Andreas Rosén – författare
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3 produkter
3 produkter
965 kr
Skickas inom 10-15 vardagar
This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions.The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.
691 kr
Skickas inom 10-15 vardagar
This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions.The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.
Immobilization of Ruthenium-Triphos Catalysts and their Application for the Hydrogenation of Polar Bonds in Batch and Continuous-Flow Systems
Häftad, Engelska, 2020
558 kr
Tillfälligt slut
The present thesis deals with the development of immobilized Ruthenium-Triphos catalysts for the selective hydrogenation of esters, amides and CO2 as potential substrates in the context of the valorization of renewable carbon resources.The highly active molecular catalyst [Ru(Triphos)TMM] (C-1a), already investigated in various catalytic approaches and mechanistic studies, was defined as target structure for immobilization. In a detailed preparative study, two synthetic pathways towards [(Ru(Ether-Triphos)TMM] (C-2a) and [(Ru(Carbamate-Triphos)TMM] (C-3a) were developed, using a triethoxysilyl-functionality as anchoring-group in the catalysts backbone, enabling the covalent immobilization on oxidic supports (section 3.1). Subsequently, the complex [(Ru(Ether-Triphos)TMM] (C-2a) was tethered on amorphous SiO2,500, leading to the heterogenized catalyst [(Ru(Ether-Triphos)TMM]@SiO2,500 (C-2b, section 3.1).The immobilized catalyst was successfully tested in ester-, amide- and CO2 hydrogenation reactions in single-batch and continuous-flow experiments. In lactam hydrogenation reactions the immobilized catalyst showed superior long-term stability and activity in comparison to its homogeneous counterpart. Since the homogeneous complex quickly forms an inactive hydridebridged dimer under the employed reaction conditions, the active-site isolation of the tethered complexes on the surface prevents self-deactivation, thus maintaining its activity in several recycling steps. For long-term continuous-flow hydrogenation tests with C-2b, DL-lactide was evaluated as a suitable benchmark-substrate in an extensive ester screening. Here, different catalyst pre-treatments were tested to maximize catalyst activity. High TON (> 4700) over multiple days in flow were reached and the changes that the catalyst material underwent were characterized (section 3.3).After the catalytic evaluation of C-2b the observed Ru leaching was determined to be the major target for further catalyst optimization. Therefore, various modifications in catalyst preparation were performed, including changes in the synthesis order and reaction conditions, additive utilization as well as the incorporation of the complex C-2a into the framework mesostructured SBA-15 towards [(Ru(Ether-Triphos)TMM]@SBA-15 (C-2k, section 3.4). In a final investigation, selected catalysts were evaluated in the direct synthesis of dimethoxy methane (DMM) from CO2, H2 and MeOH. Catalyst C-2k was highly active and superior in terms of low Ru leaching-rates and reached unpreceded activity during recycling experiments (TON >1900 of DMM, section 3.5).