With the rapid of growth of wireless connectivity more demand is placed on the need for innovative technologies capable of satisfying increasing user demand and network capacity. Adaptive antennas systems or most commonly known as Smart Antennas are expected to be implemented in the next generation of wireless systems. Their implementation avails in dynamic adaptation to spatial and temporal conditions affecting the quality of communication, while offering tremendous flexibility to wireless providers. However one of the major challenges facing Smart Antenna technology is the inherent complexity of the antenna structure, associated control algorithm and implemented RF components possibly contributing to the delay of commercial interest. This thesis will present various adaptive antenna configurations that utilize an embedded dielectric in order to achieve significant size reduction and mechanical rigidity while maintaining favorable electromagnetic performance. In order to constrict the lateral ground plane dimension, a cylindrical shaped hollow ground skirt was attached to the antenna structures effectively compromising between effective beam forming in the azimuth plane and physical size. The complexity of these antenna structures requires a more contemporary design approach which involved computer modeling using a commercial available Finite Element software package and optimization using a developed generic Genetic Algorithm based optimization program. A dielectric embedded 7-element monopole array antenna featuring switched parasitic elements is presented and optimized for maximum vertically polarized gain in the horizontal plane, producing an antenna structure with a radial length of less then 0.25λ and total height of 0.4&alamba which was shown to radiate a main lobe beamwidth of 80 degrees with an absolute gain of 4.8dBi at 2.45GHz. Further on a dielectric embedded 7-element monopole array antenna featuring parasitic elements terminated with finite set of terminating reactive loads is presented with a radial length of less then 0.25&alambda and total height of 0.4&alambda. The antenna structure and reactive load combination were optimized for maximum horizontal gain producing a principal main lobe with a measured gain of 5.1dBi and beamwidth of 110 degrees at 2.48GHz. Finally it was shown single and dual radiation lobes maybe produced when active monopoles elements are placed eccentric in a circular shaped dielectric material. A circular array of elements embedded in a dielectric material was realized with measured gains of single and dual beam radiation at 2.45GHz was shown to be 5.18dBi and 3.65Bi respectively with corresponding beamwidths of 78.5 degrees and 53 degrees.

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Microwave tomography is a classical approach for non destructive evaluation. Microwave tomography has many biomedical applications such as brain imaging, temperature sensing in different biological tissues and breast cancer detection. In a microwave tomography system, numbers of radiators are used to transmit microwave signal into an object under test and the scattered fields are recorded. The collected data is used to quantitatively reconstruct the dielectric profiles of the object under test through inverse scattering mechanism. It has been shown that by using wide band data, highly stable and high resolution reconstructions can be obtained. Lower frequency components provide stability of the reconstructions, while higher frequency components contribute to the resolution.  Accordingly, ultra wideband antennas are required in UWB microwave tomography systems. In addition to ultra wide bandwidth, the antennas in a microwave tomography system should be easy to model with computational program. In this thesis Printed elliptical monopole antenna (PEMA) is investigated for microwave tomography. It is a multi resonant antenna with simple structure and yield ultra wide bandwidth. The performances of a single antenna and an antenna array are studied. The reflection coefficients of the antenna, mutual coupling between antennas and energy distribution in the near field are obtained by means of simulations in CST microwave studio.    The simulation result shows that reflection coefficients of the designed antenna are below         -10dB over the entire frequency band of interest (1-4.5GHz), mutual coupling between antennas at different locations are below -20dB over the entire frequency band of interest and the designed antenna also has good electric field distribution in an array configuration which makes the radiated power concentrating in the imaging region. These results indicate that PEMA is a potential antenna for microwave tomography applications.

An internal small antenna usually suffers from degradation in performance of impedance bandwidth and radiation patterns. In this thesis, we design and fabricate a broadband interior type planar monopole with an omni-directional radiation pattern over a wide operation band using a slant feeding strip. It has a measured impedance bandwidth about 465MHz with center frequency at 1.66GHz (1427 ¡V 1892MHz) and the maximum cross polarization level about -13dB at 1800MHz, which is GSM1800 band in mobile communications. A modified design is an interior planar monopole with a slant slit. It has a measured impedance bandwidth about 455MHz with center frequency at 1.71GHz (1487 ¡V 1942MHz), including GSM1800 and PCS1900 band, and the maximum cross polarization level about -15dB at 1800MHz. The antennas have the dimensions of 40mm*15mm which occupies a small size on the system board and they are suitable to be mounted within the mobile handset device.

