Let d ≥ 2 and let K ⊂ R be a convex body containing the origin 0 in its interior. Let, for each direction ω, the (d − 1)–volume of the intersection of K and an arbitrary hyperplane with normal ω attain its maximum if the hyperplane contains 0. Then K is symmetric about 0. The proof uses a linear integro–differential operator on S, whose null–space needs to be, and will be determined.

Artificial life has now become a mature inter-discipline. In this contribution, its roots are traced, its key questions are raised, its main methodological tools are discussed, and finally its applications are reviewed. As part of the growing body of knowledge at the intersection between the life sciences and computing, artificial life will continue to thrive and benefit from further scientific...

We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the inand circumradius of the convex body. We show that the roots of 1-tangential ...

These lines are the intersections of the plane through the point p in the world and the centres of the left and right cameras with the two camera focal planes (see Figure 1). These epipolar lines are formed by the intersections of the pencil of planes through the line joining the image centres with the camera focal planes. Hence such lines form a pencil passing through the point of intersection...

We generalize the strong Hanani-Tutte theorem to clustered graphs with two disjoint clusters, and show that an extension of our result to flat clustered graphs with three disjoint clusters is not possible. We also give a new and short proof for a result by Di Battista and Frati about efficient c-planarity testing of an embedded flat clustered graph with small faces based on the matroid intersec...

ÐThe minimum length test sequence generation method proposed in [2] for conformance testing of a protocol uses Unique Input Sequences (UIS) for state identification. This method, called the U-method, requires that the test graph, a graph derived from the protocol, be connected. This requirement also needs to be satisfied in the case of the MU-method [31], [30], which assumes that the multiple U...

Matching 2-lattice polyhedra are a special class of lattice polyhedra that include network 3ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, etc. In this paper we develop a polynomial-time extreme point algorithm for #nding a maximum cardinality vector in a matching 2-lattice polyhedron. c © 2001 Elsevier Science B.V. All rights reserved.