Bornological convergences

We study a family of convergences (actually pretopologies) in the hyperspace of a metric space that are generated by covers of the space. This family includes the Attouch-Wets, Fell, and Hausdorff metric topologies as well as the lower Vietoris topology. The unified approach leads to new developments and puts into perspective some classical results.     

Sign Regular Matrices of Order Two

A matrix is called sign regular of order k if every minor of order i has the same sign for each i = 1,2,<, k . If an m × n matrix is sign regular of order k for k = min { m,n } then it is called sign regular. This paper studies some properties of sign regular matrices of order two. Remarkable properties are proved when the row sums of these matrices form a monotone vector.     

紧致黎曼对称空间的全测地子流形及其稳定性Ⅱ

本文决定了经典的紧致黎曼对称空间的一大批全测地子流形,并确定了它们在其包围空间中的稳定性.     

全非负阵的Hadamard—Fischer不等式的几个改进

本文讨论了全非负阵与其逆矩阵的关系，改进了关于全非负矩阵的Hadamard－Fischer不等式的几个近期结果．     

Group Codes Defined on Totally Ordered Sets

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The polytopal structure of the tight-span of a totally split-decomposable metric

The tight-span of a finite metric space is a polytopal complex that has appeared in several areas of mathematics. In this paper we determine the polytopal structure of the tight-span of a totally split-decomposable (finite) metric. These metrics are a generalization of tree-metrics and have importance within phylogenetics. In previous work, we showed that the cells of the tight-span of such a metric are zonotopes that are polytope isomorphic to either hypercubes or rhombic dodecahedra. Here, we extend these results and show that the tight-span of a totally split-decomposable metric can be broken up into a canonical collection of polytopal complexes whose polytopal structures can be directly determined from the metric. This allows us to also completely determine the polytopal structure of the tight-span of a totally split-decomposable metric. We anticipate that our improved understanding of this structure may lead to improved techniques for phylogenetic inference.     

A Pinching Theorem for Minimal Submanifolds in Sphere

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Interlacing properties of roots of certain biorthogonal polynomials

In this paper we consider the biorthogonal polynomials with respect to the measure e^-x4-y2+2τxydxdy, and show that their roots interlace. The proof involves showing total nonnegativity of matrices related to Jacobi type matrices.     

Some connections between symmetry results for semilinear PDE in real and hyperbolic spaces

Taking advantage of the “invariance” under conformal transformations of certain elliptic operators and combining it with symmetry results obtained by moving totally geodesic hypersurfaces in Hn, we are able to prove the symmetry of positive solutions of −Δu=f(r,u), in balls in Rn, for a class of nonlinearities that do not satisfy the classical hypothesis of f being decreasing in r.