3,295 research outputs found
Factorization of quadratic polynomials in the ring of formal power series over
We establish necessary and sufficient conditions for a quadratic polynomial
to be irreducible in the ring of formal power series with integer
coefficients. For and prime, we show that is reducible in if and only if it is reducible in , the
ring of polynomials over the -adic integers.Comment: 15 page
On cyclic numbers and an extension of Midy's theorem
In this note we consider fractions of the form 1/m and their floating-point
representation in various arithmetic bases. For instance, what is 1/7 in base
2005? And, what about 1/4? We give a simple algorithm to answer these
questions. In addition, we discuss an extension of Midy's theorem whose proof
relies on elementary modular arithmetic.Comment: 6 pages, aimed at undergraduate student
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
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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
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