Informacia

g) binaruli narevis Termodrekadobis TeoriaSi damtkicebulia statikis sasazRvro amocanebis amonaxsnebis erTaderTobis Teoremebi wrisa da sibrtyisaTvis wriuli xvreliT. aigo I, II da III sasazRvro amocanebis amonaxsnebi wrisa da sibrtyisaTvis wriuli xvreliT absoluturad da Tanabrad krebadi mwkrivebis saxiT, agebulia I da II sasazRvro amocanebis amonaxsnebi Sesabamisad puasonisa da dinis formulebis saxiT sibrtyisaTvis wriuli xvreliT. aigo statikis mTavari sakontaqto amocanis amonaxsni (roca sakontaqto wiri wrewiria) ubnobriv-erTgvarovani sibrtyisaTvis absoluturad da Tanabrad krebadi mwkrivebis saxiT, agebulia I sasazRvro amocanis amonaxsni wriuli rgolisaTvis absoluturad da Tanabrad krebadi mwkrivebis saxiT, damtkicebulia sasazRvro-sakontaqto amocanebis amonaxsnebis erTaderTobis Teoremebi da agebulia am amocanebis amonaxsnebi ubnobriv erTgvarovani wrisa da rgolisaTvis absoluturad da Tanabrad krebadi mwkrivebis saxiT, miRebulia binaruli narevis Termodrekadobis Teoriis statikis sasazRvro amocanebis ricxviTi amonaxsnebi wrisaTvis, rgolisaTvis, sibrtyisaTvis wriuli xvreliT, ubnobriv erTgvarovani wrisa da rgolisaTvis (Semsrulebeli ivane cagareli).

d) elementaruli funqciebis saSualebiT agebulia transversalurad izotropuli binaruli narevis drekadobis Teoriis statikis gantolebaTa sistemis fundamenturi amonaxsni da dadgenilia misi ZiriTadi Tvisebebi (sami ganzomilebis SemTxveva), am TeoriaSi agebulia martivi fenis, ormagi fenisa da moculobiTi potencialebi da Seswavlilia maTi Tvisebebi (sami ganzomilebis SemTxveva), miRebulia grinis formulebi da damtkicebulia statikis sivrciTi sasazRvro amocanebis amonaxsnebis erTaderTobis Teoremebi, dadgenilia miRebuli singularuli integraluri gantolebis Tvisebebi da damtkicebulia am Teoriis statikis sivrciTi sasazRvro amocanebis amonaxsnebis arsebobis Teoremebi, agebulia transversalurad izotropuli binaruli narevis drekadobis Teoriis statikis gadaadgilebisa da Zabvis sasazRvro amocanebis amoxsnebi naxevarsivrcisaTvis, miRebulia zogadi amonaxsnis warmodgenis formulebi transversalurad izotropuli binaruli narevis drekadobis Teoriis statikis gantolebaTa sistemisaTvis ori da sami ganzomilebebis SemTxvevebSi, aigo statikis Zabvis sasazRvro amocanis amoxsna usasrulo zolisaTvis furies gardaqmnis saxiT, damtkicebulia statikis gadaadgilebisa da Zabvis sasazRvro amocanebis amoxsnebis arsebobis Teoremebi naxevarsibrtyisaTvis mrudwiruli WrilebiT. agebilia am amocanebis amonaxsnebi erTi Wrilis SemTxvevaSi (Semsrulebeli lamara biwaZe).
1.5. saqarTvelo-aSS (CRDF-GRDF ) erToblivi sagranto programa III mecnierebis gavlena socialur problemebze
proeqtis saTauri: “miwisZvris winamorbedebis saxiT generirebuli ionosferuli ultradabali sixSiris talRebis gamokvleva”
proeqtis xangrZlioba: 2007-2009 ww.
grantis nomeri: GEP2-3340-TB-06
proeqtis xelmZRvaneli saqarTvelos mxridan; Tamaz kalaZe

