We define triangulated piecewise linear constant mean curvature surfaces using a variational characterization. These surfaces are critical for area amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the nonminimal case) the volume to one side of the surfaces. We then find explicit formulas for complete examples, such as disc...

The Laakso–Taagepera index (Laakso and Taagepera, 1979) has become the most commonly used measure to specify the ‘effective’ number of political parties in a party system where parties vary substantially in their vote and/or seat shares. It is well known that the Laakso–Taagepera index is the inverse of the even more widely used Herfindahl–Hirschman index of concentration (Hirschman, 1945; Herf...

This paper presents a classification of cavitation damage levels on spillway surface. Two important factors influencing cavitation damage have been considered in this study, flow velocity and cavitation index. Based on these factors, five different damage levels from no cavitation damage to major cavitation damage have been determined. The method was applied to data of the Shahid Abbaspour dam ...

Background An international initiative is underway to develop a revised systemic lupus erythematosus (SLE) organ damage index (SDI) using multi-phase process that supported by the SLE International Collaborating Clinics (SLICC), American College of Rheumatology (ACR) and Lupus Foundation America (LFA). The first two phases (evaluating construct item generation through literature review an Delph...

In this paper a new cluster validity index is introduced, which assesses the average compactness and separation of fuzzy partitions generated by the fuzzy c-means algorithm. To compare the performance of this new index with a number of known validation indices, the fuzzy partitioning of two data sets was carried out. Our validation performed favorably in all studies, even in those where other v...

Abstract. In 1968, Simons [9] introduced the concept of index for hypersurfaces immersed into the Euclidean sphere S. Intuitively, the index measures the number of independent directions in which a given hypersurface fails to minimize area. The earliest results regarding the index focused on the case of minimal hypersurfaces. Many such results established lower bounds for the index. More recent...