
Moore Postnikov factorization allows us to view homotopy types of topological spaces as being constructed out of standardized building blocks, i.e., EilenbergMacLane spaces.
The relevant classification result has long been known for 2stage spaces, i.e., those constructed from just two building blocks. The 3stage case is in general unresolved.
We investigate the latter question in situations where the factorizationviewed as a fibrationhas an Hcogroup base space and a product of EilenbergMacLane space fibres. A precise classification result up to fibrewise homotopy type is obtained for such cases.
This result appears to generalize to higherdimensional cases in a relatively straightforward manner.
This study focuses on free surface flow past a circular cylinder based on a two fluid model at a Reynolds number of R=200. The cylinder is forced to perform harmonic streamwise oscillations in the presence of an oncoming uniform flow. The effects of the free surface presence at a submergence depth of h=0.75 for a fixed Froude number, Fr =0.2 are investigated on the vortex shedding modes and fluid forces acting on the cylinder. Calculations are performed at a fixed displacement amplitude of A=0.13 in forcing frequencytonatural shedding frequency ratio range 1.53.5.
A (k,l)colouring of a graph G is a covering of its vertex set by k independent sets and l cliques, generalizing both the colouring and clique covering of a graph. The bichromatic number of G is defined as the minimum integer r, such that G is (k,l)colourable for all k+l=r. In this talk we will investigate some fundamental properties of the bichromatic number.
Given a graph G, an Hdecomposition of G is a partition with its edge set into subgraphs isomorphic to H. A rational Hdecomposition of G is a nonnegative rational weighting of the copies of H in G such that the total weight on any edge of G equals 1. The study of graph decompositions plays an important role in graph theory and combinatorics and has numerous applications. We will present a proof of the fact that any sufficiently large circulant (under several mild conditions) admits a rational decomposition into copies of any nontrivial graph on at most k vertices. This proof will showcase a linear algebraic connection between decomposition of these graphs and families with dominant differences.