PURPOSE This study was conducted to determine the potential influence of PaO2 fluctuation on the retinal neovascular response known to occur in newborn rats exposed to hyperoxic conditions. As an inherent corollary, the authors also defined the relationship between the fraction of inspired oxygen (FiO2) and the arterial blood oxygen tension (PaO2) in newborn rats. METHODS Experiment 1 was com...

We show that the discriminant of the generalized Laguerre polynomial L n (x) is a non-zero square for some integer pair (n, α), with n ≥ 1, if and only if (n, α) belongs to one of 30 explicitly given infinite sets of pairs or to an additional finite set of pairs. As a consequence, we obtain new information on when the Galois group of L n (x) over Q is the alternating group An. For example, we e...

Motivated by recent analytical and numerical work on two-and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the spirit of earlier work by Iooss (1986) on...

In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as subalgebra the ring invariants certain noncommutative with respect to action $S_1\times S_2\times\cdots\times S_n$, where $S_j$ is symmetric group on $j$ variables. An interesting question what similar algebra would be in invariant product alternating groups. this paper we define such an algebra, denoted $\mathscr...