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Full-Text Articles in Physical Sciences and Mathematics
The Poincaré Duality Theorem And Its Applications, Natanael Alpay, Melissa Sugimoto, Mihaela Vajiac
The Poincaré Duality Theorem And Its Applications, Natanael Alpay, Melissa Sugimoto, Mihaela Vajiac
SURF Posters and Papers
In this talk I will explain the duality between the deRham cohomology of a manifold M and the compactly supported cohomology on the same space. This phenomenon is entitled “Poincaré duality” and it describes a general occurrence in differential topology, a duality between spaces of closed, exact differentiable forms on a manifold and their compactly supported counterparts. In order to define and prove this duality I will start with the simple definition of the dual space of a vector space, with the definition of a positive definite inner product on a vector space, then define the concept of a manifold. …
The Künneth Formula And Applications, Melissa Sugimoto
The Künneth Formula And Applications, Melissa Sugimoto
SURF Posters and Papers
The de Rham cohomology of a manifold is a homotopy invariant that expresses basic topological information about smooth manifolds. The q-th de Rham cohomology of the n-dimensional Euclidean space is the vector space defined by the closed q-forms over the exact q-forms. Furthermore, the support of a continuous function f on a topological space X is the closure of the set on which f is nonzero. The result of restricting the definition of the de Rham cohomology to functions with compact support is called the de Rham cohomology with compact support, or the compact cohomology. The concept of cohomology can …
Designing A Reactor Chamber For Hot Electron Chemistry On Bimetallic Plasmonic Nanoparticles, Bryn Merrill, Bingjie Zhang, Jerry Larue
Designing A Reactor Chamber For Hot Electron Chemistry On Bimetallic Plasmonic Nanoparticles, Bryn Merrill, Bingjie Zhang, Jerry Larue
SURF Posters and Papers
Catalysis provides pathways for efficient and selective chemical reactions by lowering the energy barriers for desired products. Gold nanoparticles (AuNPs) show excellent promise as plasmonic catalysts. Plasmonic materials have localized surface plasmon resonances, oscillations of the electron bath at the surface of a nanoparticle, that generate energetically intense electric fields which rapidly decay into energetically excited electrons. The excited electrons have the potential to destabilize atoms strongly bound to the catalysts through occupation of antibonding orbitals. Tuning the antibonding orbitals to make them accessible for occupancy by electrons is achieved by coating the AuNP in a thin layer of another …