A group epimorphism Q: G+ Q preserves perfect radicals if $PG = PQ, where PC, PQ is maximal perfect in G, Q respectively. The following two questions are considered. Question 1. If P,,(B) acts trivially on H,(F; E), does the tibration F + Es B then have ~,(P)(P~,(E)) = Pm,(B)? Question 2. If f: X + Y is a map of spaces which induces an isomorphism of homology groups, is rr,(X) * rr,( Y) n,( Y)/...

A graph G = (V, E) is called factor-critical if G = ∅ and G − v has a perfect matching for every vertex v ∈ V (G). A factor-critical graph G is tight (anti-tight, respectively) if for any v ∈ V (G), any perfect matching M in G − v, and any e ∈ M , |N (v) ∩ V (e)| = 1 (|N (v) ∩ V (e)| = 2, respectively), where N (v) denotes the neighborhood of v and V (e) denotes the set of vertices incident wit...

Given a positive integer n we find a graph G = (V,E) on |V | = n vertices with a minimum number of edges such that for any pair of non adjacent vertices x, y the graph G − x − y contains a (almost) perfect matching M . Intuitively the non edge xy and M form a (almost) perfect matching of G. Similarly we determine a graph G = (V,E) with a minimum number of edges such that for any matching M̄ of t...

For perfect fields k satisfying [k ¯:k]>2, we construct new normal subgroups of the plane Cremona group and provide an elementary proof its non-simplicity, following melody recent by Blanc, Lamy Zimmermann that rank n over (subfields of) complex numbers is not simple for n≥3.

Let X be a graph on n vertices with with adjacency matrix A and let H(t) denote the matrix-valued function exp(iAt). If u and v are distinct vertices in X, we say perfect state transfer from u to v occurs if there is a time τ such that |H(τ)u,v| = 1. If u ∈ V (X) and there is a time σ such that |H(σ)u,u| = 1, we say X is periodic at u with period σ. We show that if perfect state transfer from u...

The aim of this study was to determine what factors are important for the achievement of perfect anal continence after restorative proctocolectomy. One hundred patients underwent paired studies of anorectal physiology before and one year after restorative proctocolectomy with pelvic ileal reservoir (11 S, 25 J, 64 W) with stapled ileoanal anastomosis, without mucosectomy. Fifty seven patients a...