We apologize the readers for the mistake made in equation (53) on page 531, which was found by us in paper [1] after its publication in the Robotica Journal. Namely, values of function s defined in equation (53) are always greater or equal to unity: s(t) ≥ 1 for all t ≥ 0. On the other hand, the inverse 1/s(t), which was used in the left-hand side of (53), belongs to the set (0, 1] (function s ...

This paper introduces a new method in the study of representations of groups into affine algebraic groups. In this work we focus on the study of SLnrepresentations and postpone the consideration of the theory in full to future papers. Let G be a group and let R be a commutative ring with unity. There is a commutative R-algebra Repn(G), called the universal representation algebra, and the univer...

There exists a number of known constructions for perfect sequences over roots of unity. These include Frank sequences of length n over n roots of unity [Heimiller, 1961][Frank, 1962], Chu sequences of length n over n roots of unity for n odd and length n over 2n roots of unity for n even [Chu, 1972], Milewski sequences of length m overm roots of unity [Milewski, 1983], Liu-Fan sequences of leng...