The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link and all torus links, and explore some of their properties and applications. Several examples are exhibited with color coding of tiles.

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The research in this dissertation is focused on the synthesis and characterization of sterically crowded, precisely charged polyelectrolytes based on substituted stilbene comonomers. New sterically crowded polyelectrolytes based on functionalized stilbenes with maleic anhydride or functionalized N-phenylmaleimides were prepared via a "protected" precursor polymer strategy. The polyelectrolyte precursors readily dissolved in organic solvents and were characterized by 1H NMR, SEC, TGA, and DSC. The polyelectrolytes were obtained via simple deprotection chemistries. The use of different combinations of the donor-acceptor comonomer pairs and the alternating copolymerization of these comonomers lead to precise control over charge density and placement of charged groups along the polymer backbone. Analogous styrenic copolymers, for direct comparison to the stilbene structures, were also prepared. Broad peaks in 1H NMR spectra were observed. There were no thermal transitions measured by DSC below the degradation temperature. A strong polyelectrolyte effect, for both stilbene and styrene copolymers, occurred in deionized water and was suppressed by adding NaCl to the polymer solution. These results are not consistent with "rigid" rod polyelectrolytes in which chain collapse in the presence of added salt and chain expansion on dilution should not be observed. In response to these observations persistence length measurements were conducted on the stilbene and styrene copolymers to assess directly the steric crowding effect of added phenyl groups in stilbene copolymers. Both SEC and SAXS measurements were used to obtain persistence lengths. The results from three different approaches, Bohdanecký, graphical and Sharp and Bloomfield Global, were in good agreement. The persistence lengths of stilbene containing copolymers range from 3 to 6 nm and the added phenyl groups increase the rigidity of the polymer chain by about 30-50%. This puts these polymers into a broadly defined "semi-rigid" category of polymers and is consistent with the solution polyelectrolyte effect observed. In dilute solution characterization of stilbene containing polyanions, a 2-step dissociation behavior was observed for the two adjacent carboxylic acids in maleic acid containing polyanions. Stilbene polyanion solutions showed high Rh values in deionized water as shown by DLS measurements and a decrease of Rh values followed by aggregation upon gradual addition of salt. Bimodal peaks were observed in SEC measurements with the copolymer of 4-methylstilbene and maleic anhydride. DLS measurements indicated interchain aggregation as the origin of the apparent high molecular weight fraction. The antiviral activity of the polyanion based on sodium 4-styrenesulfonate and N-(4-sodium sulfophenyl)maleimide was found to be ~50 times higher than the microbicide, sodium poly(styrene sulfonate). The early study of antiviral activities of carboxylated stilbene and styrene polyanions also showed promising results. The synthesis of methyl sulfonate ester-functionalized polyanion precursors was attempted because they can be characterized without the complications caused by directly using charged sulfonate groups. / Ph. D.

The primary purpose of this thesis is to present, in clear and logical form, an analysis of high-frequency modulation. This will be done in order to explain each of the various methods of obtaining modulation, and the characteristics of the resultant waves. The question of side bands will be considered in detail. The subject of circuits and associated apparatus is of secondary importance, emphasis being placed on the fundamental electric theory. From this point of view, possibilities for improvement and new developments will be investigated. / Master of Science

Stilbene containing polymers are a group of interesting and versatile polymers. The pendent phenyl ring along the polymer backbone can impart unusual rigidity to the polymer backbone due to steric repulsion. By functionalizing stilbene, a variety of functional groups and ionic groups can be precisely placed along the polymer chain with tunable charge density. Therefore, stilbene containing polymers are potentially rod-like polyelectrolytes with controllable charges and charge density. They are the basis of a novel group of rigid synthetic polyelectrolytes and can be used for furthering our knowledge of rigid polyelectrolytes. A novel series of methyl substituted stilbenes were synthesized and copolymerized with maleic anhydride. A conversion-time study was undertaken to understand the methyl substituent effect on copolymerization rates. Methyl substituted stilbene-maleic anhydride copolymer compositions were determined by quantitative ¹³C 1D NMR. SEC measurements showed the weight average molecular weights of these copolymers vary from 3 000 to over 1 000 000 g/mol. No glass transition temperature or crystalline melting temperature was observed between 0 °C and 250 °C by DSC. TGA showed that these polymers have 5% weight loss around 290 °C. Precursors to a polycation and a polyanion based on functionalized stilbenes and maleimides have been prepared: poly(di-t-butyl-(E)-4,4′-stilbenedicarboxylate-co- N-(4-(t-butoxycarbonyl)phenyl)maleimide) and poly(N,N,Nâ ,Nâ -tetraalkyl-4,4′-di- aminostilbenes-co-N-4-(N′,N′-dimethylaminophenyl)-maleimide). These copolymer precursors were characterized by ¹H NMR, SEC, TGA, and DSC. The ¹H NMR spectrum indicated the rigidity of copolymer backbones. SEC measurements showed the weight average molecular weights of these copolymers vary from 5 000 to 11 700 g/mol. No glass transition temperature or crystalline melting temperature was observed between 0 °C and 175 °C by DSC for poly(di-t-butyl-(E)-4,4′-stilbenedicarboxylate-co-N-(4-(t-butoxy- carbonyl)phenyl)maleimide). TGA showed that this polymer has 5% weight loss around 210 °C and 26% weight loss on the first stage of decomposition which corresponds to elimination of t-butyl functional group in the copolymer. The homopolymerization of EMS-III via free radical polymerization, anionic polymerization and cationic polymerization was attempted. However, no polymer was obtained from any of these polymerization methods. In anionic polymerization, the solution changed to red upon the addition of the initiator sec-bu-Li, indicating the successful addition of the sec-bu-Li to EMS-III. However, the initiated monomer did not propagate to form homopolymer. / Master of Science

