Browsing Mathematical Sciences by Title
-
Jevtić, Miroljub (Belgrade)[more][less]
-
Vučković, Bojan (Beograd , 2017)[more][less]
Abstract: We present original results from the following fields of discrete mathematics: chromatic graph theory, extremal set theory and Boolean matrix theory. From the chromatic graph theory we investigate edge and total colorings satisfying the condition that neighboring vertices of a graph possess different values of multi-set, set or sum, induced by the giving coloring. Multi-set neighbor-distinguishing edge coloring of a graph is an assignment of colors to edges such that, for every edge uv of a graph, multi-set of the edges incident with the vertex u differs from the multi-set of the edges incident with the vertex v. The previous best result concerning the minimum number of colors required for such a coloring of an arbitrary graph states that four colors are sufficient. The author’s contribution is a proof that such a coloring is always possible with only three colors, which is in general case the optimal number of colors. We construct a graph for which we subsequently prove that a different number of colors is required to obtain a multi-set neighbor-distinguishing coloring and neighbor-distinguishing coloring by sum. As far as we know, this is the first example of such a graph. A few results concerning the neighbor expended sum distinguishing coloring are given. The main contribution is a proof that for an arbitrary graph there exists a total coloring from the set f1; 2; 3g, such that every two adjacent vertices have different sums of its adjacent vertices and incident edges. Also, for certain classes of graphs is proved that there exists such a coloring using only the colors from the set f1; 2g. Neighbor-distinguishing edge coloring of a graph G requires that every two adjacent edges receive different colors, while the sets of the edges incident with the vertices u and v differ for every edge uv of G. The author presents a procedure of edge coloring for an arbitrary graph without isolated edges, where we a smaller number of colors is used compared to all known results. For the adjacent vertex distinguishing total coloring of a graph G the condition is that every two adjacent and incident elements of V (G) [ E(G) receive different colors, while for every edge uv of G the set composed from the colors assigned to the edges incident with u together with the color of u, differs from such a set for v. The author improves the upper bound of the minimum number of colors needed for such a coloring, relative to the maximal degree of a graph. Frankl’s conjecture from the extremal set theory states that for every family closed under union there exists an element contained in at least half of the sets of the family. We give a proof that Frankl’s conjecture holds for every family contained from 12 elements, while it is known that this is true for families contained from 11 or less elements. Our proof is based on the efficient algorithm that exhausts all the possibilities, while using the results for subfamilies that eventual counter-example cannot contain, which we obtained in a number of consecutive steps. Family of sets G is an FC-family if for every family F containing G there exists an element from S G that appears in at least half of the sets of F. NonFC-family is every family that is not FC. The author’s contribution is the complete classification of all families consisting of 6 or less elements into FC and NonFC-families. From the Boolean matrices theory we present our results concerning the row space cardinality. Boolean matrices are the matrices whose all components are from the set f0; 1g, while the row space of a Boolean matrix is the set of vectors that can be obtained by disjunction from the rows of a matrix. We present the set consisted of all values a from the interval [2n2 + 2n3; 2n2] such that there exists a matrix of dimension n n having the row space cardinality equal to a. For the least positive integer an for which there exists no matrix of dimension n n having the row space cardinality equal to an, the author gives a lower bound that is an improvement over the previously known results. All proofs for the main results in the dissertation are constructive. Proofs of some of them require the use of computers where there is a calculation of a great number of possibilities. For other proofs this was not necessity, though algorithms following the steps of the proofs can be implemented to obtain a graph coloring or a matrix with the desired properties. URI: http://hdl.handle.net/123456789/4661 Files in this item: 1
Disertacija_-_Bojan_Vuckovic.pdf ( 1.143Mb ) -
Mijajlović, Žarko (Beograd , 2010)[more][less]
-
Ivanović, Marija (Beograd , 2022)[more][less]
Abstract: This dissertation focuses on the Roman domination problem and its two modifications. Improvements and relaxations of two integer linear programming for- mulations for the Roman domination problem from the literature are introduced, proved to be equivalent to the existing ones despite of the variables relaxation and usage of fewer number of constraints and compared by standard optimization solvers, CPLEX and Gurobi. Improved formulations can be equally used as original ones, but, as it can be seen from numerical results, for some instances, they can be more useful. Given the fact that old and new formulations can not be used for some large size instances, and that algorithms for solving Roman domination problem are mostly defined for some particular graph classes, the aim of this research was to find a new algorithm that can be used for solving Roman domination problem on all graph classes and all graph sizes. Although the Roman domination problem belongs to the class NP, presented algorithm is able to find solution value equal to optimal solution value on very large number of instances in less then a second. For the first modification of the Roman domination problem, named Restrained Roman domination problem, a new mixed integer linear programming formulation is intro- duced and, to the best of the author’s knowledge, this formulation is the first in the literature. For the second modification of the Roman domination problem, the Weak Roman domination problem, an improved integer linear programming formu- lation