andria razmaZis maTematikis institutis 2008 wlis ...rmi.tsu.ge/geo/angarishi/angarishi2008.pdf · gogolauri, mecnier-TanamSromeli luiza SafaqiZe. programa # 7: “meqanikuri da eleqtromagnituri

andria razmaZis maTematikis institutis

2008 wlis

samecniero angariSi

2

Sinaarsi

Tavi 1. 2008 wlis sabiujeto samuSao programebi . . . . . . . . . . . . . 3

Tavi 2. samecniero grantebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Tavi 3. ZiriTadi samecniero Sedegebis mokle daxasiaTeba . . . . . . . 8

Tavi 4. 2008 wels Catarebuli samecniero konferenciebi . . . . . . . . 25

Tavi 5. 2008 wels gamoqveynebuli da gamosaqveyneblad gadacemuli naSromebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Tavi 6. 2008 wels sazRvargareT da saqarTveloSi gamarTul samecniero forumebze wakiTxuli moxsenebebi da moxsenebaTa Tezisebi . . . . . 27

Tavi 7. saerTaSoriso samecniero TanamSromloba . . . . . . . . . . . . . 28

Tavi 8. 2008 wlis sagamomcemlo saqmianoba . . . . . . . . . . . . . . . . . . 34

Tavi 9. damatebiTi informacia . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

danarTi 1. 2008 wels gamoqveynebuli da gamosaqveyneblad gadacemuli naSromebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

danarTi 2. 2008 wels sazRvargareT da saqarTveloSi gamarTul samecniero forumebze wakiTxuli moxsenebebi . . . . . . . . . . . . . . . 45

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andria razmaZis maTematikis institutSi aris cxra samecniero ganyofileba: algebris, maTematikuri logikis, geometria-topologiis, maTematikuri analizis, diferencialuri gantolebebis, maTematikuri fizikis, drekadobis maTematikuri Teoriis, Teoriuli fizikis, albaTobis Teoriisa da maTematikuri statistikis.

2008 wlis 31 dekembris monacemebiT institutSi iricxeba 70 mecnier-TanamSromeli, maT Soris 36 fizika-maTematikis mecnierebaTa doqtori (3saqarTvelos mecnierebaTa akademiis akademikosi da 2 wevr-korespondenti)da 31 fizika-maTematikis mecnierebaTa kandidatia.

Tavi 1. 2008 wlis sabiujeto samuSao programebi

2008 wels institutSi muSavdeboda 9 sabiujeto programa:

programa # 1: “homotopiuri algebris, K-Teoriis da kategoriaTa Teoriis zogierTi sakiTxi”programis koordinatori _ algebris ganyofilebis gamge, mTavari mecnier-TanamSromeli, akademikosi xvedri inasariZe;programis Semsruleblebi _ ufrosi mecnier-TanamSromeli Tamar daTuaSvili, ufrosi mecnier-TanamSromeli nikoloz inasariZe, ufrosi mecnier-TanamSromeli Tamaz kandelaki, ufrosi mecnier-TanamSromeli baCuki mesabliSvili, mecnier-TanamSromeli aleqsi paWkoria, mecnier-TanamSromeli dali zanguraSvili, mecnier-TanamSromeli emzar xmalaZe.

programa # 2: “intuicionisturi logikisa da modaluri sistemebis semantikuri analizi”programis koordinatori _ maTematikuri logikis ganyofilebis gamge, ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa kandidati leo esakia;programis Semsruleblebi _ ufrosi mecnier-TanamSromeli mamuka jiblaZe, mecnier-TanamSromeli nikoloz beJaniSvili, mecnier-TanamSromeli daviT gabelaia, mecnier-TanamSromeli dimitri pataraia.

programa # 3: “topologiur sivrceTa algebruli invariantebi da maTi gamoyenebani”programis koordinatori _ geometria-topologiis ganyofilebis gamge, ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori Tornike qadeiSvili;programis Semsruleblebi _ mTavari mecnier-TanamSromeli nodar berikaSvili, mTavari mecnier-TanamSromeli giorgi ximSiaSvili, ufrosi mecnier-TanamSromeli malxaz bakuraZe, ufrosi mecnier-TanamSromeli aleqsandre elaSvili, ufrosi mecnier-TanamSromeli vaxtang lomaZe, ufrosi mecnier-TanamSromeli samson sanebliZe, mecnier-TanamSromeli

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suliko xaJomia, mecnier-TanamSromeli zurab Todua, mecnier-TanamSro-meli manana miqiaSvili.

programa # 4: “integraluri da diferencialuri operatorebi banaxis funqciur sivrceebSi, arawrfivi analizis problemebi da gamoyenebebi kerZowarmoebulebian diferencialur gantolebebSi”programis koordinatori _ maTematikuri analizis ganyofilebis gamge,mTavari mecnier-TanamSromeli, saqarTvelos mecnierebaTa akademiis wevr-korespondenti vaxtang kokilaSvili;programis Semsruleblebi _ mTavari mecnier-TanamSromeli aleqsandre xaraziSvili, ufrosi mecnier-TanamSromeli laSa efremiZe, ufrosi mecnier-TanamSromeli vaxtang paataSvili, ufrosi mecnier-TanamSromeli omar ZagniZe, ufrosi mecnier-TanamSromeli givi xuskivaZe, ufrosi mecnier-TanamSromeli aleqsandre mesxi, mecnier-TanamSromeli eTer gordaZe, mecnier-TanamSromeli Saqro tetunaSvili, mecnier-TanamSromeli avTandil saginaSvili.

programa # 5: “aralokaluri da sawyisi amocanebi Cveulebrivi da hiper-boluri tipis kerZowarmoebulebiani gantolebebisaTvis”programis koordinatori _ diferencialuri gantolebebis ganyofilebis gamge, mTavari mecnier-TanamSromeli, akademikosi ivane kiRuraZe;programis Semsruleblebi _ mTavari mecnier-TanamSromeli sergo xaribegaSvili, ufrosi mecnier-TanamSromeli malxaz aSordia, ufrosi mecnier-TanamSromeli givi berikelaSvili, ufrosi mecnier-TanamSromeli jondo gvazava, ufrosi mecnier-TanamSromeli oTar joxaZe, mecnier-TanamSromeli giorgi kvinikaZe, mecnier-TanamSromeli sulxan muxigulaSvili, institutis direqtori nino farcvania.

programa # 6: “drekadobis Teoriis nawilobriv ucnobsazRvriani da sakontaqto amocanebi; filtraciis Teoriis sivrciTi RerZsimetriuli nawilobriv ucnobsazRvriani amocanebi da blanti arakumSvadi siTxis brunviT warmoqmnili reJimebi”programis koordinatori _ drekadobis maTematikuri Teoriis ganyofilebis gamge, mTavari mecnier-TanamSromeli, saqarTvelos mecnierebaTa akademiis wevr-korespondenti revaz bancuri;programis Semsruleblebi _ ufrosi mecnier-TanamSromeli sergei kukujanovi, ufrosi mecnier-TanamSromeli avTandil cicqiSvili, ufrosi mecnier-TanamSromeli nugzar SavlayaZe, mecnier-TanamSromeli lida gogolauri, mecnier-TanamSromeli luiza SafaqiZe.

programa # 7: “meqanikuri da eleqtromagnituri velebis urTierT-qmedebis araklasikuri amocanebi”programis koordinatori _ maTematikuri fizikis ganyofilebis gamge, mTavari mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori roland duduCava;programis Semsruleblebi _ ufrosi mecnier-TanamSromeli Tengiz buCukuri, ufrosi mecnier-TanamSromeli oTar Wkadua, mecnier-TanamSromeli avTandil gaCeCilaZe, mecnier-TanamSromeli daviT kapanaZe, direqtoris moadgile roland gaCeCilaZe.

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programa # 8: “kvanturi velebis Teoriisa da mis gamoyenebasTan dakavSirebuli maTematikuri amocanebis kvleva”programis koordinatori _ Teoriuli fizikis ganyofilebis gamge, ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori merab eliaSvili;programis Semsruleblebi _ mTavari mecnier-TanamSromeli vaxtang garsevaniSvili, ufrosi mecnier-TanamSromeli aleqsandre kvinixiZe, ufrosi mecnier-TanamSromeli giorgi lavrelaSvili, ufrosi mecnier-TanamSromeli giorgi ciciSvili, ufrosi mecnier-TanamSromeli giorgi jorjaZe, mecnier-TanamSromeli badri maRraZe, mecnier-TanamSromeli avTandil SurRaia, mecnier-TanamSromeli arsen xvedeliZe, mecnier-TanamSromeli zaqro giunaSvili.

programa # 9: “optimizaciisa da albaTur-statistikuri meTodebis gamoyeneba finansuri bazrebis semimartingalur modelebSi nawilobrivi informaciiT da finansuri riskebis marTva”programis koordinatori _ ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori Teimuraz toronjaZe;programis Semsruleblebi _ ufrosi mecnier-TanamSromeli nanuli lazrieva, albaTobis Teoriisa da maTematikuri statistikis ganyofilebis gamge, ufrosi mecnier-TanamSromeli mixeil mania, ufrosi mecnier-TanamSromeli Tengiz ServaSiZe, mecnier-TanamSromeli omar furTuxia, mecnier-TanamSromeli zurab cigroSvili.

Tavi 2. samecniero grantebi

(a) 2008 wels institutSi muSavdeboda saqarTvelos erovnuli samecnierofondis grantebiT dafinansebuli 11 samecniero Tema (amaTgan dasruldamuSaoba 6 Temaze):

proeqti # GNSF/ST06/3-002: “sasazRvro amocanebi usasrulo SualedSi araavtonomiuri Cveulebrivi diferencialuri gantolebebisaTvis” _ xelmZRvaneli: ivane kiRuraZe; ZiriTadi personali: malxaz aSordia, sulxan muxigulaSvili, zaza soxaZe, nino farcvania;

proeqti # GNSF/ST06/3-003: “intuicionisturi modaluri logikis semantika: algebruli da topologiuri modelebi” _ xelmZRvaneli: leo esakia; ZiriTadi personali: dimitri pataraia, mamuka jiblaZe, nikoloz beJaniSvili, daviT gabelaia, guram beJaniSvili;

proeqti # GNSF/ST06/3-004: “algebruli da topologiuri struqturebi homotopiur da kategoriul algebraSi, K-TeoriaSi da ciklur homologiaSi” _ xelmZRvaneli: xvedri inasariZe; ZiriTadi personali: malxaz bakuraZe, Tamar daTuaSvili, dali zanguraSvili, nikoloz inasariZe, Tamaz kandelaki, baCuki mesabliSvili, zaza omiaZe, aleqsi paWkoria, zurab janeliZe, emzar xmalaZe; damxmare personali: giorgi raqviaSvili, SoTa melaZe, dimitri CixlaZe, Tamar janeliZe;

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proeqti # GNSF/ST06/3-005: “maxasiaTebeli amocanebi arawrfiv hiperbolur gantolebaTa zogierTi klasisaTvis” _ xelmZRvaneli: jondo gvazava; ZiriTadi personali: sergo xaribegaSvili, givi berikelaSvili, oTar joxaZe, avTandil gagniZe, biZina midodaSvili;

proeqti # GNSF/ST06/3-007: “topologiur sivrceTa da fibraciaTa axali algebruli modelebi da maTi gamoyeneba homotopiis TeoriaSi” _ xelmZRvaneli: Tornike qadeiSvili; ZiriTadi personali: nodar berikaSvili, samson sanebliZe, suliko xaJomia;

proeqti # GNSF/ST06/3-010: “arastandartuli funqciuri sivrceebi da funqciebi da maTi gamoyeneba kerZowarmoebulebian diferencialur gantolebaTa TeoriaSi” _ xelmZRvaneli: vaxtang kokilaSvili; ZiriTadi personali: aleqsandre xaraziSvili, vaxtang paataSvili, givi xuskivaZe, aleqsandre mesxi, eTer gordaZe, Saqro tetunaSvili, aleqsi kirTaZe, cira canava;

proeqti # GNSF/ST06/4-050: “ZiriTadi mdgomareobis problema velis kvantur Teoriasa da kvantur statistikaSi” _ xelmZRvaneli: merab eliaSvili; ZiriTadi personali: giorgi jorjaZe, aleqsandre kvinixiZe, arsen xvedeliZe, giorgi ciciSvili, avTandil SurRaia, giorgi WavWaniZe, badri maRraZe, zaqro giunaSvili, giorgi lavrelaSvili.

proeqti # GNSF/ST07/3-169: “harmoniuli da arawrfivi analizis zogierTi sakiTxi araklasikuri dasmiT da maTi gamoyenebebi diferencialur gantolebebSi” _ vaxtang kokilaSvili (proeqtis samecniero xelmZRvaneli), vaxtang paataSvili (proeqtis menejeri), ZiriTadi personali: laSa efremiZe, aleqsandre mesxi, Saqro tetunaSvili, aleqsandre xaraziSvili, aleqsi kirTaZe;

proeqti # GNSF/ST07/3-172: “optimaluri marTvisa da statistikis martingaluri meTodebi finansur maTematikaSi” _ Teimuraz toronjaZe (proeqtis samecniero xelmZRvaneli da proeqtis menejeri), ZiriTadi personali: mixeil mania, nanuli lazrieva, Tengiz ServaSiZe, revaz TevzaZe, zurab cigroSvili;

proeqti # GNSF/ST07/3-174: “lis algebrebi da gansakuTrebulobaTa Teoria” _ giorgi ximSiaSvili (proeqtis samecniero xelmZRvaneli), aleqsandre elaSvili (proeqtis menejeri), grigori giorgaZe (ZiriTadi personali);

proeqti # GNSF/ST07/3-175: “kerZowarmoebulebiani diferencialuri gantolebebi hiperzedapirebze: garsTa Teoriis gantolebebi da maqsvelis sistema” _ roland duduCava (proeqtis samecniero xelmZRvaneli da proeqtis menejeri), ZiriTadi personali: daviT natroSvili, daviT kapanaZe, Tengiz buCukuri, oTar Wkadua, levan sigua.

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(b) 2008 wels institutSi muSavdeboda agreTve ucxouri grantebiTdafinansebuli 9 samecniero Tema:

INTAS Grant No. 05-1000008-8157: “Function spaces and their applications to partial differential equations”, v. kokilaSvili (xelmZRvaneli), a. mesxi, v. paataSvili, S. tetunaSvili.

INTAS Grant No. 06-1000017-8792: “Variable exponent analysis”, v. kokilaSvili(xelmZRvaneli), l. efremiZe, a. mesxi, v. paataSvili, S. tetunaSvili.

INTAS Grant No. 06 – 1000017 – 8609 “K-theory, Non-Commutative Geometry, Homology Theories, Operator and Normed Algebras”, 2007-2009, x. inasariZe (xelmZRvaneli).

INTAS Grant No. 05-1000008-7921 “Investigation of global catastrophes for nonlinear proces-ses in continuum mechanics”, j. gvazava (xelmZRvaneli), o. joxaZe.

INTAS Grant No. 06-1000017-9093 “Polynomial mappings algebra, computation and topology”, g. ximSiaSvili (xelmZRvaneli).

INTAS Grant No. 06-1000017-9258 “Testing space-time symmetry-braking in the early universe with the Cosmic Microwave Background and with sources of high frecuency radiation”, g. lavrelaSvili (xelmZRvaneli).

EPSRC EP/C014014/1,2006-2008 didi britaneTi, n. beJaniSvili.

GRDF/CRDF Grant No. GEP1-3339-TB-06 “Non-classical problems of fluid-elastic cusped plate (beam) interaction”, s. xaribegaSvili.

Royal Society Grant # 2005/ R4-JP, International Joint Project with Georgia:erToblivi qarTul-inglisuri kvleviTi proeqti “Boundary-domain integral equations with variable coefficients” _ o. Wkadua d. natroSvilTan da s. mixailovTan erTad anxorcielebda cvladi koeficientebis mqone sasazRvro ariTi (boundary-domain) integraluri gantolebebis Seswavlas.

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Tavi 3. ZiriTadi samecniero Sedegebis mokle daxasiaTeba

maTematikuri analizis ganyofileba

programa # 4: “integraluri da diferencialuri operatorebi banaxis funqciur sivrceebSi, arawrfivi analizis problemebi da gamoyenebebi kerZowarmoebulebian diferencialur gantolebebSi”programis koordinatori _ maTematikuri analizis ganyofilebis gamge, mTavari mecnier-TanamSromeli, saqarTvelos mecnierebaTa akademiis wevr-korespondenti vaxtang kokilaSvili.

damtkicebulia zomian kvazimetrikul sivrceebze gansazRvruli wiladuri integraluri operatoris (potencialebis) SemosazRvruloba moris sivrceebSi mudmivi maCveneblebiT. kerZod, dadgenilia kvalis utolobisa da xarisxovani wonebiT SemosazRvrulobis sakmarisi (zogierT SemTxvevaSi aucilebeli) pirobebi. ganzogadoebulia adamsisa da sobolevis Teoremebi [82], [147].

dadgenilia ergoduli maqsimaluri funqciebis, wiladuri da singularuli integralebis SemosazRvruloba wonian lorencis sivrceebSi cvalebadi maCveneblebiT [35].

gamokvleulia dirixles amocana smirnovis klasis harmoniuli funqciebisaTvis oradbmul areebSi aragluvi sazRvrebiT. warmoCenilia sazRvris geometriis gavlena amoxsnadobis pirobebze. aRmoCenilia, rom sazRvris kuTxian wertilebSi kuTxeebis garkveuli sidideebis SemTxvevaSi erTgvarovan amocanas SeiZleba gaaCndes aratrivialuri amonaxsnebi; dadgenilia wrfivad damoukidebel amonaxsnTa ricxvi [67].

dadgenilia borelis zomebis calmxrivi im maqsimaluri funqciebis erTaderToba, romlebic gansazRvrulia integralis niSnis qveS modulis gareSe [33].

gamokvleulia rimanis sasazRvro amocana analizuri funqciebisaTvis, roca sasazRvro pirobis koeficienti uban-uban uwyveti funqciaa, saZebn funqciaTa klasi ki _ koSis tipis integralTa klasia simkvriviT cvladmaCveneblian lebegis sivrcidan [92].

funqciur sivrceebSi, sadac Zvris operatori aRar aris uwyveti da maSasadame, klasikuri gagebiT, sigluvis modulis ganxilvas azri ekargeba, Semotanilia axali struqturuli maxasiaTbeli. miRebulia aRniSnuli maxasiaTeblis saukeTeso miaxloebebiT Sefasebebi. aRmoCenilia, rom ganzogadoebuli sigluvis modulis nulisaken krebadobis rigi damokidebulia aramarto trigonometriuli polinomebiT saukeTeso miaxloebis rigze, aramed sivrcis metrikazec [181].

