Comment: Towards a Complete Classification of Spherically Symmetric Lorentzian Manifolds According to Their Ricci Collineations

General expressions for the components of the Ricci collineation vector are derived and the related constraints are obtained. These constraints are then solved to obtain Ricci collineations and the related constraints on the Ricci tensor components for all spacetime manifolds (degenerate or non-degenerate, diagonal or non-diagonal) admitting symmetries larger than so(3) and already known results are recovered. A complete solution is achieved for the spacetime manifolds admitting so(3) as the maximal symmetry group with non-degenerate and non diagonal Ricci tensor components. It is interesting to point out that there appear cases with finite number of Ricci collineations although the Ricci tensor is degenerate and also the cases with infinitely many Ricci collineations even in the case of non-degenerate Ricci tensor. Interestingly, it is found that the spacetime manifolds with so(3) as maximal symmetry group may admit two extra proper Ricci collineations, although they do not admit a G ₅ as the maximal symmetry group. Examples are provided which show and clarify some comments made by Camci et al. [Camci, U., and Branes, A. (2002). Class. Quantum Grav. 19, 393–404]. Theorems are proved which correct the earlier claims made in [Carot, J., Nunez, L. A., and Percoco, U. (1997). Gen. Relativ. Gravit. 29, 1223–1237; Contreras, G., Núñez, L. A., and Percolo, U. (2000). Gen. Relativ. Gravit. 32, 285–294].     

De Sitter空间中具有常均曲率的类空超曲面（Ⅱ）

设Ｍ＾ｎ是Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面，若Ｓ≤２（ｎ－１）＾１／２，则Ｍ＾ｎ是等参超曲面。     

One-pot synthesis of an ionic half-sandwich complex of neodymium. Application to isoprene polymerisation catalysis

The reaction of one equivalent of Nd(BH₄)₃(THF)₃ with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene.     

Unnatural multidentate metal ligating α-amino acids

A family of penta- and hexadentate metal ligating α-amino acids, suitably protected for Fmoc solid-phase chemistry, has been prepared. These residues incorporate the mono-amides of ethanolaminetriacetic acid, ethylenediaminetriacetic acid, and ethylenediaminetetraacetic acid as side chains. Side chains are tethered varying distances (n) from the Cα-carbon to allow metal binding events to occur at distinct distances from the peptide backbone. These residues are designed to allow the facile installation of metal chelates along a peptide backbone.     

Crystal structure and magnetic structure of TbOOH

The monoclinic modification of terbium oxide hydroxide, TbOOH, was prepared using hydrothermal technique. The crystal structure was investigated by three-dimensional single-crystal X-ray analysis and was refined to a conventional R-value of 8.1%. The space group is $\text{P2}{}_1\text{m}$, No. 11, with a = 6.04 Å, b = 3.69 Å, c = 4.33 Å, and β = 109.0°. The terbium atom is seven coordinated with oxygen atoms, and the structure is not hydrogen bonded.The compound is antiferromagnetic with a Néel temperature of 10°K. Neutron diffraction powder patterns were measured at 300°K and 4.2°K. The magnetic super lattice reflections were indexed on the basis of a monoclinic unit cell with the dimensions a_M = 2a, b_M = b, c_M = c, and β_M = β, where a, b, c, and β are the dimensions of the chemical unit cell. The structure contains two independent magnetic atoms. A nonclinear antiferromagnetic arrangement of the spins describes the magnetic structure. The spin at one atom has an angle of 43° with the ac plane and the projection of the spin on the ac plane has an angle of 59° with the a axis. The spin on the other atom has an angle of ?43° with the ac plane, the projection having the same angle of 59° with the a axis.     

Zinc porphyrin sensitized redox processes in microemulsions

Photoinduced electron transfer from Zn tetraphenylporphyrin to acceptors solubilized either in the lipid interior or aqueous bulk of anionic oil-in-water microemulsions has been investigated by nanosecond laser photolysis. While intimate cosolubilization appears to decrease the efficiency of electron transfer in the former, enhanced charge separation of the redox products has been observed in the latter.     

The de novo design of median molecules within a property range of interest

Summary In this paper an application is presented of the median molecule workflow to the de novo design of novel molecular entities with a property profile of interest. Median molecules are structures that are optimised to be similar to a set of existing molecules of interest as an approach for lead exploration and hopping. An overview of this workflow is provided together with an example of an instance using the similarity to camphor and menthol as objectives. The methodology of the experiments is defined and the workflow is applied to designing novel molecules for two physical property datasets: mean molecular polarisability and aqueous solubility. This paper concludes with a discussion of the characteristics of this method.     

Rearrangements of the carbanions derived from allyl benzyl thioether

The metalation of allyl benzyl thioether involves the benzylic or the allylic hydrogens. The benzylic carbanion undergoes a rapid[2,3] sigmatropic shift whereas the allylic carbanion gives rise to various rearrangements, among them migration of the allylic unit to the para position with allylic inversion. The temperature dependence of the ratio of products arising from the benzylic carbanion vs those from the allylic carbanion shows that the allylic-to-benzylic carbanion transformation occurs only under special conditions: (a) with slow addition of the base; (b) with thioether in excess relative to the base, and (c) on raising the temperature of the reaction medium from ?78° to ?15°. In the last instance, the proton transfer is intramolecular as shown with labeled thioethers. The extent of the different rearrangements depends on the temperature and solvent. A choice of mechanism cannot be made at this time for the para migration 5→9a. A leaving group effect on the reaction regioselectivity of the carbanion from allyl methyl thioether with benzyl halides has been noticed. The presence of dibenzyl indicates that, in addition to S_N2 reactions, some electron transfer process is occurring.     

Non planéité de cyclopenténones substituées analyse conformationnelle par résonance magnétique nucléaire

The stereochemistry of substituted cyclopent-2-en-1-ones was studied by NMR. The existence of non-planar rings is indicated and conformational analysis, based principally upon examination of the coupling constants enables the conformational population to be estimated; trans dihalogeno derivatives, for example, occur predominantly in the diaxial form.     

Vibrational spectra,normal coordinate analyses,and molecular configurations of crystalline propionic acid

Temperature dependence of the IR spectra of crystalline propionic acid were examined in the temperature range 242–50 K. The intensities of most absorption bands increased on lowering the temperature, but some bands diminished until they disappeared at temperatures lower than about 120 K. Normal coordinate analyses indicate that the former bands are due to the stable cis dimer and the latter due to the less stable trans dimer which would be produced from the cis dimer by simultaneous proton transfer along two hydrogen bonds.