http://hdl.handle.net/123456789/1 http://hdl.handle.net/123456789/5842 MOGUĆNOSTI I OPTIMIZACIJA SLETANJA NA JUŽNU HEMISFERU MARSA Marčeta, Dušan Almost 40 years after the rst successful landing on Mars, exploration of its surface still presents enormous scienti c and technological challenge. This particularly holds for the Mars southern highlands, which cover large part of the southern hemisphere where no successful landings have been achieved up to date. On the other hand, in the northern lowlands, which spans most of the northern hemisphere, there has been 7 successful landings. This difference is consequence of the speci c topography of the Martian surface due to so-called global or hemispheric dichotomy, which is a unique characteristic in the Solar system. Due to the difference in the surface elevations, the vehicle trying to land on the southern highlands has thinner layer of the atmosphere that can use for the dissipation of its kinetic energy. Since the vehicles from the interplanetary trajectories enter the Martian atmosphere with hyperbolic velocities, their kinetic energy is extremely large and possibility for its dissipation through the interaction with the atmosphere has crucial importance for the landing on the locations with high elevations. Beside the differences in topography between northern lowlands and southern highlands, there is also a big difference in the number of impact craters between these two regions. This fact indicates that the southern highlands are several billion years older than the northern lowlands, which were exposed to strong volcanic activity in the relatively recent past. Such huge difference in age is strong motivation to explore the entire surface of Mars in order to understand its complex geological evolution. In addition, large number of open basins discovered in the southern highlands suggests that these regions could contain liquid water in the past, which is one of the most important reasons for exploring these sites. The main objective of this dissertation is to determine whether it is possible to land on the southern highlands, without advancing the technology which was used for the previous landings on Mars. Since the atmosphere of Mars is extremely dy- namic due to high sensitivity to insolation, the parameters in uencing the process of landing, especially density and temperature, have extremely large variations on the daily and annual scale. In that sense, it is necessary to accurately model the in uence of the most important parameters, such as the orbital position of Mars and local true solar time, in order to determine the optimal conditions for landing. For this purpose, a numerical algorithm for determination of the trajectory of a vehicle with arbitrary aerodynamic characteristics, moving through the atmosphere with ar- bitrary vertical and horizontal pro les, under the in uence of arbitrary gravitational eld, has been developed. Using this algorithm, large number of atmospheric tra- jectories was simulated which enabled determination of the possibilities and optimal conditions for landing on the southern highlands. http://hdl.handle.net/123456789/5841 UNAPREÐENJE HIBRIDIZACIJOM METAHEURISTIKA INTELIGENCIJE ROJEVA ZA REŠAVANJE PROBLEMA GLOBALNE OPTIMIZACIJE Bačanin Džakula, Nebojša Hard optimization problems that cannot be solved within acceptable computational time by deterministic mathematical methods have been successfully solved in recent years by population-based stochastic metaheuristics, among which swarm intelli- gence algorithms represent a prominent class. This thesis investigates improvements of the swarm intelligence metaheuristics by hybridization. During analysis of the existing swarm intelligence metaheuristics in some cases de ciencies and weaknesses in the solution space search mechanisms were observed, primarily as a consequence of the mathematical model that simulates natural process as well as inappropriate balance between intensi cation and diversi cation. The thesis examines whether existing swarm intelligence algorithms for global op- timization could be improved (in the sense of obtaining better results, faster con- vergence, better robustness) by hybridization with other algorithms. A number of hybridized swarm intelligence metaheuristics were developed and implemented. Considering the fact that good hybrids are not created as a random combination of individual functional elements and procedures from di erent algorithms, but rather established on comprehensive analysis of the functional principles of the algorithms that are used in the process of hybridization, development of the hybrid approaches was preceded by thorough research of advantages and disadvantages of each involved algorithm in order to determine the best combination that neutralizes disadvantages of one approach by incorporating the strengths of the other. Developed hybrid approaches were veri ed by testing on standard benchmark sets for global optimization, with and without constraints, as well as on well-known practical problems. Comparative analysis with the state-of-the-art algorithms from the lite- rature demonstrated quality of the developed hybrids and con rmed the hypothesis that swarm intelligence algorithms can be successfully improved by hybridization. Keywords: swarm intelligence metaheuristics, hybrid algorithms, global optimiza- tion. http://hdl.handle.net/123456789/5840 OCJENE NORME INTEGRALNIH OPERATORA NA PROSTORIMA BESOVA I BLOHA Vujadinović, Đorđije In this work we investigate the various norms of known integral operators such as Bergman projection and certain integral operators induced with Green function. We have observed acting of the Bergman projection on the weighted Lebesgue spaces with image in spaces of analytic functions, Bloch and Besov spaces. We obtained the estimate for the norm of the Bergman projection onto the Besov spaces, when 1 < p < ∞, and this estimate is asimptoticaly sharp for p → +∞. We have found norm for the special Hilbert case p = 