Seswavlilia furies orTogonaluri mwkrivebis cvladi rigebiT Sejamebadobis sakiTxebi [194].

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dadgenilia invariantuli (kvaziinvariantuli) zomebis ergodulobis kriteriumebi; agebulia ergodulobis Tvisebis mqone araseparabeluri invariantuli zomebi [162].

gaxsnil karlesonis rkalebze amoxsnilia wrfivi SeuRlebis amocana uwyveti koeficientebiT cvladmaCveneblian funqciaTa sivrceebis CarCoebSi maSin, roca rkalis boloebs oscilebadobis garkveuli piroba edeba [42].

sasruli sigrZis gawrfevad wirebze gansazRvruli wiladuri integralisaTvis gamokvleulia SemosazRvrulobis pirobebi wiris geometriis gaTvalisiwnebiT [66].

gamokvleulia cvladmaCvenebliani hardis klasis funqciaTa mimdevrobebis krebadoba, ganzogadoebulia tumarkinis cnobili Teorema klasikuri hardis klasebis funqciaTa mimdevrobebisaTvis [86], [87].

zogadi TvalsazrisiT ganxiluli iyo nawilobrivi funqciebis gagrZelebis amocana Sesabamisi struqturebis (uwyvetoba, naxevrad uwyvetoba, zomadoba, beris Tviseba da maTi SesaZlo kombinaciebi) SenarCunebiT. gansakuTrebuli yuradReba daeTmo mravali cvladis nawilobriv funqciebs da simravlis nawilobriv funqciebs (karaTeodoris tipis, zomis tipis da sxv.). am tipis nawilobrivi funqciebis gagrZelebis dros gamoyenebulia zomadi seleqtorebis teqnika da zomaTa gagrZelebis marCevskis meTodi [56].

gamokvleuli iyo nulzomis simravleebis yofaqceva standartuli algebruli operaciebis mimarT. kerZod, dadginda, rom ori absoluturad (anu universalurad) nulzomadi simravlis algebruli jami SeiZleba iyos absoluturad arazomadi [57].

Semotanil iqna universaluri simravlis qvesimravleTa nebismieri ojaxis eiler-venis ganzogadebuli diagrama da damtkicebul iqna rigi Teoremebisa qvesimravleTa ojaxebis geometriuli realizaciebis Sesaxeb. saxeldobr, dadgenili iyo, rom evklidur sibrtyeSi arsebobs amozneqil kvazipoligonTa araTvladi damoukidebeli ojaxi. es faqti dayvanil iqna amozneqil funqciaTa garkveuli Tvisebis ganxilvaze (e.w. interferenciis Tviseba). naCvenebi iyo, rom arsebobs amozneqil funqciaTa araTvladi ojaxi, romelsac aqvs interferenciis Tviseba [58].

zomis gagrZelebis amocanasTan dakavSirebiT ganxiluli iyo kodaira-kakutanis cnobili meTodis arsebiTi modifikacia iseTi funqciebis terminebSi, romelTa grafikebi eqstremalurad masiuria. am terminebSi moxerxda banaxis cnobili problemis invariantuli versiis bolomde amoxsna [161].

naCvenebi iyo metrikuli tranzitulobis (anu ergodiulobis) mniSvnelovani roli aranulovani invariantuli zomis araseparabeluri gagrZelebis arsebobis dadgenaSi. moyvanilia aseTi gagrZelebebis agebis

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sruliad axleburi meTodi ergodiuli komponentebisa da ulamis matricis gamoyenebiT [162].

namdvilmniSvnelobiani safexura funqciebi gamokvleuli iyo zomis gagrZelebis zogadi amocanis konteqstSi. dadginda, rom am tipis funqciebi savsebiT xasiaTdeba zomis gagrZelebadobis TvisebiT. amave dros, naCvenebi iyo, rom analogiur Sedegs ara aqvs adgili invariantuli (an kvaziinvariantuli) zomebisaTvis [163]

sazRvargareTuli grantebiT Sesrulebuli samuSaoebi

INTAS-is #06-1000017-8792 grantiT Sesrulebuli samuSaoebis Sedegebi

dadgenilia ganzogadoebul analizur funqciaTa i. vekuaseul TeoriaSi gaCenili ganzogadoebuli koSis singularuli integralis TiTqmis yvelgan kuTxuri sasazRvro mniSvnelobebis arseboba, roca saintegro wiri nebismieri gawrfevadi wiria da simkvrive jamebadi funqciaa [91].

SemoRebulia cvladmaCvenebliani smirnovis klasebi da dadgenilia am klasis funqciaTa mTeli rigi Tvisebebi. ase magaliTad, puasonisa da koSis integraliT warmodgenadoba risis, smirnovisa da tumarkinis cnobili Teoremebis ganzogadoeba [86].

SemoRebulia cvladmaCvenebliani woniani lorencis sivrceebi, damtkicebulia maqsimaluri funqciis, singularuli da potencialuri operatorebis SemosazRvruloba zemoaRniSnul sivrceebSi [35].

ganzogadoebuli riman-liuvilis operatorebisaTvis kvalis utolobebSi dadgenilia dasaSvebi wonebis sruli aRwera cvladmaCveneblian lebegis sivrceebSi. aRniSnuli operatorebisaTvis da sivrceebisTvis dadgenilia kompaqturobis kriteriumebi [115].

dadgenilia erTgvarovani sivrcis SemosazRvrul simravleze gansazRvruli maqsimaluri funqciebis normiT SemosazRvruloba cvladmaCveneblian lebegis wonian sivrceebSi, roca wona makenhauptis tipisaa [84].

erTgvarovan sivrceze gansazRvruli woniani banaxis funqciuri sivrceebisaTvis arastandartuli zrdadobis rigiT damtkicebulia eqstrapolaciis Teorema, romelmac saSualeba mogvca erTbaSad dagvemtkicebina harmoniuli analizis iseTi operatorebis SemosazRvruloba zemoT aRniSnul sivrceebSi, rogoricaa singularuli da wiladuri integraluri operatori, furies multiplikatorebi, furies trigonometriul mwkrivTa kerZo jamebis maJorantebi, komutatorebi, fsevdodiferencialuri operatorebi, veqtoruli maqsimaluri da singularuli operatorebi da sxva [92], [79].

amoxsnilia uban-uban uwyveti koeficientebiT riman-hilbertis amocana koSis tipis integralTa wonian klasebSi, rodesac sazRvari uban-uban gluvia da integralis simkvrive cvladmaCvenebliani lebegis woniani

11

sivrcis elementia. miRebulia amoxsnadobis sruli suraTi, amoxsnadobis SemTxvevaSi amonaxsnebi agebulia efeqturad; gamovlenilia amoxsnadobis suraTze Semdegi parametrebis gavlena: sazRvris geometria, wonebis xarisxebis maCveneblebi, sivrcis cvladi maCveneblebis mniSvnelobebi kuTxian wertilebSi, koeficientebis wyvetebis naxtomebis sidideebi [84], [177].

INTAS-is #05-1000003-8157 grantiT Sesrulebuli samuSaoebis Sedegebi

dadgenilia aucilebeli da sakmarisi pirobebi, romlebic uzrunvelhyofen orwoniani utolobebis marTebulobas Zlieri maqsimaluri funqciebisaTvis, jeradi potencialebisa da singularuli integralebisaTvis [175].

erTgvarovan jgufebze gansazRvruli maqsimaluri funqciebisa da singularuli integralebisaTvis miRebulia arakompaqturobis zomebis Sefasebebi wonebiT [7].

TiTqmis monotonuri wonaTa wyvilisaTvis dadgenilia orwoniani Sefasebebis kriteriumebi maqsimaluri funqciebisa da singularuli integralebisaTvis cvladmaCveneblian lebegis sivrceebSi [143].

dadgenilia yvelgan krebadi trigonometriuli mwkrivebis jamebis struqturuli Tvisebebi [194].

harmoniuli funqciebisaTvis amoxsnilia dirixles amocana areebSi uban-uban gluvi sazRvrebiT cvladmaCvenebliani lebegis woniani sivrceebis simkvriviani koSis tipis integralTa klasebSi. gamokvleulia aris sazRvris geometriis, xarisxovani wonis maCveneblebisa da wiris kuTxian wertilebSi cvladi maCveneblis mniSvnelobebis gavlena amoxsnadobis suraTze [177].

diferencialuri gantolebebis ganyofileba

programa # 5: “aralokaluri da sawyisi amocanebi Cveulebrivi da hiper-boluri tipis kerZowarmoebulebiani gantolebebisaTvis”

programis koordinatori _ diferencialuri gantolebebis ganyofilebis gamge, mTavari mecnier-TanamSromeli, akademikosi ivane kiRuraZe.

fazuri cvladebis mimarT swrafad zrdadi arawrfivi diferencialuri sistemebisa [172] da meore rigis arawrfivi diferencialuri gantolebebisaTvis [77], rogorc rezonansul, ise ararezonansul SemTxvevebSi dadgenilia aralokalur sasazRvro amocanaTa amoxsnadobisa da koreqtulobis optimaluri sakmarisi pirobebi.

maRali rigis arawrfivi hiperboluri gantolebebisaTvis iterirebuli talRis operatoriT mTavar nawilSi dadgenilia darbus amocanis mravalganzomilebiani

12

variantebis globaluri amonaxsnis arsebobisa da ararsebobis sakmarisi pirobebi [62], [63].

zogadi saxis meore rigis wrfivi hiperboluri gantilebebisaTvis gamokvleulia ri-manisa da grini-adamaris funqciaTa zogierTi Tviseba. kerZod, dadgenilia maTi niSan-gansazRvrulobisa da garkveuli azriT simetriulobis pirobebi. moyvanilia am faqtebis zogierTi gamoyeneba arawrfiv kerZowarmoebulebian diferencialur gantolebaTa sasazRvro amocanebis TeoriaSi, damtkicebulia Sedarebis tipis Teorema [157].

talRis erTganzomilebiani arawrfivi gantolebisaTvis dadgenilia sawyis-maxasiaTe-beli da darbus pirveli amocanebis ganzogadoebuli da klasikuri, lokaluri da globaluri amonaxsnis arsebobisa da ararsebobis, erTaderTobisa da araerTader-Tobis sakmarisi pirobebi [156], [158].

regularuli grZeli talRis gantolebisaTvis dasmuli sawyis-sasazRvro amocanis amosaxsnelad agebuli da gamokvleulia sasrul sxvaobiani sqema. pirvel Sreze saZiebeli funqciis mniSvnelobebi gamoiTvleba orSriani sqemiT. yoveli axali SrisTvis miRebuli algebruli gantolebebi wrfivia saZiebeli funqciis

mniSvnelobebis mimarT. damtkicebulia sxvaobiani sqemis mdgradoba da 22 hO rigiT krebadoba, sadac da h badis bijebia [126].

biharmoniuli gantolebisaTvis gamokvleulia aralokaluri amocana integraluri pirobebiT da dirixles pirobebiT sazRvris nawilze. damtkicebulia amonaxsnis

arseboba da erTaderToba wonian sobolevis 12W sivrceSi [123].

sagranto proeqtebiT gaTvaliswinebuli samuSaoebi

meore rigis arawrfivi diferencialuri gantolebebisaTvis dadgenilia neimanis rezonansuli amocanis amoxsnadobis aucilebeli da sakmarisi pirobebi da garkveuli azriT optimaluri pirobebi, rac uzrunvelyofs am amocanis calsaxad amoxsnadobasa da koreqtulobas [168].

dadgenilia perioduli amocanis amoxsnadobisa da calsaxad amoxsnadobis optimaluri sakmarisi pirobebi maRali rigis araavtonomiuri wrfivi diferencialuri gantolebebisaTvis niSancvladi koeficientebiT [76].organzomilebiani wrfivi diferencialuri sistemebisaTvis damtkicebulia burling-borgis tipis Teorema aratrivialuri amonaxsnebis komponentebis nulebis raodenobis zemodan Sefasebis Sesaxeb [72] da optimalurad aris aRwerili perioduli amocanis amoxsnadobis zonebi [173].

aRwerilia klasi meore rigis araavtonomiuri, arawrfivi diferencialuri gantolebebisa, romelTac gaaCniaT kontinuumis simZlavris mqone periodul amonaxsnTa simravle [169].

araavtonomiuri arawrfivi diferencialuri sistemebisaTvis fazuri cvladebis mimarT swrafad zrdadi marjvena mxareebiT:

13

a) dadebiT naxevarRerZze ganxilulia sasazRvro amocana, romelic Seicavs komponentebze dadebul pirobebs rogorc sasrul wertilSi, aseve usasrulobaSi. SemoRebulia am amocanis koreqtulobis cneba garkveuli woniT da napovnia aragaumjobesebadi pirobebi, romlebic saTanadod uzrunvelyofen aRniSnuli amocanis amoxsnadobasa da koreqtulobas. garda amisa, dadgenilia amonaxsnebis globaluri Sefasebebi da gamokvleulia maTi yofaqceva usasrulobis midamoSi [171];

b) ganxilulia amocana namdvil RerZze SemosazRvruli amonaxsnis arsebobis Sesaxeb. damtkicebulia zogadi debuleba am amocanis amoxsnadobis Sesaxeb (e. w. aprioruli SemosazRvrulobis principi), SemoRebulia amave amocanis koreqtulobis cneba da napovnia efeqturi optimaluri pirobebi, romlebic saTanadod uzrunvelyofen mis amoxsnadobas, koreqtulobas da nebismieri amonaxsnis usasrulobaSi qrobadobas [170].

impulsur da ganzogadoebul diferencialur gantolebaTa sistemebisaTvis dadgenilia perioduli amonaxsnebisa da mTel RerZsa da naxevarRerZze SemosazRvruli amonaxsnebis arsebobis sakmarisi pirobebi [3]-[5], [112].

ganzogadoebuli da impulsuri wrfivi diferencialuri sistemebisaTvis miRebulia liapunovis azriT mdgradobis aucilebeli da sakmarisi pirobebi [113], [114].

meore rigis araavtonomiuri diferencialuri gantolebebisaTvis dadgenilia: e. w. gardamavali amonaxsnis arsebobis kriteriumi [188]; iseTi amonaxsnis arsebobis kriteriumi, romelic (an romlis warmoebuli) usasrulod Soreul wertilSi winaswar dasaxelebul mniSvnelobas Rebulobs [103]; wesieri amonaxsnebis rxevadobis aucilebeli da sakmarisi pirobebi [139].

wyarosa da disipatiuri wevrebis Semcvel arawrfiv talRis gantolebaTa zogierTi klasisaTvis dadgenilia darbus amocanebis globaluri da feTqebadi amonaxsnebis arsebobisa da erTaderTobis sakmarisi pirobebi da gamokvleulia amonaxsnebis sigluvis sakiTxi [164], [159], [165].

11 -ganzomilebiani kuburi arawrfivobis mqone klein-gordonis gantolebisaTvis

ganxilulia darbus pirveli amocana. oTx-wertilovan Sablonze agebulia mdgradi sasrulsxvaobiani sqema, romelic Sridan Sreze gadasasvlelad ar moiTxovs

damatebiT iteracias. damtkicebulia sqemis krebadoba 2hO rigiT, roca zusti

amonaxsni sobolevis 22W sivrces miekuTvneba [124], [125].

Seswavlilia sawyis-sasazRvro amocana rigis gadagvarebis mqone hiperboluri ganto-lebisaTvis, romelic aRwers wamaxvilebuli Zelis drekad mdgomareobas. sobolevis Sesabamis wonian sivrceSi damtkicebulia am amocanis koreqtuloba [150].

