Related papers: Cells with many facets in a Poisson hyperplane tes…

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the…

Given a finite set of points $S\subset\mathbb{R}^d$, a $k$-set of $S$ is a subset $A \subset S$ of size $k$ which can be strictly separated from $S \setminus A $ by a hyperplane. Similarly, a $k$-facet of a point set $S$ in general position…

In this paper we present an explicit combinatorial description of a special class of facets of the secondary polytopes of hypersimplices. These facets correspond to polytopal subdivisions called multi-splits. We show a relation between the…

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…

It is shown phenomenologically that the fractional derivative $\xi=D^\alpha u$ of order $\alpha$ of a multifractal function has a power-law tail $\propto |\xi| ^{-p_\star}$ in its cumulative probability, for a suitable range of $\alpha$'s.…

Let $G$ be a connected complex semi-simple Lie group, and let $Z_{{\bf u}}$ be an $n$-dimensional Bott-Samelson variety of $G$, where ${\bf u}$ is any sequence of simple reflections in the Weyl group of $G$. We study the Poisson structure…

We consider the typical Poisson-Voronoi cell in the Euclidean space R d and in particular the maximal distance D from a vertex of that cell to its nucleus. We provide a sharp asymptotics for the tail distribution of D. As a byproduct, we…

In this paper we introduce a family of Poisson-Laguerre tessellations in $\mathbb{R}^d$ generated by a Poisson point process in $\mathbb{R}^d\times \mathbb{R}$, whose intensity measure has a density of the form $(v,h)\mapsto f(h){\rm d} h…

We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do…

Let $P_n$ be an $n$-dimensional regular polytope from one of the three infinite series (regular simplices, regular crosspolytopes, and cubes). Project $P_n$ onto a random, uniformly distributed linear subspace of dimension $d\geq 2$. We…

We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…

We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell…

In coverage-oriented networks, base stations (BSs) are deployed in a way such that users at the cell boundaries achieve sufficient signal strength. The shape and size of cells vary from BS to BS, since the large-scale signal propagation…

From a three-dimensional boundary value problem for the time harmonic classical Maxwell equations, we derive the dispersion relation for a surface wave, the edge plasmon-polariton (EP), that is localized near and propagates along the…

Fine and Gill (1973) introduced the geometric representation for those comparative probability orders on n atoms that have an underlying probability measure. In this representation every such comparative probability order is represented by…

With suitable order of limits, as p, m, and n all tend to infinity, the distribution of the normalized trace of Frobenius on H^1 of a "random" plane curve of degree n over the field with p^m elements, tends to a Gaussian distribution. The…

We study the geometry of complex Poisson bivectors over smooth manifolds. We show that under mild regularity conditions any complex Poisson bivector has associated a complex presymplectic foliation. After that, we use techniques of Dirac…

Let $\Phi$ be an irreducible crystallographic root system with Weyl group $W$ and coroot lattice $\check{Q}$, spanning a Euclidean space $V$. Let $m$ be a positive integer and $\aA^m_\Phi$ be the arrangement of hyperplanes in $V$ of the…

We have known that most sequences in $\mathcal{M}=\{1,2,\dots, M\}$ with length $n$ will miss $Me^{-\lambda}$ of the total numbers of $\{1,2,\dots,M\}$ as the ratio $n/M$ tends to $\lambda$. Now we consider a more general case where the…

The well-known Heyde theorem characterizes the Gaussian distributions on the real line by the symmetry of the conditional distribution of one linear form of independent random variables given another. We generalize this theorem to groups of…