A novel approach is proposed to design optimal finite word length (FWL) realizations of digital controllers implemented in fixed-point arithmetic. An analytical method is first formulated to obtain a global optimal controller realization that optimizes an FWL closed-loop stability measure. Since this FWL closed-loop stability measure is solely linked to the fractional part or precision of fixed...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

Cross Coherence time frequency transform and independent component analysis (ICA) method were used to analyse the electroencephalogram (EEG) signals in resting and action states during open and close eyes conditions. From the topographical scalp distributions of delta, theta, alpha, and beta power spectrum can clearly discriminate between the signal when the eyes were open or closed, but it was...

In this note we work with untyped lambda terms under β(η)-conversion and consider the possibility of extending Böhm’s theorem to infinite RE sets. Of course, it is well known that Böhm’s theorem will fail in general for such sets even if it holds for all finite subsets. It turns out that generalizing Böhm’s theorem to infinite sets involves three other superficially unrelated notions; namely, C...

We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $L^{N/2}(mathb...