When Can Matrix Query Languages Discern Matrices?

We investigate when two graphs, represented by their adjacency matrices, can be distinguished by means of sentences formed in MATLANG, a matrix query language which supports a number of elementary linear algebra operators. When undirected graphs are concerned, and hence the adjacency matrices are real and symmetric, precise characterisations are in place when two graphs (i.e., their adjacency matrices) can be distinguished. Turning to directed graphs, one has to deal with asymmetric adjacency matrices. This complicates matters. Indeed, it requires to understand the more general problem of when two arbitrary matrices can be distinguished in MATLANG. We provide characterisations of the distinguishing power of MATLANG on real and complex matrices, and on adjacency matrices of directed graphs in particular. The proof techniques are a combination of insights from the symmetric matrix case and results from linear algebra and linear control theory

Continuity and change in the treatment of frightening subject matter: contemporary retellings of classical mythology for children in the Low Countries

Ever since its origins, children's literature has dealt with frightening subject matter. The forms of such frightening fiction for children are, however, continuously changing. Retellings of classical mythology are a case in point as myths contain subjects that might be considered a threat to the romantic notion of the innocent child. As such, a focus upon the way authors deal with sex, death and violence in retellings of classical mythology reveals how the paradoxical impulses that govern the act of retelling that is, a desire for preserving and challenging cultural tradition alter under the influence of society's changing ideas about children and their literature. This paper concentrates on the rich and vivid tradition of retelling classical myths in the Low Countries. Shifts in the choice of pretext and in the age of the intended audience reveal a change of attitude towards frightening subjects in classical myths during the last decades. A closer look at retellings of the creation myths, dealing with sexual and lethal violence between parents and children, and the subject of death in the myth of Orpheus shows how the retellings of frightening myths range from unequivocal presentations as cautionary tales to demanding narratives generating unfixed meanings

Coordinate-free interpretations of the optimal costs for LQ-problems subject to implicit systems

Control Systems;operations research

Free end-point linear-quadratic control subject to implicit continuous-time systems: Necessary and sufficient conditions for solvability

Optimal Control;operations research

Regularity and singularity in linear-quadratic control subject to implicit continuous-time systems

Optimal Control;operations research

Solvability conditions, consistency and weak consistency for linear differential-algebraic equations and time-invariant singular systems: The general case

Control Systems;operations research

Invariant subspaces and invertibility properties for singular systems: The general case

Control Systems;operations research

The algebraic Riccati equation and singular optimal control: The discrete-time case

Optimal Control;mathematics