Generalised 2D-correlation NMR analysis of a wine fermentation

A wine fermentation has been monitored on a daily basis by (1)H NMR spectroscopy. Following data pre-processing that includes synthesis of the spectra to ensure all peaks are of constant half-width, the series of spectra were examined using generalised two-dimensional correlation techniques. Synchronous and asynchronous data maps have been generated and employed to interpret the changes in the fermentation process as a function of time. The results illustrate the potential of high resolution NMR with multivariate data analysis as a tool for process monitoring and the manner in which two-dimensional correlation mapping can aid in data interpretation.     

The development of novel organically modified sol-gel media for use with ATR/FTIR sensing

The ability to prepare and develop novel pre-concentration media by the sol-gel process, and their integration with mid-infrared transparent waveguides has been demonstrated. This research approach resulted in a mid-infrared sensing methodology in which the properties (porosity, functionality, polarity, etc.) of the recognition layer could be tailored by variation of the sol-gel precursors and processing conditions. Cross-linker type and concentration notably influenced p-xylene absorption and diffusion rate. Unreacted silanol groups appeared to be the dominant factor in the hydrophobicity of sol-gel layers. Variation of sol-gel precursors and thermal treatment altered both film cross-link density and polarity, as demonstrated by variation in the rate of analyte diffusion and equilibrium analyte concentration. The use of a novel 1 : 1 PTMOS : DPDMS material as pre-concentration medium in this analytical sensing approach was validated through the determination of p-nitrochlorobenzene in an aqueous environment. The response demonstrated linearity between 0-30 mg L(-1) with a correlation coefficient of 0.989 and a limit of detection of 0.7 mg L(-1). Sensing times for p-nitrochlorobenzene were also reduced from several hours to 24 minutes, without loss of measurement accuracy or sensitivity, by a 10 degrees C increase in the sensing temperature and the use of a predictive Fickian model previously developed by this research group.     

Extremal Homogeneous Polynomials on Real Normed Spaces

IfPis a continuousm-homogeneous polynomial on a real normed space andPis the associated symmetricm-linear form, the ratio P/P always lies between 1 andm^m/m!. We show that, as in the complex case investigated by Sarantopoulos (1987,Proc. Amer. Math. Soc.99, 340–346), there areP's for which P/P=m^m/m! and for whichPachieves norm if and only if the normed space contains an isometric copy of ℓ^m₁. However, unlike the complex case, we find a plentiful supply of such polynomials providedm4.     

The efficiency of immobilised glutamate oxidase decreases with surface enzyme loading: an electrostatic effect, and reversal by a polycation significantly enhances biosensor sensitivity

The apparent Michaelis constant, K(M), for glutamate oxidase (GluOx) immobilised on Pt electrodes increased systematically with enzyme loading. The effect was due, at least in part, to electrostatic repulsion between neighbouring oxidase molecules and the anionic substrate, glutamate (Glu). This understanding has allowed us to increase the Glu sensitivity of GluOx-based amperometric biosensors in the linear response region (100+/-11 nA cm(-2)microM(-1) at pH 7.4; SD, n=23) by incorporating a polycation (polyethyleneimine, PEI) to counterbalance the polyanionic protein. Differences in the behaviour of glucose biosensors of a similar configuration highlight a limitation of using glucose oxidase as a model enzyme in biosensor design.     

Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularisations

This paper studies intersection theory on the compactified moduli space of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface of genus where n and d may have common factors. Because of the presence of singularities we work with the intersection cohomology groups defined by Goresky and MacPherson and the ordinary cohomology groups of a certain partial resolution of singularities of Based on our earlier work [25], we give a precise formula for the intersection cohomology pairings and provide a method to calculate pairings on The case when n = 2 is discussed in detail. Finally Witten's integral is considered for this singular case.     

Co-constructive development of a green chemistry-based model for the assessment of nanoparticles synthesis

Nanomaterials (materials at the nanoscale, ${10}^{?9}$ meters) are extensively used in several industry sectors due to the improved properties they empower commercial products with. There is a pressing need to produce these materials more sustainably. This paper proposes a Multiple Criteria Decision Aiding (MCDA) approach to assess the implementation of green chemistry principles as applied to the protocols for nanoparticles synthesis. In the presence of multiple green and environmentally oriented criteria, decision aiding is performed with a synergy of ordinal regression methods; preference information in the form of desired assignment for a subset of reference protocols is accepted. The classification models, indirectly derived from such information, are composed of an additive value function and a vector of thresholds separating the pre-defined and ordered classes. The method delivers a single representative model that is used to assess the relative importance of the criteria, identify the possible gains with improvement of the protocol’s evaluations and classify the non-reference protocols. Such precise recommendation is validated against the outcomes of robustness analysis exploiting the sets of all classification models compatible with all maximal subsets of consistent assignment examples. The introduced approach is used with real-world data concerning silver nanoparticles. It is proven to effectively resolve inconsistency in the assignment examples, tolerate ordinal and cardinal measurement scales, differentiate between inter- and intra-criteria attractiveness and deliver easily interpretable scores and class assignments. This work thoroughly discusses the learning insights that MCDA provided during the co-constructive development of the classification model.     

The Pontryagin Rings of Moduli Spaces of Arbitrary Rank Holomorphic Bundles Over a Riemann Surface

The cohomology of M(n, d), the moduli space of stable holomorphicbundles of coprime rank n and degree d and fixed determinant,over a Riemann surface of genus g 2, has been widely studiedfrom a wide range of approaches. Narasimhan and Seshadri [17]originally showed that the topology of M(n, d) depends onlyon the genus g rather than the complex structure of . An inductivemethod to determine the Betti numbers of M(n, d) was first givenby Harder and Narasimhan [7] and subsequently by Atiyah andBott [1]. The integral cohomology of M(n, d) is known to haveno torsion [1] and a set of generators was found by Newstead[19] for n = 2, and by Atiyah and Bott [1] for arbitrary n.Much progress has been made recently in determining the relationsthat hold amongst these generators, particularly in the ranktwo, odd degree case which is now largely understood. A setof relations due to Mumford in the rational cohomology ringof M(2, 1) is now known to be complete [14]; recently severalauthors have found a minimal complete set of relations for the‘invariant’ subring of the rational cohomology ofM(2, 1) [2, 13, 20, 25]. Unless otherwise stated all cohomology in this paper will haverational coefficients.     

Extendibility of homogeneous polynomials on Banach spaces

We study the -homogeneous polynomials on a Banach space that can be extended to any space containing . We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible -homogeneous polynomials on and we characterize the extendible 2-homogeneous polynomials on when is a Hilbert space, an -space or an -space.

     

Localized oscillator expansions of nuclear two-body wave functions

Harmonic oscillator expansions are applied to two-body systems simulating the deuteron, triton and alpha particle. Convergence rates in energies and wave functions can be significantly improved when the expansions are localized by first subtracting an approximate asymptotic wave function.