Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field \mathbb{F}_{q}(y), where \mathbb{F}_{q} is the finite field with q elements. In this thesis we will present new efficient probabilistic algorithms for Wedderburn decomposition and the computation of the radical.

This thesis provides the first example of coordination of a 1,2,3-dithiazolyl (1,2,3-DTA) ligand through a N, O bidentate pocket that is reproducible in high purity and bulk quantities. More importantly, it reports the first magnetometry measurements on metal complexes of a 1,2,3-DTA ligand. The radical ligand 1,2,3-dithiazolyl-6,7-dimethyl-1,4-naphthoquinone (6,7-Me2DTANQ) has been prepared and fully characterized. Coordination complexes of 6,7-Me2DTANQ have also been prepared and the resulting species’ structural and magnetic properties are presented. The transition metal ions Ni2+ and Mn2+ produce volatile trinuclear M(hfac)2-Rad-M(hfac)2-Rad-M(hfac)2 complexes. The spin ground state of the trinuclear Mn complex ST = 13/2 results from antiferromagnetic (AFM) coupling. Short sulfur-sulfur contacts and sulfur-oxygen contacts between trinuclear complexes produce weak AFM coupling interactions between trimer units. The lanthanide ions Nd3+, Gd3+ and Dy3+ produce volatile [Ln(hfac)3-Rad]n complexes. The spin ground state of the Gd polymer is ST = 3 per monomeric unit due to Gd3+‒radical AFM coupling.

A 1,2,3-dithiazolyl radical, [1,2,3]dithiazolyl[4,5-f][1,10]phenanthroline, has been prepared and characterized. The EPR spectrum in toluene supports a delocalized structure with an experimental g-factor of 2.0081. Cyclic voltammetry in CH2Cl2 reveals an Ecell of 1.30 V vs. SCE with a reversible +1/0 and irreversible 0/-1 redox couple. The structure belongs to the space group P-1. Complexes of the radical with Mn2+ and Dy3+ have been obtained. The mononuclear Mn2+ complex was confirmed by elemental analysis; however, no structure was determined. The structure of the mononuclear Dy3+ complex was determined by X-ray crystallography and belongs to the space group C2/c. An isopropyl-substituted oxobenzene-bridged bis-1,2,3-dithiazolyl radical has been prepared and characterized by EPR and cyclic voltammetry. The EPR in toluene supports a delocalized structure with an experimental g-factor of 2.0091. Cyclic voltammetry in CH3CN reveals an Ecell of 0.64 V vs SCE with a reversible +1/0 and irreversible 0/-1 and +2/+1 redox couples.

Verdazyl radicals, discovered in 1963, are a family of exceptionally stable radicals defined by their 6-membered ring containing four nitrogen atoms. Verdazyl radicals are highly modular compounds with a large assortment of substitution patterns reported. Their stability and high degree of structural variability has been exploited in the fields of materials, inorganic, polymer and physical chemistry; however their deliberate use as starting materials towards organic synthesis had only been reported in recent years by the Georges lab. In 2008, the Georges group reported a disproportionation reaction that was observed to a occur with 6-oxoverdazyl radicals resulting in azomethine imines capable of undergoing 1,3-dipolar cycloaddition reactions. With this discovery, the door to using verdazyl radicals as substrates towards organic synthesis had been opened. Their utility in synthesis was soon discovered not to be limited to just the cycloadducts their azomethine imine derivatives could generate but also the increasing number of N-heterocycles that could be generated from these cycloadducts via unique rearrangement reactions, a major theme of this thesis. In addition, triphenyl verdazyl radicals, a distinct class of verdazyl radicals, has been shown to react with alkynes by direct radical addition and rearrangement to afford isoquinolines. As part of this thesis, a new synthetic methodology of generating 6-oxoverdazyl radicals is reported that does not rely on the use of phosgene or hydrazines. This new synthesis allows for the expansion of available alkyl substituents possible on N1 and N5 positions of 6-oxoverdazyl radicals, as well as, generation of unsymmetrical examples of 6-oxoverdazyl radicals with non-identical N1 and N5 alkyl substituents. Employing the new 6-oxoverdazyl radicals synthesized via this method, a study on the effects of different alkyl substituents on the disproportionation reaction of 6-oxoverdazyls was undertaken. Lastly, given the assortment of N-heterocyclic molecular scaffolds capable of being synthesised starting from verdazyl radicals as precursors, the applicability of verdazyl radicals in making a diversity oriented synthesis (DOS) based library was explored. In a group effort with other Georges lab members, a small library composed of various classes of verdazyl radical derived compounds was synthesized and non-specifically tested for cytotoxicity against acute myeloid leukemia and multiple myeloma cell lines in collaboration with The Princess Margaret Hospital. One example was shown to effectively kill cancer cells in both these lines in 250 μM concentration pointing out the potential of using verdazyl radical based chemistry in drug discovery.