Several novel designs of printed monopole antennas are proposed and experimentally studied. These antennas have the advantages of low profile, light weight and easy construction and can be printed on dielectric substrates and integrated with associated circuitry on the same substrates, which not only reduces the manufacturing cost but also decreases the required size of the complete system. This dissertation mainly consists of four sections and several novel designs are introduced in each section. First, a novel dual-band antenna with two stacked inverted-F strips and a CPW-fed folded inverted-F strip antenna are proposed. Second, a novel printed dual-band double-T monopole antenna, comprising two stacked T-shaped monopoles, is discussed. Third, three diversity antenna designs obtained by protruding a ground plane with optimal dimensions between two printed monopoles for WLAN communication applications in the 2.4 GHz and 5.2 GHz bands are presented. Good dual-polarized radiation with an enhanced port decoupling (isolation less than ¡V27 dB) for the two feeding ports is obtained. Finally, a novel printed ultra-wideband diversity monopole antenna is shown. The operating bandwidth of the ultra-wideband antenna reaches about 5.4 GHz, covering the WLAN bands at 2.4, 5.2 and 5.8 GHz, and the antenna can provide spatial diversity to combat the multipath fading problem.

In this thesis, two novel antennas and three advanced design concepts for further studies are presented. Firstly, the design of diversity dual-band inverted-F monopole antenna using two back-to-back stacked metallic strips for operating in the 2.4 and 5.2 GHz WLAN band is presented. Secondly, the diversity dual-band inverted-F monopole antenna mounted vertically at the edge of a system circuit board is studied. Finally, three advanced design concepts are discussed to demonstrate the methods of controlling radiation patterns to achieve better radiation characteristics of the antenna.

Title: Giant monopole resonances in deformed nuclei Author: Daniel Božík Department: Institute of particle and nuclear physics Supervisor: prof. RNDr. Jan Kvasil, DrSc., ÚČJF, MFF UK Abstract: The study of giant monopole resonances is important, because of its di- rect connection to the incompressibility of the nuclear matter, and its importance has risen with new experimental data obtained in recent years from the experi- ments TAMU and RCNP. The current work brings a study of the giant monopole resonances for chains of spherical (Pb, Sn, Zr) as well as deformed (Sm, Mo, Cd) isotopes. The calculations were carried out within the HFB + SRPA method, which was developed at MFF UK in cooperation with JINR Dubna and the University of Erlangen. We were as first able to confirm, from the microscopic theory, the appearance of a double-peak structure of GMR strength functions for deformed nuclei, and its connection with E0-E2 coupling. We showed the importance of using strength functions in the study of GMR. Keywords: HFB, SRPA, giant monopole resonances 1

This thesis is concerned with the quantum Dirac magnetic monopole and two classes of its generalisations. The first of these are certain analogues of the Dirac magnetic monopole on coadjoint orbits of compact Lie groups, equipped with the normal metric. The original Dirac magnetic monopole on the unit sphere S^2 corresponds to the particular case of the coadjoint orbits of SU(2). The main idea is that the Hilbert space of the problem, which is the space of L^2-sections of a line bundle over the orbit, can be interpreted algebraically as an induced representation. The spectrum of the corresponding Schodinger operator is described explicitly using tools of representation theory, including the Frobenius reciprocity and Kostant's branching formula. In the second part some discrete versions of Dirac magnetic monopoles on S^2 are introduced and studied. The corresponding quantum Hamiltonian is a magnetic Schodinger operator on a regular polyhedral graph. The construction is based on interpreting the vertices of the graph as points of a discrete homogeneous space G/H, where G is a binary polyhedral subgroup of SU(2). The edges are constructed using a specially selected central element from the group algebra, which is used also in the definition of the magnetic Schrodinger operator together with a character of H. The spectrum is computed explicitly using representation theory by interpreting the Hilbert space as an induced representation.

