Free boson representation of DYℏ(sl^(M+1∣N+1))DY_{\hbar}(\hat{sl} (M+1|N+1)) at level one

We construct a realization of the central extension of super-Yangian double $DY_{\hbar}(\hat{sl}(M+1|N+1))$ at level-one in terms of free boson fields with a continuous parameter.Comment: 9 pages, latex, reference revise

A Symmetric Rank-one Quasi Newton Method for Non-negative Matrix Factorization

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix approximation is proposed. This method mainly bases on the active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. Our method improves the recent results of those methods in [Pattern Recognition, 45(2012)3557-3565; SIAM J. Sci. Comput., 33(6)(2011)3261-3281; Neural Computation, 19(10)(2007)2756-2779, etc.]. Moreover, the object function decreases faster than many other NMF methods. In addition, some numerical experiments are presented in the synthetic data, imaging processing and text clustering. By comparing with the other six nonnegative matrix approximation methods, our experiments confirm to our analysis.Comment: 19 pages, 13 figures, Submitted to PP on Feb. 5, 201

On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In \cite{HL09}, Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler and Navier-Stokes equations is that the convection term is neglected in the 3D model. In \cite{HSW09}, the authors proved that the 3D inviscid model can develop a finite time singularity starting from smooth initial data on a rectangular domain. A global well-posedness result was also proved for a class of smooth initial data under some smallness condition. The analysis in \cite{HSW09} does not apply to the case when the domain is axisymmetric and unbounded in the radial direction. In this paper, we prove that the 3D inviscid model with an appropriate Neumann-Robin boundary condition will develop a finite time singularity starting from smooth initial data in an axisymmetric domain. Moreover, we prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition.Comment: Please read the published versio

Evolution and control of the phase competition morphology in a manganite film

The competition among different phases in perovskite manganites is pronounced since their energies are very close under the interplay of charge, spin, orbital and lattice degrees of freedom. To reveal the roles of underlying interactions, many efforts have been devoted towards directly imaging phase transitions at microscopic scales. Here we show images of the charge-ordered insulator (COI) phase transition from a pure ferromagnetic metal with reducing field or increasing temperature in a strained phase-separated manganite film, using a home-built magnetic force microscope. Compared with the COI melting transition, this reverse transition is sharp, cooperative and martensitic-like with astonishingly unique yet diverse morphologies. The COI domains show variable-dimensional growth at different temperatures and their distribution can illustrate the delicate balance of the underlying interactions in manganites. Our findings also display how phase domain engineering is possible and how the phase competition can be tuned in a controllable manner.Comment: Published versio

How Massless Neutrinos Affect the Cosmic Microwave Background Damping Tail

We explore the physical origin and robustness of constraints on the energy density in relativistic species prior to and during recombination, often expressed as constraints on an effective number of neutrino species, Neff. Constraints from current data combination of Wilkinson Microwave Anisotropy Probe (WMAP) and South Pole Telescope (SPT) are almost entirely due to the impact of the neutrinos on the expansion rate, and how those changes to the expansion rate alter the ratio of the photon diffusion scale to the sound horizon scale at recombination. We demonstrate that very little of the constraining power comes from the early Integrated Sachs-Wolfe (ISW) effect, and also provide a first determination of the amplitude of the early ISW effect. Varying the fraction of baryonic mass in Helium, Yp, also changes the ratio of damping to sound-horizon scales. We discuss the physical effects that prevent the resulting near-degeneracy between Neff and Yp from being a complete one. Examining light element abundance measurements, we see no significant evidence for evolution of Neff and the baryon-to-photon ratio from the epoch of big bang nucleosynthesis to decoupling. Finally, we consider measurements of the distance-redshift relation at low to intermediate redshifts and their implications for the value of Neff.Comment: 11 pages. Replaced version extends our discussion of origin of constraints and updates for current data, submitted to PR