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).     

Vacancies in the solids of low molecular weight organic compounds observed by positron annihilation

PAL were measured for several low molecular organic compounds, normal and cyclic-hydrocarbons and their perfluorinated ones, from room temperature down to about 40 K, and information about the vacancies in them has been extracted from ₃ andI ₃. Normally the size of vacancies were larger in the solids comprising larger molecules, showing thato-Ps can represent the vacancy size. In a special case of perfluorocyclohexane whose solid had to be prepared by sublimation the vacancy size was larger than expected. In all the solid molecules studied twoo-Ps states could be observed and their relative importance could easily change showing a hysteresis-like behavior. At further lower temperatures of around 40 K theo-Ps state with longer lifetime and larger intensity became overwhelming for all molecules. Also ₃ andI ₃ were not very sensitive to most of the phase transitions, including the melting points.     

Chromium(III) complexes of naturally occurring amino acids

Summary Amino acid complexes of CrCl₃Py₃ have been prepared and studied by elemental analysis, magnetic susceptibility, vibrational (i.r.), electronic and circular dichroism spectroscopy. Two peaks in the visible spectra are assigned to a d-d transition in pseudo octahedral symmetry. The spectrochemical parameters (Dq, B and ₃₅) for the complexes were calculated which confirm that pyridine nitrogen and/or chlorine are not removed. Prolonged heating or bubbling of air through the solution of CrCl₃-Py₃ containing l-(-)-histidine or l-(-)-threonine for several hours enhanced formation of chromium (VI).     

Synthetic strategies and functional reactivity of versatile thiophene synthons

Abstract

Thiophenes are a highly important group of heterocycles and have been of great interest to researchers due to their various reactivities. Many synthetic strategies are used to generate functionalized thiophene derivatives. Several reactions are described, depending on the reactivity of the substituents attached to the thiophene nucleus toward different nucleophiles to yield the versatile thiophene products. Many diverse applications have been utilized for thiophenes from medicinal chemistry to material science.     

Negative ion mass spectra of some unsaturated C-glycosides following keV ion bombardment

A series of anomeric unsaturated C-glycosides were studied by negative ion mass spectrometry following keV ion bombardment The compounds bearing an acidic hydrogen show a prominent [M ? H]^? peak; in the other cases, the [M ? H]^? peak is of very low intensity. A retro-Diels–Alder fragmentation and the abstraction of a hydrogen atom from the aglycon residue are observed in all cases.     

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.

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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.