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We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourier finite element methods (Fourier-FEMs) in weighted function spaces. Closed Hilbert complexes and commuting projectors are used as in the work of Arnold, Falk & Winther, (2010, Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Amer. Math. Soc. (N.S.) , 47 , 281–354), by using the new family of finite element spaces for general axisymmetric problems introduced in Oh, (2015, de Rham complexes arising from Fourier-FEMs in axisymmetric domains. Comput. Math. Appl. , 70 , 2063–2073). In order to get stability results and error estimates for the discrete mixed formulation, we construct commuting projectors that can be applied to functions with low regularity. [ABSTRACT FROM AUTHOR]

The question of whether bilingualism conveys a broader advantage in executive functions has recently been controversially discussed, with the empirical findings presenting a complex pattern of positive and null results. Here we present results from three standard tasks measuring executive functions (Flanker; Simon; Spatial Stroop) in which we compared performance of English monolingual to Chinese–English bilingual young adults. Participants provided responses via movement of a computer mouse rather than the conventional key presses, which provides a rich signal of the unfolding response dynamics. Clear differences between bi- and monolinguals emerged, with the former providing more 'efficient' responses than the latter. Results are discussed regarding the extent to which these results can be characterised as a genuine "bilingual advantage". [ABSTRACT FROM AUTHOR]

This paper builds a new framework to analyse axisymmetric problems through differential forms and exterior calculus. We construct a new weighted L2 de Rham complex that arises when analysing axi-symmetric problems. By constructing its dual complex, we obtain a Hodge decomposition and a Poincaré inequality in weighted spaces, and the well-posedness of the weighted mixed Hodge Laplacian problem. The stability and convergence of the discrete weighted mixed Hodge Laplacian problem are also achieved by using bounded cochain projections. [ABSTRACT FROM AUTHOR]

In this paper, we will construct and analyze a multigrid algorithm that can be applied to weighted H (div) problems on a two-dimensional domain. These problems arise after performing a dimension reduction to a three-dimensional axisymmetric H (div) problem. We will use recently developed Fourier finite element spaces that can be applied to axisymmetric H (div) problems with general data. We prove that if the axisymmetric domain is convex, then the multigrid V-cycle with modern smoothers will converge uniformly with respect to the meshsize. [ABSTRACT FROM AUTHOR]