The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients a are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume...

Shabir and Naz in [27] introduced the notion of soft topological spaces. They defined soft topology on the collection τ of soft sets over X . Consequently, they defined soft separation axioms, soft regular spaces and soft normal spaces and established their several properties. Min in [30] investigate some properties of these soft separation axioms. Kandil et al. [12] introduce the notion of sof...

Article history: Received 21 September 2008 Received in revised form 14 July 2009 Accepted 24 July 2009

A new class of functions called fuzzy semi α-irresolute functions in fuzzy topological spaces are introduced in this paper. Some characterizations of this class and its properties and the relationship with other classes of functions between fuzzy topological spaces are also obtained.

Probability distributions and histograms are natural representations for product ratings, traffic measurements, and other data considered in many machine learning applications. Thus, this paper introduces a technique for graph-based semisupervised learning of histograms, derived from the theory of optimal transportation. Our method has several properties making it suitable for this application;...

Semi supervised methods involve converting unlabelled data into high quality labelled data that can be used to improve the performance of conventional supervised methods that had previously been given a small training set. Unlabelled data has also been shown to be helpful in a supervised setting called ‘bridging’ where unlabelled data have been used to help relate labelled instances to those th...

This work tackles the problem of learning a robust classification function from a very small sample set when a related but unlabeled data set is provided. To this end we define a new semi-supervised method that is based on a stability criterion. We successfully apply our proposal in the specific case of automatic diagnosis of intestinal motility disease using video capsule endoscopy.