Ferric ferrocyanide (Prussian blue) and its analogues are renowned for the variety of properties and applications associated with them. At the same time, however, they suffer from issues related to their variable composition and poor crystallinity. As a result, we are preparing discrete cyanide-bridged clusters both to mimic these materials and to search for properties unique to the molecule, such as single molecule magnetism. The work in this dissertation has focused on the expansion of series of trigonal bipyramidal (TBP) cyanide-bridged clusters, [M(tmphen)2]3[M′(CN)6]2, that exhibit a variety of properties including spin crossover, charge-transfer-induced spin transition, and photomagnetism. One goal of the work was focused on the preparation of new paramagnetic TBP clusters incorporating various 3d metal ion combinations. Nine new clusters were prepared and characterized, including several “model compounds” with only one type of paramagnetic metal ion. The magnetic properties of these model compounds were combined to better explain the coupling through the cyanide ligands in clusters with two paramagnetic metal centers. An additional two clusters were also prepared that were found to exhibit a thermally induced LS Fe^II -> HS Fe^II transition. The spin crossover event was confirmed by magnetic susceptibility and Mössbauer spectroscopy, and variable temperature X-ray crystallography revealed the transitions to be distinct for each FeII center and dependant on the interstitial solvent. Another major goal of the work was to investigate the TBP clusters for their potential to be used as building-blocks to prepare 1-D extended structures of linked clusters, such as a {[Co(tmphen)2]3[Fe(CN)6]2[Mn(MeOH)4]}∞(ClO4)3 chain. A final research goal was a search for photomagnetic behavior, the change in magnetic properties with irradiation, related to spin transitions in several key TBP clusters. The Fe3Fe2 and Fe3Co2 TBP clusters were found to exhibit a light-induced excited spin state trapping (the LIESST effect) similar to that observed in mononuclear FeII compounds, and the photo-induced charge transfer that has been observed in Co-Fe Prussian blue materials is mimicked by the Co3Fe2 TBP molecular analogue.

Submitted by Michele de Souza Lopes null (michele_slopes2006@hotmail.com) on 2017-05-13T00:16:52Z No. of bitstreams: 2 Dissertação_Arquivamento_Michele de Souza Moraes.pdf: 6181011 bytes, checksum: b3192423a64e91b48893e8a4e263a0cd (MD5) Produto_Michele de Souza Moraes.pdf: 16061853 bytes, checksum: 354e98ade11a1c55818ccade4d870da3 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-05-16T13:40:54Z (GMT) No. of bitstreams: 1 moraes_ms_me_bauru.pdf: 6181011 bytes, checksum: b3192423a64e91b48893e8a4e263a0cd (MD5) / Made available in DSpace on 2017-05-16T13:40:54Z (GMT). No. of bitstreams: 1 moraes_ms_me_bauru.pdf: 6181011 bytes, checksum: b3192423a64e91b48893e8a4e263a0cd (MD5) Previous issue date: 2017-03-20 / Esta dissertação foi desenvolvida a partir do estudo de um tratado intitulado The Trigonall Sector. A obra foi publicada por John Chatfeilde, em 1650, e mostra a descrição e o uso de um instrumento matemático chamado setor trigonal. O documento apresenta relações geométricas e trigonométricas verificadas nas propriedades dos triângulos, incluindo senos, tangentes, secantes, como também cordas e relações de proporção. O objetivo geral foi investigar o movimento do pensamento de estudantes do ensino médio na formação dos conceitos inerentes ao uso do instrumento setor trigonal e seu respectivo tratado em uma atividade didática. A pesquisa é exploratória, orientada por uma interface entre história e ensino de matemática fundamentada na relação entre o movimento do pensamento na formação de conceito e o contexto no qual os conceitos foram desenvolvidos. Realizou-se estudo sobre a história de instrumentos matemáticos, o tratado e o próprio instrumento, a partir dos quais inferem-se potencialidades didáticas que desencadearam a realização de uma atividade orientadora de ensino com estudantes do ensino médio de uma escola pública. A análise das ações dos estudantes pautou-se na perspectiva lógico-histórica e dos pensamentos empírico e teórico. Verificou-se que a atividade orientadora de ensino proporcionou um diálogo entre os conhecimentos matemáticos de uma época com os atuais, o que permitiu aos participantes mobilizar conceitos matemáticos durante a atividade e auxiliá-los na compreensão do movimento do pensamento. Dentre os resultados destaca-se a relação do simples ao complexo no que tange a representação direta de um triângulo e as elaborações conceituais necessárias quanto a aparente limitação do instrumento, e o movimento do pensamento empírico para o teórico por meio de análises das classificações dos triângulos quanto aos seus lados e ângulos. A partir desta pesquisa elaborou-se um produto final em formato de livreto contendo contribuições para o ensino dos triângulos por meio do instrumento setor trigonal e seu tratado. / This dissertation was developed from a study of a treatise, titled The Trigonall Sector. This work was published by John Chatfeilde, in 1650, and shows the description and use of a mathematical instrument called trigonal sector. The document presents geometric and trigonometric relations verified in the properties of triangles, including sines, tangents, secants, as well as strings and proportion ratios. The general objective was to investigate the thinking process of students from high school when formulating inherent concepts to the use of the trigonal sector instrument and its respective treatise in a didactic activity. The research is exploratory, oriented by an interface between history and the teaching of Mathematics, based in a relation between the thinking process in forming concepts and the context in which the concepts were developed. It was conducted a study on the history of mathematical instruments, the treatise and the instruments themself, from where it is inferred didactic potentialities which resulted in the performance of an oriented teaching activity with high school students from a public school. The analyses of students’ actions were guided by a logic-historical perspective and by empirical and theoretical thinking. It was verified that this activity provided a dialogue between mathematical knowledge from a time with the present day, which allowed to the participants to mobilize mathematical concepts during the activity and assist them in the comprehension of thinking process. Among the results, it can be highlighted the relation from the simple to the complex in what regards the direct representation of a triangle and the conceptual elaboration necessary as to the apparent limitation of the instrument, and the empirical to the theoretical thinking process by the analyses of the classification of the triangles as to their sides and angles. From that research, a final product was elaborated as a booklet with contributions to the teaching of triangles by the instrument of trigonal sector and its treatise.

