Factorization of quadratic polynomials in the ring of formal power series over Z\Z

We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring $Z[[x]]$ of formal power series with integer coefficients. For $n,m\ge 1$ and $p$ prime, we show that $p^n+p^m\beta x+\alpha x^2$ is reducible in $Z[[x]]$ if and only if it is reducible in $Z_p[x]$, the ring of polynomials over the $p$-adic integers.Comment: 15 page

Comments on "Observation of Long-Range, Near-Side Angular Correlations in Proton-Proton Collisions at the LHC" by the CMS collaboration(arXiv:1009.4122v1 [hep-ex])"

It is the purpose of this note to point out that the CMS observation is in line with previous observations in particle physics at large transverse momenta and/or high multiplicities at lower energies, which were interpreted as possible evidence for quark-gluon plasma (QGP), and to suggest other features of the QGP observed in A+A collisions such as radial flow and jet quenching, which should be investigated in p-p collisions in order to provide further evidence for QGP production

Magnetic Resonance Spectroscopy of the Brain in Alcohol Abuse.

Magnetic resonance (MR) technology produces data on brain structure and activity without relying on radiation or invasive surgery. Magnetic resonance imaging (MRI) creates images, and magnetic resonance spectroscopy (MRS) produces spectra based on the ability of atomic nuclei in tissues to absorb and release pulses of energy. MRS studies of alcohol in the brain reveal that only a portion of the alcohol in the brain can be detected by MR technology, suggesting that alcohol there exists in multiple pools. The pools not visible using MRS is hypothesized to be bound to cell membranes. Indirect evidence from MR studies of chronic alcohol abusers suggests that tolerance to alcohol's effects results in an increased rigidity of cell membranes that forces more alcohol to remain in the MR-visible pool (i.e., the pool not bound to membranes) compared with alcohol in the brains of nontolerant people

On factor-free Dyck words with half-integer slope

We study a class of rational Dyck paths with slope (2m+1)/2 corresponding to factor-free Dyck words, as introduced by P. Duchon. We show that, for the slopes considered in this paper, the language of factor-free Dyck words is generated by an auxiliary language that we examine from the algebraic and combinatorial points of view. We provide a lattice path description of this language, and give an explicit enumeration formula in terms of partial Bell polynomials. As a corollary, we obtain new formulas for the number of associated factor-free generalized Dyck words.Comment: 13 pages. To appear in Advances in Applied Mathematic