Posets of Matrices and Permutations with Forbidden Subsequences

The enumeration of permutations with specific forbidden subsequences has applications in areas ranging from algebraic geometry to the study of sorting algorithms. We consider a ranked poset of permutation matrices whose global structure incorporates the solution to the equivalent problem of enumerating permutations which contain a required subsequence. We describe this structure completely for saturated chains of lengths one and two, so settling several new and general instances of the original problem, and conclude with a superficial asymptotic investigation of arbitrary chains whose length is small by comparison with the rank of its constituent permutations. The value of this approach is reflected in the appearance of closed polynomial formulae (related to the Robinson-Schensted correspondence) and of a framework for the systematic analysis of associated combinatorial questions; indeed, we begin by studying a simpler poset of 0-1 sequences as the natural environment in which to introduce our insertion and deletion operators.     

Gel permeation chromatography: Effect of pore-size distribution

The pore-size distributions of various grades of porous glass were determined by gas desorption and mercury porosimeter measurements. This allowed the calculation of elution volumes as a function of pore diameters. The coil sizes of polystyrenes in toluene were obtained for a series of molecular weights from hydrodynamic theory and matched with pore diameters. In this manner, expected calibration curves for gel permeation chromatography could be calculated. Good agreement was found with experimental data.     

A wavelet,fourier, and PCA data analysis pipeline: application to distinguishing mixtures of liquids

Using a new optical engineering technique for the "fingerprinting" of beverages and other liquids, we study and evaluate a range of features. The features are based on resolution scale, invariant frequency information, entropy, and energy. They allow mixtures of beverages to be very precisely placed in principal component plots used for the data analysis. To show this we make use of data sets resulting from optical/near-infrared and ultrasound sensors. Our liquid "fingerprinting" is a relatively open analysis framework in order to cater for different practical applications, in particular, on one hand, discrimination and best fit between fingerprints, and, on the other hand, more exploratory and open-ended data mining.     

Total synthesis of deoxymannojirimycin and d-mannolactam via carbonylation of 5-vinyloxazolidin-2-ones

The stereoselective synthesis of piperidine alkaloids deoxymannojirimycin and d-mannolactam from d-serine has been achieved. The key step involves palladium-catalysed decarboxylative carbonylation of a serine-derived 5-vinyloxazolidin-2-one to give 6-(tert-butyldimethylsilyloxymethyl)-3,6-dihydro-1H-pyridin-2-one which was subsequently converted into the title compounds.     

Primary photochemical processes in the photolysis of alkyl nitrites at 366 NM and 23°c in the presence of 15NO

The alkyl nitrites, C₂H₅ONO, n-C₃H₇ONO, n-C₄H₉ONO, and i-C₄H₉ONO were photolyzed at 23°C in the presence of ¹⁵NO at 366-nm incident radiation. The quantum yields of the corresponding isotopically-enriched alkyl nitrites were measured by mass spectrometry. The results indicated that only part of the absorption leads to photodecomposition. The remainder forms an electronically excited state which isotopically exchanges with ¹⁵NO. The indicated reactions of the electronically excited state RONO*, are where k₃/k₂ = 0.50 ± 0.10, 0.62 ± 0.20, 0.42 ± 0.06, and 0.24 ± 0.03 torr, and that k_2a/k₂ = 1.0, 1.0, 0.64 ± 0.04, and 0.56 ± 0.03, respectively, for C₂H₅ONO, n-C₃H₇ONO, n-C₄H₉ONO, and i-C₄H₉ONO.