Sorted term-position algebras are an extension of term algebras. In addition to sorted terms with constructor and selector functions, they provide term positions as algebra elements and functions that relate term positions. This paper describes possible applications of termposition algebras and investigates their formal specification in existing specification frameworks. In particular, it prese...

This paper presents the use of an iteration method to solve the identifiability problem for a class of discretized linear partial differential algebraic equations. This technique consists in replacing the partial derivatives in the PDAE by differences and analyzing the difference algebraic equations obtained. For that, the theory of discrete singular systems, which involves Drazin inverse matri...

The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying dynamic and static (in the form of algebraic constraints) relations on the evolution of state trajectories, an appropriate notion of observability is presented wh...

A new method to decide the invertibility of a given high-dimensional function over a domain is presented. The problem arises in the field of verified solution of differential algebraic equations (DAEs) related to the need to perform projections of certain constraint manifolds over large domains. The question of invertibility is reduced to a verified linear algebra problem involving first partia...

This paper presents using a new modified homotopy perturbation method (NHPM) for solving linear and nonlinear systems of differential-algebraic equations (DAEs) of index one or higher index without index reduction. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. Some examples are given to illustrate the simp...

Differential-algebraic equations (DAEs) naturally arise in many applications, but present numerical and analytical difficulties. The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. Therefore, it is desirable to transform the original DAE into an equivalent DAE with lower index. In this paper, we p...

A regular matrix pencil sE − A and its rank one perturbations are considered. We determine the sets in C ∪ {∞} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE − A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in C∪...