In this paper, we analyze the Bohr ρ-almost periodic type sequences and generalized of form F:I×X→Y, where ∅≠I⊆Zn, X Y are complex Banach spaces ρ is a general binary relation on Y. We provide many structural results, observations open problems about introduced classes sequences. Certain applications established theoretical results to abstract Volterra integro-difference equations also given.

A scaling theory of the sub atto-molar (aM) detection limits of magnetic particle (MP) based biosensors (e.g., bio-barcode assays) is developed and discussed. Despite the dramatic differences of sensing protocols and detection limits, the MP-based sensors can be interpreted within the same theoretical framework as any other classical biosensor (e.g., nanowire sensors), except that these sensors...

Let G be a connected graph with vertex set V and a weight function ρ that assigns a nonnegative number to each of its vertices. Then, the ρ-moment of G at vertex u is defined to be M G(u) = ∑ v∈V ρ(v) dist(u, v), where dist(·, ·) stands for the distance function. Adding up all these numbers, we obtain the ρ-moment of G: M G = ∑ u∈V M G(u) = 1 2 ∑ u,v∈V dist(u, v)[ρ(u) + ρ(v)]. This parameter ge...

BACKGROUND Computer based surgical training is believed to be capable of providing a controlled virtual environment for medical professionals to conduct standardized training or new experimental procedures on virtual human body parts, which are generated and visualised three-dimensionally on a digital display unit. The main objective of this study was to conduct virtual phacoemulsification cata...

It is discussed the problem of the ρ ± − ρ 0 mass splitting. It is suggested to use the φ → ρπ → 3π decay to measure the ρ ± − ρ 0 mass splitting.