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1. The Torelli theorem for gravitational instantons

   https://doi.org/10.1017/fms.2022.67  

   Collins, Tristan; Jacob, Adam; Lin, Yu-Shen (January 2022, Forum of Mathematics, Sigma)

   Abstract We give a short proof of the Torelli theorem for $ALH^*$ gravitational instantons using the authors’ previous construction of mirror special Lagrangian fibrations in del Pezzo surfaces and rational elliptic surfaces together with recent work of Sun-Zhang. In particular, this includes an identification of 10 diffeomorphism types of $$ALH^*_b$$ gravitational instantons. 

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2. Polymeric Interfaces for Renewable Fuel Production

   Wadsworth, B; Khusnutdinova, D; Beiler, A; Moore, G. (January 2018, Materials Research Society symposia proceedings)

   Rational design of soft-to-hard material interfaces offers new opportunities to control matter and energy across the nano- and meso-scales, thus providing a chemical strategy to tailor the structural and physical properties of surfaces with molecular level precision. In the context of energy transduction, interfacing molecular catalysts with solid-state substrates is a promising approach to developing hybrid materials for generating solar fuels. However, effective integration of the requisite components, while controlling their redox properties and stability, remains a major challenge. Taking inspiration from nature, where specific amino acid residues and soft-material coordination environments control the redox properties of metal centers in proteins during enzymatic catalysis, we show that thin-film polymer surface coatings provide a novel strategy for assembling human-engineered catalysts onto solid supports. This presentation describes recent results from our laboratory aimed at better understanding the electrochemical and optical properties of hydrogen production catalysts assembled onto polymer-modified electrode surfaces. The polymer immobilization method results in unique electronic and vibrational spectroscopic signals associated with the immobilized molecular species. In addition, the use of discrete polymer architectures, coupled with rational synthetic modifications to the catalyst’s ligand environment, affords control over the chemical stability and redox potentials of surface immobilized molecular complexes, spanning a ~250 mV range. 

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3. The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems

   https://doi.org/10.1007/978-3-319-94881-2_4  

   Cosun, I.; Huizenga, J. (November 2018, Abel symposia)

   Brill-Noether Theorems play a central role in the birational geometry of moduli spaces of sheaves on surfaces. This paper surveys recent work on the Brill-Noether problem for rational surfaces. In order to highlight some of the difficulties for more general surfaces, we show that moduli spaces of rank 2 sheaves on very general hypersurfaces of degree d in P3 can have arbitrarily many irreducible components as d tends to infinity. 

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4. Generalizations of non-uniform rational B-splines via decoupling of the weights: theory, software and applications

   https://doi.org/https://doi.org/10.1007/s00366-019-00799-w  

   Alireza H. Taheri, Saeed Abolghasemi (October 2019, Engineering with computers)

   We introduce a new class of curves and surfaces by exploring multiple variations of non-uniform rational B-splines. These variations which are referred to as generalized non-uniform rational B-splines (GNURBS) serve as an alternative interactive shape design tool, and provide improved approximation abilities in certain applications. GNURBS are obtained by decoupling the weights associated with control points along different physical coordinates. This unexplored idea brings the possibility of treating the weights as additional degrees of freedoms. It will be seen that this proposed concept effectively improves the capability of NURBS, and circumvents its deficiencies in special applications. Further, it is proven that these new representations are merely disguised forms of classic NURBS, guaranteeing a strong theoretical foundation, and facilitating their utilization. A few numerical examples are presented which demonstrate superior approximation results of GNURBS compared to NURBS in both cases of smooth and non-smooth fields. Finally, in order to better demonstrate the behavior and abilities of GNURBS in comparison to NURBS, an interactive MATLAB toolbox has been developed and introduced. 

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5. Selectivity for ethanol partial oxidation: the unique chemistry of single-atom alloy catalysts on Au, Ag, and Cu(111)

   https://doi.org/10.1039/C9TA04572D  

   Li, Hao; Chai, Wenrui; Henkelman, Graeme (October 2019, Journal of Materials Chemistry A)

   Recently, we found that the atomic ensemble effect is the dominant effect influencing catalysis on surfaces alloyed with strong- and weak-binding elements, determining the activity and selectivity of many reactions on the alloy surface. In this study we design single-atom alloys that possess unique dehydrogenation selectivity towards ethanol (EtOH) partial oxidation, using knowledge of the alloying effects from density functional theory calculations. We found that doping of a strong-binding single-atom element ( e.g. , Ir, Pd, Pt, and Rh) into weak-binding inert close-packed substrates ( e.g. , Au, Ag, and Cu) leads to a highly active and selective initial dehydrogenation at the α-C–H site of adsorbed EtOH. We show that many of these stable single-atom alloy surfaces not only have tunable hydrogen binding, which allows for facile hydrogen desorption, but are also resistant to carbon coking. More importantly, we show that a rational design of the ensemble geometry can tune the selectivity of a catalytic reaction. 

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