Jet launching and field advection in quasi-Keplerian discs

The fact that self-confined jets are observed around black holes, neutron stars and young forming stars points to a jet launching mechanism independent of the nature of the central object, namely the surrounding accretion disc. The properties of Jet Emitting Discs (JEDs) are briefly reviewed. It is argued that, within an alpha prescription for the turbulence (anomalous viscosity and diffusivity), the steady-state problem has been solved. Conditions for launching jets are very stringent and require a large scale magnetic field $B_z$ close to equipartition with the total (gas and radiation) pressure. The total power feeding the jets decreases with the disc thickness: fat ADAF-like structures with $h\sim r$ cannot drive super-Alfv\'enic jets. However, there exist also hot, optically thin JED solutions that would be observationally very similar to ADAFs. Finally, it is argued that variations in the large scale magnetic $B_z$ field is the second parameter required to explain hysteresis cycles seen in LMXBs (the first one would be $\dot M_a$).Comment: 4 pages, 1 figure, proceedings of IAU 275 "Jets at all scales" (Gustavo E. Romero, Rashid A. Sunyaev and Tomaso Belloni, eds

A herbrandized functional interpretation of classical first-order logic

We introduce a new typed combinatory calculus with a type constructor that, to each type σ, associates the star type σ^∗ of the nonempty finite subsets of elements of type σ. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements.info:eu-repo/semantics/publishedVersio