A recurrent set of words is such that its minimal automaton is strongly connected. This class of sets does not seem to have been studied before. It contains the submonoids generated by prefix codes but also more general sets. We prove some properties of recurrent sets and investigate their relation with a natural generalization of prefix codes called weakly prefix codes, and also known as codes...

We consider the existence and regularity of weakly polyharmonic almost complex structures on a compact Hermitian manifold $$M^{2m}$$ . Such objects satisfy elliptic system $$[\varDelta ^m J, J]=0$$ weakly. prove general theorem for semilinear systems in critical dimensions (with growth nonlinearities), which includes dimension four six.

Abstract. Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated when multiple measurements are ava...