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...

Abstract Given a holomorphic self-map $\varphi $ of $\mathbb {D}$ (the open unit disc in {C}$ ), the composition operator $C_{\varphi } f = \circ \varphi , $f \in H^2(\mathbb {\mathbb {D}})$ defines bounded linear on Hardy space $H^2(\mathbb . The model spaces are backward shift-invariant closed subspaces which canonically associated with inner functions. In this paper, we study that invariant ...

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...

Quantitative materials characterization using electron holography frequently requires knowledge of the mean inner potential, but reported experimental mean inner potential measurements can vary widely. Using density functional theory, we have simulated the mean inner potential for materials with a range of different surface conditions and geometries. We use both "thin-film" and "nanowire" speci...

The method to study oscillating potentials of double bars, based on invariant loops, is introduced here in a new way, intended to be more intelligible. Using this method, I show how the orbital structure of a double-barred galaxy (nested bars) changes with the variation of nuclear bar’s pattern speed. Not all pattern speeds are allowed when the inner bar rotates in the same direction as the out...

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 ...