We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject and the resul...

We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject and the resul...

In this article we establish an asymptotic formula for the number of rational points, with bounded denominators, within a given distance to compact submanifold M RM certain curvature condition. Our result generalises earlier work Huang hypersurfaces (J.-J. (2020) [18]), as our condition reduces Gaussian being away from 0 when M−dim⁡M=1. An interesting feature is that holds beyond conjectured ra...