The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

Admissible equilibria of non-neutral plasmas in a Malmberg-Penning trap

A "parallel current constraint" is derived, that in combination with the Poisson equation allows one to select admissible equilibria of non-neutral plasmas in a Malmberg-Penning trap in the presence of a nonuniform and nonaxisymmetric magnetic field. Asymmetry-induced currents (analogous to the Pfirsch-Schluter currents in Tokamaks) appearing in a non-neutral plasma even in the absence of magnetic drifts are explicitly computed in the case of a uniformly tilted magnetic field

Equilibrium of non-neutral plasmas in a Malmberg\u2013Penning trap with a weakly tilted magnetic field

The effect of small asymmetric magnetic perturbations on the equilibrium of a non-neutral plasma confined in a Malmberg-Penning trap is analyzed. A constraint, known in the theory of tandem mirrors as the condition of current closure, is derived for non-neutral plasmas. Together with Poisson's equation, this constraint provides a set of equations for determining self-consistent asymmetric equilibria of non-neutral plasmas in Malmberg-Penning traps. As an example of this approach, the non-neutral plasma equilibrium in the presence of a weak magnetic tilt is analyzed. Analytical and semianalytical solutions for the electric potential variations inside the trap are found in a paraxial limit for various radial density profiles of the plasma, including the case of global thermal equilibrium. The numerical procedure aimed to obtain self-consistent plasma equilibria for a magnetic field with a large asymmetry is also discussed. The newly developed method can be straightforwardly applied to determine plasma equilibria under the effect of the magnetic perturbations of higher multipolarity (such as, quadrupole or octupole fields)

Geological-morphological description of the Sedna and Guinevre planitiae on Venus (photomap sheets B-11, B-20, B-21)

Presented are descriptions and maps of the region of Sedna and Guinevra Planitiae--representatives of the largest geological providense on Venus comprised of volcanic rock. Units of different age are isolated and their relations are given, as well as interpretations of proposed mechanisms of formation

Geological-morphological description of the Ishtar Terra (photomap of the Venusian surface sheet B-5)

The main part of the Ishtar Terra east of the Maxwell Montes is covered with systems of areal dislocations of several directions, which are called Parquet. According to the structural patterns these may be divided into: (1) the central stable block; (2) the lesser peripheral blocks separated from the central one by gaps and grabens; (3) the zones of mobilized parquet, whose substance flowed downward at an incline in the directions away from the central block in the form of plastic flows; and (4) the partially parqueted lava sheets. The Maxwell Montes were formed as a result of the collision between the central parquet block and the Lakshmi Planum