Seiberg–Witten theory is used to obtain new obstructions to the existence of Einstein metrics on 4-manifolds with conical singularities along an embedded surface. In the present article, the cone angle is required to be of the form 2π/p, p a positive integer, but we conjecture that similar results will also hold in greater generality. Recent work on Kähler–Einstein metrics by Chen, Donaldson, S...

Consider a proper cone K ⊂ < and its dual cone K. It is well known that the complementary slackness condition xs = 0 defines an n-dimensional manifold C(K) = { (x, s) : x ∈ K, s ∈ K, xs = 0 } ⊂ <×<. When K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. This fact proves to be very useful when optimizing over such cones, therefore it is natural to look for ...

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we present observation of polar coronal hole plumes with foot point jets that shows evidence of longitudinal acceleration. the series of event, occurring in the north coronal hole on 10 july 2010, was observed by the aia telescopes of the solar dynamic observatory (sdo mission) in the euv lines, with unprecedented details. the structures along the plume show a propagating outward velocity of ab...

Intact chicken sensory neurites have the same microtubule polarity reported for nongrowing axons in intact organisms. The assembly-favored or + ends of the microtubules are found at the distal terminal (growth cone) of the neuron. After amputation of chicken sensory neurites, the fragment removed from the cell body collapsed to a bead of axoplasm from which neurites rapidly regrew. In nine such...

A molecular basket with four cholate units assembled on a cone-shaped calix[4]arene assumed reversed micelle-like conformation in 5% methanol/carbon tetrachloride. The inwardly facing hydroxyl groups on the cholates concentrated the polar solvent from the mostly nonpolar mixture. Methanolysis of alkyl halides benefited from the concentrated pocket of methanol if the substrate was capable of ent...

Constraint qualifications (CQ) are assumptions on the algebraic description of the feasible set of an optimization problem that ensure that the KKT conditions hold at any local minimum. In this work we show that constraint qualifications based on the notion of constant rank can be understood as assumptions that ensure that the polar of the linear approximation of the tangent cone, generated by ...

In this short communication, we observe that the Graphical Traveling Salesman Polyhedron is the intersection of the positive orthant with the Minkowski sum of the Symmetric Traveling Salesman Polytope and the polar of the metric cone. This follows trivially from known facts. There are two reasons why we find this observation worth communicating none-the-less: It is very surprising; it helps to ...

In this paper we study uniqueness of Lagrange multipliers in optimization problems subject to cone constraints. The main tool in our investigation of this question will be a calculus of dual (polar) cones. We give sufficient and in some cases necessary conditions for uniqueness of Lagrange multipliers in general Banach spaces. General results are then applied to two particular examples of the s...

In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or “lift” of the convex set is especially useful if the cone admits an efficient algorithm for linear optimization over its affine slices. We show that the existence of a lift of a convex set to a cone is equival...