Given a line arrangement A with n lines, we show that there exists a path of length n/3−O(n) in the dual graph of A formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring ...

Using partitionings of quadrics we give a geometric construction of certain symmetric group divisible designs. It is shown that some of them at least are self-dual. The designs that we construct here relate to interesting work — some of it very recent — by D. Jungnickel and by E. Moorhouse. In this paper we also give a short proof of an old result of G. Pellegrino concerning the maximum size of...

Under certain conditions, a recent method of Barlet and Koziarz [2] constructs enough holomorphic functions to give a direct proof of the Stein condition for a cycle space. Here we verify those conditions for open G0–orbits on X, where G0 is the group of a bounded symmetric domain and X is its compact dual viewed as a flag quotient manifold of the complexification G of G0 . This Stein result wa...

We consider the following class of unitary representations π of some (real) Lie group G which has a matched pair of symmetries described as follows: (i) Suppose G has a period-2 automorphism τ , and that the Hilbert space H(π) carries a unitary operator J such that Jπ = (π ◦ τ)J (i.e., selfsimilarity). (ii) An added symmetry is implied if H(π) further contains a closed subspace K0 having a cert...

The following are notes on stochastic and parametric PDEs of the short course in Paris. 1 Lecture 4: Capturing Functions in Infinite Dimensions Finally, we want to give an example where the problem is to recover a function of infinitely many variables. We will first show how such problems occur in the context of stochastic partial differential equations. 1.1 Elliptic equations: general principl...

Abstract. In this article, we study the Berglund–Hübsch transpose construction W T for invertible quasihomogeneous potential W . We introduce the dual group G and establish the state space isomorphism between the Fan–Jarvis–Ruan–Witten A-model of W/G and the orbifold Milnor ring B-model of W T /G . Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for G...

We introduce observation frames as an extension of ordinary frames. The aim is to give an abstract representation of a mapping from observable predicates to all predicates of a specific system. A full subcategory of the category of observation frames is shown to be dual to the category of F! topological spaces. The notions we use generalize those in the adjunction between frames and topological...

The dual of the James Tree space is asymptotically uniformly convex.

We prove that two unital dual operator algebras A,B are stably isomorphic if and only if they are ∆-equivalent [7], if and only if they have completely isometric normal representations α, β on Hilbert spaces H,K respectively and there exists a ternary ring of operators M ⊂ B(H,K) such that α(A) = [M∗β(B)M]−w and β(B) = [Mα(A)M∗]−w .