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maTematikuri fizikis ganyofileba

programa # 7: “meqanikuri da eleqtromagnituri velebis urTierT-qmedebis araklasikuri amocanebi”programis koordinatori _ maTematikuri fizikis ganyofilebis gamge, mTavari mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori roland duduCava.

gamokvleulia talRis difraqciis amocana 270 -iani kuTxis mqone waxnagovan usasrulo areSi dirixles, neimanisa da impedansis tipis sasazRvro pirobebiT. miRebulia amonaxsnis arsebobis, erTaderTobisa da regularobis Teoremebi beselis potencialTa sivrceebSi. dasrulda 2007 wels dawyebuli kvlevebi helmholcis gantolebisTvis dasmuli talRis difraqciis amocanebisTvis sxvadasxva konfiguraciis mqone areebisTvis. [21], [22], [25]-[28], [133].

gamokvleulia drekadobis Teoriis statikis Siga da gare sasazRvro amocanebi erTgvarovani hemitropuli sxeulebisaTvis, rodesac drekadi sxeulis sazRvris dadebiTi zomis nawilze an mTlianad mTel sazRvarze gaTvaliswinebulia xaxunis efeqti, romelic aRiwereba kulonis kanoniT. sivrciT da sasazRvro variaciul utolobebze ekvivalenturad dayvanis meTodiT Seswavlilia susti amonaxsnis arsebobis da erTaderTobis, agreTve monacemebze uwyvetad damokidebulebis sakiTxi [149].

grantiT Sesrulebuli samuSaoebi

drekad garsTa gantolebebi Caiwera samganzomilebiani drekadobis wrfivi gantolebebi mrudwirul koordinatebSi, metrikuli tenzoris deformacia mrudwirul koordinatebSi.Camoyalibda koreqtuli sasazRvro amocanebi samganzomilebiani dreka-dobisTvis, damtkicda kornis utoloba da lema xisti gadaadgilebis (kilingis veqtoruli velebis) Sesaxeb mrudwirul koordinatebSi. damtkicda sasazRvro amocanebis amonaxsnis arsebobisa da erTaderTo-bis Teoremebi.Seswavlilia hiperzedapirze metrikuli da simrudis tenzorTa deformacia, damtkicebulia kornis utoloba da Seswavlilia xisti gadaadgileba (kilingis veqtoruli velebi). Fdamtkicda fundamenturi amonaxsnis arseboba lames gantolebisaTvis hiperzedapirze.gamoyvanilia 2-ganzomilebiani wrfiv garsTa gantolebebi sisqis mimarT skalirebis saSualebiT, rac amzadebs niadags garsTa asimptoturi analizisaTvis rodesac sisqe miiswrafis nulisaken [29], [140].

maqsvelis gantolebebiCamoyalibda ZiriTadi sasazRvro amocanebi maqsvelis sistemisaTvis bianizotropul/qiralur garemoSi: talRis gabneva Ria zedapiris mier (Sereuli tipis amocanebi) Sesabamis sivrceebSi, amonaxsnis erTaderToba. gamokvleulia bianizotropul/qiralur garemoSi maqsvelis sistemis fundamenturi amonaxsnisa da Sesabamisi martivi da ormagi fenis potencialTa Tvisebebi. Gdamtkicebulia grinisa da amonaxsnis war-

15

modgenis formulebi da momzadebulia aparati potencialTa meTodis gamosayeneblad. sasazRvro amocanebi dayvanilia eqvivalentur sasazRvro fsevdodiferen-cialur gantolebebze da dadgenilia maTi fredholmurobis Tvisebebi. damtkicebulia sasazRvro fsevdodiferencialuri gantolebebis amo-naxsnTa arseboba funqciaTa ZiriTad sivrceebSi. maqsvelis sistema Caiwera giunterisa da stoqsis warmoebulebis meSveobiT da moxda misi zogierTi Tvisebis Seswavla (preprinti mzaddeba dasabeWdad).

helmholcis gantoleba areebSi aragluvi (kuTxovani) sazRvriT.Sesrulda mosamzadebeli samuSao kuTxovan da ukuqcevis wertilebian areebSi mocemuli helmholcis gantolebis gadasawerad erTeulovan wreSi konformuli asaxvis saSualebiT varSavskis Teoremis daxmarebiT. dasmulia koreqtuli amocanebi helmholcis gantolebisaTvis sasazRvro amocanebis kuTxovan areebSi. Ddasmuli amocanebi dayvanilia konformuli asaxvis saSualebiT eqvivalentur amocanaze erTeulovan wreSi.damtkicda helmholcis gantolebisaTvis ZiriTadi sasazRvro amocanebis amonaxsnis erTaderToba kuTxovan areebSi.damtkicda helmholcis gantolebisaTvis ZiriTadi sasazRvro amocanebis amonaxsnis arseboba kuTxovan areebSi (preprinti mzaddeba dasabeWdad).

Seswavlilia eleqtromagnituri harmoniuli, brtyeli talRebisTvis sakontaqto amocana, rodesac orTotropuli sxeuli Cadgmulia izotropul garemoSi. miRebulia amonaxsnis arsebobisa da erTaderTobis Teoremebi (preprinti mzaddeba dasabeWdad).

sasazRvro amocanebi bzarebis Semcveli keramikul_metaluri tipis kompozitebisTvisbzarebis Semcveli keramikul_metaluri tipis kompozitebisTvis dasmuli sasazRvro-sakontaqto amocanebi dayvanilia fsevdodiferencialur gantolebaTa sistemaze, damtkicebulia sasazRvro-sakontaqto amocanebis amonaxsnebis arsebobis da erTaderTobis Teoremebi, Seswavlilia amona-xsnebis asimptoturi Tvisebebi gansakuTrebuli wirebis midamoSi [101], [131].

mikrostruqturis mqone drekadi sxeulebis maTematikuri problemebis gamokvleva.variaciuli meTodebiT gamokvleulia drekadi hemitropuli sxeule-bisaTvis dasmuli statikis unilateruli amocanebi xaxunis gaTvaliswinebiT. damtkicebulia susti amonaxsnis arseboba da erTader-Toba [149].

drekadobis maTematikuri Teoriis ganyofileba

programa # 6: “drekadobis Teoriis nawilobriv ucnobsazRvriani da sakontaqto amocanebi; filtraciis Teoriis sivrciTi RerZsimetriuli nawilobriv ucnobsazRvriani amocanebi da blanti arakumSvadi siTxis brunviT warmoqmnili reJimebi”

16

programis koordinatori _ drekadobis maTematikuri Teoriis ganyofilebis gamge, mTavari mecnier-TanamSromeli, saqarTvelos mecnierebaTa akademiis wevr-korespondenti revaz bancuri.

Seswavlilia daZabul-deformirebuli mdgomareoba ubnobriv-erTgvarovani sibrtyisa, romelic Sedgeba myarad SeerTebuli, gansxvavebuli drekadi mudmivebis mqone ori orTotropuli kuTxis formis arisagan, romelTagan erT-erTs biseqtrisis gaswvriv aqvs Wrili, romelic kveTs gamyof sazRvars da gadis meore garemoSi. Wrilis sasrul nawilSi modebulia simetriuli normaluri Zala. amocana amoxsnilia kvadraturebSi da gamokvleulia Zabvebis xasiaTi gamyof sazRvarze da Wrilis boloSi [118]-[120].

agebulia idealuri siTxis dinebis Wavluri Teoriis nawilobriv ucnobsazRvriani sivrciTi RerZsimetriuli stacionaruli amocanebis amonaxsnebis moZebnis zogadi meTodi. idealuri siTxis dinebis Teoriidan amoxsnilia amocana siTxis nakadis mier dakavebuli iseTi arisaTvis, romelic nawilobriv aris SemosazRvruli myari siTxeSeuRwevadi zedapiriT da ucnobi Tavisufali zedapirebiT, romlebzedac damatebiT mocemulia mudmivi wneva [110], [111], [196], [197].

ganxilulia drekadobis Teoriis sakontaqto amocana ubab-uban erTgvarovani firfitisaTvis, romelic gamagrebulia gamyof sazRvarze gamavali CarTviT. amocana miiyvaneba integro-diferencialur gantolebaTa sistemaze ucnobi sakontaqto Zabvebis mimarT. miRebulia cxadi amoxsnebi zogierT konkretul SemTxvevaSi [108], [193].

miRebulia nebismieri sigrZis winaswar daZabuli orTotropuli cilindruli garsebis rxevis sistema da Sesabamisi amoxsnadi gantoleba. gantolebaTa sistema miRebulia garsebis Teoriis dazustebuli Tanafardobebidan. Gganxilulia winaswar daZabuli orTotropuli garsebis rogorc RerZsimetriuli, ise arasimetriuli sakuTari rxevebi. miRebuli gantolebebis safuZvelze gamomdinareobs rogorc cnobili, aseve zogierTi axali formula umciresi da praqtikulad yvelaze mniSvnelovani sixSiris gansazRvrisaTvis. Gganxilulia ricxviTi magaliTebi [93], [182].

Seswavlilia or mbrunav forovan cilindrs Soris siTxis dinebis mdgradobis amocana, rodesac dinebaze moqmedebs mudmivi transversaluri wnevis gradienti.Hhidrodinamikuri dinebebis bifurkaciis Teoria ricxviT meTodebTan erTad iZleva saSualebas mocemuli amocanisaTvis gamokvleul iqnas gadasvlebi siTxis dinebis rTuli reJimebisaken [107].

Seswavlilia optimaluri xvrelebis moZebnis amocana kvadratSi [151].

17

algebris ganyofileba

programa # 1: “homotopiuri algebris, K-Teoriis da kategoriaTa Teoriis zogierTi sakiTxi”programis koordinatori _ algebris ganyofilebis gamge, mTavari mecnier-TanamSromeli, akademikosi xvedri inasariZe.

gagrZelda lokalurad amozneqili algebrebis homotopiuri Tvisebebis Seswavla gluvi K-funqtorebis saSualebiT. damtkicda gluvi da algebruli K-funqtorebis izomorfizmi dadebiT ganzomilebebSi kvazi stabiluri freSes algebrebisaTvis, riTac dasturdeba karubis hipoteza freSes algebrebisaTvis [44], [155].

nebismieri interesis kategoriaSi misi nebismieri obieqtisaTvis Semotanilia universaluri, mkacri, zogadi aqtoris cneba, romelic SeiZleba ganvixiloT rogorc Sinagani avtomorfizmebis obieqti da romelic yovelTvis arsebobs zogadi interesis kategoriaSi. Seswavlilia misi Tvisebebi, dadgenilia misi arsebobis pirobebi,mocemulia misi konstruqcia da ganxilulia konkretuli magaliTebi [132].

agebuli da Seswavlili iqna Sinagani homologiis Teoria lis algebrebis jvaredini modulebis kategoriaSi. dadgenilia misi kavSiri lis algebrebis jvaredini modulebis Sevalei-eilenbergis homologiebTan grZeli zusti mimdevrobis terminebSi [204].

damtkicebulia, rom sasruli poliedris klasikuri n-uri homotopiisjgufi izomorfulia am poliedris bakis n-uri homotopiis jgufisa. garda amisa, damtkicebulia, rom yoveli proeqciuli naxevradmoduli naxevradrgolze valuaciiT arauaryofiT ricxvebSi Tavisufalia [206].

naCvenebia, rom SesaZlebelia racionaluri modulebis da komodulebis urTierTkavSirebis wminda kategoriuli aRwera, rac saSualebas iZleva es cnebebi ganzogaddes zogadi kategoriebisaTvis. miRebuli Sedegebi gamoyenebulia erTeulis mqone rgolze racionaluri modulebis Sesaswavlad. garda amisa, ganzogadebulia zogad bikategoriebze masuokas erT-erTi Sromis ZiriTadi Sedegi, romelic exeba mkacrad brtyeli homomorfizmiT gansazRvruli Sebrunebadi qvemodulebis monoidis aRweras. agreTve ganzogadebulia joialis da tirneis Sedegi efeqturi dawevis morfizmis Sesaxeb [201], [100]. asociuri algebrebis jvaredini modulebisaTvis agebulia hoxSildis da cikluri homologiebi. dadgenilia maTi Tvisebebi, miRebulia xuTwevra zusti mimdevrobebi da Cadgmis jvaredini modulis hoxSildis da cikluri homologiebisaTvis damtkicebulia amoWris Tviseba. kosameuliT warmoebuli funqtorebis saSualebiT ganmartebulia asociuri algebrebis jvaredini modulebis kosameuli cikluri homologia da grZeli zusti mimdevrobis terminebSi gamokvleulia misi kavSiri jvaredini modulebis ciklur homologiasTan. agebulia lis algebrebis meore araabeluri kohomologia da daxasiaTebulia gafarToebebiT [45].

18

Seswavlili iqna jvaredini algebrebi hoxSildisa da cikluri homologiebis TvalsazrisiT. jvaredini algebrisaTvis daiwera xuTwevrazusti mimdevrobebi, romlebic erTmaneTTan akavSireben hoxSildisa daciklur homologiebs dabal ganzomilebebSi. garda amisa, Tu ρ aris ineqcia, maSin dadginda aucilebeli da sakmarisi pirobebi, Tu rodis kmayofildeba amoWris aqsioma hoxSildisa da ciklurihomologiisaTvis jvaredini algebrebis kategoriaSi [203]. Seswavlilia sxvadasxva universalur-algebruli termuli aqsiomebis kategoriuli analogebi, romlebsac akmayofilebs yvela protomodularuli kategoria, da kerZod, jgufTa, rgolTa da sxva msgavs algebrul struqturaTa kategoria. zogierT SemTxvevaSi es aqsiomebi eqvivalenturia protomodularobis, da amgvarad moxerxda am kategoriebis garkveuli azriT wminda algebruli daxasiaTebebis povna, rac warmoadgens saintereso siaxles protomodularul kategoriaTa TeoriaSi. sxvaobiani kategoriebisTvis msgavsi Sedegebi (romelic miRebuli iyo 2007 wels) gamoyenebulia am kategoriebis erTi homologiuri Tvisebis dadgenaSi [130], [16], [17].

geometria-topologiis ganyofileba

programa # 3: “topologiur sivrceTa algebruli invariantebi da maTi gamoyenebani”programis koordinatori _ geometria-topologiis ganyofilebis gamge, ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori Tornike qadeiSvili.

dadgenilia maryuJTa sivrcis betis ricxvebis QSemousazRvrelobis kriteriumi [191].

Seswavlilia sasruli jgufebisTvis kompleqsurad orientirebuli kohomologiebi [8].

aRwerilia wrfivi dinamiuri sistemebi lokalurad integrebadi traeqtoriebiT [190].

Seswavlilia orientirebuli farTobi, rogorc funqcia saxsruli oTxkuTxedebis da xuTkuTxedebis konfiguraciul sivrceebze. damtkicebulia, rom aragadagvarebuli mravalkuTxedis SemTxvevaSi farTobis yoveli kritikuli wertili aragadagvarebulia. miRebulia kritikuli wertilebis raodenobis zusti Sefasebebi da gamoTvlis efeqturi meTodebi. Ddamtkicebulia agreTve, rom yoveli kritikuli konfiguracia wrewirSi Caxazvadia [2], [166].

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erovnuli samecniero grantebiT Sesrulebuli samuSaoebi

agebulia kojaWvur operaciaTa koSkebi, da maTi meSveobiT igeba kohomologiis Teoria braunis azriT. am Teoriis terminebSi mocemulia asaxvaTa postnikovis klasifikaciis Teoremebi [122].

adre agebuli modelis daxmarebiT damtkicebulia Teorema, rom Tu mocemuli sivrcis kohomologiebi polinomuri algebraa, maSin maryuJTa sivrcis kohomologiuri algebra aris gare, roca koeficientebi mTel ricxvTa rgolia, xolo mod 2 SemTxvevaSi maSin da mxold maSin aris gare, roca bazis kohomologiebze stinrodis pirveli operacia multiplikaturad daSladia. Aam Teoremis bolo nawili faqtiurad Seicavs borelis 1953 wels damtkicebuli Teoremis Sebrunebuls [191].

grZeldeba kvleva im pirobebis dasadgenad, roca mocemuli uwyveti asaxvis mier inducirebuli kohomologiuri homomorfizmis ganuleba iwvevs TviT asaxvis nulTan homotopiurobas. kerZod, erT-erT pirobaSi moxsnilia Zlieri SezRudva asaxvis formalurobaze [192].

gamoTvlilia transferis homomorfizmi sxvadasxva magaliTebisaTvis [8].

aRwerilia saxsruli mravalkuTxedis modulebis sivrcis gansakuTrebu-lobebi. gamoTvlilia binomur izolirebul gansakuTrebulobaTa lis algebrebi [64].


gamoTvlilia moravas Teoria metacikluri jgufebisTvis [8].

SemuSavebulia tensegritis tipis konstruqciis mdgradi konfiguraciebis raodenobis gamoTvlis efeqturi meTodi. aRwerilia saxsruli oTxkuTxedis wonasworobis konfiguraciebi sxvadasxva energiis funqciis mimarT [64].

maTematikuri logikis ganyofileba

programa # 2: “intuicionisturi logikisa da modaluri sistemebis semantikuri analizi”programis koordinatori _ maTematikuri logikis ganyofilebis gamge, ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa kandidati leo esakia.

agebulia ara–ailenberg–makleinis tipis umartivesi speqtrebis smeS–namravlis algebruli modeli sqver–jgufebis kategoriaze ori simetriuli monoiduri struqturis agebis meSveobiT [9].

20

am Sedegebze dayrdnobiT miRebulia rgolTa makleinis kohomologiis mesame jgufis elementTa interpretacia sqver–rgoluri gafarToebebis saSualebiT [10].

Semotanilia standartuli damtkicebadobis predikatis alternatiuli, polinomialurad gansazRvruli predikatebi da daxasiaTebulia Sesabamisi modaluri sistemebi [197].

Semotanili da gamokvleulia topologiur sivrceTa ramdenime klasi, romlebic Ria simravleTa meseris TvisebebiT axlos dganan aleqsandrovis sivrceTa klasTan. agebulia ramdenime madiskriminirebeli magaliTi am klasebis gansasxvaveblad da damtkicebulia am klasebs Soris zogierTi CarTvis faqti [198].

gamokvleulia namdvil ricxvTa sivrcis Caketviani algebris qvealgebraTa mier warmoqmnili modaluri sistemebi. naCvenebia, rom sasruli modelebis Tvisebis mqone logikebs Soris aseTi sistemebi emTxveva, erTi mxriv, raime gza–bmuli kvazidalagebis mier waroqmnil sistemebs, xolo meore mxriv, raime bmuli topologiuri sivrcis mier warmoqmnil logikebs [199].

gamokvleulia stounis sivrceebis modaluri logika zRvris operatoris terminebSi. naCvenebia, rom es logika emTxveva K4 modalur sistemas [200].

mocemulia zaxariaSCevis kanonikuri formulebis sruli algebruli daxasiaTeba [201].

topologiuri kripke freimebis terminebSi mocemulia solovais modaluri sistemis Tavisufali cikluri algebris sruli aRwera [36].

mocemulia profinituli haitingis algebrebis sruli algebruli, topologiuri da freimuli daxasiaTeba. kerZod, damtkicebulia, rom haitingis algebra profinitulia maSin da mxolod maSin, roca is izomorfulia imij–sasruli freimis yvela konusebis haitingis algebrisa [14].

mocemulia zaxariaSCevis kanonikuri formulebis sruli algebruli daxasiaTeba [129].

gansazRvrulia freimuli formulebi da mocemulia kriteriumi Tu rodis aris logika aqsiomatizebadi freimuli formulebiT. am kriteriumis gamoyenebiT damtkicebulia, rom yoveli lokalurad sasruli intuicionisturi logika aqsiomatizebadia iankov–de iongis formulebiT [13].

mocemulia gerCius Teoremis (niSimuras logikis yvela gafarToebas aqvs sasruli modelebis Tviseba) martivi damtkiceba. agreTve mocemulia niSimuras logikis yvela gafarToebis lokalurad sasrulobis kriteriumi [15].

