Browsing Mathematical Sciences by Title
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Danić, Dr Dimitrije (Branislav Cerović - Ajhštet , 1920)[more][less]
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Jočić, Radivoje; Danić, Dimitrije (Belgrade , 1920)[more][less]
URI: http://hdl.handle.net/123456789/437 Files in this item: 1
RadivojeJocicDiferencijalniRacun.pdf ( 13.94Mb ) -
Bilimović, Anton (Beograd , 1961)[more][less]
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Bojović, R. Dejan (Kragujevac, Serbia , 1999)[more][less]
Abstract: The field of research in this dissertation is consideration of convergence of finite differnce method for parabolic problems with generalized solutions. The research in this dissertation is connected with the following subjects: Numerical Analysis and Partial Differential Equations. This dissertation, beside Preface and References with 56 items, consists of five chapters: 1. Introductory Topics; 2. Parabolic Problems with Variable Operator: Convergence in W(2,1)-norm; 3. Parabolic Problems with Variable Operator: Convergence in W(1,1/2)-norm; 4. Convergence in L-2 norm; 5. Application of Interpolatyion theory In Chapter 1 a brief review of the Sobolev spaces, anisotropic Sobolev spaces, multipliers in Sobolev spaces, interpolation theory of Banach spaces and existence of generalized solution of parabolic problems are presented. Initial-boundary-value problems with variable (time-dependent) operator are considered in Chapters 2 and 3. In Chapter 2 is proved convergence of finite difference scheme in discrete W(2,1) Sobolev norm. Convergence in W(1,1/2) norm is proved in Chapter 3. In Chapter 4, parabolic problem with variable coefficients is considered and convergence in L-2 norm is proved. Finally, in Chapter 5 , interpolation theory is applied to the convergence analysis. URI: http://hdl.handle.net/123456789/1915 Files in this item: 1
doktorska disertacija Scan reduce.pdf ( 1.523Mb ) -
Hodžić, Sandra (Beograd , 2016)[more][less]
Abstract: In recent years there has been increasing interest in modeling the physical and chemical processes with equations involving fractional derivatives and integrals. One of such equations is the subdi usion equation which is obtained from the di usion equation by replacing the classical rst order time derivative by a fractional derivative of order with 0 < < 1: The subject of this dissertation is the initial-boundary value problem for the subdi usion equation and its approximation by nite di erences. At the beginning, the one-dimensional equation is observed. The existence and the uniqueness of weak solution is proved. The stability and the convergence rate estimates for implicite and the weighted scheme are obtained. The main focus is on two-dimensional subdi usion problem with Laplace operator as well as problem with general second-order partial di erential operator. It is assumed that the coe cients of the di erential operator satisfy standard ellipticity conditions that guarantees existence of solution in appropriate spaces of Sobolev type. In that case, apart from above mensoned, we constructed the additive and the factorized di erence schemes. We investigated their stability and convergence rate depending on the smoothness of the input data and of generalized solution. URI: http://hdl.handle.net/123456789/4455 Files in this item: 1
Disertacija_Sandra_Hodzic.pdf ( 913.2Kb ) -
Budimir, Srđan (Beograd , 2013)[more][less]
URI: http://hdl.handle.net/123456789/4911 Files in this item: 1
S Budimir MASTER RAD.pdf ( 837.9Kb ) -
Pejović, Tadija (BEOGRAD , 1936)[more][less]
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Bejtullahu, Rasim (Pristina , 1976)[more][less]
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Delić, Aleksandra (Beograd , 2016)[more][less]
Abstract: The time fractional di usion-wave equation can be obtained from the classical diffusion or wave equation by replacing the rst or second order time derivative, respectively, by a fractional derivative of order 0 < 2. In particular, depending on the value of the parameter , we distinguish subdi usion (0 < < 1), normal di usion ( = 1), superdi usion (1 < < 2) and ballistic motion ( = 2). Fractional derivatives are non-local operators, which makes it di cult to construct e cient numerical method. The subject of this dissertation is the time fractional di usion-wave equation with coe cient which contains a singular distribution, primarily Dirac distribution, and its approximation by nite di erences. Initial-boundary value problems of this type are usually called interface problems. Solutions of such problems have discontinuities or non-smoothness across the interface, i.e. on support of Dirac distribution, making it di cult to establish convergence of the nite di erence schemes using the classical Taylor's expansion. The existence of generalized solutions of this initial-boundary value problem has been proved. Some nite di erence schemes approximating the problem are proposed and their stability and estimates for the rate of convergence compatible with the smoothness of the solution are obtained. The theoretical results are con rmed by numerical examples. URI: http://hdl.handle.net/123456789/4337 Files in this item: 1
