Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
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: Inner structure of Spinc(4) gauge potential on 4-dimensional manifolds
abstract: The decomposition of Spinc(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation ΔAμ=-λAμ has been discovered. Here, λ is the vacuum expectation value of the spinor field, λ=Φ2, and Aμ the twisting U(1) potential. It is found that when λ takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg–Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

title: Decomposition of $Spin^c(4)$ Gauge Potential and Determinant Equation for Twisting U(1) Potential in Seiberg-Witten Theory
abstract: The Seiberg-Witten equations are studied from the viewpoint of gauge potential decomposition. We find a determinant equation ∆Aμ = −λAμ for the twisting U(1) potential Aμ of the Seiberg-Witten theory, which is in itself an eigenvalue problem of the Laplacian operator, with the eigenvalue being the vacuum expectation value of the field function, λ = ‖Φ‖ /2. This establishes a direct relationship between the spectral theory of the Laplacian operator and the classification of the moduli space of the Dirac operator. Topological characteristic numbers of instantons in the self-dual SU(2)+ sub-space are also discussed.

title: Free field realization of current superalgebra $gl(m|n)_k$
abstract: We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$.

title: Drinfeld twist and symmetric Bethe vectors of open XYZ chain with non-diagonal boundary terms
abstract: With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.

title: The Lax pair for C2-type Ruijsenaars- Schneider model
abstract: We study the C-2 Ruijsenaars-Schneider model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameters are constructed. Also given are the involutive Hamiltonians for the system. Taking a non-relativistic limit, we obtain the Lax pair of C-2 Calogero-Moser model.

title: Axial form-factor and induced pseudoscalar form-factor of the nucleons
abstract: We calculate the axial and the induced pseudoscalar form-factors GA(t=-Q2) and GP(t=-Q2) of the nucleons in the framework of the light-cone QCD sum-rules approach up to twist-6 three valence quark light-cone distribution amplitudes, and observe that the form-factors GA(t=-Q2) and GP(t=-Q2) at intermediate and large momentum transfers with Q2>2 GeV2 have significant contributions from the end-point (soft) terms. The numerical values for the axial form-factor GA(t=-Q2) are compatible with the experimental data and theoretical calculations; for example, the chiral quark models and lattice QCD. The numerical values for the induced pseudoscalar form-factor GP(t=-Q2) are compatible with the calculation from the Bethe–Salpeter equation.

title: Solar models with revised abundances and opacities
abstract: Using reconstructed opacities, we construct solar models with low heavy-element abundance. Rotational mixing and enhanced diffusion of helium and heavy elements are used to reconcile the recently observed abundances with helioseismology. The sound speed and density of models in which the relative and absolute diffusion coefficients for helium and heavy elements have been increased agree with seismically inferred values at better than the 0.005 and 0.02 fractional levels, respectively. However, the surface helium abundance of the enhanced diffusion model is too low. The low-helium problem in the enhanced diffusion model can be solved to a great extent by rotational mixing. The surface helium and the convection zone depth of rotating model M04R3, which has a surface Z of 0.0154, agree with the seismic results at the levels of 1 sigma and 3 sigma, respectively. M04R3 is almost as good as the standard model M98. Some discrepancies between the models constructed in accord with the new element abundances and seismic constraints can be solved individually, but it seems difficult to resolve them as a whole.

title: The frequency separations of stellar p-modes
abstract: The purpose of this work is to investigate the characteristics of a new frequency separation of stellar p-modes.  Frequency separations are deduced from the asymptotic formula of stellar p-modes. Then, using the theoretical adiabatic frequencies of stellar model, we compute the frequency separations.  A new separation sigma(l-1l+ 1)( n), which is similar to the scaled small separation d(ll+ 2)( n)/(2l + 3), is obtained from the asymptotic formula of stellar p-modes. The separations sigma(l-1l+ 1)( n) and d(ll+ 2)( n)/(2l+ 3) have the same order. And like the small separation, sigma(l)-(1l+ 1)( n) is mainly sensitive to the conditions in the stellar core. However, with the decrease in the central hydrogen abundance of stars, the separations sigma(02) and rho(13) deviate more and more from the scaled small separation. This characteristic could be used to extract the information on the central hydrogen abundance of stars.

title: Magnetic moment of the pentaquark Θ+(1540) as diquark-diquark-antiquark state with QCD sum rules
abstract: In this article, we study the magnetic moment of the pentaquark state Θ+(1540) as a diquark-diquark-antiquark ($[ud][ud]\bar{s}$) state with the QCD sum rules in an external weak electromagnetic field (EFSR) and the light-cone QCD sum rules (LCSR) respectively. The numerical results indicate that the magnetic moment is about $\mu_{\Theta^ + } = -(0.11\pm 0.02)\mu_N$ for the EFSR and $\mu_{\Theta^ + }\approx-(0.1$-$0.5)\mu_N$ for the LCSR. As the values obtained from the EFSR are more stable than the corresponding ones from the LCSR, $\mu_{\Theta^ + } = -(0.11\pm 0.02)\mu_N$ is more reliable.

title: A Model of Fermion Flavor and Leptogenesis and Cold Dark Matter
abstract: I suggest a new particle model to integrate the fermion flavor, the TeV scale Leptogenesis and cold dark matter. The model has a local gauge symmetry $U(1)_{B-L}$ at the TeV scale and a flavor family symmetry SO(3), in addition, it also contains the fourth generation fermions in which including a cold dark matter neutrino. The model can simultaneously account for the fermion masses and flavor mixings, and the baryon asymmetry and cold dark matter. It not only excellently fits all the current experimental data, but also predicts some new results which are promising to be test in future experiments.