The general crossing relation for boundary reflection matrix
In this paper, we give the general crossing relation for boundary reflection matrix $R(\beta)$, which is the extension of the work given by Ghoshal and Zamolodchikov .We also use the first non-trivial extended crossing relation to determine the scaler factor of $R(\beta)$ which is the rational diagonal solution to the boundary Yang-Baxter equation in the case of l=2 and n=3.

title: Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism
abstract: Ruijsenaars–Schneider models associated with An−1 root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are given in terms of the Bethe ansatz formulas. Taking the “nonrelativistic” limit, we obtain the spectrum of the corresponding Calogero–Moser systems in the third formulas of Felder et al.

title: Primary fields and screening currents of gl(2|2) non-unitary conformal field theory
abstract: The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.

title: THE DRESSING TRANSFORMATION OF THE CONFORMAL AFFINE TODA
abstract: We study the dressing transformations of the conformal affine Todal which can be obtained from a Hamiltonian reduction. As a special case, we obtain the dressing transformations of the sinh-Gordon model. We will show that the dressing group is the semiclassical limit of the quantum group . We will also obtain the algebra of the charges which generate the infinitesimal dressing transformations.

title: Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
abstract: A bstractThe Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

title: Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models
abstract: We construct the Drinfeld twists (factorizing F-matrices) of the gl(m|n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix (the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m|n) supersymmetric model.

title: Decay constants of the pseudoscalar charmonium and bottomonium
abstract: In this Letter, we investigate the structures of the pseudoscalar charmonium and bottomonium in the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). As the current masses are very large, the dressing or renormalization for the c and b quarks are tender, however, mass poles in the timelike region are absent. The Euclidean time Fourier transformed quark propagator has no mass poles in the timelike region which naturally implements confinement. The Bethe–Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around zero momentum with spatial extension to about q 2 = 1 GeV 2 which happen to be the energy scale for chiral symmetry breaking, the strong interactions in the infrared region result in bound states. The decay constants for those pseudoscalar heavy quarkonia are compatible with the values of experimental extractions and theoretical calculations.

title: Ground state mass spectrum for scalar diquarks with Bethe-Salpeter equation
abstract: In this article, we study the structures of the pseudoscalar mesons $\pi$, $K$ and the scalar diquarks $U^a$, $D^a$, $S^a$ in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential. The $u$, $d$, $s$ quarks have small current masses, and the renormalization is very large, the mass poles in the timelike region are absent which implements confinement naturally. The Bethe-Salpeter wavefunctions of the pseudoscalar mesons $\pi$, $K$ and the scalar diquarks $U^a$, $D^a$, $S^a$ have the same type (Gaussian type) momentum dependence, center around zero momentum and extend to the energy scale about $q^2=1GeV^2$ which happen to be the energy scale for the chiral symmetry breaking, the strong interactions in the infrared region result in bound (or quasi-bound) states. The numerical results for the masses and decay constants of the $\pi$, $K$ mesons can reproduce the experimental values, the ground state masses of the scalar diquarks $U^a$, $D^a$, $S^a$ are consistent with the existing theoretical calculations. We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks .

title: The Color Excesses of Type Ia Supernovae from Single-Degenerate Channel Model
abstract: Single Degenerate model is the most widely accepted progenitor model of type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from a main sequence or a slightly evolved star (WD +MS) to increase its mass, and explodes when its mass approaches the Chandrasekhar mass limit. During the mass transfer phase between the two components, an optically thick wind may occur and the material lost as the wind may exist as circumstellar material (CSM). Searching the CSM around progenitor star is helpful to discriminate different progenitor models of SNe Ia. Meanwhile, the CSM is a source of color excess.The purpose of this paper is to study the color excess produced from the single-degenerate progenitor model with optically thick wind, and reproduce the distribution o f color excesses of SNe Ia. Meng et al. (2009) systemically carried out binary evolution calculation of the WD +MS systems for various metallicities and showed the parameters of the systems before Roche lobe overflow and at the moment of supernova explosion in Meng & Yang (2009). With the results of Meng et al. (2009), we calculate the color excesses of SNe Ia at maximum light via a simple analytic method.We reproduces the distribution of color excesses of SNe Ia by our binary population synthesis approach if the velocity of the optically thick wind is taken to be of order of magnitude of 10 km s −1 . However, if the wind velocity is larger than 100 km s −1 , the reproduction is bad.

title: A New approach for calculating the Nambu-Gorkov propagator in color superconductivity theory
abstract: In this article, we propose a new approach to calculate the Nambu-Gorkov propagator intuitively with some linear algebra techniques in presence of the scalar diquark condensates. With the help of energy projective operators, we can obtain relatively simple expressions for the quark propagators, which greatly facilitate the calculations in solving the Schwinger-Dyson equation to obtain the gap parameters.

title: Decay constants of the pion and B mesons with the Bethe–Salpeter equation
abstract: In this Letter, we investigate the under-structures of the π and B mesons in the framework of the Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). In bare quark–gluon vertex approximation, we obtain the algebraic expressions for the solutions of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation. Firstly, we neglect the rainbow Schwinger–Dyson equation, take the bare quark propagator and solve the Bethe–Salpeter equation numerically alone. Although the bare quark propagator cannot embody dynamical chiral symmetry breaking and has a mass pole in the time-like region, it can give reasonable results for the values of decay constants f π and f B compared with the values of experimental data and other theoretical calculations, such as lattice simulations and QCD sum rules. Secondly, we explore those mesons within the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation. The Schwinger–Dyson functions for the u and d quarks are greatly renormalized at small momentum region and the curves are steep at about q 2 =1 GeV 2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier-transformed quark propagator has no mass poles in the time-like region which naturally implements confinement. As for the b quark, the current mass is very large, the renormalization is more tender, however, mass pole in the time-like region is also absent. The Bethe–Salpeter wavefunctions for both the π and B mesons have the same type (Gaussian type) momentum dependence as the corresponding wavefunctions with the bare quark propagator, however, the quantitative values are changed and the values for the decay constants f π and f B are changed correspondingly.