The acoustic transmission loss of a finite periodic array of long rigid cylinders, without and with porous absorbent covering, is studied both theoretically and in the laboratory. A multiple scattering model is extended to allow for the covering and its acoustical properties are described by a single parameter semi-empirical model. Data from laboratory measurements and numerical results are fou...

Let the lattice Λ have covering radius R, so that closed balls of radius R around the lattice points justcover the space. The covering multiplicity CM(Λ) is the maximal number of times the interiors of theseballs overlap. We show that the least possible covering multiplicity for an n-dimensional lattice is n ifn ≤ 8, and conjecture that it exceeds n in all other cases. We determine ...

Given a sphere of radius r > 1 in the n-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growing n, we obtain the covering density of (n lnn)/2. This new upper bound is half the order n lnn established in ...

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck’s discrete transformation group) of a digital covering. By using these to...

In this note we prove that for any compact subset S of a Busemann surface (S, d) (in particular, for any simple polygon with geodesic metric) and any positive number δ, the minimum number of closed balls of radius δ with centers at S and covering the set S is at most 19 times the maximum number of disjoint closed balls of radius δ centered at points of S: ν(S) ≤ ρ(S) ≤ 19ν(S), where ρ(S) and ν(...