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Additional file 1. Table S1. Indications for initiation of KRT in patients with acute kidney injury. Table S2. Predictive accuracy of [TIMP-2]*[IGFBP7] for renal non-recovery at different cutoff values. Table S3. Predictions of secondary outcome of urinary biomarkers on day 0. Table S4. Multivariable regression analysis of clinical variables. Table S5. Urinary biomarkers on day 0 for predicting renal non-recovery in patients with AKI stage 2-3.

This paper presents a property of geometric and topological nature of Gateaux differentiability points and Frechet differentiability points of almost CL-spaces. More precisely, if we denote by M a maximal convex set of the unit sphere of a CL-space X, and by C M the cone generated by M, then all Gateaux differentiability points of X are just Un-s(C M ), and all Frechet differentiability points of X are ∪ int(C M ) (where n-s(C M ) denotes the non-support points set of CM).

This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi–dual can never have such a one; consequently, every non–separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.

Every real-valued convex and locally Lipschitzian function f defined on a nonempty closed convex set D of a Banach space E is the local restriction of a convex Lipschitzian function defined on E. Moreover, if E is separable and int ⁡ D ≠ ∅ \operatorname {int} D \ne \emptyset , then, for each Gateaux differentiability point x ( ∈ int ⁡ D ) ( \in \operatorname {int} D) of f, there is a closed convex set C ⊂ int ⁡ D C \subset \operatorname {int} D with the nonsupport points set N ( C ) ≠ ∅ N(C) \ne \emptyset and with x ∈ N ( C ) x \in N(C) such that f C {f_C} (the restriction of f on C) is Fréchet differentiable at x.