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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.

In this paper, we give a number of characterizations for a Banach space X which is isometric to a subspace of c0, or, c0(Γ), successively, in terms of extreme points of its dual unit ball BX*, Frechet and Gâteaux derivatives of its norm, or, in terms of w*-strongly exposed points and w*-exposed points of BX*.

In this paper, we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract, and that it also admits the uniform compact approximation property. These can be regarded as extensions of Lindenstrauss and Kalton’s corresponding results.

By characterizing Asplund operators through Frechet differentiability property of convex functions, we show the following Bishop-Phelps-Bollobes theorem: Suppose that X is a Banach space, T: X → C(K) is an Asplund operator with ∥T∥ = 1, and that x0 ∈ SX, 0 < e satisfy $$\left\| {T\left({{x_0}} \right)} \right\| > 1 - {{{\varepsilon^2}} \over 2}$$ . Then there exist xe ∈ SX and an Asplund operator S: X → C(K) of norm one so that $$\left\| {S\left({{x_\varepsilon}} \right)} \right\| = 1,\,\,\,\,\,\,\left\| {{x_0} - {x_\varepsilon}} \right\| < \varepsilon \,\,\,\,\,{\rm{and}}\,\,\,\,\,\,\,\left\| {T - S} \right\| < \varepsilon .$$ Making use of this theorem, we further show a dual version of Bishop-Phelps-Bollobas property for a strong Radon-Nikodym operator T: l1 → Y of norm one: Suppose that y0* ∈ Sy*, e ≥ 0 satisfy $$\left\| {{T^*}\left({y_0^*} \right)} \right\| > 1 - {{{\varepsilon^2}} \over 2}$$ . Then there exist y*µ ∈ Sy*, xe∈ (±en), ye∈Sy, and a strong Radon-Nikodym operator S: l1→ Y of norm one so that $$\begin{array}{*{20}{c}} {(i)}&{\left\| {S({x_\varepsilon })} \right\| = 1;}&{(ii)S({x_\varepsilon }) = {y_\varepsilon };}&{(iii)\left\| {T - S} \right\| < \varepsilon ;} \end{array}$$ $$\begin{array}{*{20}{c}} {(iv)\left\| {{S^*}(y_\varepsilon ^*)} \right\| = \left\langle {y_\varepsilon ^*,{y_\varepsilon }} \right\rangle = 1;}&{(v)\left\| {y_0^* - y_\varepsilon ^*} \right\| < \varepsilon }&{and}&{(vi)\left\| {{T^*} - {S^*}} \right\| < \varepsilon ,} \end{array}$$ where (en) denotes the standard unit vector basis of l1.

Suppose that X, Y are two real Banach Spaces. We know that for a standard ∈-isometry f: X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of Y*. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ∈-isometry to be stable in assuming that N is w*-closed in Y*. Making use of this result, we improve several known results including Figiel’s theorem in reflexive spaces. We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then $$L(f) \equiv \overline {span} [f(x)]$$ contains a complemented linear isometric copy of X; Moreover, if X = Y, then for every ∈-isometry f : X → X, there exists a surjective linear isometry S : X → X such that f − S is uniformly bounded by 2∈ on X.

In this paper, we show that a closed convex subset C of a Banach space is strongly proximinal (proximinal, resp.) in every Banach space isometrically containing it if and only if C is locally (weakly, resp.) compact. As a consequence, it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it, the metric projection from Y to C is nonempty set-valued and upper semi-continuous.

The purpose of this paper is to discuss those kinds of statistical convergence, in terms of filter F, or ideal I-convergence, which are equivalent to measure convergence defined by a single statistical measure. We prove a number of characterizations of a single statistical measure μ-convergence by using properties of its corresponding quotient Banach space l ∞/l ∞(I μ ). We also show that the usual sequential convergence is not equivalent to a single measure convergence.

In this paper, with the help of spectral integral, we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces. Precisely, let H be a complex Hilbert space and 0 < ɛ < 1/2. Then for every bounded linear operator T: H → H and x 0 ∈ H with ‖T‖ = 1 = ‖x 0‖ such that ‖Tx 0‖ > 1 − g3, there exist x ɛ ∈ H and a bounded linear operator S: H → H with ‖S‖ = 1 = ‖x ɛ ‖ such that $$\left\| {Sx_\varepsilon } \right\| = 1, \left\| {x_\varepsilon - x_0 } \right\| \leqslant \sqrt {2\varepsilon } + \sqrt[4]{{2\varepsilon }}, \left\| {S - T} \right\| \leqslant \sqrt {2\varepsilon } .$$

This paper presents two counterexamples about ball-coverings of Banach spaces and shows a new characterization of uniformly non-square Banach spaces via ball-coverings.

In order to minimize the impact of anthropogenic factor and to study the relationships between dimple diameter and common mechanical properties,computer image processing technology is introduced to measure and count the size and number of dimples in metallographic image formed by ductile fracture.The dimples are segmented very well by using an adaptive method for image thresholding based on index of fuzziness.An improved multiregional area algorithm based on Freeman chain is presented.It proves that this algorithm can detect and measure dimple diameter rapidly and accurately.It also provides quantitative results for further classify and analysis of dimples.

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).

To guarantee every real-valued convex function bounded above on a set is continuous, how ”thick” should the set be? For a symmetric set A in a Banach space E, the answer of this paper is: Every real-valued convex function bounded above on A is continuous on E if and only if the following two conditions hold: i) spanA has finite co-dimentions and ii) coA has nonempty relative interior. This paper also shows that a subset A ⊂ E satisfying every real-valued convex function bounded above on A is continuous on E if (and only if) every real-valued linear functional bounded above on A is continuous on E, which is also equivalent to that every real-valued convex function bounded on A is continuous on E.

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.

To study on effects of injection of Huangqi Injectio into Zusanli (ST 36) on the hospital infection and immune function in the patient of schizophrenia.Thirty inpatients of chronic schizophrenia were treated with injection of Huangqi Injectio into bilateral Zusanli (ST 36), 2 mL each point, thrice each week, for 8 weeks. Relative immune indexes and the hospital infection were investigated.The hospital infection and the sub-infection were 4 cases (13.3%), 7 cases-times (23.3%) in the injection group; and 9 cases (15.0%), 19 cases-times (31.7%) in the control group, respectively, with no significant difference between the two groups (P0.05). The drug-administration duration was 7.77 days/case and 11.87 days/case in the two groups, respectively (P0.01). In the injection group, as compared with that of last 3 years the duration was 7.77 days/case and 14.08 days/case (P0.01). IgG, IgA, IgM and T-cell subgroups did not have significant changes, but there was the most different value before and after injection in SIL-2R of the no-infection group, and the longer the drug administration duration, the smaller the different values.Injection of Huangqi Injectio into Zusanli (ST 36) has definite effect for prevention of the hospital infection in inpatients of chronic schizophrenia, and SIL-2R is a valuable index for investigation of the hospital of infection.

To study the relationship between estrogen and the development of hemangioma.The expression of EST and ER in samples from the thirty-eight cases of hemangioma and six cases of normal control group was examined with the immunohistochemical steptavidin peroxidase conjugated method (SP method).The EST in capillary hemangioma expressed significantly higher than in the cavernous hemangioma, the racemose hemangioma or the control group. Although the EST in cavernous hemangioma and racemose hemangioma also expressed higher than in the control, there are no statistical differences among them. The ER only expressed in some cases in the capillary hemangioma group. No sexual difference was shown in the expressions of the EST and the ER.This study shows that there may be a relationship existed between the estrogen and the capillary hemangioma. It may indicate that some capillary hemangioma may be possibly treated by the drugs.