In this paper, an anomaly detection method in cluster-based mobile ad hoc networks with ad hoc on demand distance vector (AODV) routing protocol is proposed. In the method, the required features for describing the normal behavior of AODV are defined via step by step analysis of AODV and independent of any attack. In order to learn the normal behavior of AODV, a fuzzy averaging method is used fo...

Article history: Received 22 November 2010 Received in revised form 11 February 2011 Accepted 14 February 2011 Available online 25 February 2011

Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: (?) v(x)xis equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). We prove that if the averaging operator (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞), is bounded from the weighted Lebesgue space Lp((0,+∞); v) into the weighted Lebesgue space Lq((0,+∞);w), then there exists ε0 ∈ (0, p−...

The Catmull-Clark subdivision algorithm consists of an operator that can be decomposed into a refinement and a smoothing operator, where the refinement operator splits each face with m vertices into m quadrilateral subfaces and the smoothing operator replaces each internal vertex with an affine combination of its neighboring vertices and itself. In this paper, we generalize the Catmull-Clark sc...