Graded Lie Algebra Generating of Parastatistical Algebraic Structure
A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.

title: Scalar form-factor of the proton with light-cone QCD sum rules
abstract: We calculate the scalar form factor of the proton in the framework of the light-cone QCD sum rules approach with the three valence quark light-cone distribution amplitudes up to twist-6 and observe the scalar form factor {sigma}(t=-Q{sup 2}) at intermediate and large momentum transfers Q{sup 2}>2 GeV{sup 2} has significant contributions from the end point (or soft) terms. The numerical values for the {sigma}(t=-Q{sup 2}) are compatible with the calculations from the chiral quark model and lattice QCD at the region Q{sup 2}>2 GeV{sup 2}.

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: A Model of Fermion Masses and Flavor Mixings with Family Symmetry $SU(3)\otimes U(1)$
abstract: The family symmetry SU(3)⊗U(1) is proposed to solve flavor problems about fermion masses and flavor mixings. It’s breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group Z2 is introduced to generate tiny neutrino masses, which is broken by a real singlet scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of θ l 13 and J l CP in neutrino physics. All of the results are promising to be tested in the future experiments.

title: The new extended left–right symmetric grand unified model with SO(3) family symmetry
abstract: We suggest a new left–right symmetric grand unified model by extending Pati–Salam group to contain an isospin SU ( 2 ) and a flavor SO ( 3 ) subgroup, where the superheavy fermions are introduced as a mirror to the low-energy standard model fermions. The model undergoes three steps to break to the SM by means of the specified Higgs multiplets. The model few parameters can elegantly accommodate whole mass spectra for all the particles at the electroweak scale, especially, two different flavor mixing for the quark and lepton sectors are reproduced in agreement with the current experimental data very well. The strong CP violation is excellently explained. The matter–antimatter asymmetry in the universe is successfully implemented through the B − L violating decays of the superheavy gauge bosons. The model also predicts that the lightest right-handed Majorana neutrino, whose mass is about several hundred GeVs and energy is about 10 16 GeV, is possibly a candidate for the dark matter.

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: Exact solution of the XXZ Gaudin model with generic open boundaries
abstract: The XXZ Gaudin model with generic integrable boundaries specified by generic non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

title: The classical exchange algebra of a Green-Schwarz sigma model on supercoset target space with Z4m grading
abstract: We investigate the classical exchange algebra of the monodromy matrix for a Green-Schwarz sigma model on supercoset target space with Z4m grading by using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution in the Poisson bracket sense. Our calculation is based on a general world-sheet metric. Taking a particular case of m = 1 (and a particular choice of supergroup), our results coincide with those of the Green-Schwarz superstring theory in AdS5 × S5 background obtained by Magro

title: The nondynamical r-matrix structure of the elliptic Ruijsenaars-Schneider model with N=2
abstract: We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider model with N=2 admits a nondynamical r-matrix structure and the corresponding classical r-matrix is the same as that of its non-relativistic counterpart (Calogero-Moser model) in the same gauge.The relation between our (classical)Lax operator and the Lax operator given by Ruijsenaars is also obtained.

title: Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric Model Associated with Uq(gl(m|n))
abstract: We construct the Drinfeld twists (or factorizing F-matrices) of the super-symmetric model associated with quantum superalgebra Uq(gl(m|n)), and obtain the completely symmetric representations of the creation operators of the model in the F-basis provided by the F-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the F-basis for the Uq(gl(2|1))-model (the quantum t-J model).

title: Determinant representation of correlation functions for the Uq(gl(1∣1)) free Fermion model
abstract: With the help of the factorizing F-matrix, the scalar products of the Uq(gl(1∣1)) free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.