21

albaTobis Teoriisa da maTematikuri statistikis ganyofileba

programa # 9: “optimizaciisa da albaTur-statistikuri meTodebis gamoyeneba finansuri bazrebis semimartingalur modelebSi nawilobrivi informaciiT da finansuri riskebis marTva”programis koordinatori _ ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori Teimuraz toronjaZe.

mocemulia optimaluri strategiis konstruqcia saSualo kvadratuli hejirebis amocanisTvis arasruli informaciis pirobebSi [99], [187]. Seswavlilia saSualo kvadratuli azriT robastuli hejirebisamocanebi arasruli finansuri bazrebisaTvis [95]. Magebulia parametris rekursiuli Sefasebis procedurebi semimartinga-luri statistikuri modelebisaTvis da Seswavlilia maTi zRvariTi yofaqceva [96]. kompensirebuli puasonis procesis funqcionalebisaTvis ganmartebulia sobolevis tipis sivrceebi da dadgenilia okone-hausman-klarkis formulaSi monawile integrandis cxadi saxe. puasonis xarisxovani funqcionalebisaTvis SemoRebulia sqoqasturi warmoebulis eqvivalen-turi ganmarteba, romelic ar iyenebs qaotur gaSlas [105]. dadgenilia, rom zog SemTxvevaSi binomuri ganawilebis maqsimaluri albaToba ar aRemateba missave muavr-laplasis asimptotikas da ganxilulia momijnave utolobebi [152].

erovnuli samecniero grantebiT Sesrulebuli samuSaoebi gamoyvanilia sargeblianobis maqsimizirebis da hejirebis amocanebis fasebTan dakavSirebuli Seqceuli stoqasturi diferencialuri gantolebebi semimartingaluri finansuri bazris modelisTvis da miRebulia am gantolebebis amoxsnadobis sakmarisi pirobebi [98], [186]. Seswavlilia robins-monros tipis stoqasturi diferencialuri gantolebebis amoxsnaTa da gasaSuloebul amoxsnaTa asimptoturiTvisebebi [184]. vineris procesis mravalganzomilebiani stoqasturad aragluvi funqcionalebisaTvis miRebulia stoqasturi integraluri warmodgena, dadgenilia integrandis cxadi saxe [104].

diskontirebuli jamebis veqtoruli analogisaTvis miRebulia centra-luri zRvariTi Teorema [109]. Ddadgenilia krebadobis versia perio-dulad cvalebadi madiskontirebeli operatorisaTvis [94]. miRebulia zRvariTi Teorema mimdevrobiTi mravaljeradi investiciisaTvis

22

markovul SemTxveviT garemoSi, rac horizontis zrdisas saSualo madiskontirebeli faqtoris fluqtuaciis Seswavlis saSualebasac iZleva am faqtoris ganawilebis markovuli gadarTvebisas ([94]).

Teoriuli fizikis ganyofileba

programa # 8: “kvanturi velebis Teoriisa da mis gamoyenebasTan dakavSirebuli maTematikuri amocanebis kvleva”programis koordinatori _ Teoriuli fizikis ganyofilebis gamge, ufrosi mecnier-TanamSromeli, fizika-maTematikis mecnierebaTa doqtori merab eliaSvili.

dabalganzomilebiani kvanturi velebis Teoriebi, integrebadi sistemebi da maTi gamoyeneba simebis Teoriisa da Zlierad korelirebuli eleqtronuli sistemebis aRsawerad. a) Catarebuli iqna SL(2,R)/U(1) koseturi modelis Hhamiltonuri reduqcia fadeev-jakivis meTodze dayrdnobiT da naCvenebi iqna, rom reducirebuli hamiltoniani emTxveva lagranJiseuli reduqciiT miiRebuli SL(2,R)/U(1)evkliduri Savi xvrelis modelis Hhamiltonians [12], [30].b) holis kvanturi sistemebisaTvis damaxasiaTebeli arakomutaciuri Tvisebebis gaTvaliswinebiT SemuSavebulia holis (ganivi) eleqtrodenis mikroskopuli Teoria. uwyvetobisa da haizenbergis moZraobis gantolebebze dayrdnobiT naCvenebia, rom SreTaSorisi spontanuri koherentoba warmoqmnis fazur dens. fazuri denis analizuri gamosaxulebebis gamoyenebiT miRebuli holis eleqtrodenis Teoriuli monacemebi karg TanxmobaSia sxvadasxva reJimSi mopovebul eqsperimentul monacemebTan [37], [38].

kvanturi velebis Teoriis arastandartuli formulirebebi da maTi gamoyeneba adronul da maRalenergetikul birTvul fizikaSi nambu-iona-lazinios modelSi Seswavlilia feradi zegamtarobis faza kvarkebis ori aromatis SemTxvevisaTvis. gamoyenebulia regularizaciis CamoWriTi da ganzomilebiTi meTodebi. gamoTvlilia kavSiri varskvlavebis masasa da radiuss Soris [43]. gamzomilebiTi regularizaciis meTodis gamoyenebiTGganxilulia nambu-iona-lazinios modeli sasruli temperaturebisaTvis mocemuli qimiuri potencialiT. Seswavlilia feradi zegamtarobis sakiTxic. miRebulia feradi da kiraluri simetriebis fazuri struqtura. Sedegebi Sedarebulia CamoWriTi regularizaciiT miRebul SedegebTan [49].SemuSavebulia sinaTlis frontis formalizmi Sedgenili sistemebisaTvis. Gganxilulia uspino da naxevarspiniani Semadgenlebis SemTxvevebi. Fformalizmi gamoyenebulia Sedgenili sistemis drekadi da Rrmad aradrekadi form-faqtorebis asagebad. Seswavlilia pionis form faqtoris asimptoturi yofaqceva didi gadacemuli impulsebis dros. naCvenebia, rom kvarkebis ganivi moZraobis gaTvaliswinebas mivyavarT biorkenis skaiingis darRvevamde.Gganxilulia Sedgenili sistemebis urTierTqmedebis sakiTxebi. kerZod, Seswavlilia SemadgenelTa urTierTgacvlis meqanizmi.Gganxilulia msubuqi birTvebis talRuri funqciebis relativizaciis sakiTxebi. experimentul monacemebTan

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Sedarebis gziT Semowmebulia relativisturi talRuri funqciebis masStaburi Tvisebebi [39].

erovnuli samecniero fondis grantebiT Sesrulebuli samuSaoebi

liuvilis Teoria zolze lorenciseuli signaturiTa da noimanis ganzogadoebuli sasazRvro pirobebiT.SemoTavazebuli iqna diskretuli speqtris, arekvlis amplitudisa da korelaciuri funqciebis gansazRvris axali meTodebi liuvilis sazRvriani TeoriisaTvis. es meTodebi dafuZnebulia verteqsuli operatoris sruqturaze da maTi efeqturoba Tavdapirvelad Semowmebuli iqna nawilakis dinamikis asaRwerad morsis potencialSi, sadac msgavsi operatoruli struqturaa. axali meTodikiT miRebuli Sedegebi ZiriTadad TanxvdenaSia `bootstrap’-is formalizmTan, Tumca dadgenili iqna SedegTa garkveuli gafarToebac, rodesac modelis parametrebi axlosaa kritikulTan. kerZoT, aseT SemTxvevebSi napovni iqna eqvidistanciur speqtrTa ramodenime (erTidan oTxamde) seria da arekvlis amplituda Sesabamisad iqna modificirebuli [30].

SL(2,R)/U(1) evkliduri Savi xvrelis modeli.am amocanis erT-erTi mTavari Sedegia ara-Tanadrouli komutatoris gamoTvla, romelic liuvilis Teoriis msgavsad kompaqtur da lokalur formiT moicema. aRsaniSnavia agreTve diskretuli speqtris gamoTvla modelis elifsur seqtorSi [121].

Seswavlilia holis orSriani sistemebis gaswvrivi gamtareblobis Tvisebebi. standartuli SemTxvevebSi gaswvrivi gamtarebloba nulis tolia, Tumca paraleluri magnituri velis Sedegad eqsperimentuli monacemebi miuTiTeben gaswvrivi gamtareblobis anomalur yofaqcevas. aseTi yofaqcevis aRsawerad SemuSavebulia egred wodebuli solitonuli meseris modeli. naCvenebia rom, am Teoriuli modelidan gamomdinare Sedegebi kargad eTanxmeba eqsperimentul monacemebs, rac modelis relisturobaze miuTiTebs [148].

ganxilulia intensiuri wrfivad polarizebuli monoqromatuli brtyeli talRis efetebi gadaxlarTuli spinebis precesiisaTvis sxvadassxva sawyisi mdgomareobebis SemTxvebvebisaTvis e.w. verneris mdgomareobebis CaTvliT [40], [47], [68], [144], [167].

naCvenebia, rom arsebuli sferuli protonis damasabuTebeli modelebi ar arian TanxmobaSi einSteinis specialur fardobiTobis TeoriasTan. naCvenebia, Tu rogor ganisazRvreba ganzogadoebuli partonuli ganawilebebi rodesac adronebi aRiwereba partonul Tavisuflebis xarisxebSi dinamiuri gantolebebiT. Seswavlilia lorenc invariantobis efeqtebi relativisturi Sedgenili kvarkuli modelis talRuri funqciisTvis. miRebuli iqna amonaxsni bolo xanebSi gamoyvanili vilsonis renormalizaciuri jgufis gantolebis birTvuli denis operatorebisaTvis. Aamonaxsni akmayofilebs modificirebul uord-takahaSis igiveobas romelic ar emTxveva Cveulebriv igiveobas magram uzrunvelyofs denis Senaxvas [183].

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Seswavlili iqna relativisturi nawilakis dinamika kovariantuli dakvantvis farglebSi da naCvenebi iqna am midgomis eqvivalentoba Sesabamisi reducirebuli sistemis geometriul dakvantvasTan.ganviTarebili iqna simis klasikuri konfiguraciebis agebis meTodi AdSsivrceebSi [121].

miRebulia kosmiuri mikrotalRuri gamosxivebis temperaturuli anizotropiis orwertilovani korelaciis funqcia (aradiagonaluri wevrebis gaTvaliswinebiT) nebismieraT orientirebul kosmologiur magnituri veliT sivrciTi izotropiis darRvevis SemTxvevaSi [52].

holis kvanturi sistemebisaTvis damaxasiaTebeli arakomutaciuri Tvisebebis gaTvaliswinebiT SemuSavebulia holis (ganivi) eleqtrodenis mikroskopuli Teoria. uwyvetobisa da haizenbergis moZraobis gantolebebze dayrdnobiT naCvenebia, rom SreTaSorisi spontanuri koherentoba warmoqmnis fazur dens. fazuri denis analizuri gamosaxulebebis gamoyenebiT miRebuli holis eleqtrodenis Teoriuli monacemebi karg TanxmobaSia sxvadasxva reJimSi mopovebul eqsperimentul monacemebTan [38].

25

Tavi 4. 2008 wels Catarebuli samecniero konferenciebi

2008 wlis 20 – 24 oqtombers Catarda andria razmaZis maTematikis institutis konferencia.gakeTda moxsenebebi:

a. elaSvili, lis algebrebi da gansakuTrebulobaTa Teoria

n. lazrieva, T. toronjaZe,

poliakis gasaSualebis procedura robins-monros tipis stoqasturi diferencialuri gantolebebisTvis

g. ximSiaSvili, mravalkuTxedebis konfiguraciuli sivrceebis topologiuri invariantebi

o. furTuxia, puasonis funqcionalebis stoqasturi warmoebulis Sesaxeb

m. mania, eqsponencialuri hejireba arasruli informaciis pirobebSi

g. bogveraZe, viner-hopfs plus hankelis operatorebis

Sebrunebadoba da fredholmuroba SemosazRvruli L

-simboloebiT g.lavrelaSvili, yalbi vakuumis daSlis aspeqtebi

o. Wkadua, eleqtrodrekadobis Teoriis Sereuli da bzaris tipis amocanebi

l. EefremiZe, matric funqciebis faqtorizaciis Sesaxeb

m. jiblaZe, analizis algebruli aRweris Sesaxeb (piter fraidis statiis mixedviT)

o. ZagniZe, ori cvladis funqciis gluvoba rimanis azriT

g. ciciSvili, arakomutaciuri geometriis elementebi hall-is kvantur sistemebSi

g. xaribegaSvili, zogierTi sasazRvro amocana arawrfivi hiperboluri gantolebebisaTvis

S. tetunaSvili, yvelgan krebadi trigonometriuli mwkrivebis jamebis Tvisebebis Sesaxeb

a.Mmesxi, kvalis utolobebis Sesaxeb maqsimaluri da potencialis operatorebisaTvis cvladmaCveneblian lebegis sivrceebSi

a. xaraziSvili, banaxis erTi problemis invariantuli versiis Sesaxeb

g.berikelaSvili, sxvaobiani sqemebi klein-gordonis gantolebisTvis darbus pirveli amocanis amosaxsnelad

j. gvazava, aralokaluri, arawrfivi maxasiaTebeli amocanis Sesaxeb

m. bakuraZe, maxasiaTebeli klasebi da moravas K-Teoriis rgolebi

b. maRraZe, quark-hadron dualobis koncepciis Semowmeba tau-leptonis daSlis monacemebis mixedviT

26

v. kokilaSvili, araerTgvarovan sivrceebze gansazRvruli maqsimaluri funqciebi da potencialebi arastandartul banaxis funqciur sivrceebSi

i. kiRuraZe, sasazRvro amocanebi usasrulo SualedSi araavtonomiuri diferencialuri sistemebisaTvis

r. duduCava, diferencialuri operatorebi hipersibrtyeebze da Txeli garsebis Teoria

r. gaCeCilaZe, a. gaCeCilaZe,

drekadobis Teoriis sasazRvro amocanebi hemitropuli sxeulebisaTvis xaxunis gaTvaliswinebiT

m. aSordia, sasazRvro amocanebi ganzogadoebuli wrfivi singularuli diferencialuri sistemebisaTvis

T. kandelaki, sasruli da grexvis bivariantuli K-Teoriebie. gordaZe, wrfivi SeuRlebis sasazRvro amocana karlesonis

tipis rkalisTvisv. kokilaSvili, v. paataSvili,

dirixles da neimanis amocanebi smirnovis klasis harmoniuli funqciebisaTvis

o. joxaZe, rimanisa da grini-adamaris funqciebis zogierTi Tviseba da maTi gamoyeneba arawrfiv gantolebebSi

T. ServaSiZe, zRvariTi Teoremebi damoukidebeli da pirobiTad damoukidebeli SemTxveviTi sidideebisaTvis

maTematikuri analizis ganyofilebam teqnikur universitetTan erTad Caatara saerTaSoriso konferencia International Workshop in Variable Exponents and Related Topics, Tbilisi, 2-5 seqtemberi.konferenciaze moxsenebebiT gamovidnen ganyofilebis TanamSromlebi: v. kokilaSvili “araerTgvarovan sivrceebze gansazRvruli modificirebuli maqsimaluri funqciebisa da wiladuri integraluri operatorebis SemosazRvrulobis sakiTxebi cvlad maCveneblian moris sivrceebSi’, a. mesxi „kvalis utolobebi wiladuri maqsimaluri da potencialuri

operatorebisaTvis xpL sivrceebSi“,

a.xaraziSvili “(amozneqil funqciaTa zogierTi ojaxis Sesaxeb“, v.paataSvili „analizur funqciaTa cvladmaCvenebliani hardisa da smirnovis klasebi“, l. efremiZe „diskretuli veiveletebis parametrizaciis Sesaxeb“, S. tetunaSvili “furies trigonometriul mwkrivTa Sejamebadoba cvalebadi rigebiT“.

maTematikuri logikis ganyofilebaSi Catarda saerTaSoriso konferencia International Workshop on Topological Methods in Logic. Tbilisi, June 3-5, 2008, http://rmi.acnet.ge/tolo/gakeTda moxsenebebi:

n. beJaniSvili. Bitopological duality for distributive lattices and Heyting algebras.l. esakia da d. gabelaia, Topological semantics of provability logic and related modal systems.m. jiblaZe. Almost Alexandroff topologies.

27

Tavi 5. 2008 wels gamoqveynebuli da gamosaqveyneblad gadacemuli naSromebi

2008 wels gamoqveynda institutis TanamSromelTa 111 naSromi (maT Soris 78 ucxour da 33 qarTul gamocemebSi) da gamosaqveyneblad gadaeca 85 naSromi (ix. danarTi 1).

Tavi 6. 2008 wels sazRvargareT da saqarTveloSi gamarTul samecniero forumebze wakiTxuli

moxsenebebi

2008 wels institutis TanamSromlebma miiRes monawileoba sazRvargareT gamarTul 44 samecniero forumSi (gakeTda 53 moxseneba) da saqarTveloSi gamarTul 5 samecniero forumSi (gakeTda 47 moxseneba). (ix. danarTi 2).

