The HIV/AIDS epidemic has many serious consequences for children. These consequences are, however, rarely inevitable. Families can provide a protective barrier that deflects blows, or minimises their impact and a supportive nurturing environment that can help children recover from harm. If strong enough, and with sufficient access to quality services and support from communities, families can r...

We study di erent notions of blow-up of a scheme X along a subscheme Y , depending on the datum of an embedding of X into an ambient scheme. The two extremes in this theory are the ordinary blow-up, corresponding to the identity, and the `quasi-symmetric blow-up', corresponding to the embedding of X into a nonsingular variety. We prove that this latter blow-up is intrinsic of Y and X , and is u...

Weobtain a hypergraph generalisation of the graph blow-up lemma proved byKomlós, Sarközy and Szemerédi, showing that hypergraphs with sufficient regularity and no atypical vertices behave as if they were complete for the purpose of embedding bounded degree hypergraphs. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 39, 275–376, 2011

In this paper we consider the slightly L-supercritical gKdV equations ∂tu + (uxx + u|u|)x = 0, with the nonlinearity 5 < p < 5 + ε and 0 < ε ≪ 1 . In the previous paper [10] we know that there exists an stable selfsimilar blow-up dynamics for slightly L-supercritical gKdV equations. Such solution can be viewed as solutions with single blow-up point. In this paper we will prove the existence of ...