The cohomology of operator algebras introduced by B. E. Johnson, R. V. Kadison, and J. R. Ringrose in a series of three papers is a useful tool for obtaining new invariants for operator algebras or to prove stability results by the vanishing of their cohomology groups (see [14]). If X is a von Neumann algebra and a Banach bimodule over M, and if « is a positive integer, then the nth cohomology ...

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 asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. the rigid disk is assumed to be in frictionless contact with the elastic half-space. by virtue of appropriate green's functions, the mixed boundary value problem is written as a dual integral equation. employing further mathematica...

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...