Subsets with Generalized Derivations Having Nilpotent Values on Lie Ideals

Let R be a prime ring, with no nonzero nil right ideal, Q the two-sided Martindale quotient ring of R, F a generalized derivation of R, L a noncommutative Lie ideal of R, and b ∈ Q. If, for any u, w ∈ L, there exists n = n(u, w) ≥1 such that (F(uw) ? bwu)ⁿ = 0, then one of the following statements holds:

1. F = 0 and b = 0;

2. R ? M₂(K), the ring of 2 × 2 matrices over a field K, b² = 0, and F(x) = ?bx, for all x ∈ R.

     

Nonempirical analysis of unusual chemical bonds. II. AlH2BH4 and AlH2C3H5

Ab initio computations have been performed on the compounds AlH₂BH₄ and AlH₂C₃H₅ in order to achieve a better understanding of the peculiar characteristics of the metal to ligand bond. Our results suggest a bidentate coordination for the tetrahydroborate complex and an η³ coordination for the allyl complex. Due to the nonrigidity of the BH and allyl complexes, possible interconversion paths between different coordination modes have also been analyzed.     

Structure,Stability, and Fragmentation of Sodium bis(2-ethylhexyl)Sulfosuccinate Negatively Charged Aggregates In Vacuo by MD Simulations

Negatively charged supramolecular aggregates formed in vacuo by n bis(2-ethylhexyl)sulfosuccinate (AOT^–) anions and n + n _c sodium counterions (i.e., [AOT _n Na _n+nc ] ^nc ) have been investigated by molecular dynamics (MD) simulations for n = 1 to 20 and n _c = –1 to –5. By comparing the maximum excess charge values of negatively and positively charged AOTNa aggregates, it is found that the charge storage capability is higher for the latter systems, the difference decreasing as the aggregation number increases. Statistical analysis of physical properties like gyration radii and moment of inertia tensors of aggregates provides detailed information on their structural properties. Even for n _c = –5, all stable aggregates show a reverse micelle-like structure with an internal core, including sodium counterions and surfactant polar heads, surrounded by an external layer consisting of the surfactant alkyl chains. Interestingly, the reverse micelle-like structure is retained also in proximity of fragmentation. Moreover, the aggregate shapes may be approximated by elongated ellipsoids whose longer axis increases with n and |n _c |. The fragmentation patterns of a number of these aggregates have also been examined and have been found to markedly depend on the aggregate charge state. The simulated fragmentation patterns of a representative aggregate show good agreement with experimental data obtained using low collision voltages. Figure

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Polyvalent scaffolds. Counting the number of seats available for eosin guest molecules in viologen-based host dendrimers

We have prepared and investigated two dendrimers based on a 1,3,5-trisubstituted benzenoid-type core, containing 9 and 21 viologen units in their branches, respectively, and terminated with tetraarylmethane derivatives. We have shown that, in dichloromethane solution, such highly charged cationic species give rise to strong host-guest complexes with the dianionic form of the red dye eosin. Upon complexation, the absorption spectrum of eosin becomes broader and is slightly displaced toward lower energies, whereas the strong fluorescence of eosin is completely quenched. Titration experiments based on fluorescence measurements have shown that each viologen unit in the dendrimers becomes associated with an eosin molecule, so that the number of positions ("seats") available for the guest molecules in the hosting dendrimer is clearly established, e.g., 21 for the larger of the two dendrimers. The host-guest interaction can be destroyed by addition of chloride ions, a procedure which permits eosin to escape from the dendrimer's interior in a controlled way and to regain its intense fluorescence. When chloride anions are precipitated out by addition of silver cations, eosin molecules re-enter the dendrimer's interior and their fluorescence again disappears.     

On the Wave Equation Associated to the Hermite and the Twisted Laplacian

The dispersive properties of the wave equation u _tt +Au=0 are considered, where A is either the Hermite operator −Δ+|x|² or the twisted Laplacian −(∇ _x −iy)²/2−(∇ _y +ix)²/2. In both cases we prove optimal L ¹−L ^∞ dispersive estimates. More generally, we give some partial results concerning the flows exp (itL ^ν ) associated to fractional powers of the twisted Laplacian for 0<ν<1.     

