Computing the conjugate of convex piecewise linear-quadratic bivariate functions

We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and faces. Using optimal computational geometry data structures, the algorithm has a linear time worst-case complexity. We present the algorithm, and illustrate it with numerical examples. We proceed to build a toolbox for convex bivariate PLQ functions by implementing the addition, and scalar multiplication operations. Finally, we compose these operators to compute classical convex analysis operators such as the Moreau envelope, and the proximal average.     

Structural and luminescent properties of micro- and nanosized particles of lanthanide terephthalate coordination polymers

Reaction in water between rare earth ions (Ln = Y, La-Tm, except Pm) and the sodium salt of terephthalic acid leads to a family of lanthanide-based coordination polymers of general formula [Ln2(C8H4O4)3(H2O)4] n with Ln = La-Tm or Y. The isostructurality of the compounds with the previously reported Tb-containing polymer is ascertained on the basis of their X-ray powder diffraction diagrams. The coordination water molecules can be reversibly removed without destroying the crystal structure for compounds involving one of the lighter lanthanide ions (La-Eu). For compounds involving one of the heavier lanthanide ions (Tb-Tm) or yttrium, a structural change occurs during the drying process. X-ray diffraction data show this new anhydrous phase corresponding to the linking of pairs of Er(III) ions through mu-carboxylate bridges. Porosity profiles calculated for the anhydrous phases of Tb(III) and Er(III) show the presence of channels with very small sections. The luminescent properties of all the compounds have been recorded and the two most luminescent polymers, namely, the europium- and the terbium-containing ones, have been studied in more detail. Tb(III)-containing compounds display large quantum yields, up to 43%. Polyvinylpyrrolidone nanoparticles doped with [Ln2(C8H4O4)3(H2O)4] n (Ln = Eu, Tb, Er) have also been synthesized and characterized. The encapsulation of the coordination polymers results in somewhat reduced luminescence intensities and lifetime, but the nanoparticles can be dispersed in water and remain unchanged in this medium for more than 20 h.     

A selective synthesis of hydroxyborate anions as novel anchors for zirconocene catalysts

A new family of hydroxytris(pentafluorophenyl)borate anions [B(C6F5)3OH](-) associated with organic and aprotic cations c+ (imidazolium, pyrrolidinium and phosphonium) has been prepared by a general one-pot synthesis that implies the chloride borate analogues [B(C6F5)3Cl](-)[c]+. The [c]+[B(C6F5)3OH](-) salts have been isolated and fully characterized. The borate anion [B(C6F5)3OH](-) has been shown to protonate the Zr-Me bond in the Cp2ZrMe2 complex forming CH4 and the first published example of anionic [Cp2Zr(Me)OB(C6F5)3](-) species. Standard spectroscopic methods demonstrate the covalent character of the Zr metal center and the anionic character of the boron atom. This protonolysis methodology using [B(C6F5)3OH](-) anion affords a new route for the incorporation of a covalently bonded anionic functionality on organometallic complexes. This provides a new way to immobilize transition metal complexes in ionic liquids.     

Approaches to open fullerenes: synthesis and thermal stability of cis-1 bis(isobenzofuran) Diels-Alder adducts of C60

In a quest to form wider openings within the cage of the fullerene C60 through controlled bond-breaking reactions, we have examined the double saturation of adjacent C=C bonds within a six-membered ring of C60. We have investigated the double Diels-Alder cycloaddition of two tethered isobenzofurans to the fullerene C60. We obtained cis-1 adducts in good yields after reacting the methylene- or quinoxaline-tethered bis(isobenzofuran) precursors 2a-k with parent 3,6-dihydro-1,2,4,5-tetrazine (3b). The X-ray structure of the methylene-tethered bis(isobenzofuran)-C60 adduct 4b has been obtained; four-eclipsed substituents are held rigidly by the bicyclic addends. The cis-1 bis(isobenzofuran) bisadducts 4b and 4e-j are kinetically far more stable toward thermal retro-Diels-Alder fragmentation than are mono(isobenzofuran) adducts of C60, in solution and in the solid state as determined by 1H NMR spectroscopy or thermogravimetric analysis. A methodology for the reversible solubilization of other fullerene derivatives based on this work is also presented.     

