In this article, we exhibit a large class of Banach spaces whose open unit balls are bounded symmetric homogeneous domains. These Banach spaces, which we call J*-algebras, are linear spaces of operators mapping one Hilbert space into another and have a kind of Jordan tripte product structure. In particular, all Hilbert spaces and all B*--algebras are J*-algebras. Moreover, all four types of the...

We first established a hyperplane restriction theorem for the local holomorphic mappings between projective spaces, which is inspired by an analogous of M. Green linear systems on $$\mathbb P^n$$ . The would then be used to prove existence sequence gaps rational proper maps complex unit balls, conjectured Huang–Ji–Yin. Our proof does not distinguish balls from other generalized and thus it simu...

We study a variant of intersection representations with unit balls, that is, unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far sets, the goal is to represent the vertices of the graph by unit balls so that the balls representing two adjacent vertices intersect if and only if the corresponding edge is near. ...

We prove some results about the Hadwiger problem of nding the Helly number for line transversals of disjoint unit disks in the plane, and about its higher-dimensional generalization to hyperplane transversals of unit balls in d-dimensional Euclidean space. These include (a) a proof of the fact that the Helly number remains 5 even for arbitrarily large sets of disjoint unit disks|thus correcting...

We provide a lower bound construction showing that the union of unit balls in R 3 has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir. Key-words: Computational geometry, Union of balls, Geometric example Une union de boules unités d'intersection non vide a une complexité quadratique Résumé : Nous proposons une construction d'un ensemble de boules d...

The contact graph of an arbitrary finite packing of unit balls in Euclidean 3-space is the (simple) graph whose vertices correspond to the packing elements and whose two vertices are connected by an edge if the corresponding two packing elements touch each other. One of the most basic questions on contact graphs is to find the maximum number of edges that a contact graph of a packing of n unit ...

This article extends recent results on log-Coulomb gases in a $$p$$ -field $$K$$ (i.e., nonarchimedean local field) to those its projective line $$\mathbb{P}^1(K)$$ , where the latter is endowed with $$PGL_2$$ -invariant Borel probability measure and spherical metric. Our first main result an explicit combinatorial formula for canonical partition function of arbitrary charge values. second call...

We give improved upper bounds on the radius of the largest ball of separable states of an m-qubit system around the maximally mixed state. The ratio between the upper bound and the best known lower bound (Hildebrand, quant.ph/0601201) thus shrinks to a constant c = p 34/27 ≈ 1.122, as opposed to a term of order √ m logm for the best upper bound known previously (Aubrun and Szarek, quant.ph/0503...

Abstract We consider the problem of computing (two-sided) Hausdorff distance between unit $\ell _{p_{1}}$ ℓ p 1 and _{p_{2}}$ 2 norm balls in finite dimensional Euclidean space for $1 \leq p_{1} &lt; p_{2} \infty $ ≤ <m...