COMPUTATION OF DIMENSIONS FOR STRANGE ATTRACTORS BY THE BOX COUNTING RENORMALIZATION METHOD
The scaling ansats for box counting functions is verified numerically for the reverse doubling sequence of the logistic map. A box counting renormalisation method is developed to calculate dimensions for strange attractors.

title: HOW THE ARNOLD TONGUES BECOME SAUSAGES IN A PIECEWISE LINEAR CIRCLE MAP
abstract: The width of mode-locking tongues shrinks to zero at well-defined points in a piecewise linear circle map. The dimension of the set of quasiperiodic points along its critical line appears to be zero as compared to the "universal" value . Many properties of this map can be described analytically by rational fractions.

title: ON THE RADIATIVE DECAY OF HEAVY VECTOR MESON INTO HIGGS PARTICLE
abstract: An estimation of the contribution from the vector meson intermediate state to the width of radiative decay of a heavy vector meson composed of heavy quarks into Higgs particle is given. Under some approximation, it exhibits a value four times larger than that obtained by using free quark picture. The implication of this result for interpreting as Higgs scalar is also discussed.

title: Asteroseismic constraints on the OPAL opacity interpolation
abstract: The frequency difference between a model used only two-point interpolation of opacity and a model used piecewise linear interpolation of opacity is of the order of several microHertz at a certain stage, which is almost 10 times worse than the observational precision of p-modes of solar-like stars. Therefore, the two-point interpolation of opacity is unsuitable in modelling of solar-like stars with element diffusion.

title: Correlation functions of the SU(2)-invariant Thirring model with a boundary
abstract: Using the bosonization and oscillator expressions of bulk and boundary Zamolodchikov - Faddeev algebras, the correlators of Jost functions via operators are obtained in the case of SU(2)-invariant Thirring model with a boundary.

title: Retrieve the Bethe states of quantum integrable models solved via off-diagonal Bethe Ansatz
abstract: Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, a systematic method for retrieving the Bethe-type eigenstates of integrable models without obvious reference state is developed by employing certain orthogonal basis of the Hilbert space. With the XXZ spin torus model and the open XXX spin-1/2 chain as examples, we show that for a given inhomogeneous T-Q relation and the associated Bethe Ansatz equations, the constructed Bethe-type eigenstate has a well-defined homogeneous limit.

title: Central elements of the elliptic Zn monodromy matrix algebra at roots of unity
abstract: The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.

title: An Unification Model of Fermion Flavor and Baryon asymmetry and Dark Matter with The TeV Scale $U(1)_{B-L}$
abstract: This paper has been withdrawn by the author. I suggest a new particle model to solve simultaneously the problems of fermion masses and flavor mixings, and baryon asymmetry and dark matter. The model extends the standard model by adding a local $U(1)_{B-L}$ gauge symmetry at the TeV scale, in addition, the fermion flavor structures are characterized by the original $S_{3}$ and residual $S_{2R}$ flavor family symmetries. The model can excellently fit all the current experimental data by the fewer parameters. The new results and predictions are promising to be test in future experiments.