‎In this paper‎, ‎we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps‎. ‎More precisely‎, ‎we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology‎. ‎Moreover‎, ‎we present some conditions unde...

Combinatorial testing applies factor covering arrays [6, 7] to test all t-way combinations of input or configuration state space. In some testing situations, it is not practical to use covering arrays, but any set of tests with n parameters covers at least some proportion of t-way combinations up to t ≤ n. This report describes measures of combinatorial coverage that can be used in evaluating t...

Combinatorial testing applies factor covering arrays [6, 7] to test all t-way combinations of input or configuration state space. In some testing situations, it is not practical to use covering arrays, but any set of tests with n parameters covers at least some proportion of t-way combinations up to t ≤ n. This report describes measures of combinatorial coverage that can be used in evaluating t...

A covering projection from a graph G onto a graph H is a \local isomorphism": a mapping from the vertex set of G onto the vertex set of H such that, for every v 2 V (G), the neighborhood of v is mapped bijectively onto the neighborhood (in H) of the image of v. We investigate two concepts that concern graph covers of regular graphs. The rst one is called \multicovers": we show that for any regu...

We define generalizations of classical invariants of ramification, for coverings on a variety of arbitrary dimension over a local field of mixed characteristic. For an -adic sheaf, we define its Swan class as a 0-cycle class supported on the closed fiber. We present a formula for the Swan conductor of cohomology and its relative version. Let K be a complete discrete valuation field of character...

A path covering of a graph G is a set of vertex disjoint paths of G containing all the vertices of G. The path covering number of G, denoted by P (G), is the minimum number of paths in a path covering of G. An k-L(2, 1)-labeling of a graph G is a mapping f from V (G) to the set {0, 1, . . . , k} such that |f(u) − f(v)| ≥ 2 if dG(u, v) = 1 and |f(u) − f(v)| ≥ 1 if dG(u, v) = 2. The L(2, 1)-label...

Two vectors x, y in Zg are qualitatively independent if for all pairs (a, b) ∈ Zg×Zg, there exists i ∈ {1, 2, . . . , n} such that (xi, yi) = (a, b). A covering array on a graph G, denoted by CA(n,G, g), is a |V (G)|×n array on Zg with the property that any two rows which correspond to adjacent vertices in G are qualitatively independent. The number of columns in such array is called its size. ...

Sir.?The aims of your paper in regard to the public health, as set out in your New Year's issue, are excellent. And as everyone seems to be waking up at last to the fact that the housing question overshadows every other question in domestic politics, perhaps something will be accomplished. Questions of housing and health must not, however, be allowed to become the playthings of politics. Every ...