Sesrulebuli samuSaos reziume

proeqtis mizani gaxldaT dedamiwis ionosferoSi iseTi talRuri Tvisebebis dadgena, romlebic SesaZloa aRviqvaT rogorc miwisZvrebis winamorbedebi. siTxis dinamikisa da magnitohidrodinamikis gantolebebis safuZvelze Catarebuli Teoriuli da ricxviTi analizis Sedegad miRebulia Semdegi Sedegebi:

1) akustikur-gravitaciuli talRebis gavrcelebaa Seswavlili dedamiwis sustad ionizirebul ionosferul D, E da FF-SreebSi. naCvenebia, rom roca akustikur-gravitaciuli talRebi aRigznebian gareSe bunebrivi faqtorebiT (vulkanuri amofrqveva, miwisZvrebi, elva da a.S.) maTi amplitudebi izrdeba am talRebis arawrfiv grigalur struqturebad TviTorganizaciamde. gaanalizebulia dabalsixSiriani grZelmasStabovani zonaluri nakadebis maRalsixSiriani, moklemasStabovani inerciul-gravitaciuli talRebis saSualebiT generaciis axali meqanizmi. arawrfivi generaciis es meqanizmi dafuZnebulia sasruli amplitudis inerciul-gravitaciuli talRebiT konveqciuri ujredebis parametrul aRgznebaze. Camoyalibebulia zonaluri nakadis aramdgradobis pirobebi da gansazRvrulia Sesabamisi inkrementi.

2) naCvenebia, rom seismuri aqtivobiT aRgznebuli dabalsixSiriani inerciul-gravitaciuli talRebi mdrgad stratificirebul atmosferoSi arawrfivi gavrcelebis dros iwveven atomuri Jangbadis mwvane xazis emisiis intensifikacias. Sesabamisi arawrfivi grigalebi uzrunvelyofen atomuri Jangbadis koncentraciis zrdas E-SreSi da zrdian 557.7 nanometris mwvane xazis radiaciis intensiobas.

3) ganxilulia seismuri warmoSobis maRalsixSiriani eleqtromagnituri talRebis (eleqtronul-ciklotronuli, ionur-ciklotronuli, vistlerebi) urTierTqmedeba sustad ionizirebuli ionosferos D, E da F Sreebis gazTan. gaTvaliswinebulia eleqtronebze moqmedi ponderomotoruli Zala da miRebulia Sesabamisad modificirebuli Carnis gantoleba. naCvenebia, rom mxolod uaryofiTi grigalobis mqone (anticikloni) arawrfivi grigaluri struqturebi aRiZvrebian. naCvenebia, rom sustad ionizirebul gazSi eleqtromagnituri talRebis amplitudis modulacia iwvevs rosbis talRebis aRZvras. gansazRvrulia Sesabamisi inkrementi. seismuri warmoSobis sawyisi talRebis intensiobaze damokidebulebiT napovnia oscilaciis sxvadasxva mdgradi da aramdgradi Stoebi. aseve ganxilulia eleqtromagnituri ionur-ciklotronuli struqturebis arawrfivi dinamika dedamiwis magnitosferoSi. napovnia brtyeli solitonuri struqturebi da aseve organzomilebiani grigaluri arawrfivi struqturebi.

4) miRebuli Sedegebis bazaze SemoTavazebulia ionosferos nawilakebis koncentraciisa da lokaluri qaris siCqaris gasazRvris axali meTodi.

5) Cven aRvniSnavT, rom gansazRvruli Tvisebebis mqone sxvadasxva ganmxoloebuli struqturebis arseboba SesaZlebelia ganxilul iqnas dedamiwis miwisZvrebis SesaZlo prognozirebisaTvis. 2005 wels saerTaSoriso kosmosur sadgurze LAZIO-SIRAD deteqtoris damontaJeba motivirebuli iyo aseTi eleqtromagnituri signalebis monitoringisaTvis da maTi dedamiwis miwisZvrebis prognozirebisaTvis. amitom, proeqtis CarCoebSi gamokvleuli oscilaciis axali Stoebisa da energetikulad intensirebuli ganmxoloebuli solitonuri struqturebis deteqtireba SesaZlebelia ganxilul iqnas rogorc dedamiwis miwisZvris winamorbedebi.
1.6. saqarTvelos erovnuli samecniero fondisPproeqti

