It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...

We have recast the problem of t ru th maintenance in a setting of algebraic equations over Boolean lattices. If a method of labeling propositions to justi fy them according to some reasoning agent's constraints of belief happens to conform to the postulates of Boolean lattices, the labeling system can be reformulated as an algebraic equation solving system. A l l t ru th maintenance systems kno...

In this paper an algebraic test procedure is presented to ascertain the stability of multidimensional discrete systems, which are represented in the forms of their respective characteristic equations. Further an equivalent single dimensional characteristics equation is formed for the given multidimensional characteristic equation; the coefficients of this characteristic equation are suitably ar...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

The computation of Lagrangian invariant subspaces of a Hamiltonian matrix, or the closely related task of solving algebraic Riccati equations, is an important issue in linear optimal control, stochastic control and H∞-design. We propose a new class of Riemannian Newton methods that allows to compute isolated Lagrangian invariant subspaces of a Hamiltonian matrix. The algorithm implements a vari...

An algebraic method for a general construction of intersecting p-brane solutions in diverse spacetime dimensions is discussed. An incidence matrix describing configurations of electric and magnetic fields is introduced. Intersecting p-branes are specified by solutions of a system of characteristic algebraic equations for the incidence matrix. This set of characteristic equations generalizes a s...

Abstract: We study the representative for the gauge equivalence class MF related to certain types of N by N monodromy matrices whose entries are polynomials of a spectral parameter z. Let X be the algebraic curve given by the common characteristic equation for MF . Then the representative corresponds to the matrix realization of the affine Jacobi variety of X . When we relate MF to the Lax matr...

The Σ-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the DAE that can be exploited to speed up numerical solution. The paper compares this fine BTF with the usually coarser BTF derived from the sparsity pattern of the si...

Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang–Baxter equation, which is precisely the Yang–Baxter equation satisfied by 6j-symbols. We investigate one of the simplest examples, generalizing the standard SU(2) quantum group. The matrix elements for its corepresentations are identified with Askey–Wilson polynom...