A Category of Restricted Modules for the Ovisenko-Roger Algebra

In this paper, we study a category of restricted modules for the Ovsienko-Roger algebra, which is an extension of the Virasoro algebra of its tensor density module of degree one. We construct and characterize simple modules in this category and give natural free field realizations of certain restricted modules using the Weyl vertex algebra.

     

Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

Synthesis,structures, and electrochemistry of diiron toluene-3,4-dithiolate complexes containing phosphine ligands

Transition Metal Chemistry - In this paper, four diiron toluene-3,4-dithiolate complexes with phosphine ligands were synthesized and characterized. Treatment of complex...     

Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m

In this paper, we study the explicit expansion of the first order Melnikov function near a double homoclinic loop passing through a nilpotent saddle of order m in a near-Hamiltonian system. For any positive integer $m(m\ge 1)$, we derive the formulas of the coefficients in the expansion, which can be used to study the limit cycle bifurcations for near-Hamiltonian systems. In particular, for $m=2$, we use the coefficients to consider the limit cycle bifurcations of general near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 and 16 (11, 13 and 16, respectively) limit cycles in the case that the homoclinic loop is of cuspidal type (smooth type, respectively) and their distributions. As an application, we consider a near-Hamiltonian system with a nilpotent saddle of order 2 and obtain the lower bounds of the maximal number of limit cycles.