In projective geometry, the common self-polar triangle has often been used to discuss the location relationship of two planar conics. However, there are few researches on the properties of the common self-polar triangle, especially when the two planar conics are special conics. In this thesis, the properties of the common self-polar triangle of special conics are studied and their applications to computer vision are presented. Specifically, the applications focus on the two topics of the computer vision: camera calibration and homography estimation. This thesis first studies the common self-polar triangle of two sphere images and also that the common self-polar triangle of two concentric circles, and exploits its properties to solve the problem of camera calibration. For the sphere images, by recovering the constraints on the imaged absolute conic from the vertices of the common self-polar triangles, a novel method for estimating the intrinsic parameters of a camera from an image of three spheres has been developed. For the other case of concentric circles, it is shown in this thesis that the imaged circle center and the vanishing line of the support plane can be recovered simultaneously. Furthermore, many orthogonal vanishing points can be obtained from the common self-polar triangles. Consequently, two novel calibration methods have been developed. Based on our method, one of the state-of-the-art calibration methods has been well interpreted. This thesis then studies the common self-polar triangle of two separate ellipses, and applies it to planar homography estimation. For two images of the separate ellipses, by inducing four corresponding lines from the common self-polar triangle, a homography estimation method has been developed without ambiguity. Based on these results, a special case of planar rectification with two identical circles is also studied. It is shown that given one image of the two identical circles, the vanishing line of the support plane can be recovered from the common self-polar triangle and the imaged circle points can be obtained by intersecting the vanishing line with the image of the circle. Accordingly, a novel method for estimating the rectification homography has been developed and experimental results show the feasibility of our method.

A new variation of the spherical helical antenna made of a wire wound over a hemispherical surface and backed by a conducting ground plane is introduced. A constant spacing is maintained between the turns of winding. The geometry of this antenna is fully described by the number of turns and the radius of hemispherical surface. In addition to the hemispherical geometry, truncated double spherical helices are also examined. Radiation properties of the proposed antennas are studied both theoretically and experimentally. The wire antenna code ESP (electromagnetic surface patch), which is based on the method of moments, is used to obtain simulation results. The results for far-field patterns, gain, axial ratio, bandwidth, and input impedance are presented. Several prototypes of this antenna were constructed and tested using an outdoor antenna range. Far-field patterns were measured over a wide range of frequencies. The measured and calculated radiation patterns are in good agreement. A unique property of the hemispherical helix is its broad half-power beamwidth. Furthermore, this antenna provides circular polarization and relatively high gain over a narrow frequency range. The results of this research show that, for example, a 4.5-turn hemispherical helix with a radius of 0.02 meter designed for operation around 2.8 GHz provides a half-power beamwidth of about 90 degrees, more than 9 dB gain, and less than 3 dB axial ratio over a 300 MHz bandwidth. The input impedance of the antenna is largely resistive and is about 150 ohms in the above frequency range. Compared with a full spherical helix, the hemispherical helix provides comparable radiation characteristics, but occupies only half the volume. The compact size of this antenna makes it attractive to mobile communication applications / Master of Science

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The increasing number of nucleic acid-based therapeutics demonstrates the potential to treat diseases at the genetic level. Although oligonucleotides show clinical potential, challenges remain including nuclease degradation, rapid clearance when administered systemically, low cell permeability, and limited distribution to tissues of interest. This is largely imparted by the polyanionic phosphate backbone, which produces unfavourable electrostatic interactions at cell membranes. As a result, their clinical translation is dependent on delivery technologies that improve stability, facilitate cell entry, and increase target affinity. Spherical nucleic acids (SNAs) consist of radially orienting linear nucleic acids onto a nanoparticle core, conferring them a three-dimensional, spherical architecture. These structures enter cells readily and display distinct properties that are independent of their nanoparticle core. Accordingly, we decided to replace the intrinsically anionic phosphodiester linkage of DNA with a phosphoramidate linkage (P-N), allowing us to incorporate new functionality at the phosphate backbone. With this handle, we inserted cationic and hydrophobically modified functional groups that were compatible with nanoscale architectures, giving rise to new properties relevant in biological contexts. Specifically, amine and guanidinium derivatized functional groups provided SNAs with a ~10-fold increase in cell uptake at early incubation times compared with unmodified SNAs. This demonstrates that we can tune the behaviour of SNAs with phosphate backbone modifications in a highly controlled manner. We hypothesize that the stringent control over location and placement of functional groups within the SNA framework will afford them favourable interactions at cell membranes, not only increasing their cell uptake, but also access to alternative uptake mechanisms and potency as therapeutics. / Thesis / Master of Science (MSc) / Oligonucleotides are short synthetic sequences of DNA or RNA that have the capacity to treat diseases at the genetic level. However, they face challenges such as degradation, low cell uptake, and poor tissue distribution. To overcome this issue, we plan to incorporate chemical modifications at the phosphate backbone of oligonucleotides to make them more stable and facilitate more favourable interactions at cell membranes. Conferring oligonucleotides into a 3D arrangement further enhances their stability and cell uptake relative to linear oligonucleotides. By densely functionalizing them onto a nanoparticle core, we can create spherical nucleic acids (SNAs). We hypothesize that the modifications imparted onto the phosphate backbone of linear oligonucleotides will translate their properties into SNAs. The new properties afforded to the SNAs will provide increased cell uptake, alternative uptake mechanisms, and access to cytosolic and nuclear targets, highlighting their potency and therapeutic potential.

This is Part B. / <p> Another approach is adopted for deriving the moments equations in spherical geometry using a spherical harmonics expansion of the neutron transport equation over a variable range of the direction cosine. Because of complications and uncertainties in establishing boundary conditions for the equations, only the zero'th order equations are solved, in an idealized situation, in order that a feel for equations and boundary conditions may be obtained.</p> <p> The equations are compared to equations given in a paper 'Directionally Discontinuous Harmonic Solutions of the Neutron Transport Equation in Spherical Geometry', by A. A. Harms and E. A. Attia. Analytical solutions for the zero'th order equations are given for equations developed there and to the equations developed in this paper. Numerical values are presented to give an idea of what accuracies might be expected. It is hoped that similar techniques can be used to solve the higher order equations analytically, and that appropriate boundary conditions can be found.</p> / Thesis / Master of Engineering (MEngr)

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