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- Daniel Hug, Rolf Schneider
- 2004

We strengthen some known stability results from the Brunn-Minkowski theory and obtain new results of similar types. These results concern pairs of convex bodies for which either surface area measures, or counterparts of such measures in the Brunn-Minkowski-Firey theory, or geometrically significant transforms of such measures, are close to each other. MSC… (More)

The Gram-negative bacterium Flavobacterium sp. strain R1534 is a natural producer of zeaxanthin. A 14 kb genomic DNA fragment of this organism has been cloned and a 5.1 kb piece containing the carotenoid biosynthesis genes sequenced. The carotenoid biosynthesis cluster consists of five genes arranged in at least two operons. The five genes are necessary and… (More)

- Steven IJland, Frances P. Noonan, +5 authors Edward C. De Fabo
- Photochemistry and photobiology
- 1998

Ultraviolet B (UVB, 290-320 nm) radiation initiates in vivo a dose- and wavelength-dependent down regulation of cell-mediated immunity. An action spectrum for UV-induced immunosuppression indicated that the photoreceptor for this effect is urocanic acid (UCA), which undergoes a trans to cis isomerization in the stratum corneum on UV exposure. An… (More)

For a convex body of given volume in spherical space, the total invariant measure of hitting great subspheres becomes minimal, equivalently the volume of the polar body becomes maximal, if and only if the body is a spherical cap. This result can be considered as a spherical counterpart of two Euclidean inequalities, the Urysohn inequality connecting mean… (More)

It is proved that the shape of the typical cell of a stationary Poisson-Voronoi tessellation in Euclidean space, under the condition that the volume of the typical cell is large, must be close to spherical shape, with high probability. The same holds if the volume is replaced by the surface area or other suitable functionals. Similar results hold for the… (More)

- Daniel Hug, Rolf Schneider
- Discrete & Computational Geometry
- 2004

It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex, given that the volume of the typical cell tends to infinity. This follows from an estimate for the probability that the typical cell deviates by a given amount… (More)

We consider geometric functionals of the convex hull of normally distributed random points in Euclidean space R. In particular, we determine the asymptotic behaviour of the expected value of such functionals and of related geometric probabilities, as the number of points increases.

- Daniel Hug
- 2004

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ Rd and a gauge body B ⊂ Rd such a generalized contact distribution is the conditional distribution of the random vector (dB(L,Z), uB(L,Z), pB(L,Z), lB(L,Z)) given that Z ∩L… (More)

- Daniel Hug, Rolf Schneider
- 2005

We establish a close relationship between isoperimetric inequalities for convex bodies and asymptotic shapes of large random polytopes, which arise as cells in certain random mosaics in d-dimensional Euclidean space. These mosaics are generated by Poisson hyperplane processes satisfying a few natural assumptions (not necessarily stationarity or isotropy).… (More)

For a non-empty compact set A ⊂ R , d ≥ 2, and r ≥ 0, let A⊕r denote the set of points whose distance fromA is r at the most. It is well-known that the volume,Vd(A⊕r ), ofA⊕r is a polynomial of degree d in the parameter r if A is convex. We pursue the reverse question and ask whether A is necessarily convex if Vd(A⊕r ) is a polynomial in r . An affirmative… (More)