48 research outputs found

    Extending partial isomorphisms

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    There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group

    Development of Visible-Light Photoredox Catalyzed Transformations and Applications in Total Syntheses of Natural Products

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    In Chapter 1, alkyl oxalates are described as new bench-stable alcohol activating groups for radical generation under visible light photoredox conditions. Using these precursors, the first net redox-neutral coupling of tertiary and secondary alcohols with electron-deficient alkenes is achieved. In Chapter 2, visible light photoredox-catalyzed fragmentation of methyl N-phthalimidoyl oxalates is described for the direct construction of a 1,4-dicarbonyl structural motif by a conjugate addition of the methoxycarbonyl radical to Michael acceptors. The regioselectivity of the addition of this alkoxyacyl radical species to electron-deficient olefins is found to be influenced by the electronic nature of the acceptor, behavior similar to that exhibited by nucleophilic alkyl radicals.In Chapter 3, the evolution of a convergent fragment-coupling strategy for the enantioselective total synthesis of trans-clerodane diterpenoids is described. The key bond construction is accomplished by 1,6-addition of a trans-decalin tertiary radical with 4-vinylfuran-2-one. The tertiary radical is optimally generated from the hemioxalate salt of the corresponding tertiary alcohol upon activation by visible light and an Ir(III) photoredox catalyst. The synthetic strategy described in this chapter allows a number of trans-clerodane diterpenoids to be synthesized in enantioselective fashion by synthetic sequences of 10 steps or less. In Chapter 4, the development of a convergent fragment-coupling strategy for the enantioselective total syntheses of a group of rearranged spongian diterpenoids that harbor the cis-2,8-dioxabicyclo[3.3.0]octan-3-one unit is described. The key bond disconnection relies on a late-stage fragment coupling between a tertiary carbon radical and an electron-deficient alkene to unite two ring systems and form two new stereocenters, one of which is quaternary, in a stereoselective and efficient manner. This strategy is applied towards 14-15 step syntheses of three diterpenoids, cheloviolenes A and B and dendrillolide C.In Chapter 5, the first total synthesis of a chromodorolide marine diterpenoid is described. The core of the natural product is constructed by a bimolecular radical addition/cyclization/fragmentation cascade that unites two complex fragments and forms two C-C bonds and four contiguous stereogenic centers of (-)-chromodorolide B in a single step. Computational studies guided the development of this transformation and provide insight into the origin of the observed stereoselectivity

    Total Synthesis of ()-Chromodorolide B

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