A large number of di erential equation problems which admit traveling waves have very large (typically in nite) naturally de ned domains, with boundary conditions de ned at the domain boundary. To be able to numerically solve these problems in smaller subdomains of the original domain, arti cial boundary conditions must be de ned for these subdomains. One such arti cal boundaryconditionswhich c...

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an in nitedimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. How...

The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form. The introduction schema for implicati...

A permutation Sn avoids the subpattern i has no subse quence having all the same pairwise comparisons as and we write Sn We present a new bijective proof of the well known result that jSn j jSn j cn the n th Catalan number A generalization to forbidden pat terns of length gives an asymptotic formula for the vexillary permutations We settle a conjecture of Shapiro and Getu that jSn j sn the Schr...