Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

Analysis of natural flavonoids by microchip-micellar electrokinetic chromatography with pulsed amperometric detection

Catechins (catechin and other derivatives) are naturally occurring flavonoids present in a number of plants and foods. They are also part of numerous nutraceutical formulations because they are believed to have antioxidant, cancer chemo-preventative, anti-inflammatory and antimicrobial properties. The determination of catechins has traditionally been performed by HPLC. However, this methodology is both time and sample intensive and generates large amounts of organic solvent waste. In the current report, an application of MEKC using a PDMS microchip is presented for the analysis of catechins. The system uses pulsed amperometric detection for direct analysis of important naturally occurring catechins. The effect of pH, surfactant concentration, detection potential and signal stability were analyzed. Linear relationships were found between the concentration and peak current, with good stability and limits of detection of 8 [micro sign]M for catechin, epigallocatechin gallate and epicatechin, and 14 [micro sign]M for epicatechin gallate. Optimum conditions were applied to the detection of selected catechins in a commercially available green tea extract nutraceutical and the results were compared to HPLC analysis. The analysis using microchip micellar electrokinetic chromatography and pulsed amperometric detection was completed in 4.5 min, 10 times faster than the HPLC analysis.     

Plasma desorption mass spectrometry of transition metal complexes of thio- and selenosemicarbazones of 2-acetylpyridines

Summary Californium-252 plasma desorption mass spectra were recorded for complexes of the anions of various thio-and seleno-semicarbazones of 3-acetylpyridines(1–4) with the transition metal ions iron(III) and cobalt(II). Positive ion spectra gave clear evidence of the cation present and fragmentation with loss of ligands or parts of ligands was straightforward. Negative ion spectra likewise provided evidence of the intact anion except with tetracoordinate metal halide systems [MX₄]^– which lost one or more halide atoms. Evidence of fragmentation of the ligand and recombination of the fragments with the metal ion was also observed in the negative ion mode. Spectra were used to revise the structure of a complex previously reported as [FeLCl₂]⁽¹⁾ to [FeL₂]⁺[FeCl₄]^–.     

Electron spin resonance studies of the radiolysis of bi-π-cyclopentadienylalkyls of molybdenum and tungsten

Exposure of (C₅H₅)₂MO(CH₃)₂ and (C₅H₅)₂W(CH₃)₂, prepared from the corresponding dichlorides, to ²⁰Co γ-rays at 77 K gave H₂C.CML₃ carbene species characterised by their ESR spectra, together with a central feature possibly due to the parent cations. Dilute solutions in CD₃OD gave features assigned to the parent anions which were converted on bleaching with visible light into methyl radicals, and H₂C.ML₃ radicals. From the magnitude of the ¹H and ¹⁸³W hyperfine coupling constants, it is deduced that the SOMO for H₂C.WL₃ radicals is strongly localised on carbon.Dilute solutions in aqueous sulphuric acid also gave species with A(2H) = 20 G, identified as the carbene derivatives, H₂C.Ml₃. These were formed on annealing, as signals assigned to HSO₄ · radicals were lost.     

Visualization and characterization of electroactive defects in the native oxide film on aluminium

Spatial!y localized electrochemical activity at Al/Al2O3 electrodes has been investigated using scanning electrochemical microscopy (SECM) in order to establish the relationship between localized corrosion of Al (and Al alloys) with the defect structure of the native Al2O3 film. Local electron transfer at microscopic defects (2 to 50 microm radius) was visualized in acetonitrile solutions using the nitrobenzene/nitrobenzene radical anion (Eo approximately -1.6 V vs. Ag/Ag+) and tetracyanoquinodimethane/tetracyanoquinodimethane radical anion couples (Eo approximately -0.3 V) as redox mediators for imaging. SECM investigations revealed no significant differences in electrochemical activity at Al/AI203 electrodes in the two mediator solutions, indicating that electrical conduction at the defect sites is weakly dependent on interfacial potential and the electric field across the Al2O3 film. The density of electroactive defects observed by SECM varied by 2 to 3 orders of magnitude between electrodes prepared from the same source of Al (either 99.450% and 99.9995%) suggesting that electrical conduction in the native oxide is very sensitive to surface preparation. Defect densities as low as approximately 3 sites cm(-2) were readily measured by SECM.     

Studies of lambert's reaction: The formation of [Mn2(CO)8(μ-AsR2)2] complexes from tertiary arsines and [Mn2(CO)10] at high temperatures

