A holomorphic representation formula for special parabolic hyperspheres is given.

Mohammed Kbiri Alaoui Department of Mathematics, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia Correspondence should be addressed to Mohammed Kbiri Alaoui, mka [email protected] Received 31 March 2011; Accepted 28 July 2011 Academic Editor: Mihai Putinar Copyright q 2011 Mohammed Kbiri Alaoui. This is an open access article distributed under the Creative Commons Attribution License, which...

We prove the interior and boundary null–controllability of some parabolic evolutions with controls acting over measurable sets.

We construct a family of (q−1) 2 -ovoids of Q(4, q), the parabolic quadric of PG(4, q), for q ≡ 3 (mod 4). The existence of (q−1) 2 -ovoids of Q(4, q) was only known for q = 3, 7, or 11. Our construction provides the first infinite family of (q−1) 2 -ovoids of Q(4, q). Along the way, we also give a construction of (q+1) 2 -ovoids in Q(4, q) for q ≡ 1 (mod 4).

We use the category of linear complexes of tilting modules for the BGG category O , associated with a semi-simple complex finitedimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category O(p,Λ).

Article history: Received 17 January 2012 Received in revised form 4 June 2012 Accepted 5 June 2012 Available online 15 June 2012

In this paper we give an overview on some methods that are useful to solve a class of integrodi erential inverse problems. Precisely, we present some methods to solve integrodi erential inverse problems of parabolic type that are based on the theory of analytic semigroups, optimal regularity results and xed point arguments. A large class of physical models can be treated with this procedure, fo...