Erratum to: The Wigner—Ville distribution associated with the quaternion offset linear canonical transform

Analysis Mathematica -     

Optimizing constrained subtrees of trees

Given a treeG = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the rooted subtree problem, is to find a maximum weight subtree, with a specified root, from a given set of subtrees.The second problem, called the subtree packing problem, is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root.We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial. In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by pasting together the convex hulls of the rooted subtree problems.We examine in detail the case where the set of feasible subtrees rooted at nodei consists of all subtrees with at mostk nodes. For this case we derive valid inequalities, and specify the convex hull whenk 4.Research supported in part by Nato Collaborative Research Grant CRG 900281, Science Program SC1-CT91-620 of the EEC, and contract No 26 of the programme Pôle d'attraction interuniversitaire of the Belgian government.     

Arsenic speciation in marine organisms: from the analytical methodology to the constitution of reference materials

An analytical procedure for total arsenic and arsenic species quantification in marine organisms has been developed. Fresh materials are freeze-dried and reduced to powders before analysis. Arsenic is determined either by energy dispersive X-ray fluorescence (EDXRF) directly or by inductively coupled plasma optical emission spectrometry (ICP/OES) after microwave digestion. Arsenic speciation is performed on the extracted sample using liquid chromatography coupled to ICP/OES for arsenobetaine and arsenocholine determination and to the hydride generation-quartz furnace atomic absorption spectrometric technique for arsenite, arsenate, monomethylarsonic and dimethylarsinic acids quantification. Special precautions are taken to avoid losses or contaminations as well as to prevent analytical errors during the quantification stage. Other methods are applied and the corresponding results compared for each step of the procedure. The method is finally validated by means of intercomparison studies within the Measurements and Testing Programme of the European Community (formely BCR).     

Electrochemical behaviour of an indium electrode in concentrated KOH solutions at different temperatures

Summary The electrochemical behaviour of pure indium in KOH solutions (1–4M) was studied at different temperatures (25–70°C) by potentiostatic techniques. Two anodic peaks corresponding to the formation of In(OH)₃ and In₂O₃ were observed. The heights of the two peaks increased with the increase of alkali concentration. An increase of temperature increased the peak currents and shifted their corresponding potentials to more negative values. The variation of the peak currents and peak potentials with scan rate suggested that the anodic dissolution of indium was a diffusion controlled process. In cyclic voltammetry, the reverse scan consistently showed one peak which was attributed to the reduction of anodic oxidation products into indium. X-ray diffraction analysis confirmed the presence of In(OH)₃ at the first anodic peak, In(OH)₃ and In₂O₃ at the second anodic peak and In₂O₃ in the permanent passive region.

---

Zum elektrochemischen Verhalten einer Indium-Elektrode in konzentrierter Kalilauge bei verschiedenen Temperaturen

Zusammenfassung Es wurde das Verhalten von reinem Indium in 1 – 4M KOH-Lösungen bei Temperaturen zwischen 25 und 70°C mittels potentiostatischer Methoden untersucht. Zwei anodische Peaks, entsprechend der Bildung von In(OH)₃ und In₂O₃, traten auf. Die Höhe der beiden Peaks wurde mit zunehmender Alkalikonzentration gesteigert. Eine Temperaturerhöhung verstärkte die Peakströme und verschob die entsprechenden Potentiale zu negativeren Werten. Die Abhängigkeit der Peakströme und Peakpotentiale von der Scangeschwindigkeit legte den Schluß nahe, daß die anodische Lösung von Indium in einem diffusionskontrollierten Prozeß stattfindet. Bei der cyclischen Voltammetrie zeigte der reverse Scan einheitlich einen Peak, der der Reduktion der anodischen Oxidationsprodukte zu Indium zugeschrieben wurde. Röntgendiffraktionsanalyse bestätigte die Präsenz von In(OH)₃ beim ersten anodischen Peak, In(OH)₃ beim zweiten Peak und In₂O₃ im permanent passiven Bereich.

     

Highly enantiomerically enriched chlorophosphine boranes: synthesis and applications as P-chirogenic electrophilic blocks

The stereoselective synthesis of P-chirogenic chlorophosphine boranes 4 was investigated by HCl acidolysis of the corresponding aminophosphine boranes 10. The reaction afforded the P-N bond cleavage with inversion of the configuration at the phosphorus center, leading to the chlorophosphine boranes 4 with high to excellent enantiomeric purities (80-99% ee), except in the case of the chloro-1-naphthylphenylphosphine borane 4d. Reaction conditions and workup significantly influence the enantiomeric purity of the product, with the exception of the o-anisyl- and o-tolylchlorophenylphosphine boranes, 4b and 4c, which were found to be particularly stable even after purification by chromatography on silica gel. Reaction of the chlorophosphine boranes 4 with various nucleophiles, such as carbanions, phenolates, thiophenolates, or amides, afforded the corresponding organophosphorus borane complexes via P-C, P-O, P-S, and P-N bond formation, respectively, in 34-93% yield and with up to 99% ee. This work demonstrates the importance of chlorophosphine boranes 4 as new and powerful electrophilic building blocks for the highly stereoselective synthesis of P-chirogenic organophosphorus compounds.     

Sulfation of hesperetin,naringenin and apigenin by the human cytosolic sulfotransferases: a comprehensive analysis

Abstract

Previous studies have revealed sulfation as a major pathway for the metabolism of hesperetin, naringenin and apigenin. The current study was designed to identify the human cytosolic sulfotransferase (SULT) enzyme(s) capable of sulfating these flavonoid compounds. Of the thirteen human SULTs, six (1A1, 1A2, 1A3, 1B2, 1C4, 1E1) displayed significant sulfating activity toward hesperetin, five (1A1, 1A2, 1A3, 1B2, 1C4) displayed sulfating activity towards naringenin, and four (1A1, 1A2, 1A3, 1C4) showed sulfating activity towards apigenin. Of the four human organ specimens tested, liver and intestine cytosols displayed much higher hesperetin-, naringenin- and apigenin-sulfating activity than lung and kidney cytosols. Moreover, sulfation of hesperetin, naringenin and apigenin was shown to take place in HepG2 human hepatoma cells and Caco-2 human colon adenocarcinoma cells under cultured conditions. Taken together, these results provided a biochemical basis underlying the metabolism of hesperetin, naringenin and apigenin through sulfation in humans.

     

Role of solvent in the compatibility of a vinylchloride–vinylacetate–maleic acid terpolymer and nitrocellulose blends

The compatibility of cast films of a vinylchloride–vinylacetate–maleic acid terpolymer (VMCH) and nitrocellulose (NC) blends is influenced by solvents. Transparent films of VMCH/NC blends are obtained when cast from solvents such as tetrahydrofuran or cyclohexanone, whereas hazy films are obtained when cast from solvents such as acetone or ethylacetate. Visible spectroscopy and phase morphology were used to analyse the compatibility–incompatibility of the blend. Differential scanning calorimetry (DSC) studies demonstrate that the transparent film is compatible, but the hazy film is incompatible. Fourier transform infra-red (FTIR) studies establish that a greater interaction is observed between the polymer pair in case of the compatible blend than in the case of the incompatible blend. A solvent dependency of blend compatibility is reflected in this study. The conformational state of the polymers in solution, which is responsible for the compatibility phenomena, may depend on the donor number and/or Taft-β value of the solvent. The greater the donor number and/or the Taft-β value, the higher may be the level of interaction between the solvent and the polymer molecules, which in turn may give a compatible blend after removal of the solvent.