We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results of [4]. As an application of our main result we complete and simplify the analysis in [6], showing that in a 4-dimensional subRiemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth.

A non-vacuum, two-step process has been used to prepare a series of nanocrystalline CuIn1−xGaxSe2 (x = 0, 0.25, 0.5, 0.75, 1) materials. An open-air solvothermal preparation in triethylenetetramine solvent was followed by annealing at 500 °C in a nitrogen atmosphere for 20 min. All materials have mixed clustered plate, spherical particle, and nanorod morphologies with the smallest particle diam...

Niching enables a genetic algorithm (GA) to maintain diversity in a population. It is particularly useful when the problem has multiple optima where the aim is to find all or as many as possible of these optima. When the fitness landscape of a problem changes overtime, the problem is called non–stationary, dynamic or time–variant problem. In these problems, niching can maintain useful solutions...

We define a family of non-principal ultrafilters on N ${\mathbb {N}}$ which are, in sense, very far from P-points. prove the existence such under reasonable conditions. In subsequent articles, we intend to that may exist while no P-point exists. Though our primary motivations came forcing and independence results, introduced here should be interesting combinatorial point view too.