Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by $kappa$-distributions. The free-free spectrum and radiative loss
es depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than $10^{-10}$ in units of $z^2Ry$. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the $kappa$ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing $kappa$. Tables of these Gaunt factors are provided.
Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless, we use doma
in-specific variants of the latter, as they are convenient modeling languages in which the local code of processes can be programmed explicitly, with the local state information usually managed via parameter lists of process constants. However, domain-specific process calculi are often equipped with (unlabeled) reduction semantics, building upon a rich and convenient notion of structural congruence. Unfortunately, the price for this convenience is that the analysis is cumbersome: the set of reachable states is modulo structural congruence, and the processes state information is very hard to identify. We extract from congruence classes of reachable states individual state-informative representatives that we supply with a proper formal semantics. As a result, we can now freely switch between the process calculus terms and their representatives, and we can use the stateful representatives to perform assertional reasoning on process calculus models.
We study whether, in the pi-calculus, the match prefix-a conditional operator testing two names for (syntactic) equality-is expressible via the other operators. Previously, Carbone and Maffeis proved that matching is not expressible this way under ra
ther strong requirements (preservation and reflection of observables). Later on, Gorla developed a by now widely-tested set of criteria for encodings that allows much more freedom (e.g. instead of direct translations of observables it allows comparison of calculi with respect to reachability of successful states). In this paper, we offer a considerably stronger separation result on the non-expressibility of matching using only Gorlas relaxed requirements.
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors.
