4 problems

Lions's conjecture. The compressible Navier–Stokes system may exhibit propagation of oscillations; Lions provided an example for a variant of the system that includes a forcing ter…

The perturbed network Laplacian has hybridized zero-modes, obtained from the zero-eigenspace of the disconnected-network Laplacian and associated with a chosen partition of the net…

Oscillation-pattern classification conjecture. We conjecture that $\mathcal{P}_{\textnormal{osc}}=-K_0$ characterizes stable non-standard relaxation oscillations,…

Consider a cyclic network of $n$ genes, with gene-expression levels determined by the corresponding inhibitory-loop model. Expression-level conjecture. More generally,…