The Deligne-Simpson problem is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj âŠ‚ SL(n,C) or cj âŠ‚ sl(n,C) so that there exist irreducible (p +â€¦ (More)

To the memory of my mother Abstract We consider the variety of (p + 1)-tuples of matrices A j (resp. M j) from given conju-gacy classes c j âŠ‚ gl(n, C) (resp. C j âŠ‚ GL(n, C)) such that A 1 +. .. + Aâ€¦ (More)

We describe the construction of suboptimal trajectories of the problem of a planar motion with bounded derivative of the curvature and we prove their suboptimality. â€˜Suboptimalâ€™ means longer than theâ€¦ (More)

The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj âŠ‚ GL(n,C) or cj âŠ‚ gl(n,C) so thatâ€¦ (More)

We consider the planar motion of a car-like robot with a bounded derivative of the curvature, with given initial and nal connguration (i.e. positions, tangent angles and curvatures). The tangentâ€¦ (More)

In the present paper we prove some geometric properties of clothoids. A clothoid (or Cornu's spiral) is a plane curve whose curvature is a linear function of its length. In suitably chosenâ€¦ (More)

The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj âŠ‚ GL(n,C) or cj âŠ‚ gl(n,C) so thatâ€¦ (More)

In the present paper we find a new interpretation of Narayana polynomials Nn(x) which are the generating polynomials for the Narayana numbers Nn,k = 1 n C kâˆ’1 n C k n where C i j stands for the usualâ€¦ (More)

We consider the Deligne-Simpson problem (DSP) (resp. the weak DSP): Give necessary and sufficient conditions upon the choice of the p + 1 conjugacy classes cj âŠ‚ gl(n,C) or Cj âŠ‚ GL(n,C) so that thereâ€¦ (More)

The Schur-SzegÃ¶ composition of two polynomials of degree â‰¤ n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials,â€¦ (More)