In this thesis a characterization of air showers induced by magnetic monopoles is presented. Monopoles are predicted to exist and be accelerated to relativistic velocities. High energy monopoles traversing earth’s atmosphere continuously deposit energy, inducing an air shower. These air showers have been described based on simulations run in CORSIKA. It was found that monopole air showers are continuous; they plateau after the shower maximum, and have a large electromagnetic component. As such,they can easily be distinguished from normal cosmic rays and most other air shower sources. Very high energy photons and muons could induce similar showers but do not produce identical signals in track-following detectors such as IceCube.

Cette thèse est composée de trois chapitres. Le premier chapitre, "Bertrand-Edgeworth Competition with Substantial Product Differentiation", étudie le comportement d'un duopole lorsque les deux entreprises sont caractérisées par des contraintes de capacité et produisent un bien différencié à la Hotelling. En limitant l'analyse au cas d'un degré élevé de différentiation du produit, je démontre l'existence d'au moins un équilibre en stratégie pure pour tous les niveaux de capacités. Le deuxième chapitre, "Monopoly Pricing with Dual Capacity Constraints" analyse un monopole qui est contraint par deux types de contraintes de capacité: un sur la quantité produite, l'autre sur le nombre des consommateurs. Je démontre que les prix optimaux choisis par les entreprises en court terme ne sont pas monotones dans le niveau des contraintes de capacité. En outre, le bien-être agrégé des consommateurs peut décroître si une des contraintes de capacité est augmentée. Le troisième chapitre, "Competition with Dual Capacity Constraints", étend l'analyse du deuxième chapitre au cas du duopole symétrique dans lequel les deux entreprises font face aux mêmes niveaux de capacité. Je démontre l'existence de conditions sous lesquelles la non-monotonicité des prix et du bien-être des consommateurs observée dans le 2ème chapitre est également présente dans le cas du duopole. Certains équilibres donnent naissance à des prix de duopole égaux au prix de monopole. En outre, les entreprises peuvent choisir des prix d'équilibre identiques sur les deux marchés malgré leur pouvoir de discrimination des prix. / This Ph.D. thesis is composed of three chapters. Since Kreps and Scheinkman's seminal article (1983) a large number of papers have analyzed capacity constraints' potential to relax price competition. However, the majority of the ensuing literature has assumed that products are either perfect or very close substitutes. Therefore very little is known about the interaction between capacity constraints and local monopoly power. The aim of the present paper is to shed light on this question using a standard Hotelling setup. The high level of product dierentiation results in a variety of equilibrium firm behavior and it generates at least one pure-strategy equilibrium for any capacity level. The second chapter, "Bertrand-Edgeworth Competition with Substantial Product Differentiation", studies the price-setting behavior of a monopoly facing two capacity constraints: one on the number of consumers it can serve, the other on the total amount of products it can sell. Facing two consumer groups that difer in their demands and the distribution of their willingness-to-pay, the monopoly's optimal non-linear pricing strategy consists of offering one or two price-quantity bundles. The characterization of the firm's optimal pricing as a function of its two capacities reveals a rich structure that also gives rise to some surprising results. In particular, I show that prices are non-monotonic in capacity levels. Moreover, there always exists a range of parameters in which weakening one of the capacity constraints decreases consumer surplus. In the long run, when the firms can choose how much capacity to build, prices and consumer surplus are monotonic in capacity costs. The third chapter, "Competition with Dual Capacity Constraints", studies duopoly pricing under dual capacity constraints, limiting both the total quantity and the number of consumers served. It extends both the analysis of monopoly pricing with dual capacity constraints and the symmetric models of Bertrand-Edgeworth competition with a singular capacity. By isolating parameter regions where a symmetric pure-strategy equilibrium exists, I nd that several types of equilibria are possible, depending on the model's specications. For some of them, duopoly prices are identical to monopoly prices. Equilibrium prices are non-monotonic in capacity levels if consumers' valuations are suciently heterogeneous. Moreover, I show that despite their ability to price discriminate, competition may lead firms to charge identical prices across markets.