2 problems

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Almost self-duality conjecture for effective conductivity
Consider an irreducible $n$ -component system in which the conductivity $sigma$ takes the distinct values $\sigma_1,\ldots,\sigma_n$ with positive probabilities $p_1,\ldots,p_n$ sat…
Conjectureopeneffective-conductivity random-mediaarXiv posted 2 days ago
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Monotonicity conjecture for the lattice conductivity integral $H(d)$
Monotonicity conjecture. $H(d)$ is a strictly decreasing function of $d$ . The preceding discussion identifies the two-dimensional value as $H(2)=1$ ; the conjecture concerns the beh…
Conjectureopeneffective-conductivity fourier-analysis lattice-modelsarXiv posted 2 days ago

Almost self-duality conjecture for effective conductivity