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.

Antoine and Zouaki ([1] and [16]) have given the existence of a continuous selection of (1.1) in the particular case where M − x0 and N − y0 are closed convex cones . In this paper, we extend this result when M (resp. N) approximates continuously its Clarke tangent cone at x0 (resp. y0) (see Definition 2.2). This property is verified at x0 for an important class of sets. We get among others: se...

We analyze the properties of an interior point cutting plane algorithm that is based on a semi-infinite linear formulation of the dual semidefinite program. The cutting plane algorithm approximately solves a linear relaxation of the dual semidefinite program in every iteration and relies on a separation oracle that returns linear cutting planes. We show that the complexity of a variant of the i...

We investigate the local deformation space of 3-dimensional conemanifold structures of constant curvature κ ∈ {−1, 0, 1} and coneangles≤ π. Under this assumption on the cone-angles the singular locus will be a trivalent graph. In the hyperbolic and the spherical case our main result is a vanishing theorem for the first Lcohomology group of the smooth part of the cone-manifold with coefficients ...

We present an explicit minimal set of generators for the defining ideal family Backelin semigroups and find its Betti numbers. In particular, we compute type semigroup as well, correcting a claim in literature. Additionally, show that numbers corresponding numerical ring coincide to those tangent cone.

We give a natural way to identify between two scales, potentially arbitrarily far apart, in non-compact Ricci-flat manifold with Euclidean volume growth when tangent cone at infinity has smooth cross section. The identification map is given as the gradient flow of solution an elliptic equation.