Kronecker-like forms of a system pencil are useful in solving many computational problems encountered in the analysis and synthesis of linear systems. The reduction of system pencils to various Kronecker-like forms can be performed by structure preserving 0(n) complexity numerically stable algorithms. The presented algorithms form the basis of a modular collection of LAPACK compatible FORTRAN 7...

We consider minimization of a quadratic objective function subject to a sign-indefinite quadratic equality constraint. We derive necessary and sufficient conditions for the existence of solutions to the constrained minimization problem. These conditions involve a generalized eigenvalue of the matrix pencil consisting of a symmetric positivesemidefinite matrix and a symmetric indefinite matrix. ...

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degenera...

The majority of scientific papers focusing on wood classification for pencil manufacturing take into account defects and visual appearance. Traditional methodologies are based on texture analysis by co-occurrence matrix, by image modeling, or by tonal measures over the plate surface. In this work, we propose to classify plates of wood without biological defects like insect holes, nodes, and cra...

It is proved that on a smooth algebraic variety, fibered into cubic surfaces over the projective line and sufficiently “twisted” over the base, there is only one pencil of rational surfaces – that is, this very pencil of cubics. In particular, this variety is non-rational; moreover, it can not be fibered into rational curves. The proof is obtained by means of the method of maximal singularities.

The Matrix-Pencil (MP) method is applied to the estimation of the undesired radiation from the microstrip line discontinuities. The Q factors are obtained from the complex resonant frequencies estimated from FDTD transient field by using MP. The number of the damped oscillations is estimated by using MDL which is widely used as an information theoretic criterion for the model order estimation. ...

The study aimed at defining the dual-task performance characteristics in healthy children/adolescents on the computerised and the paper and pencil dual-task methods; investigating the effect of task difficulty on dual-task performance; testing if the paper and pencil version of the dual-task method is giving the same results in ADHD and healthy controls; investigating whether the dual-task func...