The genus Haplozoon contains a group of intestinal parasites of marine worms with a bizarre cellular organization. Although the phylogenetic relationship of these parasites to other eukaryotes was once controversial, a few studies using light and transmission electron microscopy (TEM) and small subunit rDNA confirmed that they are aberrant dinoflagellates. Microscopical studies also suggested t...

We show that the subgraph of concave transform a multiplicative filtration on section ring is Newton--Okounkov body certain semigroup, and if induced by divisorial valuation, then associated graded algebra sections concrete line bundle in higher dimension. use this description to give rationality criterion for Seshadri constants. Along way we introduce bodies abstract semigroups determine condi...

In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality μ(λA+ (1− λ)B) ≥ λμ(A) + (1− λ)μ(B) holds true for an unconditional product measure μ with decreasing density and a pair of unconditional convex bodies A,B ⊂ R. We also show that the above inequality is true for any unconditional logconcave me...

We study convexity and symmetry of central configurations in the five body problem when three masses ara located at vertices an equilateral triangle, that we call Lagrange plus two configurations. First, prove bodies out triangle cannot be placed on certain lines. Next, give a geometrical characterization such sense as Dziobek, describe admissible regions where remaining can placed. Furthermore...

The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The topic has a broad audience going from algorithmic convex geometry to random matrices. We have tried to emphasize different problems relating these areas of res...

in this paper, under the condition that $k$ is concave, we characterize lacunary series in $q_{k}$ spaces. we improve a result due to h. wulan and k. zhu.

We study the numerical computation of an expectation of a bounded function f with respect to a measure given by a non-normalized density on a convex body K ⊂ Rd . We assume that the density is log-concave, satisfies a variability condition and is not too narrow. In [19, 25, 26] it is required that K is the Euclidean unit ball. We consider general convex bodies or even the whole Rd and show that...

We show that an involution T on some class of functions on Rn, which reverses order (meaning that if f g then T f T g) has, often, a very specific form, actually essentially unique. It is done in this paper for the class of s-concave functions, for which this unique formula is derived. These functions are, for integer s, exactly marginals of convex bodies of dimension n+ s. This understanding i...

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly conc...

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality The volume spline is based on use of the Green’s function for interpolation of scalar function values of a chosen “carrier” solid. Our algorithm is capable of generating highly concave and branch...