Let$D$be a relatively compact domain in$C$^{2}with smooth connected boundary ∂$D$. A compact set$K⊂∂D$is called removable if any continuous CR function defined on ∂$D/K$admits a holomorphic extension to$D$. If$D$is strictly pseudoconvex, a theorem of B. Jöricke states that any compact$K$contained in a smooth totally real disc$S⊂∂D$is removable. In the present article we show that this theorem is true without any assumption on pseudoconvexity.

In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of the formulas of Lusztig's symmetries.

In this paper, we present a new algorithm, such that, for the learning with errors (LWE) problems, if the errors are bounded -- the errors do not span the whole prime finite field F_q but a fixed known subset of size D (D<q), which we call the learning with bounded errors (LWBE) problems, we can solve it with complexity O(n^D).

We give a classification of birational transformations on smooth projective surfaces which have a Zariski-dense set of noncritical periodic points. In particular, we show that if the first dynamical degree is greater than one, the union of all noncritical periodic orbits is Zariski-dense.

No abstract uploaded!