Atom transfer radical polymerization (ATRP) is a dynamic technique that possesses tremendous potential for the synthesis of novel polymeric materials not possible through conventional free radical polymerization. However, its use on an industrial scale has been limited by the high level of transition metal complex required. Significant advances have been made in the last 5 years towards lowering the level of copper complexes used in ATRP, resulting in novel variants called “activator regenerated by electron transfer” (ARGET) and “single electron transfer-living radical polymerization” (SET-LRP). To fully realize the potential of ATRP, its use in industrially relevant processes must be studied. Continuous processes such as tubular flow reactors and stirred tank reactors (CSTR) can reduce waste, improve productivity and facilitate process scale-up when compared to common batch reactors. The combination of low copper concentration ATRP techniques and continuous processes are especially attractive towards the design of a commercially viable process. This thesis presents a study into ARGET ATRP and SET-LRP as applied to continuous tubular and stirred tank reactors for the production of acrylic and methacrylic polymers. The equilibrium which governs polymerization rate and control over molecular architecture is studied through batch ARGET ATRP experiments. The improved understanding of ARGET ATRP enabled the reduction of ligand from a 3 to 10 fold excess used previously down to a stoichiometric ratio to copper salts. ARGET ATRP was then adapted to a continuous tubular reactor, as well as to a semi-automated CSTR. The design of the reactors and the effect of reaction conditions such as reducing agent concentration and residence time are discussed. The use of common elemental copper(0) such as copper wire and copper tubing is also investigated with SET-LRP for room temperature polymerization of methyl acrylate. SET-LRP is adapted to a CSTR to observe the effects of residence time on reaction rate, molecular weight control as well as copper consumption rate. The use of copper tubing as a catalyst source for SET-LRP is demonstrated and the design of a continuous tubular reactor using a combination of copper and stainless steel tubing is discussed. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2012-04-30 16:01:28.916

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Verdazyl radicals, discovered in 1963, are a family of exceptionally stable radicals defined by their 6-membered ring containing four nitrogen atoms. Verdazyl radicals are highly modular compounds with a large assortment of substitution patterns reported. Their stability and high degree of structural variability has been exploited in the fields of materials, inorganic, polymer and physical chemistry; however their deliberate use as starting materials towards organic synthesis had only been reported in recent years by the Georges lab. In 2008, the Georges group reported a disproportionation reaction that was observed to a occur with 6-oxoverdazyl radicals resulting in azomethine imines capable of undergoing 1,3-dipolar cycloaddition reactions. With this discovery, the door to using verdazyl radicals as substrates towards organic synthesis had been opened. Their utility in synthesis was soon discovered not to be limited to just the cycloadducts their azomethine imine derivatives could generate but also the increasing number of N-heterocycles that could be generated from these cycloadducts via unique rearrangement reactions, a major theme of this thesis. In addition, triphenyl verdazyl radicals, a distinct class of verdazyl radicals, has been shown to react with alkynes by direct radical addition and rearrangement to afford isoquinolines. As part of this thesis, a new synthetic methodology of generating 6-oxoverdazyl radicals is reported that does not rely on the use of phosgene or hydrazines. This new synthesis allows for the expansion of available alkyl substituents possible on N1 and N5 positions of 6-oxoverdazyl radicals, as well as, generation of unsymmetrical examples of 6-oxoverdazyl radicals with non-identical N1 and N5 alkyl substituents. Employing the new 6-oxoverdazyl radicals synthesized via this method, a study on the effects of different alkyl substituents on the disproportionation reaction of 6-oxoverdazyls was undertaken. Lastly, given the assortment of N-heterocyclic molecular scaffolds capable of being synthesised starting from verdazyl radicals as precursors, the applicability of verdazyl radicals in making a diversity oriented synthesis (DOS) based library was explored. In a group effort with other Georges lab members, a small library composed of various classes of verdazyl radical derived compounds was synthesized and non-specifically tested for cytotoxicity against acute myeloid leukemia and multiple myeloma cell lines in collaboration with The Princess Margaret Hospital. One example was shown to effectively kill cancer cells in both these lines in 250 μM concentration pointing out the potential of using verdazyl radical based chemistry in drug discovery.