28

Tavi 7. saerTaSoriso samecniero TanamSromloba

v. kokilaSvili mivlinebuli iyo q. fraiburg-unstrutSi (germania) saerTaSoriso konferenciaSi monawileobis misaRebad 5 ivlisidan 12 ivlisamde. 22-28 agvistos mivlinebuli iyo q. helsinkiSi (fineTi) simpoziumsa da saerTaSoriso konferenciis muSaobaSi monawileobis misaRebad. 7-14 seqtembers mivlinebuli iyo q. arielSi (israeli) me-5 saerTaSoriso konferenciis muSaobaSi monawileobis misaRebad.

v. paataSvili mivlinebuli iyo q. fraiburg-unstrutSi (germania) saerTaSoriso konferenciaSi monawileobis misaRebad 5 ivlisidan 12 ivlisamde. 7-21 seqtembers mivlinebuli iyo q. arielSi (israeli) me-5 saerTaSoriso konferenciis muSaobaSi monawileobis misaRebad.

a. xaraziSvili mivlinebuli iyo lopotaSi (CexeTi) saerTaSoriso konferenciaSi monawileobis misaRebad 12 ianvridan 19 ianvramde.

l. efremiZe mivlinebuli iyo meri-landis universitetis sistemaTa kvlevis institutSi (aSS) erToblivi samecniero samuSaoebisaTvis 11 aprilidan 30 aprilamde. xolo 5 ivlisidan 12 ivlisamde mivlinebuli iyo q. fraiburg-unstrutSi (germania) saerTaSoriso konferenciaSi monawileobis misaRebad.

a. mesxi 15 ianvridan 15 martamde mivlinebuli iyo italiaSi, paduas universitetSi, sadac man aspirantebisaTvis waikiTxa leqciebis kursi. 20 martidan 23 maisamde da 5 oqtombridan 22 dekembramde igi agreTve imyofeboda lahoris (pakistani) samagistro da sadoqtoro programebis centrSi. man Seasrula erToblivi samecniero samuSao, moamzada sami erToblivi naSromi aRniSnul centrSi. a. mesxma waikiTxa leqciebi doqtorantebisTvis. 22-28 agvistos mivlinebuli iyo q. helsinkiSi (fineTi) simpoziumsa da saerTaSoriso konferenciis muSaobaSi monawileobis misaRebad.

S. tetunaSvili mivlinebuli iyo q. fraiburg-unstrutSi (germania) saerTaSoriso konferenciaSi monawileobis misaRebad 5 ivlisidan 12 ivlisamde. 22-28 agvistos mivlinebuli iyo q. helsinkiSi (fineTi) simpoziumsa da saerTaSoriso konferenciis muSaobaSi monawileobis misaRebad.

ivane kiRuraZe 1 ivnisidan 10 ivlisamde mivlinebuli iyo floridis teqnologiuri institutis (q. melburni, florida, aSS) maTematikis departamentSi, sadac amerikel kolegebTan erTad Caatara erToblivikvlevebi sasazRvro amocanaTa TeoriaSi. monawileoba miiRo arawrfiv analitikosTa me-5 msoflio kongresis muSaobaSi (q. orlando, 2-9 ivlisi), rogorc mowveulma momxsenebelma da TanaxelmZRvanelma seqciisa `sasazRvro amocanebi evoluciuri diferencialuri gantolebebisaTvis~.rogorc redkolegiis wevri TanamSromlobda ucxour samecniero JurnalebTan: “Boundary Value Problems”; “Electronic Journal of Qualitative Theory of

29

Differential Equations”; “Nonlinear Oscillations”; “Fasciculi Mathematici”; “Functional Differential Equations”; “Journal of Applied Mathematics, Statistics and Informatics”, xolo

rogorc recenzenti _ JurnalebTan: “Дифференциальные уравнения”, “Nonlinear Analysis”, “Mathematische Nachrichten”, “Mathematical and Computer Modeling”.

sergo xaribegaSvili TnamSromlobda JurnalTan “E. J. Qualitative Theory of Differential Equations”, rogorc recenzenti.

nino farcvania 2-dan 10 ivlisamde mivlinebuli iyo q. orlandoSi (florida, aSS), sadac monawileoba miiRo arawrfiv analitikosTa me-5 msoflio kongresis muSaobaSi rogorc mowveulma momxsenebelma. 3-dan 13 oqtombramde mivlinebuli iyo masarikis universitetis (q. brno, CexeTi) mecnierebaTa fakultetis maTematikisa da statistikis departamentze, sadac prof. z. doSlasTan erTad Caatara erToblivi kvleva diferencia-lur gantolebaTa oscilaciis TeoriaSi. amave departamentis seminarze diferencialur gantolebebSi waikiTxa moxseneba: `meore rigis arawrfiv diferencialur gantolebaTa rxevadi da ararxevadi amonaxsnebis Sesaxeb~. iyo saerTaSoriso konferenciis “CDDEA 2008 – Conference on Differential and Difference Equations and Applications 2008” (Strecno, Slovak Republic, June 23-27, 2008) saprogramo komitetis wevri. rogorc recenzenti, TanamSromlobda saerTaSoriso JurnalTan “Boundary Value Problems”. 2008 wlidan aris saerTaSoriso Jurnalis “Memoirs on Differential Equations and Mathematical Physics” asocirebuli redaqtori.

r. duduCava mivlinebuli iyo q. aveiroSi (portugalia) sadoqtoro disertaciis dacvis proceduraSi monawileobis misaRebad da aveiros, faros da lisabonis teqnikur universitetebSi erToblivi kvlevebis Casatareblad profesor f. o. SpekTan da profesor l. kastrosTanerTad. gaakeTa moxsenebebi seminarebze. 27 martidan 25 aprilamde. portugaliaSi yofnis periodSi 13-19 aprils r. dududCava gaemgzavra obervolfaxis (germania) maTematikur institutSi saerTaSoriso konferenciaSi Analysis of Boundary Element Methods monawileobis misaRebad. 20 ivlisidan 13 agvistomde mivlinebuli iyo viliamsburgis universitetSi (aSS) mecnieruli kvlevebisaTvis, gaakeTa plenaruli moxseneba saerTaSoriso konferenciaze IWOTA – 2008 (International Workshiop on Operator Theory and Applivcations). 14 noembridan 25 noembramde mivlinebuli iyo mexikos universitetSi (meqsika) samecniero muSaobisaTvis. gaakeTa plenaruli moxseneba saerTaSoriso konferenciaze “Toeplitz-Like Operators And Related Topics”, romelic miZRvnili iyo n. vasilevskis 60 wlis iubilesadmi.r. duduCava gaxda Jurnalis Integal Equations and Operator Theoy saredaqcio kolegiis wevri, dawera 7 recenzia msoflios wamyvan JurnalebSi gamosaqvynebel statiebze (Integal Equations and Operator Theoy, Mathematische Nachrichten, Arkiv for Rational Mechanics, Functional Analysis and Applications, Mathematical Analysis and Applications), dawera 14 referati referatuli JurnalebisaTvis (Mathematical Review, Zentralblatt fuer mathematik).

o. Wkadua mivlinebuli iyo londonSi samecniero muSaobisaTvis s. mixailovTan erTad 24 inavridan 24 Tebervlamde inglisis samefo

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sazogadoebis grantiT (UK Grant: # 2005/R4-JP of The Royal Society) gaTvaliswinebuli erToblivi kvlevisTvis.29 ivnisidan 5 ivlisamde mivlinebuli iyo q. romSi (italia) “la sapienzas” universitetSi, monawileoba miiRo v. mazias 70 wlisTavisadmimiZRvnil konferenciaSi ,,funqcionaluri analizi, kerZo warmoebuliani diferencialuri gantolebebi da maTi gamoyenebebi”.

d. kapanaZe miwveuli iyo portugaliaSi, aveiroSi, umaRles teqnikur institutSi 01.12.07-01.08.08. TanamSromlobda prof. l. kastrosTan eleqtromagnituri talRebis difraqciis sakiTxebSi.

n. SavlayaZe 22-27 seqtemberis monawileobda VI saerTaSoriso konferenciaSi `deformadi sxeulebis urTierTqmedebis dinamikis problemebi~, gorisi, somxeTi. gaakeTa moxseneba Àbout dynamic contact problem for bodies with elestic cover plate“. A

x. inasariZe aris ori saerTaSoriso eleqtronuli maTematikuri Jurnalis “Journal of Homotopy and Related Structures” da “Tbilisi Mathematical Journal”mTavari redaqtori, romelTa beWvdiTi versiebis dabeWdva daiwyeba 2009 wlidan Sesabamisad “College Publications, University of London”- is mier da “Amsterdam University Press”-is mier.

n. inasariZe mivlinebuli iyo santiago de kompostelas universitetSi (espaneTi) saerTo proeqtze samuSaod 14 aprilidan 15 maisamde, 6 ivnisidan 15 ivlisamde, 4 seqtembridan 7 oqtombramde da 17 noembridan 24 dekembramde. iyo Tanaorganizatori konferenciisa SECA V (V Seminar on Categories and Applications) , University of Vigo (Spain), September 10-12, 2008.monawileobda konferenciaSi International Conference on K-theory and Homotopy theory, University of Santiago de Compostela (Spain), September 15-20, 2008.

T. daTuaSvili mivlinebuli iyo santiago de kompostelas universitetSi (espaneTi) erToblivi samecniero kvlevebis Casatareblad 1 maisidan 30 ivnisamde, xolo 2 oqtombridan 1 noembramde mivlinebuli iyo bigos uni-ve-rsitetSi (espaneTi) erToblivi samecniero samuSaoebis Casatareblad.

d. zanguraSvili mivlinebuli iyo lesteris universitetSi (didi britaneTi) konferenciaSi monawileobis misaRebad 19-dan 27 ivlisamde.

e. xmalaZe mivlinebuli iyo santiago de kompostelas universitetSi (espaneTi) samecniero TanamSromlobisaTvis 4 seqtembridan 23 oqtombramde.xolo 24 noembridan 22 dekembramde mivlinebuli iyo vigos universitetSi (espaneTi) kvleviTi saqmianobisaTvis. monawileoba miiRokonferenciebSi SECA V (V Seminar on Categories and Applications) , University of Vigo(Spain), September 10-12, 2008 da International Conference on K-theory and Homotopy theory, University of Santiago de Compostela (Spain), September 15-20, 2008.

g. donaZe mivlinebuli iyo santiago de kompostelas universitetSi (espaneTi) samecniero TanamSromlobisaTvis 4 seqtembridan 23 oqtombramde da 28 noembridan 2009 wlis 1 ivlisamde. monawileoba

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miiRokonferenciebSi SECA V (V Seminar on Categories and Applications) , University of Vigo (Spain), September 10-12, 2008 da International Conference on K-theory and Homotopy theory, University of Santiago de Compostela (Spain), September 15-20, 2008.

T. qadeiSvili iyo direqtori sazafxulo skolisa “Mathematics, Algorithms and Proofs“, romelic Catarda 11-31 agvistos Teoriuli fizikis saerTaSoriso centrSi ICTP q. trieste (italia), waikiTxa leqciaTa cikli Operadic algebraic topology, teqsti ganTavsebulia misamarTze http://www.disi.unige.it/map/ictp/lectures_files/Kadeishvili_L.pdf.

2008 wels T. qadeiSvili airCies Teoriuli fizikis saerTaSoriso centris ICTP , trieste, italia, ufros asocirebul wevrad.

giorgi ximSiaSvili 12-15 Tebervals monawileobda INTAS-is proeqtis konferenciaSi naimexenSi, holandia. 22-25 ivniss monawileobda konferenciaSi suzdalSi, ruseTi “Differential equations and dynamical systems”. 12-19 noembers monawileonda sankt-peterburgSi gamarTul konferenciaSi.17 martidan 15 aprilamde mivlinebuli iyo naimexenis universitetSi (holandia) da kotbusis universitetSi (germania) konferenciaSi monawileobis misaRebad da saerTo gamokvlevebis Casatareblad.24 ivnisidan 7 ivlisamde mivlinebuli iyo moskovsa da sankt-peterburgSi (ruseTi) saerTaSoriso konferenciaSi monawileobis misaRebad.9 ivlisidan 26 ivlisamde mivlinebuli iyo amsterdamSi da utrextSi (holandia) saerTaSoriso konferenciis muSaobaSi monawileobismisaRebad.11 agvistodan 5 seqtembramde mivlinebuli iyo q. triestSi (italia) Teoriuli fizikis saerTaSoriso centrSi samecniero muSaobisaTvis.7-dan 19 noembramde mivlinebuli iyo q. sankt-peterburgSi (ruseTi) mecnieruli samuSaoebis Casatareblad.

a. elaSvili ianvar-TebervalSi imyofeboda vaicmanis institutSi (israeli) erToblivi muSaobisaTvis, miiRo monawileoba RonisZiebaSiEuropean School of Representation Theory, sadac gaakeTa moxseneba Lie Algebras and Singularities Theory. 1 ivnisidan 31 ivnisamde imyofeboda romis universitetSi, gaakeTa moxseneba About Index of Lie Algebras. ivlisSi imyofeboda bilefeldSi, germania, erToblivi muSaobisTvis vinbergTan erTad. noemberSi imyofeboda trentoSi, konferenciaze Grobner Basis,gaakeTa moxseneba Classification of exeptional nilpotents in simple Lie algebras. Semdgom 10 noembridan 10 dekembramde monawileoba miiRo trentoSi gamarTul konferenciaSi Computer algebra, gaakeTa moxseneba “Lie Algebras and Singularities Theory”.

m. bakuraZe mivlinebuli iyo amsterdamSi (holandia) maTematikosTa me-5 kongresze monawileobis misaRebad 13-dan 18 ivlisamde, gaakeTa moxseneba Transferred Chern classes and generalised cohomology rings.

m. jiblaZe mivlinebuli iyo naimexenis universitetSi (holandia) INTAS-is erToblivi proeqtis farglebSi gamarTul konferenciaSi monawileobis misaRebad 10-14 Tebervals.

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23-29 marts mivlinebuli iyo q. bonSi (germania) maqs plankis institutSi h. bauesisadmi miZRvnil konferenciaSi monawileobis misaRebad.

n. beJaniSvili mivlinebuli iyo lesteris universitetSi (didi britaneTi) leqciebis kursis wasakiTxad 30 ianvridan 1 aprilamde.5 maisidan 30 maisamde mivlinebuli iyo lesteris universitetSi (Pinglisi) kompiuterul mecnierebaTa departamentSi proeqtze samuSaod.8 ivnisidan 9 agvistomde mivlinebuli iyo lesteris universitetis kompiuterul mecnierebaTa departamentSi (inglisi) “Coalgebras, Modal Logic, Stone Duality” proeqtze samuSaod. 1 seqtembridan 20 oqtombramde mivlinebuli iyo did britaneTSi, londonis imperial kolejSi proeqtze “Order-topological and model-theoretic methods for modal logic” samuSaod.

d. gabelaia mivlinebuli iyo q. parizSi (safrangeTi) samuSao Sexvedraze moxsenebis gasakeTeblad 18 noembridan 25 noembramde, xolo 26 noembridan 30 noembramde q. stambulSi (TurqeTi).

g. beJaniSvili, m. jiblaZe da d.gabelaia 3-15 agvistos monawileobdnen q. hamburgSi (germania) sazfxulo skolis ESSLLI,08 muSaobaSi. waikiTxes leqciaTa ciklebi.

m. mania mivlinebuli iyo q. turinis (italia) universitetis samecniero seminarSi monawileobis misaRebad 12 Tebervlidan 27 martamde da 10 ivnisidan 25 ivlisamde.

n. lazrieva mivlinebuli iyo q. amsterdamSi (niderlandebi) sadoqtoro disertaciis dacvis proceduraSi monawileobis misaRebad, rogorc dacvis komitetis wevri 27 Tebervlidan 5 martamde.31 agvistodan 11 seqtembramde imyofeboda q. barselonaSi (espaneTi) statistikis meTodebisadmi miZRvnil konferenciis muSaobaSi monawileobis misaRebad.

T. ServaSiZe mivlinebuli iyo q. lilSi (safrangeTi) lilis mecnierebaTa da teqnologiebis universitetSi mecnieruli TanamSromlobisaTvis 29 Tebervlidan 29 martamde. gaakeTa moxseneba CLT for operator Abel summation lilis mecnierebisa da teqnologiebis universitetis albaTobisa da statistikis seminarze, 12 marti, 2008L(gamoqveynda preprintad PUB.IRMA Lille,2008,vol.68, V,7pp.; (with V. Tarieladze) .22-dan 25 maisamde mivlinebuli iyo q. baqoSi (azerbaijani) mecnierebaTa akademiis maTematikisa da meqanikis institutSi sadisertacio sabWos sxdomaze oponentad.9-13 seqtembers monawileobda azerbaijanSi kibernetikisa da informatikis problemebisadmi miZRvnil saerTaSoriso konferenciis muSaobaSi monawileobis misaRebad.

m. eliaSvili mivlinebuli iyo etore maioranas samecniero-kulturul centrSi (italia) msoflio laboratoriis sesiis muSaobaSi monawileobis misaRebad 19-26 agvistos da 16-20 dekembers. TanamSromlobda agreTve anesis Teoriuli fizikis laboratoriasa (safrangeTi) da mecnierTa saerTaSoriso federaciasTan (Sveicaria).

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g. jorjaZe mivlinebuli iyo berlinis humboltis universitetSi (germania) erToblivi samuSaoebis Casatareblad 10 martidan 31dekembramde.

g. ciciSvili TanamSromlobs tohokus universitetis nawilakebis fizikis da kosmologiis ganyofilebasTan (iaponia).

a. xvedeliZe mivlinebuli iyo q. dubnaSi (ruseTi) birTvuli kvlevis gaerTianebul institutSi erToblivi kvleviTi samuSaoebis Casatareblad 30 aprilidan 29 oqtombramde da 15 dekembridan 2009 wlis 15 martamde. TanamSromlobda agreTve plimutis universitetTan (didi britaneTi).

v. garsevaniSvili mivlinebuli iyo q. JenevaSi (Sveicaria) evropis birTvuli kvlevebis centrSi erToblivi kvlevebis Casatareblad 31 martidan 30 maisamde.

g. lavrelaSvili mivlinebuli iyo triestSi (italia) abdus salamis saxelobis Teoriuli fizikis saerTaSoriso centrSi erToblivi samuSaoebis Casatareblad 16 ivnisidan 21 agvistomde Dda parizSi (safrangeTi) kosmologiur koloqviumSi monawileobis misaRebad. TanamSromlobda agreTve a. ainStainis institutTan, golmi (germania).

a. kvinixiZe mivlinebuli iyo q. salonikSi (saberZneTi) aristoteles saxelobis universitetSi, saerTaSoriso konferenciaSi monawileobis misaRebad 12 ivnisidan 3 ivlisamde. mivlinebuli iyo q. iulixis (germania) samecniero centrSi erTobliv kvlevaSi monawileobis mizniT 15 ivli-sidan 15 oqtombramde. TanamSromlobda agreTve hiroSimas universitetTan (iaponia).