2. We have also considered some weak type inequalities for the norm of the Bergman projection onto Besov space B1 .We ob- served the adjoint operator for the Bergman projection fot the mentioned case B1. Precisely, in this case we obtained two-sided bounds of norm for the adjoint oper- ator. It was represented a method for determinig the norm of the Bergman type projection defined in weighted Lebesgue spaces and with image in Bloch space in the unit ball B in Cn. Specially, we have considered the norm of the integral operator induced with Green function in a context of the weak solutions for the Poisson’s equation with ho- mogenuous condition in the unit ball in higher dimensions. The norm for the men- tioned operator was determined for the Hilbert case and when operator is defined on L∞−spaces (and also L1−case, which is dual).Final results are related to estimating the norm of gradient for the weak solutions of Poisson’s equation. http://hdl.handle.net/123456789/5839 USAVRŠAVANjE MODELA TESNO DVOJNIH SISTEMA SAGLASNO SA REZULTATIMA POSMATRANjA VISOKE PRECIZNOSTI Čeki, Atila The dissertation presents a program for modeling binary systems, Infinity, which combines the traditional principles of modeling (Roche geometry, von Zeipel’s law of temperature distribution and so forth) with a novel geometrical representation of the system. The study of binary stars has a long tradition in Serbia, mostly due to the research done by dr Gojko Đurašević. The program presented in the dissertation is based on his program for modeling of active close binary systems with an accretion disk (Đurašević, 1991) and brings several significant improvements that can be classified in two categories: The first group of improvements has to do with generalizing the model. First and foremost, the new program is applicable to systems with eccentric orbits, and is capable of computing and solving the inverse problem for radial velocities. It also features a new algorithm for determining which elements of the stellar surface are visible during the eclipse. The new algorithm allows for computing the light curves with greater precision using a method of ‘adaptive subdivision’ in the region of eclipse. The geometrical aspects of modeling the accretion disk are also improved and now include the possibility to create both conical and toroidal disks. The second group of improvements is related to the modeling of physical processes on the binary system components. The most significant change is in the way the emergent flux is calculated. Namely, the Đurašević program assumes that the elements of stellar surface produce blackbody radiation, while the new program assigns a one-dimensional Kurucz stellar atmosphere model calculated under the LTE assumption. Improvements are also made in the treatment of the influence of photometric filters on the calculated light curve, and the list of supported filters is extended. A binary system is described by the Roche model, which assumes that the motion and shape of the components are determined by the superposition of gravitational and centrifugal forces, while all the other interactions are neglected. The stars are treated as point masses (under the assumption of total central condensation), so their internal structure is not considered. If the system contains an accretion disk, it is assumed that its mass can be neglected, and that its presence doesn’t influence the dynamics of the system and the shape of the stars. The surface of the components is represented with a polygonal mesh. The stars are approximated with a geodesic, and the accretion disk with an axially-symmetric mesh. The new algorithm for solving the problem of visibility detection, proposed in the dissertation, is based on the so called inverse painter’s algorithm that originates from the field of computer graphics. The most important property of this algorithm is that, other than the polygonal meshes representing the components, it doesn’t require any other information about the geometry of the system. This makes the modeling program easily extendable to more exotic geometric configurations such as systems with eccentric or circumbinary disks, planetary and multiple systems, and so forth. It is assumed that within a single element of stellar surface all the physical quantities – local effective temperature, gravitational acceleration, emergent flux and radial velocity – are constant. Its radiation is affected by gravity darkening, limb darkening and the reflection effect. Gravity darkening is described using von Zeipel’s law, and the limb darkening can be calculated using one of the five available approximations (linear, logarithmic, square-root, quadratic and nonlinear fourth-order approximation). The reflection effect, as well as the temperature distribution along the accretion disk, are calculated using the approach from the Đurašević program (Đurašević, 1991). The local amount of radiation can additionally be affected by active regions that are represented with dark or bright circular spots. The emergent flux is computed as the sum of fluxes from all the surface elements visible in the given moment, and the radial velocity is calculated from the superposition from three kinds of motion: the proper motion of the system center of mass, the motion of the center of the star around the center of mass due to orbital revolution, and the motion of elementary surface around the center of the star due to rotation. Synthetic light and radial velocity curves obtained in this way can be directly compared to observations. The new program solves the inverse problem – estimating the optimal model parameters to fit the given observations – using the Nelder-Mead simplex algorithm to minimize the sum of squares of deviations between the observed and calculated light and radial velocity curves. The validity of the program and the proposed improvements is done by analyzing several binary systems and comparing the results with published solutions obtained with the Đurašević program.