This thesis explores two infinite families of self-complementary arc-transitive graphs: the familiar Paley graphs and the newly discovered Peisert graphs. After studying both families, we examine a result of Peisert which proves the Paley and Peisert graphs are the only self-complementary arc transitive graphs other than one exceptional graph. Then we consider other families of graphs which share many properties with the Paley and Peisert graphs. In particular, we construct an infinite family of self-complementary strongly regular graphs from affine planes. We also investigate the pseudo-Paley graphs of Weng, Qiu, Wang, and Xiang. Finally, we prove a lower bound on the number of maximal cliques of certain pseudo-Paley graphs, thereby distinguishing them from Paley graphs of the same order.

This thesis explores two infinite families of self-complementary arc-transitive graphs: the familiar Paley graphs and the newly discovered Peisert graphs. After studying both families, we examine a result of Peisert which proves the Paley and Peisert graphs are the only self-complementary arc transitive graphs other than one exceptional graph. Then we consider other families of graphs which share many properties with the Paley and Peisert graphs. In particular, we construct an infinite family of self-complementary strongly regular graphs from affine planes. We also investigate the pseudo-Paley graphs of Weng, Qiu, Wang, and Xiang. Finally, we prove a lower bound on the number of maximal cliques of certain pseudo-Paley graphs, thereby distinguishing them from Paley graphs of the same order.

Spinal muscular atrophy is caused by mutation of the SMN1 gene resulting in the selective loss of spinal cord motor neurons. HuD has been shown to interact with SMN and to localize to RNA granules along axons. In conditions where SMN is decreased, like in SMA, HuD’s localization to RNA granules affected. Overexpression of HuD in an SMA cell culture model was shown to rescue SMA-like axonal defects. Here, existence of a signaling pathway downstream of PKC leading to the activation of HuD was investigated in MN-1 cells. Stimulation of this pathway using a pharmacological agonist of PKC increased HuD levels and enhanced its binding to GAP-43 and Tau mRNAs. An scAAV9 viral expression system to overexpress HuD in vivo was established, laying the foundation for the next phase of the study. Overall, modulating HuD expression and activity would be beneficial and could constitute an attractive therapeutic approach for SMA.

A self-complementary graph is a graph isomorphic to its complement. A set S of vertices in a graph G is a restrained dominating set if every vertex in V(G) \ S is adjacent to a vertex in S and to a vertex in V(G) \ S. The restrained domination number of a graph G is the minimum cardinality of a restrained dominating set of G. In this paper, we study restrained domination in self-complementary graphs. In particular, we characterize the self-complementary graphs having equal domination and restrained domination numbers.

Yes / The syntheses of three series of complexes designed with self-complementary motifs for formation of halogen bonds between an iodotetrafluorophenyl ligand and a halide ligand at square-planar nickel are reported, allowing structural comparisons of halogen bonding between all four halides C6F4I⋯X–Ni (X = F, Cl, Br, I). In the series trans-[NiX(2,3,5,6-C6F4I)(PEt3)2] 1pX and trans-[NiX(2,3,4,5-C6F4I)(PEt3)2] (X = F, Cl, Br, I) 1oX, the iodine substituent on the benzene ring was positioned para and ortho to the metal, respectively. The phosphine substituents were varied in the series, trans-[NiX(2,3,5,6-C6F4I)(PEt2Ph)2] (X = F, I) 2pX. Crystal structures were obtained for the complete series 1pX, and for 1oF, 1oCl, 1oI and 2pI. All these complexes exhibited halogen bonds in the solid state, of which 1pF exhibited unique characteristics with a linear chain, the shortest halogen bond d(C6F4I⋯F–Ni) = 2.655(5) Å and the greatest reduction in halogen bond distance (I⋯F) compared to the sum of the Bondi van der Waals radii, 23%. The remaining complexes form zig-zag chains of halogen bonds with distances also reduced with respect to the sum of the van der Waals radii. The magnitude of the reductions follow the pattern F > Cl ∼ Br > I, 1pX > 1oX, consistent with the halogen bond strength following the same order. The variation in the I⋯X–Ni angles is consistent with the anisotropic charge distribution of the halide ligand. The temperature dependence of the X-ray structure of 1pF revealed a reduction in halogen bond distance of 0.055(7) Å on cooling from 240 to 111 K. Comparison of three polymorphs of 1oI shows that the halogen bond geometry may be altered significantly by the crystalline environment. The effect of the halogen bond on the 19F NMR chemical shift in the solid state is demonstrated by comparison of the magic-angle spinning NMR spectra of 1pF and 1oF with that of a complex incapable of halogen bond formation, trans-[NiF(C6F5)(PEt3)2] 3F. Halogen bonding causes deshielding of δiso in the component of the tensor perpendicular to the nickel coordination plane. The results demonstrate the potential of fluoride ligands for formation of halogen bonds in supramolecular structures. / We acknowledge an Overseas Research Scholarship from the University of York to VT. We also acknowledge support from EPSRC (grants EP/J012955/1 and EP/ J012998/1).