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Tavi 8. 2008 wlis sagamomcemlo saqmianoba

2008 wels gamovida:

Jurnalis “a. razmaZis maTematikis institutis Sromebi” sami tomi: 146,147 da 148.

“saqarTvelos maTematikuri Jurnalis“ me-15 tomis oTxi nomeri.

Jurnalis „memuarebi diferencialur gantolebebsa da maTematikur fizikaSi“ sami tomi: 43, 44, 45.

Tavi 9. damatebiTi informacia

a. xaraziSvils mieniWa n. musxeliSvilis saxelobis premia.

d. gabelaiam miiRo i. vekuas stipendia axalgazrda mecnierTaTvis da axalgazrda mecnierTa samecniero granti.

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danarTi 1

2008 wels gamoqveynebuli da gamosaqveyneblad gadacemuli naSromebi

a) 2008 wels gamoqveynebul naSromTa sia

1. M. Ashordia, On the solvability of a multipoint boundary value problem for systems of nonlinear generalized ordinary differential equations. Mem. Differential Equations Math. Phys. 43 (2008), 143-152.

2. M. Ashordia, On the solvability of the periodic type boundary value problems for linear systems of generalized ordinary differential equations. Mem. Differential Equations Math. Phys. 44 (2008), 133-142.

3. M. Ashordia, On the existence of bounded solutions for systems of nonlinear generalized ordinary differential equations. Mem. Differential Equations Math. Phys. 45 (2008), 127-132.

4. M. Ashordia, On the existence of bounded solutions for systems of nonlinear impulsive equations. Mem. Differential Equations Math. Phys. 45 (2008), 133-136.

5. M. Ashordia and Sh. Akhalaia, On the solvability of the periodic type boundary value problem for linear impulsive systems. Mem. Differential Equations Math. Phys. 44 (2008), 143-150.

6. M. Ashordia and G. Ekhvaia, On the solvability of a multipoint boundary value problem for systems of nonlinear impulsive equations with finite and fixed points of impulses actions. Mem. Differential Equations Math. Phys. 43 (2008), 153-158.

7. M. Asif and A. Meskhi, Weighted estimaters of a measure of non-compactness for maximal and potential operators. J. Inequal. Appl. 2008, Article ID 697407, 19 pages, doi:10.1155/2008/697407.

8. M. Bakuradze, Morava K-theory rings for the Modular groups in Chern classes. K-theory 38(2003), No. 2, 87-94.

9. H.-J. Baues, M. Jibladze and T. Pirashvili, Quadratic algebra of square groups. Adv. Math.217 (2008), No. 3, 1236-1300.

10. H.-J. Baues, M. Jibladze and T. Pirashvili, Third Mac Lane cohomology. Math. Proc. Cambridge Philos. Soc. 144 (2008), No. 2, 337-367.

11. G. Berikelashvili, O. Jokhadze and R. Koplatadze, On an approach to the analysis of asymptotic properties of solutions of first-order ordinary delay differential equations. (Russian) Differentsial’nye Uravneniya 44 (2008), No. 1, 19-38; English transl.: Differential Equations 44 (2008), No. 1, 19-39.

12. G. Berikelashvili, O. Jokhadze, B. Midodashvili, and S. Kharibegashvili, On the existence and absence of global solutions of the first Darboux problem for nonlinear wave equations. (Russian) Differentsial’nye Uravneniya 44 (2008), No. 3, 359-372; English transl.: Differential Equations 44 (2008), No. 3, 374-389.

13. N. Bezhanishvili, Frame Based Formulas for Intermediate Logics. Studia Logica 90 (2008), 139-159.

14. G. Bezhanishvili and N. Bezhanishvili, Profinite heyting algebras. Order 25 (2008), No. 3, 211-223.

15. G. Bezhanishvili, N. Bezhanishvili and D. de Jongh, The Kuznetsov-Gerciu and Rieger-Nishimura logics: The boundaries of the finite model property. Special Issue Dedicated to A.V. Kuznetsov, Logic Log. Philos. 17 (2008), 73-110.

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16. B. Bourn and Z. Janelidze, Pointed protomodularity via natural imaginary subtractions. Theory Appl. Categ. 21 (2008), 152-171.

17. B. Bourn and Z. Janelidze, Closedness properties of internal relations V: Linear Mal’tsev conditions. Algebra Universalis 58 (2008), 105-117.

18. T. Buchukuri and O. Chkadua, Mixed and crack-type boundary value problem in mindlin’s theory of piezoelectricity. Georgian Math. J. 15 (2008), No. 3, 3-22.

19. T. Buchukuri, O. Chkadua , D. Natroshvili and A.-M. Sändig, Interaction problems of metallic and piezoelectric materials with regard to thermal stresses. Mem. Differential Equations Math. Phys. 45 (2008), 7-74.

20. L. Castro, R. Duduchava and F.-O. Speck, Solvability of Singular Integro-Differential Equations with Multiple Complex Shifts. Compl. Anal. Oper. Theory 2 (2008), 327-343 (G. Litvinchuk's memorial volume; eds. N. Vasilevskii et al).

21. L. P. Castro and D. Kapanadze, Wave diffraction by a strip with first and second kind boundary conditions: the real wave number case. Math. Nachr. 281 (2008), No. 10, 1400-1411.

22. L. P. Castro and D. Kapanadze, The impedance boundary-value problem of diffraction by a strip. J. Math. Anal. Appl. 337 (2008), 1031-1040.

23. L. P. Castro, D. Kapanadze, Pseudo-differential operators in a wave diffraction problem with impedance conditions. Fract. Calc. Appl. Anal. 11 (2008), 15-26.

24. L. P. Castro and D. Kapanadze, Diffraction by a union of strips with impedance conditions in Besov and Bessel potential spaces. Math. Model. Anal. 13 (2008), No. 2, 183-194.

25. L. P. Castro and D. Kapanadze, On wave diffraction by a strip with variable face impedances. Operator Theory Adv. Appl. 181 (2008), 159-172.

26. L. P. Castro and D. Kapanadze, A boundary-transmission problem with first and second kind boundary conditions for the Helmholtz equation in Besov and Bessel potential spaces. Bull. Greek Math. Soc. 54 (2007), 79-96.

27. L. P. Castro and D. Kapanadze, Dirichlet-Neumann-impedance boundary-value problems arising in rectangular wedge diffraction problems. Proc. Amer. Math. Soc. 136 (2008), 2113-2123.

28. L. P. Castro and D. Kapanadze, Wave diffraction by a 45 degrees wedge sector with Dirichlet and Neumann boundary conditions. Math. Comput. Modelling 48 (2008), 114-121.

29. R. Duduchava and D. Kapanadze, Extended normal vector field and the Weingarten map on hypersurfaces. Georgian Math. J. 15 (2008), No. 3, 485-500.

30. P. Dorn and G. Jorjadze, Operator approach to boundary Liouville theory. Ann. Physics 323(2008), 2799-2839.

31. D. E. Edmunds, V. Kokilashvili and A. Meskhi, One-sided operators in Lp(x) spaces. Math. Nachr. 281(2008), No. 11, 1525-1548.

32. E. Elerdashvili, M. Jibladze and G. Khimshiashvili, Cyclic configurations of pentagon linkages. Bull. Georgian Nat. Acad. Sci. (New Series) 2 (2008), No. 4, 28-31.

33. L. Ephremidze and N. Fujii, On the uniqueness of the one-sided maximal functions of Borel measures. J. Math. Soc. Japan 60 (2008), 695-717.

34. L. Ephremidze, G. Janashia and E. Lagvilava, An analytic proof of the matrix spectral factorization theorem. Georgian Math. J. 15 (2008), No. 2, 241-249.

35. L. Ephremidze, V. Kokilashvili and S. Samko, Fractional, maximal and singular integral operators in variable Lorentz spaces. Fract. Calculus and Appl. 11 (2008), No. 4, 407-420.

36. L. Esakia and G. Grigolia, Formulas of one propositional variable in intuitionistic logic with the Solovay modality. Special Issue Dedicated to A.V. Kuznetsov, Logic Log. Philos. 17(2008), 111-127.

37. Z. F. Ezawa, K. Ishii and G. Tsitsishvili, Interlayer phase coherence and dissipative soliton-lattice regime in bilayer quantum Hall systems. Physica E 40 (2008), 1557.

38. Z. F. Ezawa, K. Ishii and G. Tsitsishvili, Anomalous diagonal resistivity and soliton lattice in bilayer quantum Hall systems. Physica B 403 (2008), 1517.

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39. V. Garsevanishvili, A. Khelashvili, Z. Menteshashvili and M. Nioradze, Light front formalism for composite systems and some of its applications in particle and relativistic nuclear physics. Phys. Rep. 458 (2008), 247.

40. V. Gerdt, A. Khvedelidze and Y. Palii, Light-cone Yang-Mills mechanics: SU(2) vs. SU(3). Theoret. Math. Phys. 155 (2008), 557-566.

41. R. P. Gilbert, G. Jaiani, S. Kharibegashvili, D. Natroshvili, and N. Chinchaladze, Existence and uniqueness theorems for cusped prismatic shells in the Nth hierarchical model. Math. Methods Appl. Sci. 31 (2008), No. 11, 1345-1367.

42. E. Gordadze, One theorem on weights in the space pL . Proc. A. Razmazde Math. Inst. 146 (2008), 39-43.

43. T. Inagaki, D. Kimura and A. Kvinikhidze, π and σ mesons at finite temperature and density in the NJL model with dimensional regularization. Phys. Rev. D 77 (2008), 116004.

44. H. Inassaridze and T. Kandelaki, La conjecture de Karoubi pour la K-theorie lisse. C. R. Acad. Sci. Paris, Ser. I 346 (2008), 1129-1132.

45. N. Inassaridze, E. Khmaladze and M. Ladra, Non-abelian cohomology and extensions of Lie algebras. J. Lie Theory 18 (2008), No. 2, 413-432.

46. N. Inassaridze and M. Ladra, Hopf type formulas for cyclic homology. C. R. Math. Acad. Sci. Paris, Ser. I 346 (2008), 385-390.

47. P. Jameson and A. Khvedelidze, Classical dynamics of a charged particle in laser field beyond the dipole approximation. Phys. Rev. A 77 (2008), 053403-1-13.

48. O. Jokhadze, On existence and nonexistence of global solutions of Cauchy-Goursat problem for nonlinear wave equations. J. Math. Anal. Appl. 340 (2008), No. 2, 1033-1045.

49. O. Jokhadze and S. S. Kharibegashvili, First Darboux problem for nonlinear hyperbolic equations of second order. (Russian) Mat. Zametki 84 (2008), No. 5, 693-712.

50. O. Jokhadze and B. Midodashvili, The first Darboux problem for wave equations with a nonlinear positive source term. Nonlinear Anal. 69 (2008), No. 9, 3005-3015.

51. T. Kadeishvili and P. Real, Free resolutions for differential modules over differential algebras. J. Math. Sci. 152 (2008), No. 3, 307-322

52. T. Kahniashvili, G. Lavrelashvili and B. Ratra, CMB temperature anisotropy from broken spatial isotropy due to an homogeneous cosmological magnetic field. Phys. Rev. D 78(2008), 063012; arXiv:0807.4239 [astro-ph].

53. K. Kalashnikov and G. Khimshiashvili, On stochastically independent continuous functions. (Russian) Contemp. Math. Appl. 59 (2008), 10 pp.

54. D. Kapanadze, B.-W. Schulze and J. Seiler, Operators with singular trace conditions on a manifold with edges. Integral Equations Operator Theory 61 (2008), No. 2, 241-279.

55. A. Kharazishvili, On Absolutely Nonmeasurable Sets and Functions. Georgian Math. J. 15(2008), No. 2, 317-325.

56. A. B. Kharazishvili and A. P. Kirtadze, On extensions of partial functions. Expo. Math. 25(2008), No. 4, 345-353.

57. A. B. Kharazishvili and A. P. Kirtadze, On measurability of algebraic sums of small sets.Studia Sci. Math. Hungar. 45 (2008), No. 3, 433-442.

58. A. Kharazishvili and T. Tetunashvili, On some combinatorial problems concerning geometrical realizations of finite and infinite families of sets. Georgian Math. J. 15 (2008), No. 4, 665-675.

59. S. Kharibegashvili, On the solvability of one multidimensional version of the first Darboux problem for some nonlinear wave equations. Nonlinear Anal. 68 (2008), No. 4, 912-924.

60. S. Kharibegashvili, On the solvability of the Cauchy characteristic problem for a nonlinear equation with iterated wave operator in the principal part. J. Math. Anal. Appl. 338 (2008), No. 1, 71-81.

61. S. S. Kharibegashvili, On the solvability of the characteristic Cauchy problem for some nonlinear wave equations in the future light cone. (Russian) Differentsial’nye Uravneniya 44(2008), No. 1, 129-139; English transl.: Differential Equations 44 (2008), No. 1, 135-146.

38

62. S. Kharibegashvili and B. Midodashvili, Solvability of characteristic boundary-value problems for nonlinear equations with iterated wave operator in the principal part. Electron. J. Differential Equations 2008, No. 72, 1-12.

63. S. Kharibegashvili and B. Midodashvili, On one boundary value problem for a nonlinear equation with the iterated wave operator in the. Georgian Math. J. 15 (2008), No. 3, 541-554.

64. G. Khimshiashvili, Configuration spaces and signature formulae. (Russian) Contemp. Math. Appl. 59 (2008), 10 pp.

65. G. Khimshiashvili and G. Panina, Cyclic polygons are critical points of area. Zap. Nauchn.Semin. Sankt-Peterb. Otd. Mat. Inst. Steklova 360 (2008), 35-42.

66. G. Khuskivadze, On fractional integrals on the plane curves of finite length. Georgian Math. J. 15 (2008), No. 2, 327-332.

67. G. Khuskivadze and V. Paatashvili, The Dirichlet problem for harmonic functions of Smirnov classes in doubly connected domains with non-smooth boundaries. Proc. A. Razmazde Math. Inst. 146 (2008), 67-78.

68. A. Khvedelidze, A. Kovner and D. Mc.Mullan, Creating a monopole in 4D gauge theories. Phys. Atomic Nuclei 71 (2008), 930-936.

69. A. Khvedelidze and Y. Palii, On homogeneous Grobner basis for tensors. Progr. Comput. Software 34 (2008), 101-106.

70. I. Kiguradze, On a resonance periodic problem for non-autonomous high order differential equations. (Russian) Differentsial’nye Uravneniya 44 (2008), No. 8, 1022-1032; English transl.: Differential Equations 44 (2008), No. 8, 1053-1063.

71. I. Kiguradze, On solvability conditions for nonlinear operator equations. Math. Comput. Modelling 48 (2008), No. 11-12, 1914-1924.

72. I. Kiguradze, Beurling-Borg type theorem for two-dimensional linear differential systems. Georgian Math. J. 15 (2008), No. 4, 677-682.

73. I. Kiguradze, On periodic type boundary value problems for higher order differential systems. Mem. Differential Equations Math. Phys. 44 (2008), 155-160.

74. I. Kiguradze, Some boundary value problems on infinite intervals for functional differential systems. Mem. Differential Equations Math. Phys. 45 (2008), 135-140.

75. I. Kiguradze and T. Kiguradze, On solvability of boundary value problems for higher order nonlinear hyperbolic equations. J. Nonlinear Anal.: Theory, Methods & Appl. 69 (2008), 1914-1933.

76. I. Kiguradze and A. Lomtatidze, On periodic solutions of linear differential equations with coefficients of alternating sign. (Russian) Differentsial’nye Uravneniya 44 (2008), No. 11, 1580-1581.

77. I. Kiguradze and N. Partsvania, On a nonlocal problem at resonance for second order nonlinear differential equations. (Russian) Differentsial’nye Uravneniya 44 (2008), No. 11, 1583-1584.

78. I. Kiguradze, N. Partsvania, and B. Půža, On periodic solutions of higher order functional differential equations. Boundary Value Problems 2008, ID 389028, 18pp.

79. I. Kiguradze and Z. Sokhadze, On some nonlinear boundary value problems for high order functional differential equations. Mem. Differential Equations Math. Phys. 43 (2008), 159-163.

80. V. Kokilashvili, Boundedness in Lebesgue spaces with variable exponent of the calderon singular operator on Carleson curves. Bull. Georgian Nat. Acad. Sci. 2 (2008), No. 4, 5-8.

81. V. Kokilashvili, N. Lyall and A. Meskhi, Two-weight estimates for singular and strongly singular integral operators. Acta Math. Hungar. 116 (2008), No. 1-2, 1-25.

82. V. Kokilashvili and A. Meskhi, Boundedness of maximal and singular operators in Morrey spaces with variable exponent. Armenian J. Math. 1 (2008), No. 1, 18-28.

83. V. Kokilashvili and A. Meskhi. On the maximal and Fourier operators in weighted Lebesgue spaces with variable exponent. Proc. A. Razmadze Math. Inst. 146 (2008), 120-123.

39

84. V. Kokilashvili and V. Paatashvili, The Riemann-Hilbert problem in weighted classes of Cauchy-type integrals with density from $L^{p(\cdot)}(\Gamma)$. Complex Anal. Operator Theory. (Online First ã 2008 Birkhäuser Verlag Basel/Switzerland DOI 10.1007/s11785-008-0067-9).

85. V. Kokilashvili and V. Paatashvili, On Convergence of sequences of functions in Hardy classes with a variable exponent. Proc. A. Razmazde Math. Inst. 146 (2008), 124-126.

86. V. Kokilashvili and V. Paatashvili, On variable Hardy and Smirnov classes of analytic functions. Georgian International Journal of Sciences. Nova Science Publishers, Inc. 1(2008), No. 2, 67-81.

87. V. Kokilashvili and V. Paatashvili, On Convergence of sequences of functions in Hardy classes with a variable exponent. Proc. A. Razmazde Math. Inst. 146 (2008), 124-126.

