Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments Gi(z), Hi(z) and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real z comparison with a previous code by A.J. MacLeod (J. Comput. Appl. Math. 53 (1994)) is provided. 2000 Mathematics Subject Classification: 33C10, 65D20, 65D32, 3...

Heuristic arguments are given, that the pair of consecutive primes separated by a distance d appears for the rst time at p f (d) p d exp 1 2 q ln 2 (d) + 4d. The comparison with the results of the computer search provides the support for the conjectured formula.

The conclusion by Turi et al. (Reports, 5 August 2005, p. 914) that all experimental spectral and energetic data on water-cluster anions point toward surface-bound electrons is overstated. Comparison of experimental vertical detachment energies with their calculated values for (H2O)n- clusters with surface-bound and internalized electrons supports previous arguments that both types of clusters ...

We obtain sufficient condition for SDEs to evolve in the positive orthrant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.

This paper provides a preliminary investigation towards the definition of a general framework for the comparison of extension-based argumentation semantics with respect to the notion of skepticism. We identify seven justification states for arguments and define two alternative skepticism relations between semantics, which induce a partial order on the justification states, reflecting the releva...

This paper introduces a propositional encoding of the recursive path order (RPO) on terms which is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. The proposed encoding allows us to use SAT solvers in order to determine whether a given term rewrite system is RPO terminating. An implementation is...

In this paper, we provide a methodology to design strategies for either guaranteed capture or guaranteed evasion in the case of pursuit-evasion games with multiple players which are represented by nonlinear dynamic models. This methodology is based on the continuously differentiable upper and lower approximations of the minimum and maximum function of an arbitrary number of arguments, compariso...