We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set X in a metric space, it is proved the existence of an almost periodic sequence {ψk}k∈Z such that {ψk; k ∈ Z} = X and ψk = ψk+lq(k), l ∈ Z for all...

In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on nite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and att...

The solvability of the Riemann–Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener–Hopf-type factorization with bounded outer factors, but rather general diagonal elements of its middle factor. This covers, in particular, the almost periodic setting, when the factorization multiples belong to the algebra generated by the functions...

A crystallographic bar-joint framework, C in R, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω(C), is a singleton. Moreover, the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function, ΦC(z), on the d-torus, T, determined by a full rank t...

We consider operators of convolution generated by L func tions in L and various spaces of almost periodic functions It turns out to be that if such an operator is invertible in one of these spaces then it is in vertible in all the spaces we consider Further we prove that any convolution has identical norms in many natural couples of functional spaces

This paper answers negatively the question of whether the sets of idempotents in the weakly almost periodic compactifications of (N, +) and (Z, +) are closed.

Assessing the assumption of multivariate normality is required by many parametric multivariate statistical methods, such as discriminant analysis, principal component analysis, MANOVA, etc. Here, we present an R package to asses multivariate normality. The MVN package contains three most widely used multivariate normality tests, including Mardia’s, Henze-Zirkler’s and Royston’s multivariate nor...