In this paper, an observer based fuzzy adaptive controller (FAC) is designed fora class of large scale systems with non-canonical non-affine nonlinear subsystems. It isassumed that functions of the subsystems and the interactions among subsystems areunknown. By constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured sta...

Motivated by recent results of Tao–Ziegler [Discrete Anal. 2016] and Greenfeld–Tao (2022 preprint) on concatenating affine-linear functions along subgroups an abelian group, we show three recovering affine linearity $$f: V \rightarrow W$$ from their restrictions to lines, where V, W are $${\mathbb {F}}$$ -vector spaces $$\dim \geqslant 2$$ . First, if < |{\mathbb {F}}|$$ {\mathbb is when restri...

Boolean function in even number of variables is called bent if it is at the maximal possible Hamming distance from the class of all affine Boolean functions. We have proven that every isometric mapping of the set of all Boolean functions into itself that transforms bent functions into bent functions is a combination of an affine transform of coordinates and an affine shift.

Admissiblê sl(2|1; C) k Characters and Parafermions. Abstract The branching functions of the affine superalgebrâ sl(2|1; C) k characters into characters of the subalgebrâ sl(2; C) k are calculated for fractional levels k = 1 u − 1, u ∈ N. They involve rational torus A u(u−1) and Z u−1 parafermion characters.

We review the complex differential geometry of the space of oriented affine lines in R and give a description of Hamilton’s characteristic functions for reflection in an oriented C surface in terms of this geometry.