Resolvability: A selective survey and some new results

Resolvability: a selective survey and some new results

Following guidance from the Organizing Committee, the authors give a brief introduction to the theory of spaces which are resolvable in the sense introduced by Hewitt (1943). The new results presented here are these. (A) A countably compact regular Hausdorff space without isolated points is w-resolvable--that is, it admits an infinite family of pairwise disjoint dense subsets. (B) Among Tychono...

Path-tables of trees: a survey and some new results

The (vertex) path-table of a tree T contains quantitative information about the paths in T . The entry (i, j) of this table gives the number of paths of length j passing through vertex vi. The path-table is a slight variation of the notion of path layer matrix. In this survey we review some work done on the vertex path-table of a tree and also introduce the edge path-table. We show that in gene...

Controlling the Internet: A Survey and Some New Results

In the last few years, significant progress has been made in the mathematical modelling of congestion control and congestion feedback mechanisms in the Internet. The resulting models have proved to be very useful in improving existing control and feedback mechanisms, and to make them scalable to networks that operate at very high speeds. Tools from convex optimization, control theory and stocha...

Conditional resolvability in graphs: a survey

For an ordered setW = {w1,w2, . . . ,wk} of vertices and a vertexv in a connected graphG, the code of v with respect toW is the k-vector cW (v)= (d(v,w1),d(v,w2), . . . ,d(v,wk)), where d(x,y) represents the distance between the vertices x andy . The setW is a resolving set for G if distinct vertices of G have distinct codes with respect to W . The minimum cardinality of a resolving set for G i...

Some New Characterization Results on Exponential and Related Distributions