The problem of computing minimal realizations of a singular system decomposed into a standard dynamical system and a static system of a given improper transfer matrix is formulated and solved. A new notion of the minimal dynamical-static realization is introduced. It is shown that there always exists a minimal dynamical-static realization of a given improper transfer matrix. A procedure for the...

Baxter’s Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature regime of the XXZ spin-chain are derived. For non-vanishing magnetic field the previously known Bethe ansatz equations can be replaced by a...

F. M. Callier is a Professor at the Facultes Universitaires Notre-Dame de la Paix, Namur, Belgium and C. A. Desoer is a Professor at the University of California, Berkeley, USA. Multivariable Feedback Systems is the result •of their teaching of a first-year graduate course on multivariable feedback systems addressed to control engineers. The text covers finite-dimensional time-invariant linear ...

Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in the antiferroelectric regime. It acts on the infinite tensor product W = V ⊗ V ⊗ V ⊗ · · ·, where V is the 2-dimensional irreducible representation of the quantum affine Lie algebra Uq ( ŝl (2) ) . We observe that H is the derivation of Uq ( ŝl (2) ) , and conjecture that the eigenvectors of H form the level-1 vacuum re...

We introduce ultradiscrete tau functions associated with rigged configurations for A (1) n . They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead t...

A recently introduced extension of the Corner Transfer Matrix Renormalisation Group (CTMRG) method useful for the study of self-avoiding walk type models is presented in detail and applied to a class of interacting self-avoiding walks due to Blöte and Nienhuis. This model displays two different types of collapse transition depending on model parameters. One is the standard θ-point transition. T...

We introduce ultradiscrete tau functions associated with rigged configurations for A (1) n . They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead t...

Abstract. This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity. If the bl...

A new boundary-integral formulation is proposed to analyze the heat transfer in zoned three-dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula, and the exterior formula. An advantage of this formulation over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formul...

In this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step Timoshenko rotor carrying concentrated masses is presented. Each attached element is considered to have both translational and rotational inertia. Forward and backward frequencies and corresponding modes are obtained using transfer matrix method (TMM). The effect of the angular velocity of spin,...