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.

In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, equivalent characterizations of Bouligand tangent cone, Clarke cone and their corresponding normal cones set derived. Secondly, by using cones, four types stationary points GSCO given: TB-stationary point, NB-stationary TC-stationary point NC-stationary which used to characte...

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.

In the setup of i.i.d. observations and a real valued differentiable functional T , locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of T ) and for the confidence probability of lower confidence limits (for the value of T ), in the case that the tangent set is only a convex cone. The bounds, and the tests and estimators which achieve the ...

We show that the image cone of a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be considered as a version of the Atiyah Guillemin Sternberg convexity theorem for torus action...

We present a new proof of a result by Kodiyalam-Raghavan [7] and Kreiman-Lakshmibai [11], which gives an explicit Gröbner basis for the ideal of the tangent cone at any T -fixed point of a Richardson variety in the Grassmannian. Our proof uses a generalization of the RobinsonSchensted-Knuth correspondence.

We construct a template with two ribbons that describes the topology of all periodic orbits of the geodesic flow on the unit tangent bundle to any sphere with three cone points with hyperbolic metric. The construction relies on the existence of a particular coding with two letters for the geodesics on these orbifolds.