We classify flat strict nearly Kähler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-Kähler factor of maximal dimension and a strict flat nearly Kähler manifold of split signature (2m, 2m) with m ≥ 3. Moreover, the geometry of the second factor is encoded in a complex three-form ζ ∈ Λ3(Cm)∗. The first nontrivial example occurs in dimens...

We prove L estimates for the maximal Riesz transform in terms of the Riesz transform itself, for 1 < p ≤ ∞. We show that the corresponding weak L1 estimate fails for the maximal Riesz transform, but surprisingly does hold for the maximal Beurling transform.

Movement control responsible for generation of maximal hand velocity was studied on the example of horizontal arm swing that is a component of various sports activities. The movement was performed with the nondominant arm in similarity with the baseball bat swing. The task was to generate maximum hand velocity at a target. The movement included trunk long-axis rotation and horizontal shoulder a...

Let (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the L boundedness of the maximal commutator with RBMO functions

Students are often suggested to provide feedback to teachers on lectures, learning materials and tests among other things. While such information can considerably improve the learning process it is necessary to find an effective way to obtain feedback and at the same time decrease the amount of time students use to deliver it. This article is a step towards extracting maximal knowledge with min...

A case of a fetus with multiple malformations is described. The mother showed a 46,XX,rcp(10;22) (p11;p11) karyotype. Amniocentesis at the 16th week of gestation revealed that the male fetus had a der(22) chromosome--that is, he was trisomic for a large part of 10p (10pter leads to 10p11). Clinical findings of cases with 10p, 10q, and mosaic 10 trisomies are briefly reviewed.

10. In this note we consider complete Riemannian manifolds with Ricci curvature bounded from below. The well-known theorems of Myers and Bishop imply that a manifold M n with Ric ~ n 1 satisfies diam(1l1n) ~ diam(Sn(I)), Vol(Mn) ~ Vol(Sn(I)). It follows from [Ch] that equality in either of these estimates can be achieved only if M n is isometric to Sn (1). The natural conjecture is that a manif...

We show that the maximal number of singular moves required to pass between any two regularly homotopic plane or spherical curves with at most n crossings grows quadratically with respect to n. Furthermore, for any two regularly homotopic curves with at most n crossings, there exists such a sequence of singular moves, satisfying the quadratic bound, for which all curves along the way have at mos...