Sedegebi (anotacia)
ganxilulia difuziuri procesebis aRmweri arawrfivi diferencialuri da integro-diferencialuri modelebisaTvis dasmuli sawyis-sasazRvro amocanebis amonaxsnebis Tvisobrivi da struqturuli maxasiaTeblebi. integro- diferencialuri sistemebisTvis Seswavlilia sawyis-sasazRvro amocanebis amonaxsnebis arseboba, erTaderToba da asimptoturi yofaqceva, roca ∞ → t . agebuli da gamokvleulia naxevrad-diskretuli da diskretuli sqemebi. damtkicebulia algoriTmebis krebadobis Teoremebi. agebul algoriTmebze dayrdnobiT Seqmnilia programuli paketebi. Catarebulia Sesabamisi ricxviTi eqsperimentebi da maTi analizi. Seswavlilia rogorc erTganzomilebiani aseve organzomilebiani SemTxvevebi. ganxilulia adre Seswavlilze farTo klasis arawrfivobebi.
722
# 10 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis Semsruleblebi 10 SezRudvebiani logikuri progra-
mireba urango
Te- rmebze da maT mimdev- robebze aRweris
operatorebiT (DI/16/4-120/11, 2012-2015) SoTa rusTavelis erovnuli samecniero fondi T.kucia (iohan kepleris universiteti, linci, avstria), T.jangvelaZe (saqarTvelo s mxridan) T. kucia T. jangvelaZe x. ruxaia l. tibua g. WankvetaZe b. dundua g. miqanaZe s. fxakaZe dasrulebuli proeqtis (etapis) Sedegebi (anotacia)
Camoyalibebulia SezRudvebis gadawyvetadobis da amoxsnis procedura urango termebisTvis da maTi mimdevrobebisTvis, aRweris operatorebis gareSe. damtkicebulia proceduris gaCerebis, koreqtulobis da sisrulis Teoremebi.
# 11 # proeqtis dasaxeleba damfinansebeli organizacia proeqtis xelmZRvaneli proeqtis partniori universitetebi 11
maTematikis programebis modernizacia sainJinro da sabunebismetyvelo specialobebisaTvis: 543868-TEMPUS-1-2013-1- DE-TEMPUS -JPCR, MathGeAr 1.12.2013 - 1.12.2016 evrokavSiris (tempusis) granti
sergei sosnovski (saarbrukenis universiteti, germania) lionis
universiteti (safrangeTi), tamperes universiteti (fineTi);
saqarTvelos teqnikuri universiteti (Tbilisi): (daviT
natroSvili - proeqtis sakoordinacio bordis wevri, saqarTvelos jgufis
xelmZRvaneli; SoTa zazaSvili);
723
publikaciebi: a) saqarTveloSi saxelmZRvaneloebi # avtori/avtorebi saxelmZRvanelos saxelwodeba gamocemis adgili, gamomcemloba gverdebis raodenoba 1
z. qvaTaZe, a. kirTaZe, g. fanculaia maTematikuri statistika biznessa da ekonomikaSi informatikisa da marTvis sistemebis fakultetis eleqtronuli saxelmZRvanelo 246
anotacia gadmocemulia maTematikuri statistikisa da albaTobis Teoriis ZiriTadi principebi da moyvanilia maTi gamoyenebebi biznessa da ekonomikaSi 2
l. beriZe, r. gogiberiZe, n. kaWaxiZe MMMatlab-i studentebisaTvis q. Tbilisi, sagamomcemlo saxli `teqnikuri universiteti 274
ganxilulia gamoyenebiTi maTematikis Tanamedrove efeqturi programuli sistema Matlab-i (matrix laboratory), rogorc modelirebis mZlavri sistema. `Matlab -i studentebisaTvis~ gankuTvnilia yvela specialobis im studentebisa- Tvis, romelTa programaSic Sedis Matlab-i. igi gamoadgebaT magistrantebsa da doqtorantebs,romlebsac sxvadasxva amocanebis amosaxsnelad esaWiroebaT maTematikuri gamoTvlebis Catareba, grafika da a. S. aseve sxva dainteresebul saqarTvelos universiteti, quTaisis universiteti, baTumis
universiteti, erevnis sainJinro universiteti. dasrulebuli proeqtis (etapis) Sedegebi (anotacia)
muSavdeba maTematikis silabusebis modernizebuli versiebi sainJinro da sabunebismetyvelo specialobebis programebisaTvis. 724