<p>A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis will characterize the Riemann surfaces of genus 4 wiht non-unique trigonal morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4.</p> / Report code: LiU-Tek-Lic-2004:54. The electronic version of the printed licentiate thesis is a corrected version where errors in the calculations have been corrected. See Errata below for a list of corrections.

We construct several modular compactifications of the Hurwitz space \(H^d_{g/h}\) of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the cover to collide to a variable extent, generalizing the spaces of twisted admissible covers of Abramovich, Corti, and Vistoli. The resulting spaces are very well-behaved if d is small or if relatively few collisions are allowed. In particular, for d = 2 and 3, they are always well-behaved. For d = 2, we recover the spaces of hyperelliptic curves of Fedorchuk. For d = 3, we obtain new birational models of the space of triple covers. We describe in detail the birational geometry of the spaces of triple covers of \(P^1\) with a marked fiber. In this case, we obtain a sequence of birational models that begins with the space of marked (twisted) admissible covers and proceeds through the following transformations: (1) sequential contractions of the boundary divisors, (2) contraction of the hyperelliptic divisor, (3) sequential flips of the higher Maroni loci, (4) contraction of the Maroni divisor (for even g). The sequence culminates in a Fano variety in the case of even g, which we describe explicitly, and a variety fibered over \(P^1\) with Fano fibers in the case of odd g. / Mathematics

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis characterizes the cyclic trigonal Riemann surfaces of genus 4 with non-unique trigonal morphism using the automorphism groups of the surfaces. The thesis shows that Accola’s bound is sharp with the existence of a uniparametric family of cyclic trigonal Riemann surfaces of genus 4 having several trigonal morphisms. The structure of the moduli space of trigonal Riemann surfaces of genus 4 is also characterized. Finally, by using the same technique as in the case of cyclic trigonal Riemann surfaces of genus 4, we are able to deal with p-gonal Riemann surfaces and show that Accola’s bound is sharp for p-gonal Riemann surfaces. Furthermore, we study families of p-gonal Riemann surfaces of genus (p − 1)2 with two p-gonal morphisms, and describe the structure of their moduli space.

