On the Stephani universes

The spacetimes corresponding to a weak version of the cosmological principle are considered. It appears that, starting from very different criteria, they were already obtained by Stephani and studied by Krasinski and Barnes. The only barotropic universes of this class are the Friedmann-Robertson-Walker ones. Among the others, some admit a general thermodynamic scheme; it is shown that, as for barotropic fluids, such a scheme also imposes additional symmetries.     

Present and future applications of carbon nanotubes to analytical science

This article reviews the impact of carbon nanotubes on analytical science, and the main current and future applications of carbon nanotubes in this field. Given that it is necessary to solubilize carbon nanotubes for many applications, we consider the procedures developed to achieve this. The use of carbon nanotubes in analytical chemistry as a target analyte and as an analytical tool is also discussed. Chromatographic and electrophoretic methods used to separate and characterize carbon nanotubes are presented. The use of carbon nanotubes as an analytical tool in filters and membranes, as sorbent material for solid phase extraction, in electrochemical (bio)sensors, and in separation methods is discussed. It is clear that while nanotubes are being tested for use in many different fields, their truly enormous potential has yet to be realized in analytical chemistry.Dedicated to the memory of Wilhelm Fresenius     

Magnetic relaxation of interacting co clusters: crossover from two- to three-dimensional lattices

The influence that dipole-dipole interactions exert on the dynamics of the magnetization of nanometer-sized Co clusters has been studied by means of ac and dc susceptibility experiments. These clusters grow in a quasiordered layered structure, where all relevant parameters can be tailored and measured independently. Our data show without ambiguity that the magnetic relaxation becomes slower as the degree of interaction increases. The effective activation energy increases linearly with the number of nearest neighbor clusters, evolving from the value for a 2D layer to the fully 3D behavior, which is nearly reached for five layers. The experimental results agree quantitatively with the predictions of a simple model.     

Diastereoselective synthesis of fluorinated,seven-membered beta-amino acid derivatives via ring-closing metathesis

[reaction: see text] Cis and trans seven-membered gamma,gamma-difluorinated beta-amino acid derivatives (III) have been prepared with a sequence that starts with imidoyl halides (I), which are condensed with suitable ester enolates to give intermediates (II). These, in turn, can be cyclized by means of a ring-closing olefin metathesis reaction and the product stereoselectively reduced to yield compounds (III) in good overall yields.     

Gold(I) complexes with hydrogen-bond supported heterocyclic carbenes as active catalysts in reactions of 1,6-enynes

Complexes [AuCl{C(NHR)(NHPy-2)}] (Py-2 ) 2-pyridyl; R ) Me, tBu, nBu, iPr, nheptyl) have been prepared in amodular way from [AuCl(CNPy-2)]. The carbene moiety has a hydrogen-bond supported heterocyclic structure similar to the nitrogen heterocyclic carbenes in the solid state, and in CH2Cl2 or acetone solution, which is open in the presence of MeOH. The compounds are good catalysts for the skeletal rearrangement of enynes, and for the methoxycyclization of enynes. In contrast, the complexes [AuCl{C(NHR)(NHPy-4)}] are scarcely active due to the blocking effect of the coordination position required for the catalysis by the nitrogen of the NHPy-4 group.     

Kerr–Schild Symmetries

We study continuous groups of generalized Kerr–Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.     

A special integral basis for a plane model of the Drinfeld modular curve X1(<?) mod T

In this work we get some properties of the plane model C ₁(?) (Section 3) of the reduction mod T of the Drinfeld modular curve X ₁(?). The main result is the explicit presentation of a special integral basis for this model (4.5). This integral basis is close to be minimal. Received: 23 October 1998     

Design and synthesis of a new binucleating ligand via cobalt-promoted C-N bond fusion reaction. Ligand isolation and its coordination to nickel,palladium, and platinum

A new polydentate bridging ligand, NH(4)C(5)N=NC(6)H(4)N(H)C(5)H(4)N (HL(2)), is synthesized by the cobalt-mediated phenyl ring amination of coordinated NH(4)C(5)N=NC(6)H(5). The green cobalt complex intermediate [Co(L(2))(2)](ClO(4)), [1](ClO(4)), and the free ligand HL(2) were isolated and characterized. The X-ray structure of [H(2)L(2)](ClO(4)) is reported. The ligand, upon deprotonation, behaves as a bridging ligand. It reacts with NiCl(2).6H(2)O and Na(2)[PdCl(4)] to produce dimetallic complexes, [Ni(2)Cl(2)(L(2))(2)], 2, and [Pd(2)(L(2))(2)](ClO(4))(2), [3](ClO(4))(2), respectively. X-ray structures of these two dimetallic complexes are reported. The structure of the dinickel complex, in particular, is unique. In this complex, the two deprotonated secondary amine nitrogens of the two [L(2)](-) ligands bind to two nickel centers simultaneously forming a planar Ni(2)N(2) arrangement. The complex [3](ClO(4))(2) is diamagnetic while the complex 2 is paramagnetic. The results of magnetic measurements on the dinickel complex in the temperature range 1.8-300 K are reported. The system can be described as a single spin S = 2 in the low-temperature range T < J/k whereas at high temperatures, T > J/k, it behaves as two independent spins S = 1.The reaction of [L(2)](-) with K(2)[PtCl(4)], however, yielded a monometallic platinum complex, [PtCl(3)(L(2))], 5, where the pyridyl nitrogen of the aminopyridyl function remained unused. The X-ray structure of the complex 4a is reported. The bond lengths along the ligand backbones in all the complexes indicate extensive pi-delocalization. Spectral data of the complexes are reported and compared.