A New Loop Algebra and Corresponding Computing Formula of Constant γ in Quadratic-Form Identity

A new loop algebra containing four arbitrary constants is presented, whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper,which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.     

A New Loop Algebra and the Corresponding Computing Formula of Constant γ in the Quadratic-Form Identity, as Well as the Generalized Burgers Hierarchy

A new loop algebra containing four arbitrary constants is presented, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy which possess bi-Hamiltonian structure and generalized Burgers hierarchy are derived.     

A Multi-component Matrix Loop Algebra and Its Application

A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra A^- M-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.     

A 9× 9 Matrix Representation of Birman-Wenzl-Murakami Algebra and Berry Phase in Yang-Baxter System

We present a 9×9 S-matrix and E-matrix. A representation of specialized Birman-Wenzl-Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix \breve{R}(x,φ₁,φ₂) is generated via theYang-Baxterization approach. Then we construct a Yang-BaxterHamiltonian through the unitary matrix \breve{R}(x,φ₁,φ₂). Berry phase of this Yang-Baxter system is investigated in detail.     

A New Formula for the Spectra of Axial Symmetric and Transition Nuclei and a Quantity to Identify the Nuclear γ Deformation

The analytical limits of a speacial potential of the Bohr Hamiltonian are discussed in detail.A new formula for the axial symmetric,triakial deformed and the γ-soft nuclei is presented.The nuclear γ deformation can be identified with this formula.The calculations of some nuclear yrast lines seproduce the experiment al results very Well,and the degree of the nuclear γ deformation is obtained.