Let E ⊂ Rn+1, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A∞ property of harmonic measure, for the open set Ω := Rn+1 \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, p-harmonic measure, associated to the p-Laplace operator, 1 < p < ∞.

We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is possible and we give an efficient sampling algorithm. The combination of these two properties may be appealing to risk modellers.

A Krausz partition of a graph G is a partition of the edges of G into complete subgraphs. The Krausz dimension of a graph G is the least number k such that G admits a Krausz partition in which each vertex belongs to at most k classes. The graphs with Krausz dimension at most 2 are exactly the line graphs, and graphs of the Krausz dimension at most k are intersection graphs of k-uniform linear h...

It can be expected that the respective endpoints of the Gregory-Laflamme black brane instability and the Rayleigh-Plateau membrane instability are related because the bifurcation diagrams of the black hole-black string system and the liquid drop-liquid bridge system display many similarities. In this paper, we investigate the non-linear dynamics of the Rayleigh-Plateau instability in a range of...

Chiral nematic liquid crystals (CLCs), with a unique helix structure, have attracted immense recognition over the last few decades owing to abundant presence in natural phenomena and their diverse applications. However, optical properties of CLC are usually hindered by abundance so-called fingerprint domains. Up now, studies worked on controlling in-plane orientation lying through surface rubbi...

this study aimed to investigate the effects of stiffeners on buckling of thin cylindrical shells under uniform axial compression. to this end, more than 300 finite element models of stiffened cylindrical shells were prepared. the variables considered are shell thickness, number, dimension and the location of the vertical and horizontal stiffeners as well as circular symmetrical imperfections. r...

The present paper links the concepts of Kolmogorov complexity (in Complexity theory) and Hausdorr dimension (in Fractal geometry) for a class of recursive (computable) !-languages. It is shown that the complexity of an innnite string contained in a 2-deenable set of strings is upper bounded by the Hausdorr dimension of this set and that this upper bound is tight. Moreover, we show that there ar...

In this paper we propose several equivalent definitions of digital curves and hypersurfaces in arbitrary dimension. The definitions involve properties such as one-dimensionality of curves and (n − 1)dimensionality of hypersurfaces that make them discrete analogs of corresponding notions in topology. Thus this work appears to be the first one on digital manifolds where the definitions involve th...

It is known that the gas has a fractal structure in a wide range of spatial scales with a fractal dimension that seems to be a constant around Df ≃ 2.7. It is expected that stars forming from this fractal medium exhibit similar fractal patterns. Here we address this issue by quantifying the degree to which starforming events are clumped. We develop, test, and apply a precise and accurate techni...