A bstract We holographically compute the Rényi relative divergence D α ( ρ + ||ρ − ) between two density matrices , prepared by path integrals with constant background fields λ ± coupled to a marginal operator in JT gravity. Our calculation is non-perturbative difference sources . When this large, bulk geometry becomes black hole maximal temperature allowed index In limit, we find an analytical...

The following combinatorial theorems, some of which were known for every finite n in all infinite structures, are proved in ZFC for every infinite cardinal ν in all sufficiently large structures. (a) A new extension of Miller’s theorem [18]. (b) An upper bound of ρ on the list-conflict-free number of ρ-uniform families of sets which satisfy C(ρ, ν) for cardinals ν and ρ ≥ iω(n). (c) An upper bo...

(1.2) (∂t + V ∂k)ρ+ ρdivV = 0, divV = ∂kV k in D where the velocity v = (v1, ..., vn), the density ρ and the domain D ⊂ [0, T ]×Rn are to be determined. Here the pressure p = p(ρ) is assumed to be a given function of the density which is strictly increasing at the boundary where the density is assume to be constant. Furthermore V k = δvi = vk and we have used the summation convention that repea...

Let μ be a Borel probability measure on compact path-connected metric space (X,ρ) for which there exist constants c,β≥1 such that μ(B)≥crβ every open ball B⊂X of radius r>0. For class Lipschitz functions Φ:[0,∞)→R are piecewise within finite-dimensional subspace continuous functions, we prove under certain mild conditions the ρ and each positive integer N≥2, g∈L∞(X,dμ) with ‖g‖∞=1, points y1,…,...

Weighted Poincaré-type and related inequalities provide upper bounds of the variance functions. Their applications in sensitivity analysis allow for quickly identifying active inputs. Although efficiency prioritizing inputs depends on those bounds, latter can take higher values, therefore useless practice. In this paper, an optimal weighted inequality gradient-based expression (integral equalit...