# GNSF/ST08/5-442 2009 wlis angariSi
proeqtis saTauri: dedamiwis ionosferoSi rosbisa da akustikur-gravi­taciuli eleqtromagnituri talRebis gavrce­lebis dinami-kis fizikuri modelireba

proeqtis xangZlivoba: 1.03.1009 – 1.03.2012, 12 kvartali

proeqtis xelmZRvaneli: Tamaz kalaZe

proeqtis menejeri: luba wamalaSvili

Semsruleblebi: Tamaz kalaZe

luba wamalaSvili

dasaxuli amocanebi

akustikur-gra­vita­ciuli eleqtro­ma­g­nituri talRebis io­­nosferos E, F--Sre­ebSi gavrcelebis fi­­zi­ku­ri modelireba.

A akustikur –gravi­taciuli eleqtro magnituri tal­Re­bis zonalur qar­­Tan arawrfivi ur­Ti­­erTobebis Ses­wavla ionos­feros E, F—SreebSi.
ganxorcielebuli amocanebis mokle aRwera

dedamiwis ionosferos E, F –SreSi damuxtuli nawila­kebis mier aRZruli denisa da magnituri velis urTierTqmedebis gaTva­lis­winebiT miRebu­lia aku­s­ti­kur-gravitaciuli tal­Rebis ara­­wrfivi gavr­ce­lebis dinami­kis aRmweri ganto­lebe­­bis sis­te­ma. Seswavlilia Sesa­bamisi mcire SeSfoTebebis gav­r­cele­bis eleqtromagnituri bu­­neba. Ggarda amisa gamokvleulia am­p­litiduri modulaciis saSu­alebiT rosbis talRebis aRZ­vris axali meqanizmi.

gamokvleuli iqna ionos­fe­ros E, F--SreSi akustikur-gra­vitaciuli eleqtro­magni­turi talRebis zonalur qar­Tan ur­Ti­erTqmedebis SesaZ­leb­lo­ba. hasegava-mimas arawrfivi dife­rencialuri gantolebis gamo­ye­nebiT dadginda zonaluri qa­ris aRZvris meqanizmebi, Sefa­sebuli iqna aRZvris siCqare.

Seswavlili iqna eleq­tro­magnituri iner­ci­ul-gra­vita­ciu­li talRebis gavrce­leba deda­miwis ionosferos E- da F- SreebSi geomagnituri velis pa­ra­leluri denis arsebobis pirobebSi. gamo­kv­leuli iqna aseTi talRebis gavrcelebis SesaZlebloba da Sesabamisi aramdgrado­be­bi.

plazmuri mdgomareoba xSir SemTxvevebSi warmoadgens sami komponentis, eleqtronebis, po­zitronebisa da ionebis narevs. Seswavlili iqna aseT plaz­maS­i zonaluri nakadis aRZvris SesaZlebloba.
1.7. saxelmwifo samecniero granti # ____ GGNSF/ST08/3-395 sxvadasxva fizikuri velis zemoqmedebis Seswavla periodul da kvaziperiodul struqturebze
proeqtis samecniero xelmZRvaneli

nino xatiaSvili
gamokvleulia Semdegi amocanebi:

1. 
   amoxsnilia laplasis org­a­n­zo­mi­lebiani gan­to­­leba oradperi­odul are­­Si elifsoidaluri WrilebiT uban-uban uwyveti sasazRvro pirobebiT. amocana amoxsnilia rogorc integralur gantolebaTa meTodiT, aseve sxvaobiani sqemebiT. miRebulia efeqturi amoxsnebi.
   

es amocana dakav­Sirebulia kapilarSi eriTrocitis moZraobasTan, agreTve marTkuTxa badis tipis nanostruqturaSi nawilakebis moZraobasTan.

am amocanasTan dakavSirebiT gamoqveynebulia naSromebi [1,2], gakeTebulia moxseneba gamoyenebiTi maTematikis institutis seminarze da saerTaSoriso konfe­renciaze (ix. monawileoba konferenciebSi).

