On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Astronomy: Starbursts near and far

Observations of intensely bright star-forming galaxies both close by and in the distant Universe at first glance seem to emphasize their similarity. But look a little closer, and differences emerge.Comment: 6 pages including 1 figur

The Generalized Counting Rule and Oscillatory Scaling

We have studied the energy dependence of the $pp$ elastic scattering data and the pion-photoproduction data at 90$^\circ$ c.m. angle in light of the new generalized counting rule derived for exclusive processes. We show that by including the helicity flipping amplitudes (with energy dependence given by the generalized counting rule) and their interference with the Landshoff amplitude, we are able to reproduce the energy dependence of all cross-section and spin-correlation (A$_{NN}$) data available above the resonance region. The pion-photoproduction data can also be described by this approach, but in this case data with much finer energy spacing is needed to confirm the oscillations about the scaling behavior.Comment: 5 pages, 4 figs, submitted to PRC rapid com

Analytic description of atomic interaction at ultracold temperatures II: Scattering around a magnetic Feshbach resonance

Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$, and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary $l$, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary $l$, (b) rigorous definitions of "broad" and "narrow" resonances of arbitrary $l$ and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.Comment: 13 pages, 4 figure