We define the notion of a generic integral element for the Griffiths distribution on a weight two period domain, draw the analogy with the classical contact distribution, and then show how to explicitly construct an infinite-dimensional family of integral manifolds tangent to a given element.

We say that a C∗-algebra A is approximately square root closed, if any normal element in A can be approximated by a square of a normal element in A. We study when A is approximately square root closed, and have an affirmative answer for AI-algebras, Goodearl type algebras over the torus, purely infinite simple unital C∗-algebras etc.

A partial ordering P is chain-Ramsey if, for every natural number n and every coloring of the n-element chains from P in finitely many colors, there is a monochromatic subordering Q isomorphic to P. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a c...

The problem of estimation of a regression curve in an infinite dimensional space is considered. Such problems arise in the statistics of random processes. Observation data in such processes is a pair whose one component is an element of an infinite dimensional space. It is shown that the finite dimensional projections of observations and the regression curve estimators constructed on their basi...