1. CJM 2009 (vol 62 pp. 74)
 Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre

Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces
We present the explicit formulas for the projectors on the generalized
eigenspaces associated with some eigenvalues for linear neutral functional
differential equations (NFDE) in $L^{p}$ spaces by using integrated
semigroup theory. The analysis is based on the main result
established elsewhere by the authors and results by Magal and Ruan
on nondensely defined Cauchy problem.
We formulate the NFDE as a nondensely defined Cauchy problem and obtain
some spectral properties from which we then derive explicit formulas for
the projectors on the generalized eigenspaces associated with some
eigenvalues. Such explicit formulas are important in studying bifurcations
in some semilinear problems.
Keywords:neutral functional differential equations, semilinear problem, integrated semigroup, spectrum, projectors Categories:34K05, 35K57, 47A56, 47H20 

2. CJM 2007 (vol 59 pp. 127)
 Lamzouri, Youness

Smooth Values of the Iterates of the Euler PhiFunction
Let $\phi(n)$ be the Euler phifunction, define
$\phi_0(n) = n$ and $\phi_{k+1}(n)=\phi(\phi_{k}(n))$ for all
$k\geq 0$. We will determine an asymptotic formula for the set of
integers $n$ less than $x$ for which $\phi_k(n)$ is $y$smooth,
conditionally on a weak form of the ElliottHalberstam conjecture.
Categories:11N37, 11B37, 34K05, 45J05 