Advances in technology have placed a great emphasis on the design of broadband antennas as well as antenna miniaturization to cope with the demands of making electronic and handheld communication devices smaller and more efficient. In this thesis, the design and fabrication of a frequency independent antenna and a narrow-band planar microstrip Balun are presented. An analysis of frequency selective surfaces is also introduced in order to demonstrate their capability to miniaturize antenna thickness. Lastly, s-parameters measurements and efficiency characterization are performed to determine the radiation properties of surface mount chip inductors in order to determine the feasibility of using them as electrically small antennas.Two types of frequency independent antennas are considered due to their planar geometries, the Equiangular and Archimedean spiral antennas. Frequency independent antennas are radiating devices that have frequency independent impedance and pattern properties because their shape is specified only in terms of angles.The Balun is designed to meet the need of a feeding element for the Archimedean spiral antenna. A Balun is a three port device that connects an unbalanced transmission line such as a coaxial line to a balanced feed line such as the one required by two-arm spiral antennas. The Balun discussed in this work is designed to operate at 2.4 GHz with a 200 MHz bandwidth and to transform the antenna input impedance to a 50-ohm reference impedance. The main characteristics from this device that distinguish it from commercially available structures are its low cost, planarity, and compact footprint. The balancing capability of this Balun is shown by the close agreement between the measured and simulated results. Antennas can be potentially miniaturized in the z-direction by replacing the PEC ground plane separated from the antenna by a lambda /4 thick substrate with a frequency selective surface (FSS) structure that allows the ground plane conductor to be in close proximity to the antenna without affecting its radiation performance. The FSS layer operating at 2.4 GHz presented in this thesis is static (not tuned) and thus the overall bandwidth reduces approximately to the bandwidth obtained with the narrow-band Balun.

A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex of S. We study graphs whose vertex set can be partitioned into two total dominating sets. In particular, we develop several sufficient conditions for a graph to have a vertex partition into two total dominating sets. We also show that with the exception of the cycle on five vertices, every selfcomplementary graph with minimum degree at least two has such a partition.

A set S of vertices in a graph G is a global dominating set of G if 5 simultaneously dominates both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We study the graphs for which removing any arbitrary edge from G and adding it to G decreases the global domination number.

Une antenne auto-complémentaire possède des caractéristiques radioélectriques très intéressantes en ce qui concerne l’élargissement de sa bande passante. Basée sur le principe de Babinet, l’auto-complémentarité permet en effet de maximiser la largeur de bande de par la complémentarité air-métal dans la structure de l’antenne. L’objectif de cette thèse est d’étudier quels pouvaient être les apports de l’auto-complémentarité dans le cas d’antennes à fortes contraintes d’intégration telles que celles utilisées pour les terminaux mobiles. Pour tester les limites de notre étude, nous avons choisi d’appliquer nos résultats à l’intégration d’antennes auto-complémentaires dans un objet communicant de type Smartphone multi-standards. Les antennes dites AC doivent par conséquent satisfaire de nombreux critères de performances tout en montrant leur capacité d’intégration. Celle-ci est rendue d’autant plus délicate, que la miniaturisation implique à son tour des phénomènes physiques limitant certaines performances, notamment en basse fréquence avec la nouvelle bande LTE. Dans une première étude, nous avons considéré différentes antennes et opté pour les antennes IFA-AC sur un plan de masse fini afin de couvrir initialement les bandes hautes DCS/PCS/UMTS et WLAN/LTE2600. Dans une seconde étude, nous avons amélioré leurs performances à l’aide d’éléments structurels nouveaux et interdépendants (éléments rayonnants de type double IFA), qui nous ont permis d’obtenir des résultats probants relatifs notamment à la couverture des bandes LTE800 et GSM. Enfin, nous avons complété notre projet en optimisant le lien radio par l’intégration de plusieurs éléments rayonnants AC sur un même PCB. / In this thesis we present the design and optimization of self-complementary antennas to be integrated into a Smartphone. A self-complementary antenna is known as a radio antenna with very interesting bandwidth characteristics. Self-complementarity is based on the Babinet’s principle which aims to maximize bandwidth by considering the complementarity of the air and metal in the construction of an antenna. To achieve an objective, the antennas must satisfy a number of criteria, both in terms of performance and also for the design methods and integration. Miniaturization is very sensitive and it is more difficult to implement an antenna because of the physical phenomena limiting performance, especially at low frequency with the new 4G band. In this study we considered initially the self-complementary-IFA on a finite ground plane size: 120x60mm² in order to cover the high frequencies: DCS/PCS/UMTS and WLAN/LTE2600. In the second part, we focused on the possibility of using some improvement techniques by adding structural element (capacitive elements and radiating elements). Various geometrical modifications applied to antenna structures have also been used to obtain results satisfying all criteria, including coverage of LTE800 bands and GSM bands. Several prototypes were used to compare the theoretical results and validate the concept of self-complementarity. We completed the project by developing a way to improve the radio link in natural environments. We have implemented several radiating self-complementary miniature multiband/broadband elements on the same PCB in order to implement the principles of diversity or MIMO.

This diploma thesis deal with the design of log-periodic antenna. The log-periodic antenna is self-complementary and broadband antenna. Antenna self-complementary structures are described only by angles. Input impedance of log-periodic antenna is equal to theoretical impedance ohms. The input impedance and radiation patterns of broadband antenna structures are independent of frequency over theoretically unlimited bandwidths. The log-periodic antennas provide linearly polarized radiation pattern. In this thesis is designed antenna for bandwidths 1 to 5GHz. In this diploma thesis is introduced design balanced unit, this is compound broadband balun and broadband impedance transformer. The broadband balun is based on conversion of microstrip line to balanced stripline. The Klopfenstein impedance taper is used for design. For simulation was used software from firma Zeland software IE3D.