The symmetric eigenvalue complementarity problem

In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent local optimization method to converge to a solution of the (EiCP). It is further shown that similar results apply to the Symmetric Generalized Eigenvalue Complementarity Problem (GEiCP). Computational tests show that these reformulations improve the speed and robustness of the solution methods.

     

On Translation and Affine Systems Spanning L1(ℝ)

We show that the discrete translation parameter sets Λ ⊂ ℝ for which some φ ∈ L¹(ℝ) exists such that the translates φ(x − λ), λ ∈ Λ, span L¹(ℝ) are exactly the uniqueness sets for certain quasianalytic classes, and give explicit constructions of such generators φ. We also consider a similar situation for affine systems of the type φ(μx − λ), μ ∈ Γ, λ ∈ Λ.     

Marcinkiewicz–Zygmund inequalities

We study a generalization of the classical Marcinkiewicz–Zygmund inequalities. We relate this problem to the sampling sequences in the Paley–Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz–Zygmund inequalities.     

Evaluation and application of bismuth as an internal standard for the determination of lead in wines by simultaneous electrothermal atomic absorption spectrometry

A method for the direct determination of Pb in wines by simultaneous multi-element atomic absorption spectrometry (SIMAAS) using a transversely heated graphite atomizer, Zeeman-effect background corrector and internal standardization is proposed. Bismuth was used as an internal standard and Pd(NO3)2 plus Mg(NO3)2 as chemical modifier to stabilize both the analyte and the internal standard. The implementation of two pyrolysis steps avoided any build-up of carbonaceous residues on the graphite platform. All diluted samples (1 + 1 v/v) in 0.2% v/v HNO3 and reference solutions (5.0-50 microg l(-1) Pb in 0.2% v/v HNO3) were spiked with 25 microg l(-1) Bi. For a 20 microl aliquot dispensed into the graphite tube, a good correlation (r = 0.9997) was obtained between the ratio of the analyte signal to the internal standard signal and the analyte concentration of the reference solutions. The electrothermal behaviour of Pb and Bi in red, white and rosé wines were compared. In addition, absorbance variations due to changes in experimental conditions, such as atomizer temperature, integration time, injected sample volume, radiation beam intensity, graphite tube surface, dilution and sample composition, were minimized by using Bi as internal standard. Relative standard deviations of measurements based on integrated absorbance varied from 0.1 to 3.4% and from 0.5 to 7.3% (n = 12) with and without internal standard correction, respectively. Good recoveries (91-104%) for Pb spikes were obtained. The characteristic mass was 45 pg Pb and the limit of detection based on integrated absorbance was 0.9 microg l(-1) Pb. Internal standardization increased the lifetime of the tube by 25%. Direct determinations of Pb in wines with and without internal standardization approaches were in agreement at the 95% confidence level. The repeatability and the tube lifetime were improved when using Bi as internal standard. The improvement in accuracy using an internal standard was only observed when the analytical results were affected by errors.     

Chemometric interpretation of pesticide occurence in soil samples from an intensive horticulture area in north Portugal

An extensive monitoring programme of pesticides was carried out in soil samples from an intensive horticulture area in north of Portugal, putting into practice the needs for increased control of soil quality as far as organic pollution is concerned. The area under investigation was additionally defined as vulnerable to nitrates due to local soil and aquifer characteristics, which might be extended to pesticides contamination. Five sampling sites were selected and soils analysed at three depths in eight sampling campaigns, for the period of 2 years. A stepwise multivariate statistical approach was selected to uncover most relevant patterns inside a complex environmental data matrix. Cluster analysis was applied both to group pesticides and samples, giving a primary and unsupervised overlook of privileged relationships. Clusters of persistent pesticides and selected herbicides were identified, whereas sample classes were also formed and disposed geographically. Thirty eight percent of analysed soils samples fell into one class characterized by low contamination (class 1 in cluster analysis), which is entirely representative of the sampling site no. 1. Afterwards, linear discriminant analysis was applied to identify those pesticides, which had a higher impact in the definition of classes. Finally, factor analysis using a five component model was implemented in order to bring to light the constitution and data variance explained by each of the five main principal components, as well as, their relation to pest management practices. A factor was identified (PC1 – 22% variance) composed of chlorinated pesticides, which was representative of one of the investigated sites indicating its high contamination status. Qualitative main findings and class average concentration values were obtained through this multivariate statistical approach.     