is presented. Improved formulation is also proved to be correct, equivalent to the existing formulation from the literature and compared using standard op- timization solvers, CPLEX and Gurobi. Numerical results showed the advantage of the improved formulation on almost all tested instances. Additionally, an im- proved linear-time algorithm for solving the Weak Roman domination problem on block graphs is introduced and, similarly to the Roman domination problem, a new algorithm, based on the variable neighborhood search method is presented. With the new variable neighborhood search based algorithm we aimed to find solution of the Weak Roman domination problem equal to the optimal on very large number of tested instances. For instances for which some solution value is found but not proved to be an optimal, presented algorithm provided the new lower-bounds. Even more, for some instances, where optimization solvers were not able to prove optimality or to find any solution, new solutions are found. URI: http://hdl.handle.net/123456789/5431 Files in this item: 1
MarijaIvanovic_ ... a_saPotpisanimIzjavama.pdf ( 1.958Mb ) -
Pejović, Tadija (Belgrade)[more][less]
-
Milić Žitnik, Ivana (Beograd , 2017)[more][less]
Abstract: The subje t of this dissertation is intera tion between the mean motion resonan- es and the Yarkovsky e e t. This intera tion o urs when an asteroid due to the hanges of its orbital semi-major axis ( aused by the Yarkovsky e e t) rea h the re- sonan e. The resonan e indu es a periodi os illations in the asteroid's semi-major axis around its enter. The Yarkovsky e e t exa tly auses the permanent (se ular) evolution of the orbital semi-major axis. As a result of their intera tion the mean semi-major axis drift speed is modi ed with respe t to the one aused solely by Yarkovsky. One of the main goals of this investigation was to study this intera tion, and to establish and de ne how the time that an asteroid spend in the resonan e depends on some hara teristi s of this resonan e, as well as of the asteroid itself. So far, the impa t of the resonan e on the semi-major axis drift speed has not been studied to that extent neither from that point of view. In order to study the afo- rementioned intera tion the orbital motion of test parti les a ross the resonan es is numeri ally simulated using ORBIT9 integrator. The most important result of this dissertation ertainly is determination of fun tional relation between on one side the time-period that obje ts spend inside a resonan e, and, on the other side, the semi- majors axis drift speed, the orbital e entri ity and the resonan e strength. In this work not only that existen e of the above-mentioned relationship is on rmed, but for the rst time it was expli itly de ned. Two the most interesting results are that the time spent in the resonan e is inversely proportional to the semi-major axis drift speed aused by the Yarkovsky e e t, and that this time is dire tly proportional to the resonan e strength. URI: http://hdl.handle.net/123456789/4651 Files in this item: 1
Milic-Zitnik_Ivana.pdf ( 40.69Mb ) -
Milovanović, V. Gradimir (Beograd, Naučna Knjiga , 1988)[more][less]
-
Milovanović, V. Gradimir (Beograd, Naučna Knjiga , 1991)[more][less]
-
Milovanović, V. Gradimir (Beograd, Naučna Knjiga , 1991)[more][less]
-
Radunović, Desanka (Beograd , 2003)[more][less]
-
Radunović, Desanka (Beograd , 2007)[more][less]
-
Jovanović, Boško (Belgrade , 1989)[more][less]
URI: http://hdl.handle.net/123456789/440 Files in this item: 1
BoskoJovanovicN ... ferencijalnihJednacina.PDF ( 4.592Mb ) -
Simeunović, Dragomir (Rudarsko-Geološki fakultet Beograd , 1985)[more][less]
-
Gardašević Filipvić, Milanka (Beograd , 2011)[more][less]
-
Radunović, Desanka; Samardžić, Aleksandar; Marić, Filip (Beograd , 2005)[more][less]
-
Milošević, Stanislav (Beograd , 2023)[more][less]
Abstract: In this dissertation, we presented galaxy mergers and the forming of stellar morphological substructures. We assume a large spiral galaxy and dwarf galaxy which is a satellite of the first one. We used N-body simulations to present different scenarios for the merger of two galaxies, and after that, we analyzed the properties of formed structures. The investigation of the formation of these structures and their properties is important for understanding the dynamics and evolution of galaxies. First, we did simulations where we investigated the influence of the properties of dwarf galaxies on the forming structures. We tested: 1. morphology of the dwarf galaxy where we used two models – dwarf with a disk and spheroidal dwarf galaxy; 2. inclination of the orbit in the case of a very radial merger, because in that case, we have the formation of the stellar shells and streams; 3. direction of rotation of the dwarf in the case of a dwarf with a disk. In each case, after the merger, we have stellar shells and streams formed. Morphology, inclination of the orbit, and direction of rotation have their influence on the properties of formed substructures, and on the timescale of disruption of the remnant of the dwarf. In the case of the merger of Andromeda galaxy (M31) and dwarf galaxy, the satellite of M31, we investigate the properties of the Giant Stellar Stream (GSS), as well as the Northeast shell (NE) and West shell (W). The orientation of the GSS, distances, and velocities of the GSS, NE, and W shells from our simulation are in agreement with the observed one. For the first time, we explained the observed metallicity distribution in these substructures. With a linearly decreasing gradient of the initial metallicity in the dwarf galaxy before the merger, using Monte Carlo (MC) simulations, we successfully explained the observed metallicity distribution in these substructures. These results are a contribution to the investigation of metallicity gradients in dwarf galaxies which is important for galaxy evolution in general. URI: http://hdl.handle.net/123456789/5583 Files in this item: 1
SM_Doktorat_18_07_2023.pdf ( 18.08Mb ) -
Jovanikić, Branko (Belgrade)[more][less]
-
Torgašev, Aleksandar (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/101 Files in this item: 1
phdAleksandarTorgasev.pdf ( 83.67Mb ) -
Milanković, Milutin (Beograd , 1932)[more][less]
-
Milanović, Nevena (Beograd , 2022)[more][less]