A Runge theorem for generalized analytic functions

We show an approximation theorem of Runge type for solutions of the generalized Vekua equation $Lu=Au+B\overline{u}$, where L belongs to a class of degenerate elliptic planar vector fields and $A,B\in L^p$. To prove the theorem, we make use of an integral representation for the solutions of the generalized Vekua equation valid on relatively compact sets. As an application, we study the global solvability of the equation $Lu=Au+B\overline{u}+f$ with $f\in L^p$ and some of its consequences.     

Supercharged CO2 Photothermal Catalytic Methanation: High Conversion,Rate, and Selectivity

To overcome the thermodynamic and kinetic impediments of the Sabatier CO₂ methanation reaction, the process must be operated under very high temperature and pressure conditions, to obtain an industrially viable conversion, rate, and selectivity. Herein, we report that these technologically relevant performance metrics have been achieved under much milder conditions using solar rather than thermal energy, where the methanation reaction is enabled by a novel nickel-boron nitride catalyst. In this regard, an in situ generated HOB⋅⋅⋅B surface frustrated Lewis's pair is considered responsible for the high Sabatier conversion 87.68 %, reaction rate 2.03 mol g_Ni⁻¹h⁻¹, and near 100 % selectivity, realized under ambient pressure conditions. This discovery bodes well for an opto-chemical engineering strategy aimed at the development and implementation of a sustainable ‘Solar Sabatier’ methanation process.