2. 
   gamokvleulia helmholcis organ­zo­mile­biani gan­to­­leba orad­­peri­odul Wri­lebian are­­ebSi, kerZod, poligonalur badeebSi. saTa­na­do sa­sa­z­­R­vro pi­ro­be­biT. amocana gamokvleulia integralur gantolebaTa meTodiT. miRebulia integraluri gantolebis miaxloebiTi amoxsnebi.
   

amocana aRwers poligonaluri badis mqone nanostruqturaSi nawilakis moZraobas.

amasTan dakavSirebiT gakeTebulia moxseneba saerTaSoriso kongresze praRaSi, agreTve saerTaSoriso konferenciaze TbilisSi (ix. konferenciebi). gamoqveynebulia 2 naSromi [3,4].

3. 
   Seswavlilia Sredingeris ganto­leba oradperiodul areSi. kon­for­mul asaxvaTa da poten­cia­lis meTodis gamoyenebiT miRebu­lia amoxsnis integraluri war­modgenebi uban-uban uwyvet fun­qcia­Ta klasSi. Seswavlilia agreTve neitronebis gadatanis integro-diferencialuri gantoleba sibrtyeze. miRebulia ekonomiuri sxvaobiani sqemebi.
   

es gantoleba aRwers mraval process, Cven SeviswavleT igi did hedronul ko­­la­i­derSi protonebis nakadis Sejaxebis TvalsazrisiT.

am amoca­nasTan dakavSirebiT gakeTda moxseneba saerTaSoriso konferenciaze TbilisSi da saqarTvelos maTematikosTa mexuTe yrilobaze (ix. mona­wileoba konferenciebSi). gamoqveynebulia 3 naSromi [5,6,7].

4. 
   gamokvleulia difuziis wrfivi or­­ga­­n­­­zo­­milebiani gan­to­­leba ora­d­­­­perioul are­Si uban-uban uwyveti sawyisi da sasaz­Rvro piro­be­biT, difuziis gantoleba reducirebu­lia in­te­g­­ra­luri ganto­lebaze, rome­lic gamokvleulia uban-uban uwyvet funqciaTa klasSi. zo­gi­erT ker­Zo SemTxve­va­Si mi­i­Re­ba efeqturi amoxsne­bi.
   

es gantoleba aRwers mraval process, Cven SeviswavleT igi cocxali organizmis kapilarSi nivTierebaTa cvlis TvalsazrisiT, agreTve Seswavlilia naxSirbadis mier war­­mo­qm­nil nanostru­q­­tu­rebSi eleqtro­nebis ga­data­nis erTi maTematikuri modeli.

1.8. “zogierTi diskretuli maTematikuri struqturis logikuri aspeqtebi da maTi gamoyenebebi”
granti # GNSF/ST07/3-178
proeqtis samecniero xelmZRvaneli: roland omanaZe

Semsruleblebi: roland omanaZe

revaz grigolia

gogi fanculaia

arCil yifiani

ramaz liparteliani
wamyvani organizacia: iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti
proeqtis dawyebis TariRi: 01.01.2008

proeqtis dasrulebis TariRi: 31.12.2009


mokle samecniero angariSi

proeqtis farglebSi Catarebuli gamokvlevebiT miRebul iqna Semdegi Sedegebi:

1. rekursiulad gadaTvladi (r.g.) A simravle aris efeqturad gawonasworebadi maSin da mxolod maSin, Tu arsebobs iseTi uniformulad rekursiuli mwkrivi { R_n }_nϵω , romelic aris efeqturad kofinaluri A-Si.

2. yoveli ararekursiuli r.g. A simravlisaTvis arsebobs iseTi ararekursiuli r.g. qvesimravle B , rom yoveli r.g. ararekursiuli W simravlisaTvis gvaqvs : W araa QQ-dayvanadi A-B –ze da A-B Q-dayvanadia A-ze.

3. vTqvaT K aris Q-sruli r.g. simravle . maSin arsebobs sigma 0_2 simravle B iseTi, rom (degQ(K) , degQ(B)) aris minimaluri wyvili r.g. Q-xarisxebSi.

