Parents frequently check up on what their children mean. They often do this by reformulating with a side sequence or an embedded correction what they think their children said. These reformulations effectively provide children with the conventional form for that meaning. Since the child's utterance and the adult reformulation differ while the intended meanings are the same, children infer that ...

Extension of components should be consistent in the sense that the extending component does not introduce any unexpected behaviour. We formulate requirements which allow consistent extension of components in presence of explicit invariants. We concentrate on the issue of extension consistency with forwarding as the reuse mechanism, and discuss the additional problems which require solution when...

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.

The correction procedure via reconstruction (CPR, also known as flux reconstruction) is a framework of high order semidiscretisations used for the numerical solution of hyperbolic conservation laws. Using a reformulation of these schemes relying on summation-by-parts (SBP) operators and simultaneous approximation terms (SATs), artificial dissipation / spectral viscosity operators are investigat...

Existing models have developed computational Hall thruster codes to a level where qualitative features of the plasma and electric field can be reproduced. These results are possible only with the use of corrections to various transport and energy parameters; however, these corrections are not rigorously defined by the actual physics governing these processes. This paper presents a 2-D hybrid PI...

In this paper, we consider construct high order semi-implicit integrators using integral deferred correction (IDC) to solve stiff initial value problems. The general framework for the construction of these semi-implicit methods uses uniformly distributed nodes and additive RungeKutta (ARK) integrators as base schemes inside an IDC framework, which we refer to as IDC-ARK methods. We establish un...

To produce accurate editing results, the ambiguity of editing scopes related to marked correction signs should be solved. Proofreading the web document modifies the document structures, and the modified structures should be robustly valid for the defined DTD. This paper presents a pen-based proofreading interface in the XML document. In the proposed interface, correction signs are free-drawn, a...

Gravitational physics of VLBI experiment conducted on September 8, 2002 and dedicated to measure the speed of gravity is treated in the first post-Newtonian approximation. Explicit speed-of-gravity parameterization is introduced to the Einstein equations to single out the retardation effect associated with the finite speed of gravity in the relativistic time delay of light propagating in the gr...

In this paper we study the oneand two-loop corrections to the four-point amplitude of N = 6 Chern-Simons matter theory. Using generalized unitarity methods we express the oneand two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the twoloop result is non-vanishing and matches with the W...

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this “Schur Low Rank” (SLR) preconditioning approach, the coefficient matrix is first decoupled by DD, and then a low-rank correction is exploited to compute an approximate inverse of the Schur compleme...