ADelicDisertacija.pdf ( 1.356Mb ) -
Kapunac, Stefan (Beograd , 2020)[more][less]
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Mijajlović, Žarko (Beograd , 2007)[more][less]
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Korać, Vanja (Beograd , 2012)[more][less]
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Korać, Vanja (Beograd , 2014)[more][less]
Abstract: Digitalna forenzika je multidisciplinarna nauka koja podrazumeva spoj razlicitih nauĉnih disciplina (raĉunarske nauke, pravo, kriminologija) sa brojnim izazovima u uslovima masovnog generisanja digitalnih podataka (Big Data), virtuelizacije klijentske i serverske strane (Cloud Computng), neusaglašenosti standardizacionih tela i opšteg nedostatka brojnih standarda i eksperata u svim disciplinama. Kako se digitalna forenzika odnosi na sve digitalne uraĊaje, uţa nauĉna oblast uklјuĉuje brojne aplikacije digitalne forenzike, kao što su raĉunarska forenzika, forenzika mobilnih ureĊaja, forenzika na sistemima savremenih automobila, senzorskih mreţa itd. U ovom radu je analizirana i primenjena uţa nauĉna oblast raĉunarske forenzike. Opisana je digitalna forenzika raĉunarskih sistema baziranih na Windows i Linux platformi, sa fokusom na odreĊena mesta u implementiranom sistemu proaktivne digitalne forenzike koja mogu ukazati na forenziĉki relevantne dogaĊaje kritiĉne za bezbednost sistema. Opisane su brojne metodologije, tehnologije i tehnike istrage visokotehnološkog kriminala. Proces prikuplјanja podataka i digitalne forenziĉke analize „uţivo―, detalјno je razmatran. Izvršena je kratka revizija karakteristika i tipiĉno zahtevanih funkcionalnosti softverskih forenziĉkih alata, za inicijalni odgovor i oporavak podataka i particija magnetnih diskova. Opisani su i najvaţniji digitalni forenziĉki kompleti alata i njihove osnovne funkcionalnosti. U radu se istiĉu i najznaĉajniji elementi kojima treba posvetiti posebnu paţnju prilikom digitalne forenziĉke analize u virtuelnom okruţenju. TakoĊe su objašnjeni i najvaţniji segmenti samog virtuelnog okruţenja i naĉin na koji oni mogu biti znaĉajni alati, za postupak digitalne forenziĉke analize. U poslednjem delu ovog rada, fokus je usmeren na ranjivosti Windows i Linux platformi sa prikazanim naĉinima zlonamernog proboja sistema. Opisane su opšte ranjivosti i specifiĉne ranjivosti koje se odnose samo na Windows, odnosno samo na Linux platforme. TakoĊe, navedeni su i najĉešći naĉini zlonamernog iskorišćavanja sistema. Ranjivosti raĉunarskih sistema i mreţa mogu se odnositi na programe, hardver, konfiguraciju i lјude. Isklјuĉujući lјude kao najznaĉajniji i istovremeno najkritiĉniji faktor u zaštiti informacija, programske ranjivosti se tipiĉno koriste za online direktne napade, ili napade malicioznim programima. Otkrivanje i otklanjanje ranjivosti sistemskih programa je jedan od glavnih cilјeva digitalne forenzike. Pored skuplјanja forenziĉki relevantnih digitalnih podataka i izgradnje ĉvrstih digitalnih dokaza o kompjuterskom incidentu ili kriminalu za potrebe pravosudnog sistema, cilј digitalne forenziĉke analize je da se iskorišćene ranjivosti trajno otklone i da se incident/protivpravna aktivnost takve vrste više nikada ne ponovi. U tom smislu je doprinos ovog rada veoma znaĉajan. Praktiĉan primer ispitivanja ranjivosti servisa na Windows i Linux platformama obuhvatio je 80 operativnih sistema. Od tog broja, 51 se odnosi na Windows operativne sisteme, a 29 na Linux operativne sisteme. Dobijeni rezultati su rezultat dvogodišnjeg istraţivanja, jer je ispitivanje sistema vršeno u 2011. i 2013. godini. Kroz skeniranje i prikaz ranjivosti difoltno instaliranih Windows i Linux sistema preventivno se otkrivaju ranjivosti koje potencijalno mogu biti iskorišćene od strane bezbednosnih pretnji (maliciozni programi ili zlonamerni napadaĉi) i time ugroziti raĉunarske sisteme i informacije. Proaktivnim otklanjanjem ovih ranjivosti realizuje se preventivna zaštita. Uspostavlјanjem sistema proaktivne forenzike, obezbeĊuje se logovanje forenziĉki relevantnih dogaĊaja, tj. tragova pokušaja napada u realnom vremenu, ĉime se bitno olakšava forenziĉka istraga u sluĉaju incidenta ili protivpravne aktivnosti. URI: http://hdl.handle.net/123456789/3869 Files in this item: 1
doktorat_Vanja_Korac.pdf ( 9.093Mb ) -
Mijajlović, Žarko (Beograd , 2008)[more][less]
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Mijajlović, Žarko (Belgrade , 2004)[more][less]
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Ilić, Dragana (Belgrade , 2008)[more][less]
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Zougdani, Hassan (Belgrade , 1984)[more][less]
URI: http://hdl.handle.net/123456789/148 Files in this item: 1
phdHassanKhalifaZougdani.pdf ( 4.157Mb ) -
Ilić, Dejan (Beograd , 2011)[more][less]
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Radak, Vladislav (Beograd , 2013)[more][less]
URI: http://hdl.handle.net/123456789/4873 Files in this item: 1
Dinami_ki model ... anju - Vladislav Radak.pdf ( 1.434Mb ) -
Radak, Vladislav (Beograd , 2013)[more][less]
URI: http://hdl.handle.net/123456789/2800 Files in this item: 1
masterVladislavRadak.pdf ( 1.334Mb )