Recently, the ideal free dispersal strategy has been proven to be evolutionarily stable in the spatially discrete as well as continuous setting. That is, at equilibrium a species adopting the strategy is immune against invasion by any species carrying a different dispersal strategy, other conditions being held equal. In this paper, we consider a two-species competition model where one of the sp...

We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n] that was first considered by Petersen et al. [J. Algebra 324(5) (2010), 951–969]. We give an alternative approach to their result that the flag simplicial complex on ([n] k ) induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset ...

We give various characterizations of k-vertex connected graphs by geometric, algebraic, and "physical" properties. As an example, a graph G is k-connected ff and only if, specifying any k vertices of G, the vertices of G can be represented by points of R ~-a so that no k are on a hyper-. plane and each vertex is in the convex hull of its neighbors, except for the k specified vertices. The proof...

Size-controlled synthesis of metal nanostructures has opened many new possibilities to design ideal building blocks for future nanodevices. By solution-based method, silver triangular nanoprisms of different sizes (edge length) have been synthesized. First hyper-polarizabilities of silver triangular nanomaterials were measured using hyper-Rayleigh scattering technique. We have shown that both l...

This paper is part of the program of reverse mathematics. We assume the reader is familiar with this program as well as with RCA,, and WKL,, the two weak subsystems of second-order arithmetic we are going to work with here. (If not, a good place to start is [2].) In [2], [3], [4], many well-known theorems about countable rings, countable fields, etc. were studied in the context of reverse mathe...