The 4-substituted glutarimide required for the synthesis of sesbanimide (53) was obtained by free radical addition of iodoacetamide onto the $ alpha, beta$-unsaturated ester (81) mediated by tributyltin; the lactol ring C was prepared by the analogous free radical cyclization of the $ alpha$-bromo-dipropargyl ketal 73. / The syntheses of tricyclic carbapenems involved appropriately substituted monocyclic azetidinone precursors. Free radical 5- exo cyclizations led to the relatively unstable benzo carbapenems 116, 119 and 120. The 6- exo mode, however, afforded stable benzo carbacephems 125, 127, 132 and 133. / $ alpha$-Bromo- and $ alpha{,} alpha$-dibromoazetidinones were converted stereoselectively to the $ alpha$-alkylazetidinones 149 and 153, or to $ beta$-alkylazetidinones 151, 154 and 159 by a free radical addition onto olefins 148 or allyltributyltin.

A review of organic, π-electron donor molecules is given. The focus is on non- tetrathiafulvalene based systems. Polycyclic arenes, thioalkyl substituted arenes, chalcogenated fulvalenes, peri-dichalcogen bridged polycyclic arenes and heteroarenes are covered. Various π-electron donor molecules based on acenaphtho[ 1,2-b][ 1,4]-dithin have been synthesised via various methodologies. The redox properties of these molecules, as studied by cyclic voltammetry, provide evidence that these species are efficient π-electron donors. A selection of these compounds have also been studied by Electron Spin Resonance. Two ring expansion methodologies have been utilised in the synthesis of acenaphtho[l,2-b][l,4]-dithin based systems from 1,2-dithiols. Complexation of 7,12- dithia-benzo[k]fluoranthene, thus synthesised, with 2,5-dibromo-7,7,8,8-tetracyano-p- quinodimethane and iodine (I(_4) counter ion) yielded highly crystalline but poorly conducting salts.1,2-Dibromoacenaphthylene and benzo-l,2-dithiolate species have been reacted to form new 7,12-dithia-benzo[k]fluoranthene derivatives, two of which have been studied by X-ray diffraction. The versatile oligo(l,3-dithiole-2,4,5-trithione) compound has been used to generate various compounds containing the 1,4-dithiin ring including 8,9- di(methylsulfanyl)acenaphthyleno[l,2-b][l,4]dithine, which forms complexes with 7, 7,8,8-tetracyano-p-quinodimethane, 2,5-dibromo-7,7,8,8-tetracyano-p-quinodimethane and iodine (I(_7) counter ion) all three of which have been studied by X-ray diffraction. A novel 1,2,4-trithiolane has also been synthesised and characterised by X-ray diffraction.

The aim of the current study was to examine the radical right-wing sympathizers in Sweden. To fulfill this aim, a quantitative case study on Sweden Democrats sympathizers was conducted. More specifically, this study has examined socio-economic backgrounds and political attitudes of the Sweden Democrat sympathizers. The results show that sympathizers of Sweden Democrats are higher among younger people and men. The results also show a higher support for Sweden Democrats among people with lower education and low income that also live in small towns and in the countryside. These individuals also have lower trust in political institutions at the national and European level and are less satisfied with democracy at both levels and believe that Sweden should reduce immigration. The theory explains that these results are also consistent in other parts of Europe. The underlying explanation for these results seems to be that the world has become amore globalized, and these individuals who sympathize with radical right-wing populist parties are the ones who are negatively affected by a globalized world.