In-vial pyrolysis (PyroVial) with pre- and post-sample treatment combined with different chromatographic techniques

A new generic pyrolysis unit (PyroVial) is presented. Pyrolysis is carried out in a 2 mL autosampler vial placed in a XYZ robot for automated pyrolysis as well as for pre- and post-pyrolysis treatment of the sample. Analysis of the volatiles is performed by headspace analysis while the semi- and non-volatiles are extracted from the pyrolysate with an organic solvent. The features of the PyroVial are such that all chromatographic techniques can be applied. The pyrolysis unit is discussed in terms of its technical features and its performance is illustrated with applications including conventional pyrolysis, in situ and post-pyrolysis derivatization, reaction pyrolysis and catalytic cracking.     

Temperature program optimization by computer simulation for the capillary GC analysis of fatty acid methyl esters on biscyanopropyl siloxane phases

The selectivity of capillary columns coated with biscyanopropyl siloxane stationary phases for the separation of fatty acid methyl esters has been optimized by means of computer-assisted column temperature optimization software. Temperature programming rates yielding the highest resolution in the shortest analysis time were selected for split, splitless, and on-column injection operated in the constant pressure and pressure programmed modes.     

Considerations on the possibilities and limitations of comprehensive normal phase-reversed phase liquid chromatography (NPLC x RPLC)

A comprehensive normal phase system LC-reversed phase LC (NPLC x RPLC) was evaluated for the separation of a pharmaceutical mixture and citrus oil extracts. NPLC was performed on a 25 cm x 1 mm ID x 5 microm dp diol phase. In the second dimension, an RP 18 monolithic column (10 cm L x 4.6 mm ID x 2 microm macropore size) and an octadecyl silicagel-packed column (5 cm L x 4.6 mm ID x 3.5 microm dp) were applied for the analyses of the pharmaceutical sample and the citrus oil extracts, respectively. A two-position/ten-port switching valve was used as interface. Under optimised LC conditions, the high degree of orthogonality between NP and RP resulted in peak capacities of 300 for the pharmaceutical sample and of 450 for the citrus oil extract composed of lemon and orange oil. Despite the features of NPLC x RPLC, several shortcomings related with the solvent incompatibility between the two LC modes were identified and the practical consequences were discussed.     

A stability result using the matrix norm to bound the permanent

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose A is an n × n matrix over C (resp. R), and let P denote the set of n × n matrices over C (resp. R) that can be written as a permutation matrix times a unitary diagonal matrix. Then it is known that the permanent of A satisfies |per(A)| ≤ ||A|| ⁿ ₂ with equality iff A/||A||₂ ∈ P (where ||A||₂ is the operator 2-norm of A). We show a stability version of this result asserting that unless A is very close (in a particular sense) to one of these extremal matrices, its permanent is exponentially smaller (as a function of n) than ||A|| ⁿ ₂. In particular, for any fixed α, β > 0, we show that |per(A)| is exponentially smaller than ||A|| ⁿ ₂ unless all but at most αn rows contain entries of modulus at least ||A||₂(1?β).     

MODELS AND SUPER-MODELS: WAYS OF THINKING ABOUT PROFESSIONAL KNOWLEDGE IN MATHEMATICS TEACHING[1]

Teaching about teaching is a complex process requiring knowledge about teaching as well as knowledge about teaching about teaching. We have published findings on research carried out over the last few years about teachers’ subject knowledge. This research led to the proposal of a model for thinking about subject knowledge which distinguishes between knowledge needed to pass an examination and knowledge needed to help someone else to come to know that knowledge. The first is necessary but not sufficient for the latter. This model for thinking about subject knowledge has led to proposals for similar models for thinking about other aspects of teacher knowledge and has more recently developed into a parallel model for thinking about teacher education.