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1	Zakoni održanja u heterogenim sredinama / Conservation laws in heterogeneous media Aleksić Jelena 16 October 2009 (has links) <p>Doktorska disertacija posve¶cena je re·savanju nelinearnih hiperboli·cnih skalarnih zakona odr·zanja u heterogenim sredinama, prou·cavanjem osobina kompaktnosti re·senja familija aproksimativnih jedna·cina. Ta·cnije, u cilju dobijanja re·senja u = u(t; x) problema @ t u + divx f (t; x; u) = 0;uj t=0 = u 0(x); gde su promenljive x 2 R d i t 2 R+<br />, posmatramo familije problema koji na neki na·cin aproksimiraju po·cetni problem, a koje znamo da re·simo, i ispitujemo familije dobijenih re·senja koja zovemo aproksimativna re·senja. Cilj nam je da poka·zemo da je dobijena familija u nekom smislu prekompaktna,<br />tj. da ima konvergentan podniz ·cija granica re·sava po·cetni problem.</p> / <p>Doctoral theses is dedicated to solving nonlinear hyperbolic scalar conservation laws in heterogeneous media, by studying compactness properties of the family of solutions to approximate problems. More precise, in order to obtain solution u = u(t; x) to the problem @ t u + divx f (t; x; u) = 0; uj t=0 = u 0 (x); (4.18) where x 2 R d and t 2 R+<br />, we study the solutions of the families of problems that, in some way, approximate previously mentioned problem, which we know how to solve. We call those solutions approximate solutions. The aim is to show that the obtained family is in some sense precompact, i.e. has convergent subsequence that solves the problem (4.18).</p>
2	On some results of analysis in metric spaces and fuzzy metric spaces Aphane, Maggie 12 1900 (has links) The notion of a fuzzy metric space due to George and Veeramani has many advantages in analysis since many notions and results from classical metric space theory can be extended and generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, completion of spaces as well as extension of maps. The layout of the dissertation is as follows: Chapter 1 provide the necessary background in the context of metric spaces, while chapter 2 presents some concepts and results from classical metric spaces in the setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy metric spaces, among others we show that: the product of two complete fuzzy metric spaces is also a complete fuzzy metric space. Our main contribution is in chapter 4. We introduce the concept of a standard fuzzy pseudo metric space and present some results on fuzzy metric identification. Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics) Metric space Cauchy sequence Compactness Precompactness Completeness Continuity Uniform continuity Isometry Uniform convergence Seperable Nested Closed sets Diameter Pseudo metric space Fuzzy metric space Standard fuzzy metric space Fuzzy pseudo metric space Metric identification Fuzzy metric identification Nonexpansive map t-nonexpansive map t-uniformly continuous map t-isometry map Quotient map Quotient topology Quotient space Natural map Topological space 514.325 Metric spaces Fuzzy topology
3	On some results of analysis in metric spaces and fuzzy metric spaces Aphane, Maggie 12 1900 (has links) The notion of a fuzzy metric space due to George and Veeramani has many advantages in analysis since many notions and results from classical metric space theory can be extended and generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, completion of spaces as well as extension of maps. The layout of the dissertation is as follows: Chapter 1 provide the necessary background in the context of metric spaces, while chapter 2 presents some concepts and results from classical metric spaces in the setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy metric spaces, among others we show that: the product of two complete fuzzy metric spaces is also a complete fuzzy metric space. Our main contribution is in chapter 4. We introduce the concept of a standard fuzzy pseudo metric space and present some results on fuzzy metric identification. Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics) Metric space Cauchy sequence Compactness Precompactness Completeness Continuity Uniform continuity Isometry Uniform convergence Seperable Nested Closed sets Diameter Pseudo metric space Fuzzy metric space Standard fuzzy metric space Fuzzy pseudo metric space Metric identification Fuzzy metric identification Nonexpansive map t-nonexpansive map t-uniformly continuous map t-isometry map Quotient map Quotient topology Quotient space Natural map Topological space 514.325 Metric spaces Fuzzy topology

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