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis will characterize the Riemann surfaces of genus 4 wiht non-unique trigonal morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4. / <p>Report code: LiU-Tek-Lic-2004:54. The electronic version of the printed licentiate thesis is a corrected version where errors in the calculations have been corrected. See Errata below for a list of corrections.</p>

The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P3 (or SP3) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP3 transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP3 and diffusion equations, which guarantees high accuracy. The SP3 equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP3 transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP3 transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.

The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P3 (or SP3) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP3 transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP3 and diffusion equations, which guarantees high accuracy. The SP3 equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP3 transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP3 transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.

Silylamide ligands have been used throughout the Periodic Table since the 1960s. They have delivered landmark complexes by providing the first three co-ordinate f-element complexes, the first trigonal planar f-element complexes and the first near-linear f-element complexes. This area is reviewed in Chapter 2.Herein, this work presents the first uses of several novel bis-silylamide ligands developed at Manchester which take the form {N(SiR3)2} where R = Me, iPr or tBu to afford four novel ligands: N ʹ, {N(SiMe3)(SiiPr3)}; N**, {N(SitBuMe2)2}; N* {N(SitBuMe2)(SiiPr3)}; and N , {N(SiiPr3)2}. Group 1 and 2 complexes of all of these ligands are presented along with the previously reported N*ʹ [N*ʹ = {N(SitBuMe2)(SiMe3)}]; which show variable bonding motifs based on the steric bulk. The N** and N ligands have formed the bulk of the work presented and were used to stabilise the first trigonal planar actinide complex [U(N**)3], as well as the first near-linear Ln(II) (Ln = lanthanide) complexes [Ln(N )2] (Ln = Sm, Eu, Yb, Tm). Additionally the trigonal planar Ln(II) complexes [K(2.2.2-cryptand)][Ln(N**)3] (Ln = Sm, Eu, Yb, Tm) have also been synthesised to compare the physicochemical properties of trigonal planar and near-linear geometries on the same elements with similar ligands.

Natural product synthesis has been a most exciting and challenging branch of organic chemistry in view of its creative power and unlimited scope. Natural product synthesis witnessed an unprecedented growth and innovative developments, especially during the later half of the 20th century. This can be attributed to a number of factors, one of which has been the isolation and characterization of growing number of compounds from natural sources through availability of newer techniques of isolation and purification and advances in the incisive tools (eg. 2D NMR, X-ray, HRMS) of structure determination. Many natural products, though scarce from natural resources, possess wide ranging biological activity and need to be accessed through synthesis for clinical development and evaluation, particularly of analogs. This has been one of the main stimuli in recent years for undertaking the synthesis of natural products. Among the diverse architecture created by Nature, terpenoids are the most variegated in terms of the presence of a bewildering array of carbocyclic frameworks with unusual assemblage of rings and functionalities. This phenomenal structural diversity of terpenoids makes them challenging targets for total synthesis and for the articulation of new synthetic strategies for carbocyclic ring construction. One of the major concerns in organic chemistry, particularly of relevance in synthesis is the control of diastereoselectivity in nucleophilic and electrophilic additions to trigonal carbon atoms as this is the fundamental step in stereogenesis. Several approaches have been devised to achieve diastereoselection and to understand the interplay of underlying stereoelectronic factors. In this context, introduction of newer probe systems and search for incisive interpretations are continuously enriching the area. The present thesis addresses both the above mentioned themes of contemporary interest in organic chemistry and is presented in two main parts. Part-1: A Total Synthesis of Novel Sesquiterpenoid Natural Product (±)-Merrilactone A. Part-2: A Study of -Face Selectivity in Additions to Trigonal Carbon Centers in Iso-steric Environments. The Part-1 describes our travails towards a stereoselective construction of the complex framework present in the biologically potent and structurally novel sesquiterpene natural product Merrilactone A culminating in its total synthesis. The Part-2 narrates the results of -face selectivity in addition reactions to two novel systems, exo-5-subtituted bicyclo[2.1.1]hexan-2-ones, 5-exo-substituted 2-methylene-bicyclo[2.1.1]hexane and 1-substitued tricyclo[2.1.0.02,5]pentan-3-ones, employing various nucleophiles and electrophiles