The classical Bernstein pointwise estimate of the (first) derivative of a univariate algebraic polynomial on an interval has natural extensions to the multivariate setting. However, in several variables the domain of boundedness, even if convex, has a considerable geometric variety. In 1990, Y. Sarantopoulos satisfactorily settled the case of a centrally symmetric convex body by a method we may...

The paper is a supplement to [2]. Let L be a lattice and U an o-symmetric convex body inR n. The Minkowski functional I[ I1~ of U, the polar body U ~ the dual lattice L*, the covering radius/z(L, U), and the successive minima ~.i(L, U), i = 1 . . . . . n, are defined in the usual way. Let 12, be the family of all lattices in R". Given a convex body U, we define mh(U) = sup max ~.i(L, U)~.n-i+l(...

a r t i c l e i n f o a b s t r a c t We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating ...

It has been noticed long ago that many results on sections and projections are dual to each other, though methods used in the proofs are quite different and don't use the duality of underlying structures directly. In the paper [KRZ], the authors attempted to start a unified approach connecting sections and projections, which may eventually explain these mysterious connections. The idea is to us...

Geometrical and statistical properties of polarization of CMB are analyzed. Singular points of the vector field which describes CMB polarization are found and classified. Statistical distribution of the singularities is studied. A possible signature of tensor perturbations in CMB polarization is discussed. For a further analysis of CMB statistics Minkowski functionals are used, which present a ...

We investigate the use of wavelet transforms in detecting and characterising non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the Kaiser-Stebbins effect due to cosmic strings onto which Gaussian signals of varying amplitudes are superposed. We find the method significantly outperforms standard techniques based on measuring the mom...