Es wird eine notwendige Optimalitaets-Bedingung fuer das linear-quadratische Optimierungsproblem mit differentiell-algebraischen Gleichungen im Fall Index 2 bewiesen. Im ersten Schritt wird die kausale DAE betrachtet. Im ...

Let W be a closed algebraic subvariety of the n-dimensional projective space over the complex or real numbers and suppose that W is non--empty and equidimensional. In this paper we generalize the classic notion of polar ...

We deal with linear multi-step methods for SDEs and study when the numerical appro\-xi\-mation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a ...

Several features and interrelations of projector methods and reduction techniques for the analysis of linear time-varying differential-algebraic equations (DAEs) are addressed in this work. The application of both methodologies ...

Stochastic differential-algebraic equations (SDAEs) arise as a mathematical model for electrical network equations that are influenced by additional sources of Gaussian white noise. We sketch the underlying analytical ...

Nowadays the semiconductor devices in an electrical circuit are modelled by equivalent circuits containing basic network elements described by algebraic and ordinary differential equations. But the correct adjustment of ...

For a refined network analysis, we are interested in circuit simulation including distributed models of semiconductors. We construct a mathematical model for nonlinear electric networks containing semiconductors described ...

By the use of the corresponding shift matrix, the paper gives a criterion for the unique solvability of linear boundary value problems posed for linear differential algebraic equations up to index 2 with well-matched leading ...

Let l be a prime number. For $n \ge 1$ the L-function of the Kummer Curve $C_n :y^l = x(x^{l^n} - 1)$ over the cyclotomic field $\Bbb{Q} (\zeta_{l^{n+1}}, \zeta_{l^{n+1}} := {\rm exp} \frac{2\pi i}{l^{n+1}}$, is a product ...

In a linear differential algebraic equation with properly stated leading term, the involved derivatives of the unknown function are figured out by an additional matrix coefficient being in some sense well matched with the ...