Gorenstein rings and irreducible parameter ideals

Given a Noetherian local ring it is shown that there exists an integer such that is Gorenstein if and only if some system of parameters contained in generates an irreducible ideal. We obtain as a corollary that is Gorenstein if and only if every power of the maximal ideal contains an irreducible parameter ideal.

     

On multiplicative independence of rational function iterates

We give lower bounds for the degree of multiplicative combinations of iterates of rational functions (with certain exceptions) over a general field, establishing the multiplicative independence of said iterates. This leads to a generalisation of Gao’s method for constructing elements in the finite field $${\mathbb {F}}_{q^n}$$ whose orders are larger than any polynomial in n when n becomes large. Additionally, we discuss the finiteness of polynomials which translate a given finite set of polynomials to become multiplicatively dependent.     

¹⁵C(d,p)¹⁶C reaction and exotic behavior in ¹⁶C

We have studied the 1?C(d,p)1?C reaction in inverse kinematics using the Helical Orbit Spectrometer at Argonne National Laboratory. Prior studies of electromagnetic-transition rates in 1?C suggested an exotic decoupling of the valence neutrons from the core in that nucleus. Neutron-adding spectroscopic factors give a different probe of the wave functions of the relevant states in 1?C. Shell-model calculations reproduce both the present transfer data and the previously measured transition rates, suggesting that 1?C may be described without invoking very exotic phenomena.     

Nucleon transfer reactions with exotic beams at ATLAS

We present some recent results from studies of light nuclei using exotic beams from ATLAS at Argonne National Laboratory. Light nuclei far from stability provide ideal testing grounds for modern theoretical methods, and may provide information about astrophysical environments. We focus on the nuclei ⁹Li and ⁷He, populated with the (d,p) and (d,³He) reactions.     

NOX production by impulse sparks in air

An experimental study on the production of NO_X by impulse sparks in air is presented. The emphasis is placed on the dependence of the NO_X yield on the signature of the discharge current waveforms. A voltage and two current impulses were used in the experiments to create a spark and the NO_X production was measured by the method of chemiluminescence. The results show that, for a given current waveform, the NO_X production varies linearly with the peak current and the gap length. In addition, it was found that the NO_X yield increases with the duration of the current for a given peak current.