The Cauchy–Schwarz Master Class: References

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Wasserstein Stability for Persistence Diagrams (2020, unknown): “This corollary states that for X a triangulable, compact metric space that implies bounded degree-k total persistence for some real number k ≥ 1 , and f, g two tame Lipschitz functions we have See Section 3 for some limitations in terms of k and C X,k .”
Thirty-two Goldbach Variations (2005, unknown): “7) is best possible [52, 70].”
Reynolds-averaged Navier–Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned (2018, unknown): “Using the Schwartz inequality (Steele 2004; Debnath & Mikusiński 2005) leads to: |δu(x′)| 6 ‖Gx′‖Ω ‖δb‖Ω (A 9) = ‖Gx′‖Ω ‖∇ · δτ‖Ω (A 10) As in A.1, the pressure gradient is assumed constant and thus δb = ∇ · δτ .”
Advances in operator cauchy-schwarz inequalities and their reverses (2015, background): “The general form of the C-S inequality for inner product spaces was proved by Hermann Amandus Schwarz in 1885; see also [45].”
Nonextensive Information Theoretic Kernels on Measures (2009, unknown): “To show the (2 − q)-convexity of −1/ϕ′′q (x) = −(1/q)x2−q, for xt ≥ 0, and q ∈ [0, 1], we use a version of the power mean inequality (Steele, 2006), − ( l∑ i=1 λi xi )2−q ≤ − l∑ i=1 (λi xi) 2−q = − l∑ i=1 λ2−qi x 2−q i , thus concluding that −1/ϕ′′q is in fact (2− q)-convex.”