This paper presents a decomposition scheme for a large class of greyscale structuring elements from mathematical morphology. In contrast with many existing decomposition schemes, our method is valid in the continuous domain. Conditions are given under which this continuous method can be properly discretized. The class of functions that can be decomposed with our method contains the class of qua...

We introduce a new class of cooperative games by using the notion of local supermodularity. Therefore locally convex games can be considered as relaxations of convex games. Moreover, we obtain a characterization of a subclass of locally concave games in terms of the rank function of a matroid.

Surface water is a primary concept of human experience but concepts are captured in cultures and languages in many different ways. Still, many commonalities exist due to the physical basis of many of the properties and categories. An abstract ontology of surface water features based only on those physical properties of landscape features has the best potential for serving as a foundational doma...

Concave compositions are ordered partitions whose parts are decreasing towards a central part. We study the distribution modulo a of the number of concave compositions. Let c(n) be the number of concave compositions of n having even length. It is easy to see that c(n) is even for all n 1. Refining this fact, we prove that #{n < X : c(n) ⌘ 0 (mod 4)} p X and also that for every a > 2 and at leas...

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland’s branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we...

we provide a continuous representation of quasi-concave mappings by their upper level sets. A possible motivation is the extension to quasi-concave mappings of a result by Ulam and Hyers, which states that every approximately convex mapping can be approximated by a convex mapping. Keyword: quasi-concave, upper level set AMS classification: 47N10

We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman’s reverse Brunn-M...

A new class of gold nanostructures, concave nanocubes, enclosed by 24 high-index {720} facets, have been prepared in a monodisperse fashion by a modified seed-mediated synthetic method. The Cl(-) counterion in the surfactant plays an essential role in controlling the concave morphology of the final product. The concave nanocubes exhibit higher chemical activities compared with low-index {111}-f...

kermanshah province is the main producer of various chickpea cultivars in iran. in this study a laboratory peg-tooth thresher was employed for chickpea threshing. the effect of cylinder speed (9, 12, 15 m/s), concave clearance (12, 14, 16 mm), feed rate (80, 160, 240 kg/h) and material moisture content (5, 10, 15% w.b.) was studied on percentage of grain damage, threshing efficiency and percent...

In this paper we present a new method for Boolean operations (intersection, union and difference) of triangulated solids, and its applications in three-dimensional (3D) computerized geological modelling (3DGM). This method is adapted to arbitrary (convex or concave), close geological solids. Three major steps are included in this method: (1) Calculate intersection points between triangles. Our ...