Although very bulky ligands e.g.(o-MeC₆H₄)₃E or (μ-C₁₀H₇)₃E (E = P or As) are inert, the normal photochemical or thermal reaction of tertiary phosphines or arsines, L, with [Mn₂(CO)₁₀] is CO substitution with the formation of [Mn₂(CO)₈(L)₂] derivatives (I). At elevated temperatures some triarylarsines, R₃As, undergo Lambert's reaction with ligand fragmentation to give [Mn₂(CO)₈(μ-AsR₂)₂] complexes (II) (R = Ph, p-MeOC₆H₄, p-FC₆H₄, or p-CIC₆H₄) even though, in the absence of [Mn₂(CO)₁₀] R₃As are stable under the same conditions. Exceptional behaviour is exhibited by (p-Me₂NC₆H₄)_3- As which forms a product of type I; by some HN(C₆H₄)₂AsR which give a product of type II as a result of loss of the non-aryl groups R = PhCH₂, cyclo-C₆H₁₁, or MeO; and by Ph(α-C₁₀H₇₂P which is the only phosphine to form a product of type II, albeit in trace amounts only. The thermal decomposition of a n-butanol solution of [Mn₂(CO)₈(AsPh₃)₂] in a sealed tube gives C₆H₆ and [Mn₂(CO)₈(α-AsPh₂)₂], whilst in an open system in the presence of various tertiary phosphines, L, [Mn(H)(CO)₃(L)₂] are obtained. It is suggested that Lambert's reaction is a thermal fragmentation of [Mn(CO)₄(AsR₃]^* radicals, the first to be recognised. They lose the radical R^* which abstracts hydrogen from the solvent. The resulting [Mn(CO)₄(AsR₂)] moiety dimerises to [Mn₂(CO)_8-(α-AsR₂)₂]. the reaction is facilitated by the stability of the departing radical (e.g. PhCH₂ or MeO) and, as the crowding about As is relieved, by its size (e.g. Ph, cyclo-C₆H₁₁, o-MeC₆H₄, or α-C₁₀H₇). In general, phosphine-substituted radicals [Mn(CO)₄(PR)₃]^* do not undergo this decomposition, probably because the PC bonds are much stronger than AsC.     

Efforts to expand the genetic alphabet: identification of a replicable unnatural DNA self-pair

Six unnatural nucleotides featuring fluorine-substituted phenyl nucleobase analogues have been synthesized, incorporated into DNA, and characterized in terms of the structure and replication properties of the self-pairs they form. Each unnatural self-pair is accommodated in B-form DNA without detectable structural perturbation, and all are thermally stable and selective to roughly the same degree. Furthermore, the efficiency of polymerase-mediated mispair synthesis is similar for each unnatural nucleotide in the template. In contrast, the efficiency of polymerase-mediated self-pair extension is highly dependent on the specific fluorine substitution pattern. The most promising unnatural base pair candidate of this series is the 3-fluorobenzene self-pair, which is replicated with reasonable efficiency and selectivity.     

Development of a stabilized low temperature infrared absorption cell for use in low temperature and collisional cooling experiments

We have constructed a stabilized low temperature infrared absorption cell cooled by an open cycle refrigerator, which can run with liquid nitrogen from 250 to 80K or with liquid helium from 80K to a few kelvin. Several CO infrared spectra were recorded at low temperature using a tunable diode laser spectrometer. These spectra were analyzed taking into account the detailed effects of collisions on the line profile when the pressure increases. We also recorded spectra at very low pressure to accurately model the diode laser emission. Spectra of the R(2) line in the fundamental band of 13CO cooled by collisions with helium buffer gas at 10.5K and at pressures near 1 Torr have been recorded. The He-pressure broadening parameter (gamma(0) = 0.3 cm(-1) atm(-1)) has been derived from the simultaneous analysis of four spectra at different pressures.     

Molecular structure-activity relationships for the oxidation of organic compounds using mesoporous silica catalysts derivatised with bis(halogeno)dioxomolybdenum(VI) complexes

Mo K-edge XAFS spectra have been measured for ordered mesoporous silica MCM-41 grafted with the complexes [MoO2X2(thf)2] (X=Cl, Br). For grafting reactions in the absence of triethylamine, materials with 1 wt. % Mo are obtained; the Mo K-edge EXAFS results indicate the co-existence of isolated surface-fixed monomeric species [MoO2[(-O)3SiO]2(thf)(n)] and [MoO2[(-O)3SiO]X(thf)(n)]. When Et3N is used in the grafting reactions, materials with 4 wt. % Mo are obtained. The EXAFS data for the material prepared using [MoO2Cl2(thf)2] and Et3N indicate the presence of dinuclear species with two Mo(VI) centres, each with two Mo=O groups and each linked by one or two oxo bridges (Mo...Mo 3.27 A). The molybdenum centres in the material prepared using the dibromo complex comprise mainly isolated four-coordinate dioxomolybdenum(VI) and trioxomolybdenum(VI) monomeric species, with a small contribution from dimeric species. All materials were further characterised in the solid state by powder X-ray diffraction, N2 adsorption analysis, MAS NMR (13C, 29Si) and FTIR spectroscopy. The derivatised MCMs perform differently as catalysts in the liquid-phase oxidation of various olefins and alcohols with tert-butyl hydroperoxide. The highest alkene epoxidation activity was recorded for the catalysts with low metal loading, whereas the material containing oxo-bridged dimers had the highest activity for oxidation of alcohols. The recyclability of all the catalysts was tested: the catalytic activity of the derivatised materials tended to stabilize with ageing.     

Diode laser emission linewidth determination: application to H2O line profile studies in the 5 and 1.4 microm regions

In order to study absorption line profiles using the stabilized diode laser spectrometer of Laboratoire de Physique Moléculaire et Applications (LPMA), a reliable determination of the emission line shape of different diodes laser is needed. In the near infrared region (1.39 and 1.66 microm) we used Distributed Feed Back diode lasers which operate around room temperature and in the middle infrared (5 and 8 microm) we used lead salt diode lasers cooled in a helium closed cycle cryostat or in a liquid nitrogen dewar. Some results obtained in H2O line profile studies in the 1.39 and 5 microm regions are presented as examples demonstrating how absorption line profile measurements can lead to erroneous values of the spectroscopic parameters when the contribution of the diode laser emission line width is neglected.