4. nebismieri MVN_n-algebra (A, ,,,1, 1/2,0) izomorfulia (S_m, ,,,1, 1/2,0) algebrebis qvepirdapiri namravlisa, sadac m,n > 2 da m 1 yofs n 1.

5. formula  aris NL_n logikis Teorema maSin da mxolod maSin, roca  tavtologiaa, e. i. |   |= .

6. sasrulad warmoqmnili MVN_n-algebra A aris proeqciuli maSin da mxolod maSin, roca A izomorfulia S₃  A’, sadac A’ aris sasruli MVN_n-algebra.

7. napovnia uniformuli grafebis avtomorfizmTa jgufebis simZlavreTa simravle, es simravle gansxvavdeba -xeebis avtomorfizmTa jgufebis simZlavreTa simravlisagan da cxadi saxiTaa Cawerili; magaliTad es simravle Seicavs yvela mTel dadebiT ricxvs, am faqtidan ki gamomdinareobs avtomorfizmebis Sesaxeb ulamis erTi amocanis amoxsna

8. SeuZlebelia nebismieri jgufis warmodgena uniformuli grafis avtomorfizmTa jgufiT da e.i SeuZlebelia jgufTa warmodgenadobis Sesaxeb kionigis cnobili amocanis uniformizacia.

9. arsebobs ω₁ -xe T, romlis uniformizaciac SeuZlebelia Aut(T) –s simZlavris SenarCunebiT.

10. miRebul iqna kardinalur ricxvTa ( , 2^ ) Ria Sualedis daxasiaTeba binarul damokidebulebaTa avtomorfizmebis terminebSi.

11. damtkicda, rom winadadeba: „nebismieri α ordinalisaTvis arsebobs uniformuli binaruli mimarTeba, romlis avtomorfizmTa jgufi ω_α+1 simZlavrisaa“ ganzogadoebuli kontinuum- hipoTezis eqvivalenturia.

12. soloveis DmodelSi damtkicebulia, rom bazisian separabelur banaxis sivrceebSi sasrul-ganzomilebiani veqtoruli sivrciT gansazRvruli yoveli simravle warmoadgens shy-simravles. AamasTan yoveli aseTi simravlisaTvis agebulia lebegis zomis garkveuli usasrulo analogi, romlis mimarTac aRniSnuli simravle aris nul-zomadi. Aaqve naCvenebia rom analogiuri Sedegi ara marTebuli AAC modelebisaTvis.

13. mocemulia meTodi, romelic iZleva saSualebas evklides n-ganzomilebiani sivrcis lebegis azriT nulzomadi universaluri simravle davxliCoT n-cal iseT universalur qvesimravled, romelTagan TiToeuli aris gansazRvruli sakoordinato RerZis ortebiT warmoqmnili erTganzomilebiani veqtoruli qvesivrceebiT(Hhonjoia Sis (Hongjia Shi) I amocanis amoxsna).

14. Seswavlilia zogadi sistemebis zogierTi Tviseba sxvadasxva simravlur-Teoriul modelebSi. kerZod, soloveisa da ZFC modelebSi, da sivrceebSi ganxilulia ostrogradskis, kramerisa da liuvilis Teoremebis usasrulo analogebi.

1.9. “algoriTmuli da kombinatoruli meTodebis zogierTi gamoyeneba algebruli da diskretuli tipis struqturebSi” granti # GNSF/ST08/3-391

proeqtis samecniero xelmZRvaneli: roland omanaZe

Semsruleblebi: roland omanaZe

A aleqsandre xaraziSvili

gogi fanculaia

arCil yifiani

aleqxi kirTaZe
wamyvani organizacia: iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti
proeqtis dawyebis TariRi: 01.03.2009

proeqtis dasrulebis TariRi: 28.02.2010


mokle samecniero angariSi

proeqtis farglebSi Catarebuli gamokvlevebiT miRebul iqna Semdegi Sedegebi:

