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.

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

In this note we communicate some important remarks about the concepts of almost periodic time scales and almost periodic functions on time scales that are proposed by Wang and Agarwal in their recent papers ( see [7]-[10]).

During decision making, valuation of different types of rewards may involve partially distinct neural systems, but efficient choice behavior requires a common neural coding of stimulus value. We addressed this issue by measuring neural activity with functional magnetic resonance imaging while volunteers processed delayed and probabilistic decision options. Behaviorally, participants discounted ...