High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in [32, 7, 6]. Recently, it has been observed in [3] that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in [7], based on the high order finite volume WENO scheme with subcell resolution and utilizing...

Abstract Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature this We offer series formal results in support thesis that disquotational truth device simulate higher-order resources first-order setting. More specifically, we show any theory formulated language can naturally and conservat...

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM J. Numer. Anal. 44:300–321, 2006; Castro et al., Math. Comput. 75:1103–1134, 2006; J. Sci. Comput. 39:67–114, 2009). Recently, it has been observed in (Abgrall and Karni, J. Comput. Phys. 229:2759– 2763, 2010) that this approach may have some computational issues and shortcomi...

A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are s...