The cohomology ring of the complement of a central complex hyperplane arrangement is the well-studied Orlik-Solomon algebra. The homotopy group of the complement is interesting, complicated, and few results are known about it. We study the ranks for the lower central series of such a homotopy group via the linear strand of the minimal free resolution of the field C over the Orlik-Solomon algebra.

This training study investigates how children learn to refer to things unambiguously. Two hundred twenty-four children aged 2.6, 3.6, and 4.6 years were pre- and posttested for their ability to request stickers from a dense array. Between test sessions, children were assigned to a training condition in which they (a) asked for stickers from an adult, (b) responded to an adult's requests for sti...

Fitting response surface models is usually carried out using statistical packages to solve complicated equations in order to produce the estimates of the model coefficients. This paper proposes a new procedure for fitting response surface models to mixed two-level and four-level factorial designs. New and easier formulae are suggested to calculate the linear, quadratic and the interaction coeff...

Let L be the noncrossing partition lattice associated to a finite Coxeter group W. In this paper we construct explicit bases for top homology groups of intervals and rank-selected subposets L. We define multiplicative structure on Whitney in terms basis, resulting algebra has similarities Orlik-Solomon algebra. As an application, obtain four chain complexes which compute integral Milnor fibre r...

A molecular Solomon link was synthesized through the assembly of an interwoven molecular grid consisting of four bis(benzimidazolepyridyl)benzthiazolo[5,4-d]thiazole ligands and four zinc(II), iron(II), or cobalt(II) cations, followed by ring-closing olefin metathesis. NMR spectroscopy, mass spectrometry, and X-ray crystallography confirmed the doubly interlocked topology, and subsequent demeta...

We show the necessary conditions are su6cient for the existence of GDD(n; 2; 4; 1, 2) with two groups and block size four in which every block intersects each group exactly twice (even GDD’s) or in which every block intersects each group in one or three points (odd GDD’s). We give a construction for near 3-resolvable triple systems TS(n; 3; 6) for every n¿ 4, and these are used to provide const...