Showing papers on "Antisymmetry published in 2016"

An Introduction To Syntactic Analysis And Theory

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Language Evolution And Syntactic Theory

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Time periodic problem for the compressible Navier-Stokes equation on R^2 with antisymmetry

Abstract: The compressible Navier-Stokes equation is considered on the two dimensional whole space when the external force is periodic in the time variable. The existence of a time periodic solution is proved for sufficiently small time periodic external force with antisymmetry condition. The proof is based on using the time-T -map associated with the linearized problem around the motionless state with constant density. In some weighted L∞ and Sobolev spaces the spectral properties of the time-T -map is investigated by a potential theoretic method and an energy method. The existence of a stationary solution to the stationary problem is also shown for sufficiently small time-independent external force with antisymmetry condition on R2.

Hierarchical relations and linear ordering

Abstract: The present squib’s discussion is centered on Kayne’s (1994, 2010) proposals, which postulate a direct relation between the order of asymmetric c-command relations and linear precedence relations at PF. To put it briefly, Kayne argues that asymmetric c-command is mapped to linear precedence at PF and concludes that there is a universal hierarchical/linear order: Specifier Head-Complement. This universal order would predict the canonical order SVO found in many languages. Any other linear order, whether canonical or not, would then be obtained through movement operations. Details of the arguments in Kayne (1994, 2010) are presented and discussed in the present squib with focus on two goals: first, to show that the strict mapping of asymmetric c-command to linear precedence is questionable and, second, that linear precedence relations are not relevant for syntax, with only hierarchy playing a fundamental role — as also argued elsewhere (see CHOMSKY, 1995, 2004, 2005, 2008; URIAGEREKA, 1999; GUIMARA˜ ES, 2000). In doing this, circularity problems in Kayne’s arguments are highlighted as well as other issues. Subsequently, an alternative account of the relationship between syntax and PF is suggested, in an effort to maintain the spirit of Kayne’s LCA while at the same time making it compatible with more recent minimalist views.

Consequences of spatial antisymmetry on light

Abstract: Light propagation in two and three dimensional lattices for which the index of refraction exhibits spatial antisymmetry is investigated in the ray and photonic crystal regimes. In these regimes, all the two dimensional antisymmetry groups for which light fails to propagate are identified. In the ray-regime, it is observed that in tilings described by 7 of the 46 two dimensional antisymmetric groups, light is localized within a fundamental domain and does not propagate through the tiling, in contrast to the behavior in the other 39 groups. To understand the above phenomenon, a rule based on the number of anti-mirror planes passing through a single Bravais lattice point is derived. In the wave regime for photonic crystals, it is observed that there are no propagating eigensolutions for the same 7 tilings as above, whereas propagating solutions and energy pass band dispersion curves can be obtained for the other 39 groups. The reasons underlying this peculiar behavior are analyzed using the topological approach for modeling flow in dynamical billiards to shed light on the applicability of Bloch’s theorem for these periodic antisymmetric lattices.