and Applied Analysis 3 Definition 2.4. M is called c-porous if for any x ∈ X and every r > 0, there are y ∈ B x, r and φ ∈ X∗ \ {0} such that { z ∈ X : φ z > φy ∩M ∅. 2.2 C-porosity turns out to be the suitable notion to describe the smallness of convex nowhere dense sets see Proposition 2.5 and is a stronger form of 0-angle porosity x ∈ X instead x ∈ M . Indeed, consider the unit sphere S of a...

????. Figure 1. Elevation profiles of a crater over a pure ice half-space and heat flow of 1 mW m, after 100 Myr. Surface temperature is indicated in the legend box. 1798.pdf 44th Lunar and Planetary Science Conference (2013)

The initial temperature of a heat conductor is zero and its boundary temperature is kept equal to one at each time. The conductor contains a stationary isothermic surface, that is, an invariant spatial level surface of the temperature. In a previous paper, we proved that, if the conductor is bounded, then it must be a ball. Here, we prove that the boundary of the conductor is either a hyperplan...

Consider a family of Boolean models, indexed by integers n ≥ 1, where the n-th model features a Poisson point process in R of intensity en with ρn → ρ as n → ∞, and balls of independent and identically distributed radii distributed like X̄n √ n, with X̄n satisfying a large deviations principle. It is shown that there exist three deterministic thresholds: τd the degree threshold; τp the percolatio...

Let (W,S) be a Coxeter system. An element in W and an ordered list of elements in S give us a subword complex, as defined by Knutson and Miller. We define the “fish product” between an involution in W and a generator in S, which is also discussed by Hultman. This “fish product” always produces an involution. The structure of the involution subword complex ∆̂(Q,w) behaves very similarly to the re...

We consider a time-dependent brane configuration that corresponds to the Q-ball in the effective Lagrangian. We discuss the brane Q-balls, branonium and brane Q-ball inflation, which might have the same origin. We show the allowed parameter regions for these configurations. It is shown that the brane Q-ball looks similar to a conventional Q-ball when it is large, but its decay is dominated by t...

Robots perceiving their environment using cameras usually need a good representation of how the camera is aligned to the body and how the camera is rotated relative to the ground. This is especially important for bearing-based distance measurements. In this paper we show how to use reference objects to improve vision-based distance measurements to objects of unknown size. Several methods for di...

Let K be a convex body in Rd, let j ∈ {1, . . . , d − 1}, and let K(n) be the convex hull of n points chosen randomly, independently and uniformly from K. If ∂K is C2 +, then an asymptotic formula is known due to M. Reitzner (and due to I. Bárány if ∂K is C3 +) for the difference of the jth intrinsic volume of K and the expectation of the jth intrinsic volume of K(n). We extend this formula to ...

For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to...

In dieser Arbeit wird die technische Effizienz von Biogasanlagen mit Hilfe der Data Envelopment Analyse bestimmt. Als Datengrundlage dient eine Befragung des KTBL bei deutschen Biogasanlagenbetreibern, die sich auf das Jahr 2004 bezieht. Die Auswertung zeigt deutliche Unterschiede in der Produktivität der Anlagen. Als wesentlicher Einflussfaktor stellt sich die Auslastung heraus. 1 Problemstell...