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

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

Integrating Transmission and Energy Markets Mitigates Market Power

Integrating Transmission and Energy Markets Mitigates Market Powe

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

"The Functioning of the Payment System"

[From the Introduction]. Today, most payments consist of electronic transfer of information and book-entries. The domestic financial infrastructure in the EU is generally highly developed, with large and small value systems, central securities depositories, and modern exchanges. Until recently, the cross-border infrastructure was virtually non-existent. Central banks have traditionally played an important role in payment systems. This role has been based on both the operational and the oversight responsibilities of central banks

Auslander-Reiten theory for simply connected differential graded algebras

Peter Jorgensen introduced the Auslander-Reiten quiver of a simply connected Poincare duality space. He showed that its components are of the form ZA_infty and that the Auslander-Reiten quiver of a d-dimensional sphere consists of d-1 such components. In this thesis we show that this is the only case where finitely many components appear. More precisely, we construct families of modules, where for each family, each module lies in a different component. Depending on the cohomology dimensions of the differential graded algebras which appear, this is either a discrete family or an n-parameter family for all n.Comment: 58 pages, doctoral thesis University of Paderborn (2007