CHANGES IN THE PATTERNS OF BIOSYNTHESIS and COMPOSITION OF AMINO ACIDS IN A MARINE PHYTOPLANKTER EXPOSED TO ULTRAVIOLET-B RADIATION: NITROGEN LIMITATION IMPLICATED

Abstract— The impact of ultraviolet-B radiation (UVBR) on the biosynthesis and the composition of intracellular dissolved free and combined amino acids was examined in nitrate-replete and nitrate-deficient cultures of Tetraselmis sp. Several similarities were observed in the response of Tetraselmis sp. to nitrogen deficiency and exposure to UVBR, in support of a view that UVBR affects amino acid synthesis in phytoplankton via its inhibitory effects on nitrogen assimilation into the cells. At levels that still permitted the uptake of carbon into the cells, both nitrogen deficiency and UVBR exposure resulted in a reduction in the overall rates of carbon incorporated into amino acids, an increase in the absolute concentrations of amino acids within the intracellular dissolved free amino acid (INDFAA) pool and a decrease in the total cellular amino acid (TCAA) pool. An examination of the patterns of carbon assimilation into individual amino acids in cells exposed to UVBR revealed similarities with the patterns in cells subject to nitrogen deficiency. The most conspicuous changes from the controls included an increased incorporation of ¹³C into glutamic' acid (glutamic acid + glutamine) and aspartic acid and a marked reduction into alanine and valine. Changes in the concentrations of amino acids within the INDFAA and TCAA pools were also similar in nitrate-deficient and UVBR-exposed cells and resembled the carbon assimilation patterns. These results strongly suggest that UVBR-induced changes in the biosynthesis and composition of amino acids are probably via its suppression of nitrogen assimilation into the cells.     

Chemical synthesis and firefly luciferase produced dehydroluciferyl-coenzyme A

Dehydroluciferyl-coenzyme A (L-CoA) was chemically synthesized and characterized by MS, UV-vis spectrometry and RP-HPLC. The identity of the chemically synthesized compound with the one that was produced by firefly luciferase was confirmed. Moreover, the reversibility of the enzymatic conversion of dehydroluciferin ? dehydroluciferyl-adenylate ? L-CoA was also confirmed. The chemical synthesis of L-CoA, described here, may help the clarification of the activator effect of CoA on luciferase bioluminescent assays, in which the enzyme catalyzed formation of L-CoA and the consequent destruction of L-AMP is one of the possible explanations for that effect.     

Stereoselective titanium-mediated aldol reactions of (S)-2-tert-butyldimethylsilyloxy-3-pentanone

Titanium-mediated aldol reactions based on (S)-2-tert-butyldimethylsilyloxy-3-pentanone, a lactate-derived chiral ketone, provide the corresponding 2,4-syn-4,5-syn adducts in high yields and diastereomeric ratios with a wide array of achiral and chiral aldehydes. Furthermore, spectroscopic studies of intermediates involved in the process have permitted to propose a mechanism that accounts for the experimental results.     

A new procedure for bovine milk digestion in a focused microwave oven: gradual sample addition to pre-heated acid

Milk samples can be efficiently digested using a focused microwave oven, however the conventional procedure of addition of concentrated acids to the liquid sample leads to digestates with elevated acidity and residual carbon concentrations. In this work a focused microwave oven was applied for acid digestion of bovine milk samples using a conventional and an alternative procedure based on gradual sample addition to hot and concentrated acids. A two-level 2³ full factorial design experiment with eight runs was carried out to evaluate the optimum experimental conditions for reducing both the residual carbon and the final acidity of digestates. The three studied parameters were: temperature of the digestion medium for sample addition, addition of sulfuric acid before the sample or during the first step, and number of aliquots of the sample gradually added. The best conditions were attained by adding small aliquots of milk (ten-fold a volume of 0.5 ml added during 5.0 min) to a digestion mixture containing 3.0 ml nitric acid plus 1.0 ml sulfuric acid heated at 105 °C. It was demonstrated that the digestion efficiency of the alternative procedure was better than the conventional procedure, i.e. 98 and 80%, respectively. The alternative procedure was applied for determination of Ba, Ca, Cu, K, Mg, Na, P, and Zn in whole and non-fat bovine milk. The accuracy was proved using two certified reference materials (whole and non-fat milk powder).