Surjectivity of the ∂‾\overline{\partial}-operator between spaces of weighted smooth vector-valued functions

We derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator $\overline{\partial}$ between spaces of weighted smooth Fr\'echet-valued functions. This is done by establishing an analog of H\"ormander's theorem on the solvability of the inhomogeneous Cauchy-Riemann equation in a space of smooth $\mathbb{C}$-valued functions whose topologyis given by a whole family of weights. Our proof relies on a weakened variant of weak reducibility of the corresponding subspace of holomorphic functions in combination with the Mittag-Leffler procedure. Using tensor products, we deduce the corresponding result on the solvability of the inhomogeneous Cauchy-Riemann equation for Fr\'echet-valued functions

Integrating Transmission and Energy Markets Mitigates Market Power

Integrating Transmission and Energy Markets Mitigates Market Powe

Crying for Repression: Populist and Democratic Biopolitics in Times of COVID-19

We live in very Foucauldian times, as the many think-pieces published on biopolitics and COVID-19 show. Yet what is remarkable—biopolitically—about the current situation has gone largely unnoticed: We are witnessing a new form of biopolitics today that could be termed populist biopolitics. Awareness of this populist biopolitics helps illuminate what is needed today: democratic biopolitics

Tunneling characteristic of a chain of Majorana bound states

We consider theoretically tunneling characteristic of a junction between a normal metal and a chain of coupled Majorana bound states generated at crossings between topological and non-topological superconducting sections, as a result of, for example, disorder in nanowires. While an isolated Majorana state supports a resonant Andreev process, yielding a zero bias differential conductance peak of height 2e^2/h, the situation with more coupled Majorana states is distinctively different with both zeros and 2e^2/h peaks in the differential conductance. We derive a general expression for the current between a normal metal and a network of coupled Majorana bound states and describe the differential conductance spectra for a generic set of situations, including regular, disordered, and infinite chains of bound states.Comment: 6 pages, 4 figure