We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved, in a special case arising from the k-SAT problem, by Maneva, Mossel and Wainwright. We thus highlight the connection between various characterizations of convex geometries and a family of removal processes studied in the literature on random structures.

We provide a new characterization of convex geometries via a multi-variate version of an identity that was originally proved by Maneva, Mossel and Wainwright for particular combinatorial objects defined in the context of the k-SAT problem. We thus highlight the connection between various characterizations of convex geometries and a family of removal processes studied in the literature on random...

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions defined over the real space. In this paper, we consider a ...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Induction (or transformation) by bipartite graphs is one of the most important operations on matroids, and it is well known that the induction of a matroid by a bipartite graph is again a matroid. As an abstract form of this fact, the induction of a matroid by a linking system is known to be a matroid. M-convex functions are quantitative extensions of matroidal structures, and they are known as...

We propose a novel method to find approximate convex 3D shapes from single RGBD images. Convex shapes are more general than cuboids, cylinders, cones and spheres. Many real-world objects are nearconvex and every non-convex object can be represented using convex parts. By finding approximate convex shapes in RGBD images, we extract important structures of a scene. From a large set of candidates ...

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In this paper, we consider the optimal design of photonic crystal band structures for twodimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.