On the Long-Time Behaviour of Compressible Fluid Flows Subjected to Highly Oscillating External Forces

We show that the global-in-time solutions to the compressible Navier-Stokes equations driven by highly oscillating external forces stabilize to globally defined (on the whole real line) solutions of the same system with the driving force given by the integral mean of oscillations. Several stability results will be obtained.     

Oligonuclear 3d-4f complexes as tectons in designing supramolecular solid-state architectures: impact of the nature of linkers on the structural diversity

Heteronuclear cationic complexes, [LCuLn]3+ and [(LCu)2Ln]3+, were employed as nodes in designing high-nuclearity complexes and coordination polymers with a rich variety of network topologies (L is the dianion of the Schiff base resulting from the 2:1 condensation of 3-methoxysalycilaldehyde with 1,3-propanediamine). Two families of linkers have been chosen: the first consists of exo-dentate ligands bearing nitrogen-donor atoms (bipyridine (bipy), dicyanamido (dca)), whereas the second consists of exo-dentate ligands with oxygen-donor atoms (anions derived from the acetylenedicarboxylic (H2acdca), fumaric (H2fum), trimesic (H3trim), and oxalic (H2ox) acids). The ligands belonging to the first family prefer copper(II) ions, whereas the ligands from the second family interact preferentially with oxophilic rare-earth cations. The following complexes have been obtained and crystallographically characterized: [LCu(II)(OH2)Gd(III)(NO3)3] (1), [{LCu(II)Gd(III)(NO3)3}2(mu-4,4'-bipy)] (2), 1infinity[LCu(II)Gd(III)(acdca)(1.5)(H2O)2].13H2O (3), 2infinity[LCu(II)Gd(III)(fum)(1.5)(H2O)2].4H2O.C2H5OH (4), 1infinity[LCu(II)Sm(III)(H2O)(Hfum)(fum)] (5), 1infinity[LCu(II)Er(III)(H2O)2(fum)]NO3.3H2O (6), 2infinity[LCu(II)Sm(III)(fum)(1.5)(H2O)2].4H2O.C2H5OH (7), [{(LCu(II))2Sm(III)}2fum2](OH)2 (8), 1infinity[LCu(II)Gd(III)(trim)(H2O)2].H2O (9), 2infinity[{(LCu(II))2Pr(III)}(C2O4)(0.5)(dca)]dca.2H2O (10), [LCu(II)Gd(III)(ox)(H2O)3][Cr(III)(2,2'-bipy)(ox)2].9H2O (11), and [LCuGd(H2O)4{Cr(CN)6}].3H2O (12). Compound 1 is representative of the whole family of binuclear Cu(II)-Ln(III) complexes which have been used as precursors in constructing heteropolymetallic complexes. The rich variety of the resulting structures is due to several factors: 1) the nature of the donor atoms of the linkers, 2) the preference of the copper(II) ion for nitrogen atoms, 3) the oxophilicity of the lanthanides, 4) the degree of deprotonation of the polycarboxylic acids, 5) the various connectivity modes exhibited by the carboxylato groups, and 6) the stoichiometry of the final products, that is, the Cu(II)/Ln(III)/linker molar ratio. A unique cluster formed by 24 water molecules was found in crystal 11. In compounds 2, 3, 4, 9, and 11 the Cu(II)-Gd(III) exchange interaction was found to be ferromagnetic, with J values in the range of 3.53-8.96 cm(-1). Compound 12 represents a new example of a polynuclear complex containing three different paramagnetic ions. The intranode Cu(II)-Gd(III) ferromagnetic interaction is overwhelmed by the antiferromagnetic interactions occurring between the cyanobridged Gd(III) and Cr(III) ions.     

Attempts to Access a Series of Pyrazoles Lead to New Hydrazones with Antifungal Potential against Candida species including Azole-Resistant Strains

The treatment of benzylidenemalononitriles with phenylhydrazines in refluxing ethanol did not provide pyrazole derivatives, but instead furnished hydrazones. The structure of hydrazones was secured by X-ray analysis. The chemical proof was also obtained by direct reaction of 3,4,5-trimethoxybenzaldehyde with 2,4-dichlorophenylhydrazine. Newly synthesized hydrazones were tested against eight Candida spp. strains in a dose response assay to determine the minimum inhibitory concentration (MIC₉₉). Five compounds were identified as promising antifungal agents against Candida spp. (C. albicans SC5314, C. glabrata, C. tropicalis, C. parapsilosis and C. glabrata (R azoles)), with MIC₉₉ values ranging from 16 to 32 µg/mL and selective antifungal activity over cytotoxicity.     

Nitrogen-Based Linkers with a Mesitylene Core: Synthesis and Characterization

Mesitylene was used as a core in seven new tritopic nitrogen containing linkers. Three of the linkers, each containing three nitrile groups, were obtained through Suzuki, Sonogashira and Heck-type coupling reactions. Next, these were converted to tetrazol-5-yl moieties by the cycloaddition of sodium azide to the nitrile functionalities. The last linker, containing three 1,2,3-triazol-4-yl moieties, was synthesized by the Huisgen cycloaddition of phenyl azide to the corresponding alkyne. The latter was obtained via a Corey–Fuchs reaction sequence from the previously reported formyl derivative. As the proof of concept for their potential in MOF design, one of the nitriles was used to build an Ag-based network.     

A Neo2 bayesian foundation of the maxmin value for two-person zero-sum games

A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows andn columns). Preferences over acts are complete, transitive, continuous, monotonie and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the correspondingm × n utility matrix (viewed as a two-person zero-sum game). An alternative statement of the result deals simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.We are indebted to Jacques Drèze, Andreu Mas-Colell, Roger Myerson and Reinhard Selten for helpful comments.     

Formation of singularities for wave equations including the nonlinear vibrating string

Under very general assumptions, the authors prove that smooth solutions of quasilinear wave equations with small-amplitude periodic initial data always develop singularities in the second derivatives in finite time. One consequence of these results is the fact that all solutions of the classical nonlinear vibrating string equation satisfying either Dirichlet or Neumann boundary conditions and with sufficiently small nontriviai initial data necessarily develop singularities. In particular, there are no nontrivial smooth small-amplitude time-periodic solutions.     

Effects of peripheral substituents and axial ligands on the electronic structure and properties of iron phthalocyanine

The effects of peripheral substituents and axial ligands on the electronic structure and properties of iron phthalocyanine, H(16)PcFe, have been investigated using a DFT method. Substitution by electron-withdrawing fluorinated groups alters the ground state of H(16)PcFe and gives rise to large changes in the ionization potentials and electron affinity. For the six-coordinate adducts with acetone, H(2)O, and pyridine, the axial coordination of two weak-field ligands leads to an intermediate-spin ground state, while the strong-field ligands make the system diamagnetic. The electronic configuration of a ligated iron phthalocyanine is determined mainly by the axial ligand-field strength but can also be affected by peripheral substituents. Axial ligands also exert an effect on ionization potentials and electron affinity and can, as observed experimentally, even change the site of oxidation/reduction.     

Distinguishing between abstraction and addition as the first step in the reaction of a nitroxyl radical with cyclohexene

An unambiguous method for distinguishing between abstraction-addition and addition-abstraction mechanisms (and mixtures thereof) in the reaction of 4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl with a specifically deuterated cyclohexene, 1,2-dideuteriocyclohexene, is demonstrated.