Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

We consider systems of Ito’s stochastic differential equations with smooth compact invariant manifolds. The problem addressed is an exponential mean square (EMS) stabilization of these manifolds. The necessary and sufficient conditions of the stabilizability are derived on the base of the spectral criterion of the EMS-stability of invariant manifolds. We suggest methods for the design of the fe...

A b s t r a c t. The unbiased estimator of risk of the orthogonally invariant es-timator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given.

Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, . . . ,Mp : I → I the continuous means. We consider the problem of invariance of the graphs of functions φ : Jp−1 → I with respect to the mean-type mapping M = (M1, . . . ,Mp) . Applying a result on the existence and uniqueness of an M-invariant mean [7], we prove that if the graph of a continuous function φ : Jp−1...

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .

• A simple generalisation of the classical Hill estimator of a positive extreme value index (EVI) has been recently introduced in the literature. Indeed, the Hill estimator can be regarded as the logarithm of the mean of order p = 0 of a certain set of statistics. Instead of such a geometric mean, we can more generally consider the mean of order p (MOP) of those statistics, with p real, and eve...

Inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. In this paper, we derive the Horvitz-Thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. We then introduce an alternative unbiased estimator, corresponding to post-st...

When performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a bi-invariant Riemannian met...

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...