1. vTqvaT M aris maqsimaluri simravle, A Arekursiulad gadaTvladi (r.g.) simravle da AM. maSin

1. 
   Tu M araa m-dayvanadi M-A, maSin M araa Q-dayvanadi M-A.
   
2. 
   Tu M-A aris imunuri, maSin ar arsebobsi iseTi arsad martivi simravle S , rom M _Q (M-A) S.
   

2. Tu r.g. a da b aris minimaluri wyvili r.g. Q-xarisxebSi, maSin is aris minimaluri wyvili ∑ 0_2 Q-xarisxebSi.

3. rogoric ar unda iyos simravleTa araTvladi damoukidebeli ojaxi, ar arsebobs ganzogadebuli eiler-venis diagrama, romelic am ojaxs Seesabameba da romlis yvela figura amozneqil mravalkuTxeds (poligons) warmoadgens.

4. Tu mocemulia simravleTa damoukidebeli ojaxi, romlis simZlavre kontinuumis simZlavris tolia, maSin arsebobs misi Sesabamisi ganzogadebuli eiler-venis diagrama, romlis yvela figura amozneqil kvazi-poligons warmoadgens.

5. nebismieri kombinatorulad xisti kompleqsi (grafi) aranakleb or samkuTxa ares warmoqmnis;

6. arsebobs ragind didi raodenoba wveroebis mqone kombinatorulad xisti kompleqsi (grafi), romelic or samkuTxa ares warmoqmnis, magram mis mier warmoqmnili yvela danarCeni are aris oTxkuTxa.

7. Seswavlilia polonur jgufebze gansazRvruli shy-simravleTa generatorebis arsebobis, erTaderTobis, kvazi-finiturobisa da -sasrulobis sakiTxebi

8. SemuSavebulia lebegis zomis axali, kerZod standartuli da ordinaluri „lebegis zomebis“koncefciebi tixonovis topologiiT aRWurvil polonur jgufze da mocemulia misi zogierTi realizacia TeoriaSi.

9. Semotanilia - jgufze gansazRvruli marcxnidan -invariantuli araseparabeluri albaTuri zomebis ojaxebis klasifikacia da Seswavlilia maTi zogierTi Tviseba. aseve, tarskis damoukidebeli ojaxebis teqnikis saSualebiT agebulia arasigmakompaqtur lokalurad kompaqtur jgufebze gansazRvruli haaris zomaTa Tvladi ojaxebis ordinaluri da araordinaluri namravlebis marcxnidan invariantuli araseparabeluri gagrZelebebi maTTan asocirebuli metrikuli sivrceebis maqsimaluri topologiuri wonebiT.

10. Seswavlilia funqciebis zomadobis sakiTxi zogierTi simravlur-Teoriuli midgomis safuZvelze. -sasruli da zomebiT aRWurvili zomadi da sivrceebisaTvis napovnia sakmarisi pirobebi, romlebic uzrunvelyofen namravl sivrceSi masiuri grafikis mqone asaxvis arsebobas. aseTi asaxva aris fardobiTad zomadi iseT zomaTa klasis mimarT romlebic warmoadgenen originaluri zomis gagrZelebebs.

11. damtkicda, rom nebismieri usasrulo (G,.) jgufisaTvis. arsebobs araorientirebuli grafi (V,E ) iseTi, rom V  G da (G, .) jgufi (V,E) grafis yvela avtomorfizmTa jgufis izomorfulia.M

12. mocemul iqna kardinalur ricxvTa ( , 2^ ) Ria intervalis daxasiaTeba, araorientirebuli grafebisa da maTi avtomorfizmebis terminebSi.

danarTi # 2

(gverdebi 22-30)

gmi_Si same­cniero-kvleviTi muSaoba 2009 wlis manZilze mimdinareobda oTxi ZiriTadi mimarTulebiT.
mimarTuleba 1. uwyvet garemoTa meqanikis maTematikuri proble­mebi da analizis monaTesave sakiTxebi (xelmZRvaneli – giorgi jaiani). muSav­de­boda 17 individua­luri samecniero-kvleviTi Tema.

