The symmetric traveling salesman polytope and its graphical relaxation: Composition of valid inequalities

The graphical relaxation of the Traveling Salesman Problem is the relaxation obtained by requiring that the salesman visit each city at least once instead of exactly once. This relaxation has already led to a better understanding of the Traveling Salesman polytope in Cornuéjols, Fonlupt and Naddef (1985). We show here how one can compose facet-inducing inequalities for the graphical traveling salesman polyhedron, and obtain other facet-inducing inequalities. This leads to new valid inequalities for the Symmetric Traveling Salesman polytope. This paper is the first of a series of three papers on the Symmetric Traveling Salesman polytope, the next one studies the strong relationship between that polytope and its graphical relaxation, and the last one applies all the theoretical developments of the two first papers to prove some new facet-inducing results.This work was initiated while the authors were visiting the Department of Statistics and Operations Research of New York University, and continued during several visits of the first author at IASI.     

Spectrophotometric investigation of nickel(II) chloro complexes in alcoholic solutions

Summary A spectrophotometric study of Ni^II chloro complexes in the u.v.-vis. region was carried out at 25 °C and constant ionic strength of 1 mol dm^–3. A matrix rank treatment method was used to identify two successive mononuclear complexes, NiCl⁺ and NiCl₂, in the three alcohols studied viz. MeOH, EtOH and i-PrOH. The best values for the apparent overall stability constants, _j , were calculated using a program based on the least-squares method. The log ₁ and log ₂ values in MeOH, EtOH and i-PrOH are 1.3 and 1.2, 1.7 and 1.8, and 1.9 and 2.2, respectively. The stability increases directly with the mol. wt. of the solvent, or decreases as a linear function of the permittivity of the pure solvent. The electronic spectra and the formation curves of the two complexes in MeOH solutions were calculated.     

Syntheses of Strychnos and Aspidospermatan-Type Alkaloids. 8. Selective Total Syntheses of Mossambine and 14-epi-Mossambine by a Radical Cyclization Reaction(1)

Mossambine (6) was obtained by a six-step reaction sequence from the indoloazepine ester 7. Radical cyclization of the tetracyclic vinyl iodide 12a provided a racemic pentacyclic ketone 16E, which could be converted to either enantiomer by condensation with (S or R)-N,S-dimethyl-S-phenylsulfoximine and selective pyrolysis of the resulting diastereomeric alcohols 18 and 19 or 20 and 21. Selective reductions of the resolved (or racemic) ketone 16E provided mossambine (6) and its hydroxy epimer 17.     

Screening for and validated quantification of phenethylamine-type designer drugs and mescaline in human blood plasma by gas chromatography/mass spectrometry

In recent years, several newer designer drugs of the so-called 2C series such as 2C-D, 2C-E, 2C-P, 2C-B, 2C-I, 2C-T-2, and 2C-T-7 have entered the illicit drug market as recreational drugs. Some fatal intoxications involving 2C-T-7 have been reported. Only scarce data have been published about analyses of these substances in human blood and/or plasma. This paper describes a method for screening and simultaneous quantification of the above-mentioned compounds and their analog mescaline in human blood plasma. The analytes were analyzed by gas chromatography/mass spectrometry in the selected-ion monitoring mode, after mixed-mode solid-phase extraction (HCX) and derivatization with heptafluorobutyric anhydride. The method was fully validated according to international guidelines. Validation data for 2C-T-2 and 2C-T-7 were unacceptable. For all other analytes, the method was linear from 5 to 500 microg/L and the data for accuracy (bias) and precision (coefficient of variation) were within the acceptance limits of +/-15% and <15%, respectively (within +/-20% and <20% near the limit of quantification of 5 microg/L).     

Matrix influence on stability constants of 15-crown-5-alkali metal complexes measured by liquid secondary ion mass spectrometry

The liquid secondary ion mass spectra of 15-crown-5 in the presence of equimolecular mixtures of three alkali metal salts show large changes in the relative abundances of the 15-crown-5-cation complexes formed, depending on the relative concentrations of ligand and salts. These variations are due either to various desorption rates of the cationized species or to different affinities of 15-crown-5 toward the alkali metal cations. An original method allowing discrimination between desorption and complexation effects on the relative abundance of ligand-metal complex ions is described and can be applied for the calculation of their stability constants. The spectral data obtained using two different matrices demonstrate that the matrix polarity has a very important effect on the two parameters considered, i.e. the stability constants of the 15-crown-5-cation complexes and their desorption rates.     

Etude des petits cycles—XXXVII: Syntheses et proprietes spectrales du tetracyclopropylidene ([4]rotane) et des composes polycyclopropylspiraniques de la serie

The syntheses of [4]rotane and polycyclopropylspiranic derivatives are reported. One route involves the formation of cyclopropane rings from C₄-acyloins; a second route uses the dimerisation of bicyclopropylidene. Spectroscopic data do not point to any particular electronic interactions between cyclopropane rings in these compounds.     

Growth of Anodic Films on Compound Semiconductor Electrodes: InP in Aqueous (NH4)2S

Summary.  Film formation on compound semiconductors under anodic conditions is discussed. The surface properties of InP electrodes were examined following anodization in an (NH₄)₂S electrolyte. The observation of a current peak in the cyclic voltammetric curve was attributed to selective etching of the substrate and a film formation process. AFM images of samples anodized in the sulfide solution revealed surface pitting. Thicker films formed at higher potentials exhibited extensive cracking as observed by optical and electron microscopy, and this was explicitly demonstrated to occur ex situ rather than during the electrochemical treatment. The composition of the thick film was identified as In₂S₃ by EDX and XPS. The measured film thickness varies linearly with the charge passed, and comparison between experimental thickness measurements and theoretical estimates for the thickness indicate a porosity of over 70%. Cracking is attributed to shrinkage during drying of the highly porous film and does not necessarily imply stress in the wet film as grown. During the growth of the thick porous film, spontaneous current oscillations have been observed. The frequency of oscillation was found to be proportional to the current density, regardless of whether the measurements were carried out during a potential sweep or at constant potential. Thus, the charge passed per oscillation remained constant. A characteristic value of approximately 0.3 C · cm⁻² was measured under potential sweep conditions, and a similar value was obtained at constant potential. Received October 16, 2001. Accepted (revised) December 21, 2001