Supergravity inflation on a brane

We discuss supergravity inflation in braneworld cosmology for the class of potentials $V(\phi)=\alpha \phi^n\rm{exp}(-\beta^m \phi^m)$ with $m=1,~2$. These minimal SUGRA models evade the $\eta$ problem due to a broken shift symmetry and can easily accommodate the observational constraints. Models with smaller $n$ are preferred while models with larger $n$ are out of the $2\sigma$ region. Remarkably, the field excursions required for $60$ $e$-foldings stay sub-planckian $\Delta\phi <1$.Comment: 10 pages, 4 figure

Validation of BeiDou Observations

This study presents validation of BeiDou measurements in un-differenced standalone mode and experimental results of its application for real data. A reparameterized form of the unknowns in a geometry-free observation model was used. Observations from each satellite are independently screened using a local modeling approach. Main advantages include that there is no need for computation of inter-system biases and no satellite navigation information are needed. Validation of the triple-frequency BeiDou data was performed in static and kinematic modes, the former at two continuously operating reference stations in Australia using data that span two consecutive days and the later in a walking mode for three hours. The uses of the validation method parameters for numerical and graphical diagnostics of the multi-frequency BeiDou observations are discussed. The precision of the system’s observations was estimated using an empirical method that utilizes the characteristics of the validation statistics. The capability of the proposed method is demonstrated in detection and identification of artificial errors inserted in the static BeiDou data and when implemented in a single point positioning processing of the kinematic test

Chow Groups of Quadrics in Characteristic Two

Let $X$ be a smooth projective quadric defined over a field of characteristic 2. We prove that in the Chow group of codimension 2 or 3 of $X$ the torsion subgroup has at most two elements. In codimension 2, we determine precisely when this torsion subgroup is nontrivial. In codimension 3, we show that there is no torsion if {$\dim X\ge 11$.} This extends the analogous results in characteristic different from 2, obtained by Karpenko in the nineteen-nineties.Comment: 37 page