In this work I derive analytic expressions for the curvature-dependent fluid-substrate surface tension of a hard-sphere fluid on a hard curved wall. In the first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the exactly known second- and third-order cluster integrals of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions, which is equivalent to considering different positions of the dividing surface. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher-order terms in the curvature also exist. In the second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity, and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system; further, they are more accurate than any previously published expressions.

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PurposeThe objective of this paper is to address the question of whether the Balanced Scorecard (BSC) can be utilized in non‐profit organizations, in particular hospital sector organizations. A secondary objective addresses the issue of whether the BSC can be utilized employing the methodology encountered in the literature.Design/methodology/approachA case is presented of a private Spanish hospital, specializing in psychiatric patients, which is owned by a religious congregation and which utilizes a very primitive and informal information system. The case describes the design of the strategic map and the BSC for this hospital.FindingsThe paper concludes that the BSC is applicable to any type of organization, albeit with modifications; a BSC for non‐profit organizations must be modified to include a mission perspective, thus supporting Kaplan's model for non‐profit organizations. Hospitals should also include an additional perspective which provides specific information on social demographic factors regarding the hospital's operating environment.Originality/valueThe contribution of this paper is threefold. First, the case supports Kaplan's inclusion of a mission perspective for non‐profit organizations. Second, it further modifies the non‐profit BSC by including an additional perspective which provides specific information on social demographic factors regarding the hospital's operating environment. The authors are unaware of any instance where this additional perspective has been included in the model. Finally, the case provides a fully developed BSC and strategy map for a hospital which can be used as a template for other health‐care organizations.