Browsing Mathematics by Title
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Turku, Haljilj (Pristina , 1978)[more][less]
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Pažanin, Ratomir (Belgrade , 1980)[more][less]
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Lelas, Nikola (Beograd , 2022)[more][less]
Abstract: The subject of the dissertation is the problem of simultaneous nonvanishing of quadratic twists of elliptic curve 𝐿-functions and quadratic Dirichlet 𝐿-functions (and their derivatives) at the centar point 𝑠 = 1 2 , in the situation when these objects are defined over the rational function field over finite field F𝑞. For each monic polynomial 𝐷 ∈ F𝑞 [𝑡], there is a corresponding quadratic Dirichlet character 𝜒𝐷. Associated to such character, there is the corresponding Dirichlet 𝐿- function 𝐿(𝑠, 𝜒𝐷), as well as the quadratic twist 𝐸 ⊗ 𝜒𝐷 of a fixed elliptic curve 𝐸/F𝑞 (𝑡), whose 𝐿-function is denoted by 𝐿(𝑠, 𝐸 ⊗ 𝜒𝐷). A lower bound for the number of polynomials 𝐷 ∈ H∗ 2𝑔+1 such that 𝐿 URI: http://hdl.handle.net/123456789/5532 Files in this item: 1
Disertacija_nikola_lelas.pdf ( 2.523Mb ) -
Mitrinović, Dragoslav (Beograd , 1933)[more][less]
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Jaćimović, Milojica (Belgrade)[more][less]
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Alimpić, Branka (Belgrade)[more][less]
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Prešić, Marica (Belgrade)[more][less]
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Krstev, Cvetana (Beograd , 1997)[more][less]
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Marinković, Silvana (Kragujevac, Serbia , 2011)[more][less]
Abstract: In this dissertation functions and equations in some classes of lattices such as Post algebras, Stone algebras and multiple-valued logics, are studied. The dissertation, beside Preface and References with 46 items, consists of five chapters. In Introduction some basic notations which will be used in next chapters are given. Main results on Boolean functions and equations are exposed in Chapter 2. In Chapter 3, assuming that a general solution is known, the class of reproductive general solutions of the equation in Stone algebra is described. All general solutions of equations in one variable in multiple-valued logic are described in Chapter 4. A necessary and sufficient conditions that given sequence of recurrent inequalities represents solution of some consistent Post equation are given in Chapter 5. Also, it is proved that every Post transformation is the parametric solution of some consistent Post equation. URI: http://hdl.handle.net/123456789/1842 Files in this item: 1
SilvanaMarinkovicDoktorat.pdf ( 360.3Kb ) -
Stipanić, Ernest (Belgrade)[more][less]
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Dacić, Rade (Belgrade , 1965)[more][less]
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Mitrović, Slobodanka (Belgrade)[more][less]
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Lipkovski, Aleksandar (Belgrade , 1985)[more][less]
URI: http://hdl.handle.net/123456789/25 Files in this item: 1
phdAleksandarLipkovski.pdf ( 2.471Mb ) -
Miličić, Miloš (Belgrade , 1982)[more][less]
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Malinović, Todor (Novi Sad , 1986)[more][less]
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Obradović, Marko (Beograd , 2015)[more][less]
Abstract: First characterizations of probability distributions date to the thirties of last century. This area, which lies on the borderline of probability theory and mathematical statistics, attracts large number of researchers, and in recent times the number of papers on the subject is increasing. Goodness-of- t tests are among the most important nonparametric tests. Many of them are based on empirical distribution function. The application of characterization theorems for construction of goodness-of- t tests dates to the middle of last century, and recently has become one of the main directions in this eld. The advantage of such tests is that they are often free