A set is a collection of elements chosen from some domain. If S is a finite set, we use the notation |S| to denote the number of elements or cardinality of the set. The empty set is denoted by ∅. By A∪B (respectively A∩B, A− B) we mean the union of the two sets A and B (respectively intersection and set difference). The notation A means the complement of the set A with respect to some assumed u...

The spatial spread of an age-structured population in an isolated environment is commonly governed by a partial differential equation with zero-flux boundary condition for the spatial domain. The variables involved are time, age and space, which will be denoted in the following by t, a and x, respectively. We denote by Ω ⊂ R (d = 1, 2, 3) the spatial domain and we assume the age of the populati...

The paper studies the domatic numbers and the total domatic numbers of graphs having cut-vertices. We shall study the domatic number d(G) and the total domatic number d t (G) of a graph G. A survey of the related theory is given in 3]. We consider nite, undirected graphs without loops or multiple edges. A subset D of the vertex set V (G) of a graph G is called dominating (total dominating), if ...

Consider a line graph G(V,E) in which V = {0, 1, . . . , n, n + 1}, nodes s1 = 0 and s2 = n + 1 are spies, and E = {(i, i + 1) | i ∈ {0, . . . , n}}. One of the n nodes between the spies is chosen uniformly at random as a source, denoted by v∗ ∈ {1, . . . , n}. When the message reaches a spy si, the spy collects at least two pieces of metadata: the timestamp Tsi and the parent node psi that rel...

2.1. Graphs and weights. A Kontsevich graph [2] is a directed graph with two types of vertices, type I and type II. The type I vertices are usually denoted 1, . . . ,m (m ≥ 0) and the type II vertices 1̄, . . . , n̄ (n ≥ 0). The directed edges are required to start at type I vertices. In fact, we will only consider the case m = 7, n = 2. A Lie graph is a Kontsevich graph with exactly two type II ...

We propose a BB identification by simultaneity matrix (BISM) algorithm. The input is a set of -bit solutions denoted by S. The number of solutions is denoted by n = |S|. The output is a partition of bit positions {0, . . . , − 1}. The BISM is composed of Simultaneity-Matrix-Construction and Fine-Valid-Partition algorithms. Algorithm SMC is outlined as follows (aij denotes the matrix element at ...