We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.

In this paper we deal with the location of hyperplanes in n{ dimensional normed spaces. If d is a distance measure, our objective is to nd a hyperplane H which minimizes points and d(x m ; H) = min z2H d(x m ; z) is the distance from x m to the hyperplane H. In robust statistics and operations research such an optimal hyperplane is called a median hyperplane. We show that for all distance measu...

We fix three natural numbers k, n,N , such that n + k + 1 = N , and introduce the notion of two dual arrangements of hyperplanes. One of the arrangements is an arrangement of N hyperplanes in a k-dimensional affine space, the other is an arrangement of N hyperplanes in an n-dimensional affine space. We assign weights α1, . . . , αN to the hyperplanes of the arrangements and for each of the arra...

Is Hartwick’s rule a necessary condition for maximin in Solow’s [1974] model? Until recently this has been an open question; this is surprising given the prominence of the model. Cairns and Yang [2000] as well as Withagen, Asheim and Buchholz (this issue) claim that the answer is in the affirmative and claim to provide a formal proof. The latter team argues that the proof by the former is not c...

Let K be a field of characteristic zero, α algebraic of degree n over K. Given a proper parametrization ψ of a rational curve C, we present a new algorithm to compute the hypercircle associated to the parametrization ψ. As a consequence, we can decide if C is defined over K and, if not, to compute the minimum field of definition of C containing K. The algorithm exploits the conjugate curves of ...

We examine the existence of tangent hyperplanes to subriemannian balls. Strictly abnormal shortest paths are allowed.

Let S(N) ≡ PG(1, 2)×PG(1, 2)×· · ·×PG(1, 2) be a Segre variety that is N -fold direct product of projective lines of size three. Given two geometric hyperplanes H ′ and H ′′ of S(N), let us call the triple {H , H , H ∆H } the Veldkamp line of S(N). We shall demonstrate, for the sequence 2 ≤ N ≤ 4, that the properties of geometric hyperplanes of S(N) are fully encoded in the properties of Veldka...