of distribution parametres and hence enable testing of composite hypotheses. The goals of this dissertation are the formulation of new characterizations of exponential and Pareto distribution, as well as the application of the theory of U-statistics, large deviations and Bahadur e ciency to construction and examination of asymptotics of goodness-of- t tests for aforementioned distributions. The dissertation consists of six chapters. In the rst chapter a review of di erent types of characterizations is presented, pointing out their abundance and variety. The special emphasis is given to the characterizations based on equidistribution of functions of the sample. Besides, two new characterizations of Pareto distribution are presented. The second chapter is devoted to some new characterizations of the exponential distributions presented in papers [65] and [53]. Six characterizations based on order statistics are presented. A special case of one of them (theorem 2.4.3) represents the solution of open problem stated by Arnold and Villasenor [9]. In the third chapter there are basic concepts on U-statistics, the class of statistics important in the theory of unbiased estimation. Some of their asymptotic properties are given. U-empirical distribution functions, a generalization of standard empirical distribution functions, are also de ned. The fourth chapter is dedicated to the asymptotic e ciency of statistical tests, primarily to Bahadur asymptotic e ciency, i.e. asymptotic e ciency of the test when the level of signi cance approaches zero. Some theoretical results from the monograph by Nikitin [57], and papers [61], [59], etc. are shown. In the fth chapter new results in the eld of goodness-of- t tests for Pareto distribution are presented. Based on three characterizations of Pareto distribution given in section 1.1.2. six goodness-of- t tests, three of integral, and three of Kolmogorov type, are proposed. In each case the composite null hypothesis is tested since the test statistics are free of the parameter of Pareto distribution. For each test the asymptotic distribution under null hypothesis, as well as asymptotic behaviour of the tail (large deviations) under close alternatives is derived. For some standard alternatives, the local Bahadur asymptotic e ciency is calculated and the domains of local asymptotic optimality are obtained. The results from this chapter are published in [66] and [64]. The sixth chapter brings new goodness-of- t tests for exponential distribution. Based on the solved hypothesis of Arnold and Villasenor two classes of tests, integral and Kolmogorov type, are proposed, depending on the number of summands in the characterization. The study of asymptotic properties, analogous to the ones in the fth chapter is done in case of two and three summands, for which the tests have practical importance. The results of this chapter are presented in [39]. URI: http://hdl.handle.net/123456789/4288 Files in this item: 1
phdObradovicMarko.pdf ( 789.3Kb ) -
Aranđelović, Dragoljub (Belgrade)[more][less]
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Alagić, Mara (Belgrade , 1985)[more][less]
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Jokanović, Dušan (Podgorica)[more][less]
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Ivanović, Jelena (Beograd , 2020)[more][less]
Abstract: U teoriji kategorija, koherencija koja je vezana za odre eni tip kategori-ja, u najgrubljem smislu znaqi komutiranje dijagrama sastavljenih od kanonskihstrelica tih kategorija. Ovo komutiranje mo e biti bezuslovno ili uslovljenozadatim pretpostavkama. U savremenom smislu, koherencija, taqnije teoremekoherencije, podrazumevaju postojanje vernog funktora iz slobodno generisa-ne kategorije datog tipa u kategoriju koja omogu ava proveru jednakosti stre-lica. Takve su najqex e kategorije qije su strelice relacije ili dijagrami(mnogostrukosti, kobordizmi).Rezultati koherencije su od velikog znaqaja za opxtu teoriju dokaza. Naime,oni obezbe uju formiranje zadovoljavaju eg kriterijuma za jednakost izvo enjau