88. V. Kokilashvili, V. Paatashvili and S. Samko, Riemann problem in the class of Cauchy-type

integrals with density in pL . Dokl. Math. 78 (2008), No. 1, 510-513.89. V. Kokilashvili and S. Samko, Boundedness of maximal operators and potential operators on

Carleson curves in Lebesgue spaces with variable exponent, Acta Mathematica Sinica 24(2008), No. 11, 1775-1800

90. V. Kokilashvili and S. Samko, Weighted boundedness of the maximal, singular and potential operators in variable exponent spaces. In: Analytic Methods of Analysis and Differential Equations, A. A. Kilbas and S. V. Rogosin (Eds.), Cambridge Scientific Publishers, 139-164, 2008.

91. V. Kokilashvili and S. Samko, Vekua's generalized singular integrals on Carleson curves in weighted Lebesgue spaces. Operator Theory Adv. Appl. 181 (2008), 283-293.

92. V. Kokilashvili and S. Samko, Singular operators and Fourier multipliers in weighted Lebesgue spaces with variable exponent. (Russian) Vestnik St. Petersburg Univ. Math. 41(2008), No. 2, 134-144.

93. S. Kukudzhanov, Dynamic stability of orthotropic shells of revolution, close to cylindrical ones, under the action of meridional forces. (Russian) Izv. Ross. Akad. Nauk Mekh. Tv. Tela 2008, No. 3, 156-168.

94. Z. Kvatadze, T. Shervashidze, Some limit theorems for i.i.d. and conditionally independent random variables. The Second International Conference “Problems of Cybernetics and Informatics”, Materials of the Conference, vol. II , pp. 217-219. Azerbaijan National Academy of Sciences, Printing House “Information Technology”, Baku, 2008.

95. N. Lazrieva and T. Toronjadze, Optimal robust mean-variance hedging in incomplete financial markets. J. Math. Sci. 153 (2008), No. 3, 262-288.

96. N. Lazrieva, T. Sharia and T. Toronjadze, Semimartingale stochastic approximation procedure and recursive estimation. J. Math. Sci. 153 (2008), No.3, 211-259.

97. V. Lomadze, E. Rogers and J. Wood, Singular 2D behaviors: homologies. Georgian Math. J.15 (2008), No. 1, 139-157.

98. M. Mania and R. Tevzadze, Backward stochastic partial differential equations related to utility maximization and hedging. J. Math. Sci. 153 (2008), No. 3, 292-376.

99. M. Mania, R. Tevzadze and T. Toronjadze, Mean-variance hedging under partial information. SIAM J. Control Optim. 47 (2008), No, 5, 2381-2409.

100.B. Mesablishvili, Descent in * -autonomous categories. J. Pure Appl. Algebra 213 (2009), No. 1, 60-70.

101.D. Natroshvili, T. Buchukuri and O.Chkadua, Mathematical modeling and analysis of interaction problems for piezoelectric composits. Memorie di Matematica e Applicazioni, Rendiconti Accademia Nazionale delle Scienze detta dei XL. 124 (2008), 159-190.

102.N. Partsvania, On the solvability of boundary value problems for nonlinear differential systems. (Russian) Differentsial'nye Uravneniya 44 (2008), No. 2, 211-216; English transl.: Differential Equations 44 (2008), No. 2, 219-225.

103.N. Partsvania, On one problem with the condition at infinity for second order singular ordinary differential equations. Georgian Math. J. 15 (2008), No. 4, 753-758.

40

104.O. Purtukhia, Martingale representation theorems for multidimensional Wiener functionals. Bull. Georgian Nat. Acad. Sci. 2 (2008), No. 1, 41-46.

105.O. Purtukhia, An extension of the Ocone-Haussmann-Clark formula for the compansated Poisson process. (Russian) Teorija verojatn. i eje primen. 53 (2008), No. 2, 349-354.

106.S. Saneblidze, The bitwisted Cartesian model for the free loop fibration. Topology Appl.(2008), doi:10.1016/j.topol.2008.11.002.

107.L. Shapakidze, On the numerical investigation of instability and transition of a viscous flow between two porous rotating cylinders. Proc. A. Razmadze Math. Inst. 148 (2008), 78-90.

108.N. Shavlakadze, The contact problems of the mathematical theory of elasticity for plates with elastic inclusion. Podio-Guidugli (Eds.) “IUTAM” Symposium on relations of Shell, Plate, Beam and 3D models”. Springer Science+Business Media B.V., 2008, 197-204.

109.T. Shervashidze and V. Tarieladze, CLT for operator Abel sums of random elements. Georgian Math. J. 15 (2008), No.4, 785-792.

110.A. Tsitskishvili, A general method of constructing the solutions of spatial axisymmetric stationary problems of the jet and filtration theories with partially unknown boundaries. Mem. Differential Equations Math. Phys. 43 (2008), 119-140.

111.A. Tsitskishvili and N. Dzhorbenadze, On the construction of solutions of spatial axi-symmetric stationary with partially unknown boundaries problems of the theory of jet flows. Proc. A. Razmadze Math. Inst. 148 (2008), 92-112.

b) 2008 wels gamosaqveyneblad gadacemul naSromTa sia

112. M. Ashordia, On the solvability of boundary value problems on an infinite interval for nonlinear two-dimensional generalized and impulsive differential systems. Mem. Differential Equations Math. Phys. (accepted).

113. M. Ashordia, Sh. Akhalaia, N. Kekelia, On the necessary and sufficient conditions for the stability of linear generalized ordinary differential, linear impulsive and linear difference systems. Georgian Math. J. (accepted).

114. M. Ashordia, Sh. Akhalaia, N. Kekelia, On the necessary and sufficient conditions for the stability of linear systems of generalized ordinary differential equations. Mem. Differential Equations Math. Phys. (accepted).

115. U. Ashraf, V. Kokilashvili, A. Meskhi, Weight characterization of the trace inequality for the generalized Riemann-Liouville transform in $L^{p(x)}$ spaces. Math. Inequalities & Appl. (accepted).

116. U. Ashraf, M. Asif and A. Meskhi, Boundedness and compactness of positive integral operators on cones of homogeneous groups. Positivity (accepted).

117. M. Asif, V. Kokilashvili and A. Meskhi, Boundedness criteria for maximal functions and potentials on the half-space in weighted Lebesgue spaces with variable exponents. Integr. Transf. Spec. Func. (accepted).

118. Р. Банцури. Об одной смешанной задаче изгиба пластинки с частично неизвестной границей. Прикладная механика. (submitted).

119. R. Bantsuri, drekadobis brtyeli Teoriis Sereuli amocanis amoxsnanawilobriv ucnobsazRvriani arisaTvis. Proc.A. Razmadze Math. Inst.(accepted).

120. Р.Д. Банцури, Н.Н. Шавлакадзе. Контактная задача для кусочно-однородной плоскости, усиленной полубесконечным включением, пересекающим границу раздела под прямым углом. Прикладная Математика и Механика. (submitted).

41

121. N. Beck, G. Jorjadze, The SL(2,R) black hole model: scattering, bound states and causality. Math. Rev. (submitted).

122. N. Berikashvili, A version of obstruction functor. Submitted to Bull. Georgian Nat. Acad. Sci. (accepted).

123. G. Berikelashvili, D.G. Gordeziani, On a nonlocal generalization of the biharmonic Dirichlet problem. (Russian) Differentsial’nye Uravneniya (submitted).

124. G. Berikelashvili, O. Jokhadze, S. Kharibegashvili, B. Midodashvili, Finite-difference method of solving the Darboux problem for nonlinear Klein-Gordon equation. Mem. Differential Equations Math. Phys. (accepted).

125. G. Berikelashvili, O. Jokhadze, S. Kharibegashvili, B. Midodashvili, Finite difference solution of a nonlinear Klein-Gordon equation with on external source. Math. Comp.(submitted).

126. G. Berikelashvili, M. Mirianashvili On the three level difference scheme for regularized long wave equation. Mem. Differential Equations Math. Phys. (accepted).

127. G. Bezhanishvili, N. Bezhanishvili, D. Gabelaia, A. Kurz, Bitopological Duality for Distributive Lattices and Heyting Algebras. Mathematical Structures in Computer Science(accepted).

128. N. Bezhanishvili, G. Fontaine, Y. Venema, Vietoris Bisimulations. Journal of Logic and Computation (accepted)..

129. G. Bezhanishvili, N. Bezhanishvili, An algebraic approach to canonical formulas: intuitionistic case. (submitted).

130. D. Bourn, Z. Janelidze, Pointed protomodularity via natural imaginary subtractions.Journal of Pure and Applied Algebra, 2008 (to appear).

131. T. Buchukuri, O. Chkadua , D. Natroshvili, A.-M. Sandig, Solvability and regularity results to boundary-transmission problems for metallic and piezoelectric elastic materials. Math. Nach. (submitted).

132. J. M. Casas, T. Datuashvili, M. Ladra, Universal strict general actors and actors in categories of interest. Applied Categorical Structures, 2008 (accepted).

133. L. P. Castro, D. Kapanadze, Exterior wedge diffraction problems with Dirichlet, Neumann and impedance boundary conditions. Acta Appl. Math. (submitted).

134. O. Chkadua, S. Mikhailov, D. Natroshvili, Analysis of direct boundary-domain integral equations for mixed BVP with variable coefficients. Part 1. J. Integral Equations Appl.(submitted).

135. O. Chkadua, S. Mikhailov, D. Natroshvili, Analysis of direct boundary-domain integral equations for mixed BVP with variable coefficients. Part 2. J. Integral Equations Appl.(submitted).

136. O. Chkadua, S. Mikhailov, D. Natroshvili, Analysis of some localized boundary-domain integral equations. Part 1. J. Integral Equations Appl. (submitted).

137. O. Chkadua, S. Mikhailov, D. Natroshvili. Analysis of some localized boundary-domain integral equations. Part 2. J. Integral Equations Appl. (submitted).

138. G. Donadze, N. Inassaridze and M. Ladra, Derived functors and Hopf type formulas in cyclic homology. Bulletin de SMF (to appear).

139. Z. Došlá, N. Partsvania, Oscillation theorems for second order nonlinear differential equations. Nonlinear Analysis: Theory, Methods & Applications (accepted).

140. R. Duduchava, Lions’s lemma and Korn’s inequalities on hypersurfaces, Series “Operator Theory and Applications”, Volume dedicated to Prof. N. Vasilevski’s 60-th birthday anniversary (accepted).

141. O. Dzagnidze, On the derivability and representations of quaternion functions. Complex Variables and Elliptic Equations (submitted).

142. O. Dzagnidze, The smoothness of functions of two variables and double trigonometric series. Real Analysis Exchange (submitted).

42

143. D. E. Edmunds, V. Kokilashvili and A. Meskhi. Two-weight estimates in pL spaces with applications to Fourier series. Houston Journal of Mathematics (to appear in 2008).

144. M. Eliashvili, V. Gerdt, A. Khvedelidze, On precession of entangled spins in a strong laser field. Yad. Fiz. (submitted).

145. L. Ephremidze, G. Janashia, E. Lagvilava, A simple proof of the matrix-valued Fejer-Riesz theorem. J. Fourier Anal. Appl. (accepted)

146. L. Ephremidze, N. Fujii, The John-Nirenberg inequality for ergodic systems. J. Dynamical Systems (accepted).

147. Eridani, V. Kokilashvili and A. Meskhi. Morrey spaces and fractional integral operators. Expositiones Mathematicae (accepted).

148. Z. F. Ezawa, G. Tsitsishvili, Quantum Hall ferromagnets. Rep. Prog. Phys. (submitted).149. A. Gachechiladze, A. Gachechiladze, D. Natroshvili, Unilateral contact problems with

friction for hemitropic elastic solids. Georgian Math. J. (accepted).150. R. P. Gilbert, G. Jaiani, S. Kharibegashvili, D. Natroshvili, N. Chinchaladze, Cusped

elastic beam under the action of stresses and concentrated forces in approximation. Applied Mathematics, Informatics and Mechanics (accepted).

151. L. Gogolauri, optimaluri xvrelebis moZebnis amocana kvadratSi. Proc. A. Razmadze Math. Inst. (submitted).

152. V. Gupta, T. Shervashidze, An upper bound for maximal binomial probability. Georgian Math. J. (submitted).

153. A. Guven and V. Kokilashvili, Two-weight estimates for Fourier operators and Bernstein inequality. Studia Sci. Math. Hung. (accepted).

154. A. Guven and V. Kokilashvili, On the means of Fourier integrals and Bernstein inequality in two-weighted setting. Positivity (submitted).

155. H. Inassaridze and T. Kandelaki, Smooth K-theory of locally convex algebras. Journal of Topology and Analysis (to appear).

156. O. Jokhadze, The Cauchy-Goursat problem for one-dimensional semilinear wave equations. Comm. Partial Differential Equations (accepted).

157. O. Jokhadze, S. Kharibegashvili, Some properties of Riemann and Green-Adamard functions for second order linear hyperbolic equations. (Russian) Differentsial’nye Uravneniya (accepted).

158. O. Jokhadze, S. Kharibegashvili, The Darboux first problem for wave equations with nonlinear dissipative term. Math. Nachr. (submitrted).

159. O. Jokhadze, S. Kharibegashvili, The Cauchy-Goursat problem for the wave equations with dissipative term. (Russian) Mat. Zametki (submitted).

160. T. Kadeishvili. T. Lada, A small open-closed homotopy algebra (OCHA). Georgian Math. J. (accepted).

161. A. Kharazishvili, On sums of real-valued functions with extremely thick graphs.Expositiones Mathematicae (accepted).

162. A. Kharazishvili, Metrical transitivity and nonseparable extensions of invariant measures.Taiwanese J. of Mathematics (accepted).

163. A. Kharazishvili, Some properties of step-functions connected with extensions of measures, Acta Universitatics Carolinae (accepted).

164. S. Kharibegashvili, Boundary value problems for some classes of nonlinear wave equations. Mem. Differential Equations Math. Phys. (accepted).

165. S. Kharibegashvili, B. Midodashvili, Solvability of Cauchy spatial characteristic problem for one class of second order nonlinear wave equations. Electron. J. Differential Equations(submitted).

166. G. Khimshiashvili, Cyclic polygons as critical points. Proc. Intern. Conf. “Modern problems in applied mathematics”, Tbilisi 7-9.10.2008. (accepted).

167. A.Khvedelidze, Spin-flip resonance in an intense laser beam. Phys. Rev. (submitted).

43

168. I. Kiguradze, The Neumann problem for the second order nonlinear ordinary differential equations at resonance. Functional Differential Equations (accepted).

169. I. Kiguradze, Second order nonlinear differential equations with an infinite set of periodic solutions. Nonlinear Oscillations (accepted).

170. I. Kiguradze, Bounded and vanishing at infinity solutions of nonlinear differential systems. Georgian Math. J. (accepted).

171. I. Kiguradze, On boundary value problems on an infinite interval for nonlinear differential systems. Nonlinear Analysis (accepted).

172. I. Kiguradze, Nonlinear nonlocal problems for systems of ordinary differential equations. (Russian) Differentsial’nye Uravneniya (submitted).

173. I. Kiguradze and S. Mukhigulashvili, On periodic solutions of the system of two linear differential equations. Mem. Differential Equations Math. Phys. (accepted).

174. V. Kokilashvili, A. Meskhi, Maximal and potential operators in variable morrey spaces defined on nondoubling quasimetric measure spaces. Bull. Georgian Nat. Acad. Sci. (accepted).

175. V. Kokilashvili, A. Meskhi, Two-weight estimates for strong fractional maximal functions and potentials with multiple kernels. J. Korean Math. Soc. (accepted).

176. V. Kokilashvili, A. Meskhi, Maximal and potential operators in variable Morrey spaces defined on non-homogeneous spaces. Bull. Georgian Nat. Acad. Sci. (accepted).

177. V. Kokilashvili, V. Paatashvili, The Riemann-Hilbert problem in domains with piecewise-

smooth boundaries in classes of Cauchy type integrals with density from pL . Georgian Math. J. (accepted).

178. V. Kokilashvili and V. Paatashvili. The Riemann-Hilbert problem in the domains with piecewise-smooth boundaries in weighted class of Cauchy type integrals with density from

variable exponent Lebesgue spaces pL . Georgian Math. J. (accepted).179. V. Kokilashvili, S. Samko, Operators of harmonis analysis in weighted spaces with non-

standard growth. J. Math. Anal. Appl. (2008), doi: 10.1016/j.jmaa.2008.06.056.180. V. Kokilashvili, S. Samko, The maximal operator in weighted variable exponent spaces in

metric spaces. Georgian Math. J. (accepted).181. V. Kokilashvili, Y. Yildirir, On the approximation by trigonometric polynomials in

weighted Lorentz spaces, Function Spaces & Appl. (submitted).182. С. Кукуджанов, Об устойчивости длинных оболочек вращения, близких по форме к

цилиндрическим. Известия РАН, МТТ. (submitted).183. A. N. Kvinikhidze, B. Blankleider, On the Wilsonian renormalization group equation for

nuclear current operators. Phys. Rev. (submitted).184. N. Lazrieva, T. Toronjadze, Polyak’s Averaging for Robbins-Monro type stochastic

differential equation. Stochastics: An International Journal of Probability and Stochastic Processes (accepted).

185. M. Mania, M. Santacroce, Exponential hedging under partial minformation. Finance and Stochastics (submitted).

186. M. Mania, R. Tevzadze, Backward stochastic PDEs related to utility maximization and hedging, ICER working papers 2008, http://www.icer.it/papers/abstract2008.html; Annals of Applied Probability (submitted).

187. M. Mania, R. Tevzadze, T. Toronjadze, $L^2$-approximating pricing under restricted information. Applied Mathematics and Optimization (to appear).

188. N. Partsvania, A problem on transitional solutions for second order nonlinear differential equations. (Russian) Differentsial'nye Uravneniya (accepted).

189. O. Purtukhia, Stochastic integral representation of multidimensional polynomial Poisson functionals. Bull. Georgian Nat. Acad. Sci. (to appear).

190. M. Saeed Akram, V. Lomadze, On some basics of linear systems theory. Systems Control Letters (to appear).

44

191. S. Saneblidze, The loop space cohomology of a space with the polynomial cohomology algebra. Math. T/ 0810.4531v1. Journal of Topology (submitted).

