Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System

We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.Comment: To appear in the 2003 December issue of the Smarandache Notions Journa

Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the unstable solitary waves which belong to the frontier between expanding and collapsing solutions and to provide an oscillating solitonic structure, some sort of breather-type solution. We obtain precise conditions on the control parameters to achieve the stabilization and compare our results with accurate numerical simulations of the nonlinear Schrodinger equation. Because of the application of these ideas to matter waves these solutions are some sort of matter breathers

Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Characterisation of a candidate dual AGN

We present Chandra and optical observations of a candidate dual AGN discovered serendipitously while searching for recoiling black holes via a cross-correlation between the serendipitous XMM source catalog (2XMMi) and SDSS-DR7 galaxies with a separation no larger than ten times the sum of their Petrosian radii. The system has a stellar mass ratio M$_{1}$/M$_{2}\approx 0.7$. One of the galaxies (Source 1) shows clear evidence for AGN activity in the form of hard X-ray emission and optical emission-line diagnostics typical of AGN ionisation. The nucleus of the other galaxy (Source 2) has a soft X-ray spectrum, bluer colours, and optical emission line ratios dominated by stellar photoionisation with a "composite" signature, which might indicate the presence of a weak AGN. When plotted on a diagram with X-ray luminosity vs [OIII] luminosity both nuclei fall within the locus defined by local Seyfert galaxies. From the optical spectrum we estimate the electron densities finding n$_{1} < 27$ e$^{-}$ cm$^{-3}$ and n$_{2} \approx 200$ e$^{-}$ cm$^{-3}$. From a 2D decomposition of the surface brightness distribution we infer that both galaxies host rotationally supported bulges (Sersic index $< 1$). While the active nature of Source 1 can be established with confidence, whether the nucleus of Source 2 is active remains a matter of debate. Evidence that a faint AGN might reside in its nucleus is, however, tantalising.Comment: 16 pages, 9 figures. Accepted for publication on MNRAS. Comments welcom