pirebs. yvela paragrafi Sedgeba saWiro sacnobaro masalisagan, amoxsnili amocanebisa da mravalricxovani savarjiSo magaliTebisagan. 3
g. berikelaSvili, g. samsonaZe wrfivi algebrisa da diskretuli maTematikis elementebi Tbilisi 2014 „teqnikuri universiteti“ 404
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gamocemis adgili, gamomcemloba gverdebis raodenoba 1. S.Kharibegashvili, O.Jokhadze Boundary value problem for a wave equation with power nonlinearity in the angular domains
. Proc. A. Razmadze
Volume 164 ivane
javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis gamomcemloba, Tbilisi 116-120
(5) anotaciebi kuTxovan areSi arawrfivi talRis gantolebisaTvis gamokvleulia erTi sasazvro amocana dirixles da puankares pirobebiT aramaxasiaTebel mzidebze. ganxilulia globaluri amonaxsnis arsebobis, erTaderTobisa da ararsebobis sakiTxebi. Seswavlilia agreTve amocanis lokaluri amoxsnadoba da feTqebadi amonaxsnis arseboba. 2 V. Kokilashvili, A. Meskhi Some
fundamental inequalities for Proceedings of A. Razmadze Mathematical Tbilisi, Tsu-s 12
725
tri -gonometric poly -nomials and imbe -ddings of grand Besov spaces
Institute , 165
gamomcemloba Aanotacia dadgenilia bernSteinisa da zigmundis, aseve nikolskis tipis utolobebi grand lebegis sivrceebSi. miRebulia sivrcis meore parametris mniSvnelobebi aRniSnuli utolobebis marTebulobisaTvis. 3
V.Kokilashvili, A.Meskhi M.A. Zaighum On sharp weighted bounds for one–sided operators norms Proceedings of A. Razmadze Mathematical Institute , 164
Tbilisi, Tsu-s
gamomcemloba 9 Aanotacia miRebulia dazustebuli mudmivebi erTwonian utolobebSi calmxrivi integraluri operatorebisaTvis makehauptis maxasiaTeblis terminebSi. Sedegebi moicavs dazustebul Sefasebebs rogorc calmxrivi hardi- litlvudisa da wiladuri maqsimaluri operatorebisaTvis aseve cavlmxrivi rinam-liuvilisa da veilis gardaqmnebisaTvis.
4 Sh. Tetunashvili and T. Tetunashvili On coefficients of series with respect to the
Rademacher system,
Proceed- ings of A. Razma- dze Mathematical Institute
165
Tbilisi, Tsu-s
gamomcemloba 5 gv.
anotacia dadgenilia, rom 2 1
romelzedac rademaxeris mwkrivis krebadobis pirobebSi SesaZlebelia am mwkrivis koeficientebis aRdgena. amrigad dadgenilia iseTi Tvladi qvesimravlis arseboba, romelzec krebadoba uzrunvelyofs rademaxeris mwkrivis erTaderTobas. 5
Sh. Tetunashvili and T.
Tetunashvili
On divergent orthogonal series by the methods of summation with a variable exponent, Proceedings of A. Razmadze Mathematical 165
Tbilisi, Tsu-s
gamomcemloba 8 gv.
726
Institute anotacia Semotanilia cvladmaCvenebliani Sejamebadobis ramdenime axali meTodi. am meTodebisaTvis damtkicebulia Teoremebi orTogonaluri mwkrivebis ganSladobis Sesaxeb, riTac ganzogadebulia menSovis saTanado debuleba orTogonaluri mwkrivebis kerZo jamebis ganSladobis Sesaxeb. 6
M.Kintsurashvili An effective construction of the strong objective infinite-sample well-founded estimate
(2014), 113–119
Tbilisi, Tsu-s gamomcemloba 7 Aanotacia wrfiv erT-ganzomilebian stoqastur modelSi mocemulia sasargeblo signalis Zlierad obieqturi usasrulo-SerCeviTi Zaldebuli Sefasebis agebis efeqturi konstruqcia. 7
G.Pantsulaia, M.Kintsurashvili
An objective infinite sample well-founded estimates of a useful signal in the linear one- dimensional stochastic model
4
Tbilisi, Tsu-s gamomcemloba 9 Aanotacia
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