The Gibbs ensemble of a vortex filament

 We introduce a statistical ensemble for a single vortex filament of a three dimensional incompressible fluid. The core of the vortex is modeled by a quite generic stochastic process. We prove the existence of the partition function for both positive and a limited range of negative temperatures. Received: 31 July 2000 / Revised version: 6 March 2001 / Published online: 20 December 2001     

Exploring new directions for research in problem structuring methods: on the role of cognitive style

Prior research has argued that cognitive style can have a significant impact on group decision making. In addition, several scholars have proposed that cognitive style can play a key role in the design and use of group decision support systems. However, cognitive style has not received a great deal of attention in the problem structuring methods (PSMs) community. This is surprising, given that PSMs are specifically developed to support a group in their decision making. The purpose of this paper is thus to examine the significance of cognitive style within PSMs. The paper identifies and explores the role of four different cognitive style functions in problem structuring interventions. This analysis is carried out by focusing on the different tasks embedded within a group process supported by PSMs. Implications for the research and practice of PSMs are then discussed.     

Higher order shock waves

Shock waves and the relevant Rankine-Hugoniot conditions may be inadequate even in simple cases. As an example, the electromagnetic field generated by a point charge, whose velocity jumps from0 to a constant value, not only jumps across a spherical surface expanding at light speed, but also includes a-distribution term. This suggests that the concept of higher order shock waves be introduced, the associated compatibility conditions being also deduced.

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Sommario Il concetto di onda d'urto può rivelarsi inadeguato per descrivere situazioni anche semplici. A titolo di esempio, si determina esplicitamente l'espressione del campo elettromagnetico generato da una carica puntiforme la cui velocità passa istantaneamente da0 a un valore costante. Il campo elettromagnetico non solo è discontinuo attraverso una superficie sferica che si espande alla velocità della luce, ma include anche un termine che coinvolge la distribuzione. Ciò suggerisce di definire le onde d'urto di ordine superiore, per le quali si determinano le corrispondenti condizioni di compatibilità.

     

Preparation,characterization and a kinetic study oftrans-[Ru(NH3)4L(H2O)](PF6)2 [L=PPh3, AsPh3, or SbPh3]

Summary The complexestrans-[Ru(NH₃)₄(H₂O)PPh₃](PF₆)₂ and [Ru(NH₃)₅L](PF₆)₂, (L=AsPh₃ or SbPh₃) have been isolated and characterized by microanalysis, cyclic voltammetry and ultraviolet-visible spectroscopy. The specific rate constants for the aquation of [Ru(NH₃)₅L]²⁺ totrans-[Ru(NH₃)₄L(H₂O)]²⁺ are (2.5±0.1)×10^–5s^–1 and (1.8±0.1)×10^–5s^–1 for L=AsPh₃ and SbPh₃, respectively, at 25.0±0.1°C; =0.10 mol dm^–3, NaO₂CCF₃. Under the same conditions, the second-order rate constants for the substitution of water intrans-[Ru(NH₃)₄(H₂O)L]²⁺ by isonicotinamide (isn) are 1.2±0.1, (6.3±0.3)×10^–2 and (3.8±0.2)×10^–2 m ^–1s^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of decreasingtrans-effect is: PPh₃AsPh₃>SbPh₃. The formation constants for thetrans-[Ru(NH₃)₄L(isn)]²⁺ complexes are 75±3, (1.40±0.01)×10³ and (1.80±0.02)×10³M^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of increasingtrans-influence is: SbPh₃3PPh₃.     

The behaviour of alkylcobalt carbonyls under “oxo” conditions

Both normal and secondary alkylcobalt carbonyls are shown not to undergo isomerization under catalytic “oxo” conditions, and the relevance of this obervation for the mechanism of the “oxo” reaction is discussed.     

Effects of substrate relaxation in regular chemisorption. Hydrogen on graphite

Substrate relaxation is shown to play an important role in the 1 : 2 regular chemisorption of hydrogen atoms above alternate carbon atoms in a graphite monolayer. Binding energy, population analysis and electron density maps show that the direct HC bond is strengthened on relaxation.     

Inorganic-organic hybrids of the p,p′-diphenylmethylenediphosphinate ligand with bivalent metals: a new 2D-layered phenylphosphinate zinc(II) complex

By reaction of Zn(CH₃COO)₂ with p,p′-diphenylmethylenediphosphinic acid in water a new inorganic-organic polymeric hybrid of formula [Zn(CH₂(P(Ph)O₂)₂)] has been synthesized and completely characterized. The X-ray analysis established that the structure consists of 2D-layered polymeric array, the 2D-sheets being built up through strong covalent linkages between the zinc metal and the oxygen donors of the phenylphosphinate ligand. The 2D-layers, which are featuring a mesh-net fashion, present voids of various dimensionality, up to 24-membered rings. The organic parts of the hybrid ligand, namely the phenyl rings, are shielding the inorganic skeleton of the layers, preventing the propagation of the polymer in the third dimension. No water molecules are present in the lattice, both of coordination and crystallization. Crystal data are: monoclinic, P2₁/c, a=11.840(2), b=9.646(9), c=12.516(5) Å, β=95.03(2), V=1423.9(15) Å³, Z=4. The solid material has been characterized by ³¹P MAS NMR spectroscopy and thermogravimetric analysis.     

Structural and spectroscopic study on imidazole-copper(II)-N-protected amino acid complexes. Crystal and molecular structure of tetrakis(imidazole)copper(II)bis(N-tosylvalinate)

A pink-red air-stable, crystalline compound of empirical formula [Cu(Im)₄(N-tsval)₂] (Im=imidazole; ts=4-toluenesulfonyl group, hereafter abbreviated as tosyl;N-tsval=N-tosylvalinate monoanion) was synthesized and characterized by means of structural and spectroscopic measurements. The crystal structure of the compound was determined from three-dimensional diffractometer data. The crystals are monoclinic, space groupC2/c, a=18.952 (5),b=12.372 (2),c=17.594 (3) Å,=93.77 (2)°,Z=4. The structure was solved by the heavy-atom method and refined through least-squares calculations toR=0.035 for 2284 observed reflections. The coordination about the copper atom is elongated octahedral, with four imidazole molecules as equatorial ligands and two sulfonic oxygens in axial positions.     

Effect of core size on the partition of organic solutes in the monolayer of water-soluble nanoparticles: an ESR investigation

ESR spectroscopy has been used to study the interaction of para-pentylbenzyl hydroxyalkyl nitroxide with the monolayer of water-soluble protected gold clusters having a core diameter ranging from 1.6 to 5.3 nm. The solubilization of the nitroxide probe in the more hydrophobic environment of the monolayer strongly depends on the size of the gold core. In particular, the partition equilibrium constant increases as the nanoparticle diameter decreases. These results have been attributed to the different packing of the chains in the monolayer resulting from the different radius of curvature of the investigated nanoparticles. This represents, to the best of our knowledge, the first report demonstrating that the core size of metallic nanoparticles affects the solvating properties of the protective organic monolayer.