In [4] it was conjectured that for all unit vectors u1, · · · , ud in Rd, X (u1, · · · , ud) := sup x∈Rd, |x|2=d d ∏ i=1 〈x, ui〉 ≥ 1 with equality occurring iff u1, · · · , ud are orthonormal. We relate this to a conjecture about solutions of Ay = y−1, where A = (〈ui, uj〉), and show that if the conjecture fails then the u1, · · · , ud minimizing X must be linearly dependent. We also show X (u1,...

This paper presents a polarized phase semantics, with respect to which the linear fragment of second order polarized linear logic of [Laurent 99] is complete. This is done by adding a topological structure to Girard’s phase semantics [Girard 87]. The topological structure results naturally from the categorical construction developed in [Hamano-Scott 07]. The polarity shifting operator ↓ (resp. ...

Ten years of rocketsonde observations of wind and temperature in the 28-57 km height range at 12 stations (spanning 8øS to 76øN) were analyzed. The aim was to determine the geographical and seasonal variation of statistics relating to the propagation of inertia-gravity waves. As noted by earlier investigators, there is a clear tendency for the rocketsonde hodographs to display clockwise rotatio...

[1] The distribution of surficial deposits in the vicinity of impact craters on Venus was studied using measurements of the polarization properties of the reflected radar wave. Subsurface scattering of an incident circularly polarized radar signal results in a linearly polarized component in the radar echo due to the differing transmission coefficients at a smooth (at wavelength scales) atmosph...