Unit Interval Orders of Open and Closed Intervals

A poset P = (X, ?) is a unit OC interval order if there exists a representation that assigns an open or closed real interval I(x) of unit length to each x ∈ P so that x ? y in P precisely when each point of I (x) is less than each point in I (y). In this paper we give a forbidden poset characterization of the class of unit OC interval orders and an efficient algorithm for recognizing the class. The algorithm takes a poset P as input and either produces a representation or returns a forbidden poset induced in P.     

On the computation of stabilized tensor functors and the relative algebraic -theory of dual numbers

We compute the stabilization of functors from exact categories to abelian groups derived from -fold tensor products. Rationally, this gives a new computation for the relative algebraic -theory of dual numbers.

     

Characterization of pyrene end-labeled poly(ethylene glycol) by high resolution MALDI time-of-flight mass spectrometry

We report the characterization of a sample of poly(ethylene glycol) (PEG, M _n = 3841, M _w/M _n = 1.01), and its derivative end-labeled with pyrenebutyrate groups, using high resolution MALDI time-of-flight mass spectrometry. A matrix of 2-(4-hydroxyphenyl-azo)benzoic acid containing a trace of either sodium chloride or potassium chloride was employed for laser desorption. Peaks due to the sodium or potassium cationized polymers were obtained, equally spaced at 44 mass units apart. For the pyrenebutyrate diester, the analysis shows that 80 ± 2% of the chains were doubly labeled, with the ramaining chains containing only a single pyrene group. Molecular weight determinations for both sets of samples were entirely consistent with size-exclusion chromatography measurements, but were obtained with greater accuracy and less ambiguity about the influence of the end groups on the hydrodynamic radius of the polymer.