The dissertation presents a new control strategy for two terminal HVDC systems embedded in an AC network. The control is based upon real-time measurements performed on the AC/DC system. Use is made of a technique for high speed accurate measurement of positive sequence voltages and currents, first developed in the field of computer relaying. The real-time measurements provides a term in the control law to compensate for inaccuracies following departure from the operating point. The control criterion is to damp out the electromechanical oscillations following a disturbance. The main contribution of the dissertation is to describe a new optimal controller formulation which contains a measurement based component. Optimal controllers are commonly constructed using linearized equations of the system around the operating point. In DC systems this approach is of a very limited value because of a highly nonlinear nature of the system. With the controller developed in this dissertation, it becomes possible to describe the system as a nonlinear dynamic system. The approximation resulting from the usual linearization of the system equations is thus avoided, and leads to a better controller design. The control technique is illustrated with a small AC/DC system. However, the equations formulated are sufficiently general, so that the technique can be applied to a larger system. Simulation results are included to represent the effectiveness of the developed controller. / Ph. D.

Beethoven's early sonatas have already revealed a complex and varied technique that can present significant difficulties for intermediate piano students. In particular, the absence of systematic methodological guidance, as well as the lack of suitable and high-quality repertoire, can result in students struggling to learn Beethoven's piano technique and not being satisfied with the results. By examining and analyzing the theories of great educators, pedagogues, and performers, some of the standard technical patterns are identified and methods of mastering them are summarized. A sampling of related late-elementary level and intermediate level repertoire is identified, providing study material for students starting to learn the Beethoven sonatas, and serving as a guide for their teachers.

Yes / Magnetic Field Hyperthermia is a technique where tumours are treated through an increase in local temperature upon exposure to alternating magnetic fields (AMFs) that are mediated by magnetic nano-particles (MNPs). In an AMF, these particles heat-up and kill the cells. The relationship between an AMF and the heating-rate is complex, leading to confusion when comparing data for different MNP and AMF conditions. This work allows for the thermal-response to be monitored at multiple AMF amplitudes while keeping other parameters constant. An induction-heating coil was designed based on a Zero-Voltage-Zero-Current (ZVZC) resonant circuit. The coil operates at 93 kHz with a variable DC drive-voltage (12–30 V). NEC4 software was used to model the magnetic field distribution, and MNPs were synthesised by the coprecipitation method. The magnetic field was found to be uniform at the centre of the coil and ranged from 1 kAm−1 to 12 kAm−1, depending on the DC drive-voltage. The MNPs were found to have a specific absorption rate (SAR) of 1.37 Wg−1[Fe] and 6.13 Wg−1[Fe] at 93 kHz and 2.1 kAm−1 and 12.6 kAm−1, respectively. The measured SAR value was found to be directly proportional to the product of the frequency and field-strength (SARα f Ho). This leads to the recommendation that, when comparing data from various groups, the SAR value should be normalized following this relationship and not using the more common relationship based on the square of the field intensity (SARα f Ho2). / This work is partially supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/X039366/1, and HORIZON-MSCA-RISE ID: 101086492, Marie Skłodow-ska-Curie, Research and Innovation Staff Exchange (RISE), titled: FractuRe Orthopaedic Rehabilita-tion: Ubiquitous eHealth Solution (Robust).

Alternating minimization (AltMin) is a generic term for a widely popular approach in non-convex learning: often, it is possible to partition the variables into two (or more) sets, so that the problem is convex/tractable in one set if the other is held fixed (and vice versa). This allows for alternating between optimally updating one set of variables, and then the other. AltMin methods typically do not have associated global consistency guarantees; even though they are empirically observed to perform better than methods (e.g. based on convex optimization) that do have guarantees. In this thesis, we obtain rigorous performance guarantees for AltMin in three statistical learning settings: low rank matrix completion, phase retrieval and learning sparsely-used dictionaries. The overarching theme behind our results consists of two parts: (i) devising new initialization procedures (as opposed to doing so randomly, as is typical), and (ii) establishing exponential local convergence from this initialization. Our work shows that the pursuit of statistical guarantees can yield algorithmic improvements (initialization in our case) that perform better in practice. / text