Derivations having divergence zero onR[X,Y]

In this paper it is proved that for any ℚ-algebraR any locally nilpotentR-derivationD onR[X,Y] having divergence zero and 1 ∈ (D(X),D(Y)) (i) has a slice, and (ii)A ^D =R[P] for someP. Furthermore, it is shown that any surjectiveR-derivation onR[X,Y] having divergence zero is locally nilpotent. Connections with the Jacobian Conjecture are made.     

Universality of the double scaling limit in random matrix models

We study unitary random matrix ensembles in the critical case where the limiting mean eigenvalue density vanishes quadratically at an interior point of the support. We establish universality of the limits of the eigenvalue correlation kernel at such a critical point in a double scaling limit. The limiting kernels are constructed out of functions associated with the second Painlevé equation. This extends a result of Bleher and Its for the special case of a critical quartic potential. The two main tools we use are equilibrium measures and Riemann‐Hilbert problems. In our treatment of equilibrium measures we allow a negative density near the critical point, which enables us to treat all cases simultaneously. The asymptotic analysis of the Riemann‐Hilbert problem is done with the Deift‐Zhou steepest‐descent analysis. For the construction of a local parametrix at the critical point we introduce a modification of the approach of Baik, Deift, and Johansson so that we are able to satisfy the required jump properties exactly. © 2005 Wiley Periodicals, Inc.     

Raman scattering from antiferromagnetic spin fluctuations

A microscopic theory for the scattering of light from spin fluctuation pair modes in the two-dimensional Hubbard model is presented. Two-spin fluctuation processes with opposite momenta near the antiferromagnetic wave vectorQ=(, ) are shown to contribute in particular to the low energy part of the Raman cross section. We explicitly investigate the influence of the Raman vertex function that describes the coupling of the Raman vertex function that describes the coupling of the light to the electrons and distinguishes between the different scattering geometries. In addition we explore the dependence on the correlation strength and on the temperature.     

Intramolecular carbonyl?carbonyl interactions in W, Mo and Fe complexes containing the η-N-maleimidato ligand: X-ray, DFT and AIM studies

The crystal structures of (η⁵-C₅H₅)W(CO)₃(η¹-N-maleimidato) and (η⁵-C₅H₅)Fe(CO)₂(η¹-N-maleimidato) complexes were determined by single crystal X-ray diffraction. The molecular geometries of both structures are compared with those of the Mo analog of the W complex and ethyl-N-maleimide in order to find a relation between the geometrical features and the rate constants of the addition reaction of the sulfhydryl group of biomolecules to the ethylenic bond of the maleimidato fragment. For a deeper insight into the problem DFT calculation were performed. An analysis of atomic charges, using the CHELPG scheme, and of theoretical electron density function, using the AIM theory, was performed. In the (η⁵-C₅H₅)W(CO)₃(η¹-N-maleimidato), likewise in its Mo analog, the carbonyl?carbonyl interaction was found both for experimental and calculated structures. It is probably the first approach to explain this type of intramolecular interactions acting in organometallic compounds. This interaction can play the essential role in the reaction mechanism of nucleophilic addition to the maleimidato moiety. The AIM investigations indicate also the differences in the character of bonding between the η-N-maleimidato ligand and the central metal atom.     

Surface-induced hydrogelation

The first azo dye that gels from its aqueous solution was synthesized and its moist hydrogel was investigated with electron microscopy and atomic force microscopy; the anionic azo dye in aqueous solution forms a hydrogel on cationic surfaces even at concentrations 50 times below the minimal gelation concentration.     

Computational assessment of the electronic structures of cyclohexa-1,2,4-triene, 1-oxacyclohexa-2,3,5-triene (3delta(2)-pyran), their benzo derivatives, and cyclohexa-1,2-diene. An experimental approach to 3delta(2)-pyran.

The six-membered cyclic allenes given in the title have been studied theoretically by means of an MR-CI approach. For all compounds, the allene structures were found to be the ground states in the gas phase. In the cases of cyclohexa-1,2-diene (1), the isobenzene 2, and the isonaphthalene 7, the most stable structures having a planar allene moiety are the diradicals 1b, 2b, and 7b, representing the transition states for the racemization of 1a, 2a, and 7a and being less stable than the latter by 14.1, 8.9, and 11.2 kcal/mol, respectively. At variance with this order, the 3delta(2)-pyran 4 and the chromene 5 have the zwitterions 4c and 5c as the most stable planar structures, which lie only 1.0 and 5.4 kcal/mol above 4a and 5a, respectively. According to the simulation of the solvent effect, 4c even becomes the ground state of 4 in THF solution. The frontier orbitals of the respective states of 2 and 4 suggest different rates and sites for the reaction with nucleophiles. For the first time, the pyran 4 has been generated and trapped. As a precursor for 4, 3-bromo-4H-pyran (9) was chosen, the synthesis of which was achieved on two routes from 4H-pyran. The treatment of 9 with potassium tert-butoxide (KOt-Bu)/18-crown-6 gave 4-tert-butoxy-4H-pyran as the only discernible product, whether styrene or furan was present, indicating the interception of 4 by KOt-Bu. Finally, the disagreement between the experiment and the theory concerning the heat of formation and the electronic nature of the isobenzene 2 is resolved by demonstrating that the experimental data can provide only an upper limit of the DeltaH(f) degrees value.