We propose in this work to derive a CLT in the functional linear regression model. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology ...

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...

Let X be a hypergroup. In this paper, we define a locally convex topology β on L(X) such that (L(X), β) with the strong topology can be identified with a Banach subspace of L(X). We prove that if X has a Haar measure, then the dual to this subspace is LC(X) ∗∗ = cl{F ∈ L(X);F has compact carrier}. Moreover, we study the operators on L(X) and L 0 (X) which commute with translations and convoluti...

Strong dierential subordination and superordination properties are determined for some familiesanalytic functions in the open unit disk which are associated with the Komatu operator by investigatingappropriate classes of admissible functions. New strong dierential sandwich-type results arealso obtained.

Classically, a Tychonoff space is called strongly 0-dimensional if its Stone-Čech compactification is 0-dimensional, and given the familiar relationship between spaces and frames it is then natural to call a completely regular frame strongly 0-dimensional if its compact completely regular coreflection is 0-dimensional (meaning: is generated by its complemented elements). Indeed, it is then seen...

For Ω ⊂ RN open (and possibly unbounded), we consider integral functionals of the form F (u) := ∫ Ω f(x, u) dx, de ned on the subspace of Lp consisting of those vector elds u which satisfy Au = 0 on Ω in the sense of distributions. Here, A may be any linear di erential operator of rst order with constant coe cients satisfying Murat's condition of constant rank. The main results provide sharp co...

We obtain the following characterization of Hilbert spaces. Let E be a Banach space whose unit sphere S has a hyperplane of symmetry. Then E is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group Iso E of E has a dense orbit in S; b) the identity component G 0 of the group Iso E endowed with the strong operator topology acts topologically irreducible on E...