Tema 1.1. Seyursuli sakontaqto urTierTqmedebis sakiTxis gamokvleva Runvis amocanisaTvis (Semsrulebeli – giorgi jaiani).

miRebuli Sedegi. Seswavlil iqna wamaxvilebuli kirxof-lavis firfitis Runvis dros Seyursuli sakontaqto urTierTqmedebis sakiTxi. dadginda, rom wamaxvilebuli firfitis wamaxvilebul napirze gare Seyursuli mRunavi M momentis moqmedebis dros modebis wertilSi warmoiqmneba Sinagani Seyursuli mRunavi M momenti. miRebulia formula, romelic M–s gamosaxavs M-is saSualebiT.

Tema 1.2. drekad narevTa statikis mTavari sakontaqto amocanis gamokvleva (Semsrulebeli - mixeil baSeleiS­vi­li).

miRebuli Sedegi. ganxilulia ori drekadi izotropuli narevi, romelTagan erTs ukavia sasruli, xolo meores – usasrulo are, maTi gamyofi Caketili wiri ki sakmarisad gluvia. amocana mdgomareobs mocemul areebSi gadaadgilebis da Zabvis veqtorebis gansazRvraSi sakontaqto wirze mocemuli maTi sakmarisad gluvi naxtomebis saSualebiT, gadaadgilebis veqtoris usasrulobaSi yofaqcevis garkveuli SezRudvebis pirobebSi. potencialTa da integralur gantolebaTa meTodebis gamoyenebiT damtkicebulia ganxiluli amocanis arsebobisa da erTaderTobis Teoremebi.

Tema 1.3. Tanabrad mtkice konturis moZebnis amocana periodulad ganlagebuli xvrelebiT Sesustebuli drekadi naxevarsibrtyisaTvis (Semsrulebeli – giorgi kapanaZe).

miRebuli Sedegi. Seswavlilia periodulad ganlagebuli Tanabrad mtkice xvrelebiT Sesustebuli qveda naxevarsirbtyis drekadi wonasworobis amocana im daSvebiT, rom xvrelis sazRvari Tavisufalia garegani datvirTvebisagan, xolo naxevarsibrtyis sazRvarze moqmedebs absoluturad xisti Stampi sworxazovani fuZiT.

amocana mdgomareobs imaSi, rom ganisazRvros naxevarsibrtyis drekadi wonasworoba da dadgindes xvrelis sazRvris analizuri forma im pirobiT, rom masze tangencialuri normaluri Zabva mudmiv mniSvnelobas Rebulobdes. amocanis amosaxsnelad gamoyenebulia kompleqsuri analizis meTodebi, kerZod, kolosov-musxeliSvilis formulebis gamoyenebiT dasmuli amocana miyvanilia riman- hilbertis amocanaze naxevarsibrtyisaTvis da am ukanasknelis efeqturad amoxsnis safuZvelze saZiebeli kompleqsuri potencialebi da ucnobi konturis gantoleba agebulia analizuri saxiT.

Tema 1.4. arawrfivi da aradamreci garsebis Teoriis diferencialur gantolebaTa sruli sistemis ageba (Semsrulebeli – Tengiz meunargia).

miRebuli Sedegi. akad. i.vekuas mier SemoTavazebuli iyo wrfivi da damreci garsebis dazustebuli Teoriis agebis ramdenime varianti. am meTodze dayrd­nobiT miRebul iqna aradamreci garsebisaTvis geometriu­lad da fizikurad arawrfivi gantolebaTa sruli sistema. mi­Rebuli arawrfiv diferencialur gantolebaTa sistema, mcire para­metris SemoRebiT, dayvanil iqna II rigis elifsuri tipis gantoleba­Ta sistemamde, garsis Sua zedapiris izometrul koordinatTa mi­marT. am sistemis marcxena mxare wrfivia, xolo marjvena mxare war­moadgens wina miaxloebebis garkveul kombinacias. am sistemis zogadi amonaxsnis kompleqsuri saxe, nebismieri NN-uri rigis miaxloebisaTvis, Cawerilia vekua-biwaZis tipis formulis saSualebiT.