New Approach on the General Shape Equation of Axisymmetric Vesicles

The general Helfrich shape equation determined by minimizing the curvature free energy describes the equilibrium shapes of the axisymmetric lipid bilayer vesicles in different conditions. It is a non-linear differential equation with variable coefficients. In this letter, by analyzing the unique property of the solution, we change this shape equation into a system of the two differential equations. One of them is a linear differential equation. This equation system contains all of the known rigorous solutions of the general shape equation. And the more general constraint conditions are found for the solution of the general shape equation.Comment: 8 pages, LaTex, submit to Mod. Phys. Lett.

On the Three-dimensional Lattice Model

Using the restricted star-triangle relation, it is shown that the $N$-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice proposed by Mangazeev, Sergeev and Stroganov is a particular case of the Bazhanov-Baxter model.Comment: 8 pages, latex, 4 figure

Integrabilities of the t−Jt-J Model with Impurities

The hamiltonian with magnetic impurities coupled to the strongly correlated electron system is constructed from $t-J$ model. And it is diagonalized exactly by using the Bethe ansatz method. Our boundary matrices depend on the spins of the electrons. The Kondo problem in this system is discussed in details. The integral equations are derived with complex rapidities which describe the bound states in the system. The finite-size corrections for the ground-state energies are obtained.Comment: 24 pages, Revtex, To be published in J. Phys.