Let f $f$ be a noncommutative polynomial of degree m ⩾ 1 $m\geqslant 1$ over an algebraically closed field F $F$ characteristic 0. If n − $n\geqslant m-1$ and α , 2 3 $\alpha _1,\alpha _2,\alpha _3$ are nonzero elements from such that + = 0 _1+\alpha _2+\alpha _3=0$ then every trace zero × $n\times n$ matrix can written as A _1 A_1+\alpha _2A_2+\alpha _3A_3$ for some i $A_i$ in the image M ( ) ...

The magnetite (Fe3O4) – agar nanocomposite was prepared by co-precipitation of Fe (III) and Fe (II) ions for the first time. The obtained samples were characterized by x-ray diffraction, Fourier-transform infrared spectroscopy, scanning electron microscopy and transmission electron microscopy. FT-IR results confirm the formation of Fe3O4 nanoparticles...