Generalized r-matrix structure and algebro-geometric solution for integrable systems

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure. All these nonlinear systems have {\it r}-matrices, and are completely integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure

Magnetic phase diagram in the Co-rich side of LnCo1-xFexAsO (Ln=La, Sm) system

The magnetic phase diagram has been mapped out via the measurements of electronic resistivity, magnetization and specific heat in the cobalt-based layered LnCo1-xFexAsO (Ln=La, Sm) compounds. The ferromagnetic (FM) transition at 63 K for LaCoAsO is rapidly suppressed upon Fe doping, and ultimately disappears around x=0.3 in the LaCo1-xFexAsO system. When La is replaced by magnetic rare earth element Sm, the 3d electrons first undergo a FM transition at Tc = 75 K, followed by an antiferromagnetic (AFM) transition at a lower temperature TN1 = 45 K. With partial Fe doping on the Co site, both FM (Tc) and AFM (TN1) transition temperatures are significantly suppressed, and finally approach zero kelvin at x = 0.3 and 0.2, respectively. Meanwhile, a third magnetic transition at TN2 = 5.6 K for SmCoAsO, associated with the AFM order of the Sm3+ 4f-oments, is uncovered and TN2 is found to be almost robust against the small Fe-doping. These results suggest that the 4f electrons of Sm3+ have an important effect on the magnetic behavior of 3d electrons in the 1111 type Co-based LnCo1-xFexAsO systems. In contrast, the magnetism of the f-electrons is relatively unaffected by the variation of the 3d electrons. The rich magnetic phase diagram in the Co-rich side of the LnCo1-xFexAsO system, therefore, is established.Comment: 8 pages, 9 figure

Mode Repulsion and Mode Coupling in Random Lasers

We studied experimentally and theoretically the interaction of lasing modes in random media. In a homogeneously broadened gain medium, cross gain saturation leads to spatial repulsion of lasing modes. In an inhomogeneously broadened gain medium, mode repulsion occurs in the spectral domain. Some lasing modes are coupled through photon hopping or electron absorption and reemission. Under pulsed pumping, weak coupling of two modes leads to synchronization of their lasing action. Strong coupling of two lasing modes results in anti-phased oscillations of their intensities.Comment: 13 pages, 4 figure

Luminous Infrared Galaxies in the Local Universe

We study the morphology and star formation properties of 159 local luminous infrared galaxy (LIRG) using multi-color images from Data Release 2 (DR2) of the Sloan Digital Sky Survey (SDSS). The LIRGs are selected from a cross-correlation analysis between the IRAS survey and SDSS. They are all brighter than 15.9 mag in the r-band and below redshift ~ 0.1, and so can be reliably classified morphologically. We find that the fractions of interacting/merging and spiral galaxies are ~ 48% and ~ 40% respectively. Our results complement and confirm the decline (increase) in the fraction of spiral (interacting/merging) galaxies from z ~1 to z ~ 0.1, as found by Melbourne, Koo & Le Floc'h (2005). About 75% of spiral galaxies in the local LIRGs are barred, indicating that bars may play an important role in triggering star formation rates > 20 M_{sun}/yr in the local universe. Compared with high redshift LIRGs, local LIRGs have lower specific star formation rates, smaller cold gas fractions and a narrower range of stellar masses. Local LIRGs appear to be either merging galaxies forming intermediate mass ellipticals or spiral galaxies undergoing high star formation activities regulated by bars.Comment: 22 pages, 5 figures, accepted for publication in ApJ, title changed, typos corrected,major revisions following referee's comments,updated reference