Mapping semantic spaces: A constructionist account of the "light verb" xordæn 'eat' in Persian
Within the framework of Construction Grammar, the author develops an analytical tool to map semantic regularities in semantic spaces. This is illustrated with the study of the semantic spaces of the Persian “light verb” xordaen “to eat”. The light verb’s semantic space is populated by “notional islands” where groups of light verb constructions, expressing similar notions, combine the light verb with a restricted, but large, class of preverbs. The analysis shows that each notional island possesses linguistic and cognitive properties that allow intuitive disambiguation. It provides new results about meaning construction, productivity, and compositionality, and the basis of crosslinguistic investigations for processes of verb formation as they have evolved in different languages.
Given ?>0 andp?(0,1), we consider the following problem: findu such that $$\begin{gathered} - \Delta u + \lambda [u]_ + ^p = 0in\Omega , \hfill \\ u = 1on\partial \Omega , \hfill \\ \end{gathered} $$ whereΩ??2 is a smooth convex domain. We prove optimalH 1 andL ? error bounds for the standard continuous piecewise linear Galerkin finite element approximation. In addition we analyse a more practical approximation using numerical integration on the nonlinear term. Finally we consider a modified nonlinear SOR algorithm, which is shown to be globally convergent, for solving the algebraic system derived from the more practical approximation.