Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous.

10 In this work, we study the criteria of oscillatory solutions to impulsive parabolic 11 boundary value problem with delay. First, we consider two types of boundary condition 12 which resolve in oscillatory solutions in the impulsive problem with delay, then we 13 further reduce the oscillation criteria for the problem. 14 2003 Published by Elsevier Science Inc. 15

Let F be a non-Archimedean locally compact field, let G be a split connected reductive group over F . For a parabolic subgroup Q ⊂ G and a ring L we consider the G-representation on the L-module (∗) C∞(G/Q, L)/ ∑

For n ≥ 0, we exhibit CAT(0) groups that are n-connected at infinity, and have boundary which is (n− 1)-connected, but this boundary has non-trivial n-homotopy group. In particular, we construct 1ended CAT(0) groups that are simply connected at infinity, but have a boundary with non-trivial fundamental group. Our base examples are 1-ended CAT(0) groups that have non-path connected boundaries. I...

Asymmetric statistical errors arise for experimental results obtained by Maximum Likelihood estimation, in cases where the number of results is finite and the log likelihood function is not a symmetric parabola. This note discusses how separate asymmetric errors on a single result should be combined, and how several results with asymmetric errors should be combined to give an overall measuremen...

In this paper we consider the boundary null controllability of a system of n parabolic equations on domains of the form Ω = (0, π)×Ω2 with Ω2 a smooth domain of RN−1, N > 1. When the control is exerted on {0} × ω2 with ω2 ⊂ Ω2, we obtain a necessary and sufficient condition that completely characterizes the null controllability. This result is obtained through the Lebeau– Robbiano strategy and ...

In this paper, using a recent parabolic restriction estimate of Tao, we obtain improved partial results in the direction of Falconer’s distance set conjecture in dimensions d ≥ 3.

We generalize [6, Theorem 3] to a Mackey-type formula for the compact restriction of a semisimple perverse sheaf produced by parabolic induction from a character sheaf, under certain conditions on the parahoric group scheme used to define compact restriction. This provides new tools for matching character sheaves with admissible representations.

Using the representation T2(O) of Q(4, q) and algebraic methods, we prove that complete (q2 − 1)-arcs of Q(4, q) do not exist when q = ph, p odd prime and h > 1. As a by-product we prove an embeddability theorem for the direction problem in AG(3, q). © 2007 Elsevier Inc. All rights reserved.