We exhibit an example of a homogeneous Lorentzian manifold G/H whose homogeneous geodesics form just the light-cone and a hyperplane in the tangent space. For all light-like homogeneous geodesics, the natural parameter of the orbit is not the affine parameter of the geodesic.

Tangent cones Let A ⊆ R be a closed semialgebraic (s.a.) set and assume from now on that the origin O is not an isolated point of A. We recall that the tangent cone to A at O is the set C(A) = {u ∈ R|u = lim k→∞ tkxk}, where {xk} ⊂ A tends to O and {tk} ⊂ R. If we allow tk ∈ R only, we get what we call the tangent semicone to A at O, which we denote with C(A). It is easy to show that both C(A) ...

Nonsmooth operator equations in function spaces are considered, which depend on perturbation parameters. The nonsmoothness arises from a projection onto an admissible interval. Lipschitz stability in L∞ and Bouligand differentiability in L of the parameter-to-solution map are derived. An adjoint problem is introduced for which Lipschitz stability and Bouligand differentiability in L∞ are obtain...

This paper looks at the extraction of nonlinear turbulence information of the speech signal using Multi-Scale Fractal Dimension (MFD) as the additional feature to the convectional MFCC features. The MFD is estimated using both Box-Counting and Minkowiski-Bouligand dimensions. The proposed framework uses this feature extraction together with sub-band based speaker modeling rather than the wide-b...

Under the relaxed constant rank condition, introduced by Minchenko and Stakhovski, we prove that linearized cone is contained in tangent (Abadie condition) for sets represented as solution to systems of finite numbers inequalities equations given continuously differentiable functions defined on Banach spaces.

We prove the non-rationality of a double cover of P branched over a hypersurface F ⊂ P of degree 2n having isolated singularities such that n ≥ 4 and every singular points of the hypersurface F is ordinary, i.e. the projectivization of its tangent cone is smooth, whose multiplicity does not exceed 2(n− 2).

The maximization with respect to a cone of a set-valued function into possibly infinite dimensions is defined, and necessary and sufficient optimality conditions are established. In particular, an analogue of the Fritz John necessary optimality conditions is proved using a notion of derivative defined in terms of tangent cones.

We investigate barycenters of probability measures on proper Alexandrov spaces of curvature bounded below, and show that they enjoy several properties relevant to or different from those in metric spaces of curvature bounded above. We prove the reverse variance inequality, and show that the push forward of a measure to the tangent cone at its barycenter has the flat support.

We characterize C embedded hypersurfaces of R as the only locally closed sets with continuously varying flat tangent cones whose measuretheoretic-multiplicity is at most m < 3/2. It follows then that any (topological) hypersurface which has flat tangent cones and is supported everywhere by balls of uniform radius is C. In the real analytic case the same conclusion holds under the weakened hypot...

For each integer n 2 we construct a compact, geodesic, metric space X which has topological dimension n, is Ahlfors n-regular, satis es the Poincar e inequality, possesses IR as a unique tangent cone at Hn almost every point, but has no manifold points.