A Domain of Positivity D is an open convex cone associated with a nonsingular symmetric matrix S, called the characteristic, such that xÇzD if and only if x'Sy>0 for all y(~D* As such they were introduced by Koecher (1) in generalization of the cone of positive definite matrices studied by Siegel. The automorphisms of D are the nonsingular linear transformations mapping D onto itself. The group...

We show that if two gradient Ricci solitons are asymptotic along some end of each to the same regular cone ((0,∞)× Σ, dr + r2gΣ), then the soliton metrics must be isometric on some neighborhoods of infinity of these ends. Our theorem imposes no restrictions on the behavior of the metrics off of the ends in question and in particular does not require their geodesic completeness. As an applicatio...

we investigate buchbaum and eisenbud's construction of the second symmetric power $s_r(x)$ of a chain complex $x$ of modules over a commutative ring $r$. we state and prove a number of results from the folklore of the subject for which we know of no good direct references. we also provide several explicit computations and examples. we use this construction to prove the following ...

It is suggested recently that most of halo coronal mass ejections (CMEs) may be formed by an ice cream cone-like shell of dense CME electrons. We improve our cone model (Zhao, Plunkett and Liu, 2002) to include the contribution of the top surface of the ice cream part as well as the cone part to the shape of the halo CMEs. It is found that for an ice cream cone with a half sphere sitting on the...

We introduce exotic gapless states—‘composite Dirac liquids’—that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, inter...

An interior-point trust-region algorithm is proposed for minimization of general (perhaps, non-convex) quadratic objective function over the domain obtained as the intersection of a symmetric cone with an affine subspace. The algorithm uses a trust-region model to ensure descent on a suitable merit function. Convergence to first-order and second-order optimality conditions is proved. Numerical ...

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature F , where the defining cone of F is Γ+. F is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C, m ≥ 4.

Our original results refer to dualistic structure on primaldual interior-point methods for symmetric cone programs with linear constraints. It is shown that scalings by the Nesterov-Todd direction are generated by middle points of geodesics joining with primal interior points and dual interior points. Finally we relate power classes of search directions with geodesics and weighted geometric mea...

We define a generalized Springer correspondence for the group GL(n) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse sheaves on the nilpotent cone of GL(n) satisfying the ‘recollement’ properties, and with subquotients equivalent to categories of representations of a produc...

UNLABELLED PURPOSETo review the topographic patterns associated with keratoconus suspects and provide criteria for keratoconus screening. METHODS Case study using maps from the NIDEK OPD-Scan II and OPD Station to highlight patterns seen in keratoconic corneas. RESULTS Five criteria are listed for the detection of keratoconus: 1) apex of the cone is not centered at the 6-o'clock semi-meridi...