192. S. Saneblidze, On the homotopy classification of maps, AT/0810.4531. Journal of Homotopy and Related Structures (submitted).

193. N. Shavlakadze, The effective solution of a contact problem for compound plate. Int. Journal of Solids and Structures (submitted).

194. Sh. Tetunashvili, On one property of the sum of everywhere converging trigonometric series. Proc. A. Razmadze Math. Inst. (accepted).

195. Z. Tsigroshvili, Panjer’s Recursion – What does it Mean? ASTIN Bulletin (submitted).196. A. Tsitskishvili, R. Tsitskishvili, On the impact of two axially symmetric spatial streams.

Reports of enlarged session of the seminar of I. Vekua Institute of Applied Mathematics(accepted).

197. A. Tsitskishvili, Z. Tsitskishvili, R. Tsitskishvili, On the construction of solutions of the spatial axially symmetric stationary problem with partially unknown boundaries problems of the theory of jet flows. “Modern Problems in Applied Mathematics”, 7-9 october, 2008, Tbilisi, Georgia, P. 70, Tbilisi, University press (accepted).

198. L. Esakia, Around provability Logic. Annals of Pure and Applied Logic (accepted).199. M. Jibladze, Almost Alexandroff topologies. Order (submitted). 200. G. Bezhanishvili, L. Esakia, D. Gabelaia, K4 as the logic of Stone spaces. Review of

Symboloc Logic (submitted). 201. G. Bezhanishvili, D. Gabelaia, Modal logics of subsets of the real line. Review of

Symboloc Logic (submitted).202. G. Bezhanishvili, N. Bezhanishvili, An algebraic approach to canonical formulas:

Intuitionistic case. Review of Symboloc Logic (submitted).203. G. Donadze, N. Inassaridze, E. Khmaladze and M. Ladra, Cyclic homologies of crossed

modules of algebras. Compos. Math. (submitted).204. N. Inassaridze, J.M.Casas, and M. Ladra, Homological aspects of Lie algebra crossed

modules. Manuscripta Math. (submitted).205. B. Mesablishvili and J. Gomez-Torrecillas, A bicategorical version of Masuoka's theorem.

Applications to bimodules over functor categories and to firm bimodules. J. Pure Appl.Algebra (submitted).

206. A. Patchkoria, Projective semimodules over semirings with valuations in nonnegative integers. Semigroup Forum (submitted).

45

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2008 wels sazRvargareT da saqarTveloSi gamarTul samecniero forumebze wakiTxuli moxsenebebi

a) sazRvargareT gamarTuli konferenciebi

v. kokilaSvili, v. paataSvili, S. tetunaSvili, l.efremiZe. konferencia Function Spaces and Applications, 6-12 ivlisi (2008), fraiburgi (germania). moxsenebebi: v. kokilaSvili „volteras tipis arawrfivi integraluri gantolebis dadebiTi amonaxsnebi arsebobis Sesaxeb“, v. paataSvili „dirixlesa da neimanis amocanebi smirnovis klasis harmoniuli funqciebisaTvis im koSis tipis integralTa klasSi, romelTa simkvriveebi miekuTvnebian cvlad maCveneblian lebegis wonian sivrceebs“, S. tetunaSvili „furies trigonometriuli mwkrivebis cvladi rigebiT Sejamebadobis Sesaxeb“, l. efremiZe „matric-funqciebis faqtorizaciis efeqturi algoriTmis Sesaxeb“.

v. kokilaSvili da l. efremiZe. konferencia Function Spaces, Differential Operators and Nonlinear Analysis, 22-28 agvisto (2008), helsinki (fineTi). mosxenebebi: v. kokilaSvili „orwoniani utolobebis kriteriumebi furies operatorebisaTvis da bernSteinis erTi utolobis ganzogadoeba“; „integraluri gardaqmnebi funqciur sivrceebSi arastandartuli zrdadobis pirobiT araerTgvarovan zomian sivrceebze“, l. efremiZe „veiveleturi matricebis parametrizaciis Sesaxeb“.

v. kokilaSvili da v. paataSvili. konferencia International Conference on Mathematical Modeling, 8-12 seqtemberi (2008), arielis universitetis centri, (israeli). moxsenebebi: v. kokilaSvili „volteras tipis arawrfivi integraluri gantolebis dadebiTi amonaxsnebis arsebobis Sesaxeb“, v. paataSvili „sasazRvro amocanebi analizuri da harmoniuli funqciebisaTvis arastandartuli zrdadobis pirobiT funqciuri sivrceebis CarCoebSi“.

a. xaraziSvili. 36-e sazamTro skola abstraqtul analizSi, 12-19 ianvari, ihota nad rohanovem, CexeTis respublika, plenaruli moxseneba.

i. kiRuraZe. msoflio kongresi WCNA-2008 _ Fifth World Congress of Nonlinear Analysts, Orlando, Florida, USA, July 2-9, 2008. miwveuli moxseneba On boundary value problems with conditions at infinity for systems of ordinary differential equations.

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n. farcvania. msoflio kongresi WCNA-2008 _ Fifth World Congress of Nonlinear Analysts, Orlando, Florida, USA, July 2-9, 2008. miwveuli moxseneba Oscillatory and non-oscillatory solutions of second order nonlinear differential equations.

n. farcvania. On solvability of boundary value problems for nonlinear differential systems. Abstracts of the Conference on Differential and Difference Equations and Applications, Strečno, Slovak Republic, June 23-27, 2008, pp. 42-43.

j. gvazava. konferencia International Conference Dedicated to the 100th Anniversary of the Birthday of Sergei L. Sobolev (Novosibirsk, Russia, October 5-12, 2008). moxseneba On the non-local Darboux type problem for a class of non-strictly hyperbolic second order quasi-linear equations with admissible parabolic degneracy.

j. gvazava. On an nonlinear version of characteristic Goursat problem. Abstracts of the International Conference on Function Spaces, Differential Operators, General Topology Dedicated to the 85th Anniversary of the Birthday of L. D. Kudryavtsev, Moscow, 2008, pp. 205-206.

berikelaSvili, o. joxaZe, j. gvazava, s. xaribegaSvili, b. midodaSvili. Four-point finite differente scheme for a nonlinear Klein-Gordon equation with an extremal source. Abstracts of the Fourth International Conference on Numerical Analysis and Applications, Rousse, Bulgaria, June 16-20, 2008, p. 6.

r. duduCava. 13 – 19 aprili 2008, obervolfaxi (germania); mowveuli momx-senebeli saerTaSoriso konferenciaze: “Analysis of Boundary Element Methods”. 13–19 ivlisi 2008, viliamsburgi, aSS, plenaluri momxsenebeli saerTaSoriso konferenciaze IWOTA – 2008 (International Workshiop on Operator Theory and Applivcations).18–21 noemberi 2008, mexiko-sitis universitetis umaRlesi kvlevebis centris maTematikis instituti, plenaluri momxsenebeli saerTaSoriso konferenciaze “Toeplitz-Like Operators And Related Topics” miZRvnili n. vasilevskis 60 wlis iubilesadmi. 03.04.08. moxseneba analizis seminarze aveiros universiteti, portugalia“On the maxwell system".17.04.08 moxseneba seminarze ``Functional Analysis and Applications"lisabonis teqnikur universitetSi ``Partial differential equations on hypersurfaces".24.04.08 – moxseneba seminarze "Harmonic Analysis, Operator Theory and Applications", aveiros universiteti, portugalia `Òn the maxwell system". o. Wkadua. 30 ivnisi – 04 ivlisi 2008, ,,la-sapienzas” universiteti, romi, italia, moxseneba saerTaSoriso konferenciaze ,,funqcionaluri analizi, kerZo warmoebuliani diferencialuri gantolebebi da maTi gamoyenebebi” miZRvnili v. mazias 70 wlis iubilesadmi. n. SavlayaZe. VI saerTaSoriso konferencia `deformadi sxeulebis urTierTqmedebis dinamikis problemebi~, 22-27 seqtemberi, 2008, gorisi, somxeTi. moxseneba Àbout dynamic contact problem for bodies with elestic cover plate“. A

n. inasariZem, e. xmalaZem da g. donaZem monawileoba miiRes Semdeg saerTaSoriso konferenciebSi:

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International Conference on K-theory and Homotopy theory, University of Santiago de Compostela (Spain), September 15-20, 2008, (n.inasariZe iyo Tanaorganizatori). da SECA V (V Seminar on Categories and Applications) , University of Vigo (Spain), September 10-12, 2008.

T. qadeiSvili. sazafxulo skola “Mathematics, Algorithms and Proofs“, Teoriuli fizikis saerTaSoriso centri ICTP, trieste, italia, 11-31 agvisto. leqciaTa cikli Operadic algebraic topology, teqsti ganTavsebulia misamarTze http://www.disi.unige.it/map/ictp/lectures_files/Kadeishvili_L.pdf.

g. ximSiaSvili. konferencia suzdalSi, 22-25 ivnisi. moxseneba Differential equations and dynamical systems.

a. elaSvili. konferencia European School of Representation Theory, 28 ianvari -14 Tebervali. moxseneba Lie Algebras and Singularities Theory.konferencia Grobner Basis, Trento, Italia, 28-30 noemberi. moxseneba Classification of exeptional nilpotents in simple Lie algebras.konferencia Computer algebra, Trento, Italia, 15-20 ivnisi. moxseneba “Lie Algebras and Singularities Theory”.

m. bakuraZe. maTematikosTa me-5 kongresi, 15-18 ivlisi, holandia, moxseneba Transferred Chern classes and generalised cogomology rings.

g. bejaniSvili, d. gabelaia, m. jiblaZe. sazafxulo skola ESSLLI 2008 (http://www.illc.uva.nl/ESSLLI2008/), hamburgi, germania, 4-15 agvisto. leqciaTa kursebi G. Bezhanishvili and M. Jibladze, "Lattices and Topology",B. ten Cate, D. Gabelaia, "Advanced Modal Logic".

d. gabelaia. sazafxulo skola Fourth International Tbilisi Summer School in Logic and Language http://www.logic.at/tbilisi08/. leqciaTa kursi Advanced Modal Logics.konferencia International Workshop on Structural Proof Theory, parizi, 19-21 noemberi, moxseneba D. Gabelaia, L. Esakia, “Provability logic and related modal systems -semantical considerations” http://www.pps.jussieu.fr/~parigot/SPT-2008.html#Gabelaiakonferencia modaluri logikis seminari stambolis kulturis

universitetSi, 26-29 noemberi, moxseneba Modal Logics of subsets of the real line.

T. ServaSiZe. moxseneba “Some limit theorems for i.i.d. and conditionally independent random variables” konferenciaze The second international conference “Problems of cybernetics and informatics”, Baku, 10-12 september, 2008 (with Z Kvatadze).

n. lazrieva, T. toronjaZe. moxseneba The Robbins-Monro Type Stochastic Differential Equations, Conference on Asymptotic Statistics, September 1 to 5, 2008, Centre de Recerca Matemàtica Campus de la Universitat Autònoma de Barcelona, Bellaterra.

m. mania. moxseneba Mean-Variance Hedging under Partial information and Related BSDEs konferenciaze 5th Colloquium on Backward Stochastic Differential Equations, Finance and Applications, Le Mans, France, June 18 – 20.moxseneba L(2)-Approximate pricing under restricted information konferenciaze Convegno PRIN, Stochastic methods in Finance, Torino, Italy, July 3-5.

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o. furTuxia. moxseneba Stochastic Integral Representation of Poisson Functionalskonferenciaze The second international conference “Problems of cybernetics and infor-matics”, Baku, 10-12 september.

a. xvedeliZe. konferencia International Conference Symmetries in Physics, 27-29 March, 2008 Dubna, Russia, moxseneba On spin precession of two entangled spin-1/2 particles in a strong laser field.konferencia 12-TH WORKSHOP ON COMPUTER ALGEBRA, May 14-16, 2008, Dubnamoxseneba Algorithmic construction of polynomial invariants for the entanglement problem.konferencia Selected Problems of Modern Theoretical Physics', Dubna, 23-27 June, 2008. moxseneba On the entangled spins precession in a strong laser field.

a. kvinixiZe. konferencia The 6th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields 22-26 June 2008, Aristotle University, Thessaloniki, Greece, moxseneba Gauge invariance in the models of QFT.

g. jorjaZe. konferencia International Conference Exact results in low dimensional quantum systems, Sept. 8-12, 2008, Florence, Italy.konferencia 39ht International Symposium Ahrenshoop: Recent Developments in String/M Theory, Oct. 06-10, 2008, Berlin, Germany.

g. lavrelaSvili, konferencia Workshop on the Origin of P, CP and T Violations,ICTP, Trieste, Italy. July 2-5, 2008.konferencia 12th Paris Cosmology Colloquium, Observatoire de Paris, France. July 17 - 19, 2008.konferencia Summer School in Cosmology, ICTP, Trieste, Italy, July 21 - August 1, 2008.

b) saqarTveloSi Catarebul konferenciebi

zemoT naxsenebi institutSi Catarebuli 3 konferenciis garda institutis TanamSromlebma monawileoba miiRes Semdeg konferenciebSi:

g. berikelaSvili da d. gordeziani. konferencia International Conference on Modern Problems in Applied Mathematics Dedicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University & 40th Anniversary of the I. Vekua Institute of Applied Mathematics (Tbilisi, September 26-28, October 7-9, 2008). moxseneba Finite difference schemes for one nonlocal biharmonic problem.

g. berikelaSvili, o. joxaZe da s. xaribegaSvili. konferencia International Conference on Modern Problems in Applied Mathematics Dedicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University & 40th Anniversary of the I. Vekua Institute of Applied Mathematics (Tbilisi, September 26-28, October 7-9, 2008). moxseneba Difference method of solving the Darboux problem for nonlinear Klein-Gordon equation.

g. berikelaSvili da m. mirianaSvili. konferencia International Conference on Modern Problems in Applied Mathematics Dedicated to the 90th Anniversary of the Iv.

49

Javakhishvili Tbilisi State University & 40th Anniversary of the I. Vekua Institute of Applied Mathematics (Tbilisi, September 26-28, October 7-9, 2008). moxseneba On the convergence of difference schemes for RLW equation.

s. xaribegaSvili. konferencia International Conference on Modern Problems in Applied Mathematics Dedicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University & 40th Anniversary of the I. Vekua Institute of Applied Mathematics (Tbilisi, September 26-28, October 7-9, 2008). moxseneba On the characteristic boundary value problems for nonlinear equations with iterated wave operator in the principal part.

g. berikelaSvili, o. joxaZe, s. xaribegaSvili, b. midodaSvili. i. vekuas saxelobis gamoyenebiTi maTematikis institutis seminaris gafarToebuli sxdomebi, Tbilisi, 22-25 aprili, 2008. moxseneba “sasrul-sxvaobiani meTodi gare wyaros arawrfivi klein-gordonis gantolebisaTvis”.

s. xaribegaSvili. i. vekuas saxelobis gamoyenebiTi maTematikis institutis seminaris gafarToebuli sxdomebi, Tbilisi, 22-25 aprili, 2008. moxseneba “erTi sasazRvro amocanis Sesaxeb talRis gantolebebisaTvis”.

r. Bbancuri. Ìnternational Conference on Modern Problems in Applied Mathematics. Dodicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University 40th anniversary of the I. Vekua Institute of Applied Mathematics, 7-9 Oktober, 2008, Tbilisi.moxseneba `drekadobis brtyeli Teoriisa da firfitis Runvis nawilobriv ucnobsazRvriani amocanebi~.ilia vekuas saxelobis gamoyenebiTi maTematikis institutis seminaris XXII gafarToebuli sxdomebi, 23-25 aprili, 2008, Tbilisi. moxseneba `drekadobis brtyeli Teoriis nawilobriv ucnobsazRvriani amocanebi~ (g. kapanaZesTan erTad).

a. cicqiSvili. ilia vekuas saxelobis gamoyenebiTi maTematikis institutis seminaris XXII gafarToebuli sxdomebi, 23-25 aprili, 2008, Tbilisi. moxseneba `sivrciTi RerZsimetiuli nawilobriv ucnobsazRvriani amocanebis amoxsna. Wavluri nakadebis dajaxeba. Kkumulaciuri Wavlebi~ (r. cicqiSvilTan erTad). konferencia International Conference on Modern Problems in Applied Mathematics. Dodicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University 40th anniversary of the I. Vekua Institute of Applied Mathematics, 7-9 Oktober, 2008, Tbilisi. moxseneba Òn the construction of solutions of spatial axy-symmetric stationary with partiallly unknown boundaries problems of the theory of jet flows“ (r. cicqiSvilsa da z. cicqiSvilTan erTad)..

n. SavlayaZe. International Conference on Modern Problems in Applied Mathematics. Dodicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University 40th anniversary of the I. Vekua Institute of Applied Mathematics, 7-9 Oktober, 2008, Tbilisi. moxseneba „The dynamic bending problem of beam lying on the elastic basis“.

l. SafaqiZe. ilia vekuas saxelobis gamoyenebiTi maTematikis institutis seminaris XXII gafarToebuli sxdomebi, 23-25 aprili, 2008, Tbilisi.

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moxseneba `forovani cilindris brunviT gamowveuli siTxis dinebis Sesaxeb~.International Conference on Modern Problems in Applied Mathematics. Dodicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University 40th anniversary of the I. Vekua Institute of Applied Mathematics, 7-9 Oktober, 2008, Tbilisi. moxseneba `The numerical investigation instability and transition in a curved channel flows with a transwerse pressure gradient“.

r. gaCeCilaZe, a. gaCeCilaZe. 25-27 seqtemberi 2008, Tbilisi, moxseneba saerTaSoiso konferenciaze “gamoyenebiTi maTematikis Tanamedrove problemebi”. o. Wkadua. 25-27 seqtemberi 2008, Tbilisi, moxseneba saerTaSoriso konfe-renciaze: “gamoyenebiTi maTematikis Tanamedrove problemebi”.

d. kapanaZe. 25-27 seqtemberi 2008, Tbilisi, moxseneba saerTaSoiso konfe-renciaze “gamoyenebiTi maTematikis Tanamedrove problemebi”.

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