Lovelock terms and BRST cohomology

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology. © 2005 IOP Publishing Ltd.

Sobre el teorema de Liouville para funciones enteras

La idea del artículo es presentar las pruebas del teorema de Liouville sobre funciones enteras. En este trabajo recalcamos dos importantes aplicaciones, una en la demostración del teorema fundamental del álgebra y otra en el área de las aplicaciones conformes. El presente contiene una breve nota histórica de la vida de Joseph Liouville y su trabajo. También contiene la version del teorema de Liouville para funciones doblemente periódicas, funciones armónicas y aplicaciones cuasiconformes.

Low temperature X-ray structures of two crystalline forms (I) and (II) of the pyrimidine derivative and sodium channel blocker BW1003C87: 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine

The X-ray crystal structures of two crystalline forms of 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine, C10H7Cl3N4 (code name BW1003C87) (I) and (II), have been carried out at liquid nitrogen temperature. A detailed comparison of the two structures is given. Both are centrosymmetric, with structure (I) in the triclinic space group P (1) over bar unit cell a = 6.4870(10), b = 9.216(2), c = 12.016(2) angstrom, alpha = 75.78(3)degrees, beta = 89.95(3)degrees, gamma = 83.45(3)degrees, V = 691.5(2) angstrom(3), Z = 2 and density (calculated) = 1.544 Mg/m(3); and (II) in the monoclinic space group P2(1)/c, unit cell a = 12.000(2), b = 7.518(2), c = 13.450(3) angstrom, beta = 97.87(3)degrees, V = 1202.0(5) angstrom(3), Z = 4, Density (calculated) = 1.600 Mg/m(3). Structure (I) includes a solvated CH3OH in the lattice. Final R indices [I > 2sigma(I)] are R1 = 0.0427, wR2 = 0.1075 for (I) and R1 = 0.0487, wR2 = 0.1222 for (II). R indices (all data) are R1 = 0.0470, wR2 = 0.1118 for (I) and R1 = 0.0623, wR2 = 0.1299 for (II). 5-Phenyl-2,4 diaminopyrimidine and 6-phenyl-1,2,4 triazine derivatives, which include lamotrigine (3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine), have been investigated for some time for their effects on the central nervous system. Both lamotrigine and 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine (code name BW1003C87), the subject of the present study, are anticonvulsant as well as neuroprotective in models of brain ischaemia and in a model of white matter ischaemia. BW1003C87 is a sodium channel blocker which also reduces the release of the neurotransmitter glutamate. The three dimensional structures reported here form part of a newly developed data base for the detailed investigation of members of this drug family and their biological activities.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

A novel application of ratio spectra derivative spectroscopy for the determination of amphotericin in highly icteric plasma.

Derivative spectroscopy has been utilised for the determination of amphotericin in various biological matrices including plasma, serum, urine and brain tissue. Whilst these methods have all been shown to be suitable for the determination of the drug in these matrices it has been reported that the application fails in the case of highly icteric plasma, this being due to the presence of high concentrations (>50 mu M) of bilirubin. This paper details the application of ratio spectra derivative spectroscopy to overcome the interference of bilirubin with amphotericin in such situations.

Fasciola hepatica: Histological changes in the reproductive structures of triclabendazole (TCBZ)-sensitive and TCBZ-resistant flukes after treatment in vivo with TCBZ and the related benzimidazole derivative, Compound Alpha

Twenty-four shed-reared lambs were each infected orally with 250 metacercariae of Fasciola hepatica, using either the triclabendazole (TCBZ)-sensitive Cullompton isolate or the TCBZ-resistant Sligo isolate. Twelve weeks after infection the lambs were treated with TCBZ (10 mg/kg) or with the experimental fasciolicide, Compound Alpha (Cpd alpha), a benzimidazole derivative of TCBZ (15 mg/kg). The lambs were euthanised 48,72 and 96 h after TCBZ treatment, or 24, 48 and 72 h after Cpd a treatment, and flukes were collected from the liver and/or gall bladder of each animal. Untreated animals harbouring 12-week infections were euthanised 24 h after administration of anthelmintic to the treatment groups, and the untreated flukes provided control material. A semi-quantitative assessment of the degree of histological change induced by the two drugs after different times of exposure was achieved by scoring the intensity of three well-defined lesions that developed in the testes and uteri of a representative sample of flukes from each lamb. In general, it was found that in those tissues where active meiosis and/or mitosis occurred (testis, ovary, and vitelline follicles), there was progressive loss of cell content due to apparent failure of cell division to keep pace with expulsion of the mature or effete products. Further, actively dividing cell types tended to become individualised, rounded and condensed, characteristic of apoptotic cell death. Protein synthetic activity was apparently inhibited in the Mehlis' secretory cells. In the uterus, where successful formation of shelled eggs represents the culmination of a complex sequence of cytokinetic, cytological and synthetic activity involving the vitelline follicles, the ovary and the Mehlis' gland, histological evidence indicating failure of ovigenesis was evident from 24 h post-treatment onwards. The development of these lesions may be related to the known antitubulin activity of the benzimidazole class of anthelmintics, to the induction of apoptosis in cells where mitosis or meiosis has aborted due to failure of spindle formation, and to drug-induced inhibition of protein synthesis. The semi-quantitative findings indicated that Cpd a is slightly less efficacious than TCBZ itself in causing histological damage to the reproductive structures of TCBZ-sensitive flukes, and that, like TCBZ, it caused no histological damage in flukes of the TCBZ-resistant isolate. This study illustrates the potential utility of histological techniques for conveniently screening representative samples of flukes in field trials designed to validate instances of drug resistance or to test the efficacy of new products against known drug-resistant and drug-susceptible fluke isolates. It also provides reference criteria for drug-induced histopathological changes in fluke reproductive structures which may aid interpretation of TEM findings. (C) 2009 Elsevier B.V. All rights reserved.

The triazatruxene derivative azatrux binds to the parallel form of the human telomeric G-quadruplex under molecular crowding conditions: Biophysical and molecular modeling studies

The present study has employed a combination of spectroscopic, calorimetric and computational methods to explore the binding of the three side-chained triazatruxene derivative, termed azatrux, to a human telomeric G-quadruplex sequence, under conditions of molecular crowding. The binding of azatrux to the tetramolecular parallel [d(TGGGGT)](4) quadruplex in the presence and absence of crowding conditions, was also characterized. The data indicate that azatrux binds in an end-stacking mode to the parallel G-quadruplex scaffold and highlights the key structural elements involved in the binding. The selectivity of azatrux for the human telomeric G-quadruplex relative to another biologically relevant G-quadruplex (c-Kit87up) and to duplex DNA was also investigated under molecular crowding conditions, showing that azatrux has good selectivity for the human telomeric G-quadruplex over the other investigated DNA structures. (C) 2011 Elsevier Masson SAS. All rights reserved.