2 problems

Consider a one-dimensional periodic cell containing $n$ balls of each type $A$, $B$, and $C$, with positive radii parameters $\omega_i$ satisfying $\sum_i\omega_i=1$, and let…

Let $[\gamma_{ij}]$ satisfy the conditions in Theorem and have nullity $1$, with $\gamma>0$ its overall factor, so that $[\gamma_{ij}]/\gamma$ is fixed. Let $\vec u(\cdot;\gamma)$…