Jacobi fields and linear connections for arbitrary second-order ODEs

We discuss generalisations of Jacobi fields and Raychaudhuri’s equation from the geodesic case to that of an arbitrary system of second-order ODEs. Our results are obtained using a natural choice of linear connection on evolution space.     

On a new class of functional equations satisfied by polynomial functions

Aequationes mathematicae - The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known...     

Workshop on Photon and Neutron Applications to Biology and Nanoscale Systems

The vibrant state of collaboration between Australian and Italian synchrotron researchers was clearly demonstrated at the sixth bilateral Italian-Australian workshop on May 20–21, 2014. Held at the Australian Synchrotron, the workshop attracted close to 100 participants, who enjoyed presentations on subjects as diverse as advances in photon sources and instrumentation, food science, anti-bacterial and non-stick surfaces, organic electronics, and cancer therapy.     

Catalysis under ultrasonic irradiation: a sound synergy

1. Download : Download high-res image (133KB)
2. Download : Download full-size image

     

Pure partial planes of order 6 with 25 lines

We construct two pure partial planes of order 6 with 25 lines, which extend the dual of the linear space PG(3,2). One of these is of particular interest since its dual is a pseudo-complement of a triangle in a projective plane of order 6.      

The Erd?s-Lovász Tihany conjecture for quasi-line graphs

Erd?s and Lovász conjectured in 1968 that for every graph G with χ(G)>ω(G) and any two integers s,t≥2 with s+t=χ(G)+1, there is a partition (S,T) of the vertex set V(G) such that χ(G[S])≥s and χ(G[T])≥t. Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for quasi-line graphs and for graphs with independence number 2.