Application of charged single isomer derivatives of cyclodextrins in capillary electrophoresis for chiral analysis

The review focuses on the role of ionic or ionisable single isomer derivatives (SIDs) of cyclodextrins on the separation of chiral analytes in capillary electrophoresis (CE), covering the period since the year 2000. The advantages of using pure compounds are discussed, as well as the ways to optimise the separations in the context of a rational approach to these techniques. Specific attention is paid to the modulation of the selector–analyte interaction. The advantage due to a detailed knowledge of equilibria occurring in solution during the CE run is underlined, particularly in the case of the presence of metal complexes, as occurs in chiral ligand exchange capillary electrophoresis (CLECE).     

Thermodynamics of aqueous solutions of boric acid

Vapor pressures of aqueous solutions of boric acid over a wide range of acid concentrations were measured from 40 to 100°C. The results, together with solubility data taken from the literature, can be described with a thermodynamic model which uses the Wilson equations to express the activity coefficients of water and boric acid. Only three temperature independent adjustable parameters are required; one of these represents the entropy of fusion of boric acid, data which are not available in the literature.     

Eine neue Methode zum Nachweis und zur Bestimmung von Jod in organischen Substanzen

Ohne Zusammenfassung     

Mononuclear rearrangement of heterocycles in ionic liquids catalyzed by copper(II) salts

The reactivity of E- and Z-phenylhydrazones of 3-benzoyl-5-phenyl-1,2,4-oxadiazole in the presence of CuCl₂ and Cu(ClO₄)₂·6H₂O has been studied in four imidazolium ionic liquids [bmim][X] (X=BF₄⁻, PF₆⁻, SbF₆⁻ and CF₃SO₃⁻). The reaction may follow different mechanistic patterns, depending on the nature of the ionic liquid anion, accounting for both qualitative and kinetic data. In the presence of CuCl₂, two processes take place at the same time, i.e., the E?Z isomerization and the rearrangement of Z-isomer into the relevant 4-benzoylamino-2,5-diphenyl-1,2,3-triazole. In contrast, in the presence of Cu(ClO₄)₂·6H₂O, the rearrangement occurs only in solution of [bmim][BF₄] and [bmim][CF₃SO₃]. Collected data show that the effect of the ionic liquid on the isomerization and the rearrangement is different. In particular, a higher cross-linking degree seems to favour the triazole, but disfavour the E?Z isomerization.     

Absorption Spectra and Luminescence Properties of Isomeric Platinum (II) and Palladium (II) Complexes containing 1,1′-biphenyldiyl, 2-phenylpyridine,and 2,2′-bijpyridine as ligands

The absorption spectra, luminescence spectra, and luminescence lifetimes of the isomeric [M(bph)(bpy)] and [M(phpy)₂] complexes M = Pt(II) or Pd(II), bph^2? = 1,1′-biphenyl-2,2′-diyl dianion, phpy^? = 2-phenylpyridine-2′-yl anion, and bpy = 2,2′-bipyridine have been investigated and compared with those of [M(bpy)₂]²⁺ complexes and of the free protonated ligands H₂bph, Hbpy⁺, and Hphpy. In the absorption spectra, the region below 320 mm is dominated by ligand-centered (LC) transitions, whereas metal-to-ligand charge transfer (MLCT) transitions are responsible for the bands present in the near UV/VIS region. The MLCT bands move to higher energies on replacing Pt with Pd and in going from [M(bph)(bpy)] to the [M(phpy)₂] isomer. For the mixed-ligand complexes, evidence for both M → bph^2? (at higher energies) and M → bpy bands is found. The structured luminescence observed at 77 K shows lifetimes of 4.0 and 1.1 μs for [Pt(phpy)₂] and [Pt(bph)(bpy)], respectively, and 480 and 250 μs for the analogous Pd complexes. On the basis of the energy and lifetime data, the luminescence of the Pt(II) complexes is assigned to the lowest triplet MLCT excited state, whereas for the Pd complexes the luminescent state is thought to result from a mixture of MLCT and LC triplet levels.