We study the question of diagonalizability of the Hamiltonian for the FaddeevReshetikhin (FR) model in the two particle sector. Although the two particle S-matrix element for the FR model, which may be relevant for the quantization of strings on AdS5×S, has been calculated recently using field theoretic methods, we find that the Hamiltonian for the system in this sector is not diagonalizable. W...

in this paper, we give some determinantal and permanental representations of generalized lucas polynomials, which are a general form of generalized bivariate lucas p-polynomials, ordinary lucas and perrin sequences etc., by using various hessenberg matrices. in addition, we show that determinant and permanent of these hessenberg matrices can be obtained by using combinations. then we show, the ...

the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form, and the density of the electromagnetic current. Minimal and non-minimal (anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameter...

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel Hamiltonians obtained correspond to the generalization of the non-resonant Jaynes-Cummings Hamiltonian, widely used in quantized theories of laser. In this general cont...

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point ap...

Systems and control theory has long been a rich source of problems for the numerical linear algebra community. In many problems, conditions on analytic functions of a complex variable are usually evaluated by solving a special generalized eigenvalue problem. In this paper we develop a general framework for studying such problems. We show that for these problems, solutions can be obtained by eit...