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...

in dealing with uninvited guests as natural propositions and propositions that are based on primary essential predication, the term “predication” has undergone some semantic changes; according to the elements of “unity” and “difference” three periods may be distinguished: (1) the period in which “what causes the unity” is external and “what causes the difference” is in the mind, (2) the period ...

where we in introduce the standard notation e(x) = exp(2πix). Question 1.1. What is the magnitude of | ∑ x∈S e(x)|? By the trivial bound, we find that | ∑ x∈S e(x)| ≤ N , with equality whenever the terms are all equal. One can of course make the sum much smaller–simply sum the Nth roots of unity. In between these two extremes–completely in phase and maximally out of phase–we should consider wha...

In last two decades we had an intense discussion about which theory best describes how we understand other human beings. I will argue that neither Simulation Theory nor TheoryTheory nor Interaction-Theory do offer us an adequate analysis. Despite the fact that they highlight some relevant aspects, the generalization made by each theory cannot do justice to the varieties of social understanding ...