odre enim deduktivnim sistemima i na taj naqin pru aju mogu nost defini-sanja osnovnog pojma kojim se teorija dokaza bavi.Predmet ove doktorske disertacije je prouqavanje topoloxkih dokaza ko-herencije i formiranje novih klasa politopa koje u takvim dokazima koheren-cije mogu poslu iti. Sadr aj disertacije je, dakle, u najve oj meri posve enspomenutim dokazima koherencije, odnosno raznovrsnim geometrijskim realiza-cijama specifiqnih apstraktnih politopa koji su zadati kombinatorno.Naime, ranih devedesetih godina, Mihail Kapranov je uveo familiju e-lijskih kompleksa pod nazivom permutoasociedri koja predstavlja ,,hibrid” dveznaqajne familije prostih politopa–familije asociedara i familije permuto-edara. Ovaj hibrid je predstavljao prvu geometrijsku interpretaciju udru i-vanja komutativnosti i asocijativnosti. Kapranov je pokazao da je datom elij-skom strukturom proizveoCW-loptu qime je dobio direktan topoloxki dokazkoherencije u simetriqnim monoidalnim kategorijama. Ubrzo nakon toga, Vik-tor Rajner i Ginter Cigler su ove elijske komplekse realizovali kao fami-liju konveksnih politopa. Me utim, dobijena familija nije familija prostihpolitopa. S druge strane, i svi asociedri i svi permutoedri jesu prosti. Onipripadaju nestoedarima–xiroko izuqavanoj familiji prostih politopa, kako sakombinatorne strane, tako i sa strane primena u torusnoj topologiji.Polazixte ove teze je da je prirodno prona i prost hibrid ove dve fami-lije, tj. prost permutoasociedar. Koriste i kombinatornu proceduru sliqnuonoj koja je proizvela i same asociedre i permutoedre, u ovoj disertaciji seuvodi apstraktni politop koji odgovara problemu koherencije, a koji se pritommo e realizovati kao prost politop. Preciznije, formirane su klasen-dimen-zionalnih prostih permutoasociedara koje daju topoloxki dokaz simetriqnemonoidalne koherencije, a zatim su te klase i geometrijski realizovane eks-plicitnim zadavanjem nejednaqina poluprostora uRn+1koji definixu politopexiii xivu klasama. Ovan-dimenzionalna realizacija je oznaqena saPAn. Pored toga,u tezi je ponu ena i alternativna realizacija iste familije uz pomo sumaMinkovskog. Naime, uvedena je familijan-dimenzionalnih politopa, oznaqe-na saPAn,c, koja je dobijena sumiranjem odre enih politopa. PolitopPAn,cjenormalno ekvivalentan politopuPAnza svakoc∈(0,1]. Req je o specifiqnojrealizaciji, po ugledu na realizaciju nestoedara Aleksandra Postnjikov, kojapodrazumeva da svaki sabirak, grubo reqeno, doprinosi nastajanju taqno jednepljosni rezultuju e sume Minkovskog. Drugim reqima, svaki sabirak dovodi dozarubljivanja teku e parcijalne sume odsecanjem jedne njene strane. Postnjikovje za sabirke koristio simplekse, dok ova disertacija pokazuje da je, u analog-noj realizaciji prostog permutoasociedra, za odre ene sabirke neophodno uzetipolitope koji ne samo da nisu simpleksi, ve nisu nu no ni prosti politopi. Usluqaju formiranja familijePAn,1, sabirci su definisani kao konveksni omo-taqi skupova taqaka uRn+1xto je znaqajna prednost sa stanovixta programi-ranja.Osim xto predstavlja direktan topoloxki dokaz teoreme koherencije u si-metriqnim monoidalnim kategorijama, poseban znaqaj ove alternativne reali-zacije je u uspostavljanju jasne veze izme u operacije sumiranja Minkovskogi operacije odsecanja strana permutoedra, tj. njegovog zarubljivanja. Iz oveveze implicitno sledi procedura za analognu realizaciju xire klase prostihpolitopa–familije prostih permutonestoedara.Na kraju, u tezi su date ocene hromatskih brojeva prostog permutoasociedrai nekih znaqajnih nestoedara, sa ciljem prouqavanja mogu e veze ovih klasapolitopa sa torusnim i kvazitorusnim mnogostrukostima.Tokom svih spomenutih istra ivanja, za potrebe ove disertacije je razvijenonekoliko softverskih rexenja (programa i aplikacija) uz pomo raznovrsnihprogramskih jezika i paketa (Java,polymake/Perl,Rhinoceros/ Grasshopper). Naj-znaqajnija me u njima opisana su u dodatku teze programskim kodom i odgo-varaju im ilustrativnim primerima. URI: http://hdl.handle.net/123456789/5104 Files in this item: 1
Ivanovic_Jelena_disertacija.pdf ( 2.983Mb )