Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p )/2 is the fundamental unit of the real quadratic field Q(√p ). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B(p−1)/2, where Bn denotes the nth Bernoulli number. Although first published in 1952, this...

BACKGROUND Helicobacter pylori may cause many gastrointestinal problems in developing countries such as Iran. We aimed to analyze the cost- effectiveness and cost- utility of the test-and-treat and empirical treatment strategies in managing Helicobacter pylori infection. METHODS This was a Markov based economic evaluation. Effectiveness was defined as the symptoms free numbers and QALYs in 10...

The incremental elimination or hydroxy functionality in an organosolv lignin by ethylalion or acetylation dramatically innuenced the state of miscibility and resulting morphology or blends prepared with hydroxypropyl cellulose (HPC). A maximum level of interaction between the blend components, as determined from melting point depression, oa:.urred where 23-40-1. or the hydroxy groups were subst...

The hypre software library (http://www.llnl.gov/CASC/hypre/) is a collection of high performance preconditioners and solvers for large sparse linear systems of equations on massively parallel machines. This paper investigates the scaling properties of several of the popular multigrid solvers and system building interfaces in hypre on two modern parallel platforms. We present scaling results on ...