Development and validation of a sensitive and selective method using GC/MS-MS for quantification of 5-fluorouracil in hospital wastewater

Pollution of the environment by pharmaceuticals is a subject of growing scientific and societal concern. However, few quantitative data have been reported concerning hospital wastewater contamination. Among the different molecules used at hospital, antineoplastic drugs appear to be of special interest, and 5-fluorouracil (5-FU) can be considered as a key compound of this therapeutic class. To monitor this pharmaceutical in hospital wastewater, a highly specific and selective method was developed using gas chromatography tandem mass spectrometry after solid-phase extraction. This sensitive method (limit of quantification = 40 ng L⁻¹) was then applied to assess sewage contamination of a middle-size hospital with oncology service located in Paris, France. Native 5-FU was detectable in 12 of the 14 analysed samples. In positive samples, concentration range was measured from 0.09 to 4.0 μg L⁻¹. Finally, a predicting model for the hospital wastewater concentrations is presented, and results of this model are discussed.     

Insight into the reactivity of olefins in the Pauson-Khand reaction

The reactivity of different Co(2)(CO)(6)-acetylene complexes in the Pauson-Khand reaction is strongly dependent on the nature of the olefin. Theoretical calculations at both the DFT and ONIOM levels are concordant with experimental observations and suggest how the olefin-cobalt interactions in the complex could have a major effect on the relative reactivity of the olefins. This study rationalizes for the first time the experimentally observed reactivity differences of cyclohexene, cyclopentene, and norbornene.     

Structure électronique et spectres de resonance paramagnétique électronique des radicaux vinyle et cyclopropyle

Résumé Une méthode de calcul dérivant des théories de champ self-consistant est utilisé pour l'étude des radicaux vinyle et cyclopropyle. L'énergie électronique et les écarts hyperfins dûs aux hydrogènes et au ¹³C ont été évalués en fonction de la géométrie du carbone radicalaire. L'angle C=-H du radical vinyle a été trouvé de l'ordre de 150°. Il est montré que les radicaux vinyle et cyclopropyle ont une structure électronique similaire qui ne peut être totalement expliquée ni par un modèle ni par un modèle classique, chaque radical présentant à la fois les deux caractères.

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A method of calculation derived from self-consistent field theories is used for a study of vinyl and cyclopropyl radicals. Electronic energy, hydrogens and ¹³C hyperfine splittings are evaluated as a function of the carbon geometry. The C=-H bond angle is found to be about 150°. It is shown that vinyl and cyclopropyl radicals have a similar electronic structure which cannot be completely interpreted neither by a classical model nor by a one, each radical presenting both and character.

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Zusammenfassung Nach einer auf dem SCF-Verfahren basierenden Methode werden Elektronenenergie, H- und ¹³C-Hyperfeinaufspaltung in Vinyl- und Cyclopropylradikalen in Abhängigkeit vom Bindungswinkel am berechnet, der sich im ersten Fall zu 150° ergibt. Es zeigt sich, daß die Elektronenstruktur der beiden behandelten Radikale ähnlich ist und daß sie weder durch ein reines - noch ein reines -Modell zu beschreiben ist.

     

Bottleable Neutral Analogues of [B2H5]− as Versatile and Strongly Binding η2 Donor Ligands

Herein we report the discovery that two bottleable, neutral, base‐stabilized diborane(5) compounds are able to bind strongly to a number of copper(I) complexes exclusively through their B?B bond. The resulting complexes represent the first known complexes containing unsupported, neutral σ_B?B diborane ligands. Single‐crystal X‐ray analyses of these complexes show that the X?Cu moiety (X=Cl, OTf, C₆F₅) lies opposite the bridging hydrogen atom of the diborane and is near perpendicular to the B?B bond, interacting almost equally with both boron atoms and causing a B?B bond elongation. DFT studies show that σ donation from and π backdonation to the pseudo‐π‐like B?B bond account for their formation. Astoundingly, these copper σ_B?B complexes are inert to ligand exchange with pyridine under either heating or photoirradiation.     

The GSI oscillation mystery

In this talk, a short discussion of the GSI anomaly is given. We discuss the physics involved using a comparison with pion decay, and explain why the observed oscillations cannot be caused by standard neutrino mixing.