<p style='text-indent:20px;'>In this article we consider the following weighted nonlinear eigenvalue problem for <inline-formula><tex-math id="M1">\begin{document}$ g- $\end{document}</tex-math></inline-formula>Laplacian</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -{\text{ div}}\left( g...

We study the problem of constructing explicit families matrices which cannot be expressed as a product few sparse matrices. In addition to being natural mathematical question on its own, this appears in various incarnations computer science; most significant context lower bounds for algebraic circuits compute linear transformations, matrix rigidity and data structure bounds. first show, every c...