Convex Transitive Norms on Spaces of Continuous Functions

A norm on a Banach space X is called maximal when no equivalentnorm has a larger group of isometries. If, besides this, thereis no equivalent norm with the same isometries (apart from itsscalar multiples), the norm is said to be uniquely maximal,which is equivalent to the convex-transitivity of X: the convexhull of the orbits under the action of the isometry group onthe unit sphere is dense in the unit ball of X. The main resultof the paper is that the complex C₀() is convex-transitive inits natural supremum norm if is a connected manifold (withoutboundary). As a complement, it is shown that if is a connectedmanifold of dimension at least two, then the diameter norm isconvex transitive on the corresponding space of real functions.2000 Mathematics Subject Classification 46B15, 47B99     

Phosphazene spirannique a partir de derives du phophore dicoordine

The reaction of azidoalcohol $\text{2}$ on triazaphosphole $\text{1}$ takes place according to pathway $\text{a}$ and not $\text{b}$, as shown by the isolation of spirannic phosphazene $\text{3}$. The diazadiphosphetidines $\text{4}$, dimers of $\text{3}$ are also caracterized.     

Measurement of the B-->pi l nu branching fraction and determination of absolute value of V(ub) with tagged B mesons

We report a measurement of the B-->pi l nu branching fraction based on 211 fb(-1) of data collected with the BABAR detector. We use samples of B0 and B+ mesons tagged by a second B meson reconstructed in a semileptonic or hadronic decay and combine the results assuming isospin symmetry to obtain B(B(0)-->pi- l+ nu) = (1.33+/-0.17stat+/-0.11syst) x 10(-4). We determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element absolute value V(ub) by combining the partial branching fractions measured in ranges of the momentum transfer squared and theoretical calculations of the form factor. Using a recent lattice QCD calculation, we find absolute value V(ub) = (4.5+/-0.5stat+/-0.3syst(+0.7) -0.5FF x 10(-3), where the last error is due to the normalization of the form factor.     

Correlation of F0F1-ATPase inhibition and antiproliferative activity of apoptolidin analogues

[structure: see text] Apoptolidin (1) exhibits potent and highly selective apoptosis inducing activity against sensitive cancer cell lines and is hypothesized to act by inhibition of mitochondrial F(0)F(1)-ATP synthase. A series of apoptolidin derivatives, including a new intermolecular Diels-Alder adduct, were analyzed for antiproliferative activity in E1A-transformed rat fibroblasts. Potent F(0)F(1)-ATPase inhibition was not a sufficient determinant of antiproliferative activity for several analogues, suggesting the existence of a secondary biological target or more complex mode of action for apoptolidin.     

Zero‐valent Iron Nanoparticles Modified Screen‐printed Electrode for FIA or HPLC Amperometric Detection of Metronidazole in Pharmaceutical Formulations

A zero‐valent iron nanoparticles modified electrode was employed as an amperometric detector in flow conditions to determine metronidazole and 2‐methyl‐5‐nitroimidazole in pharmaceutical formulations. Flow injection analysis at ?0.6 V (vs. Ag) achieved limits of detection of 2 and 6 μM for metronidazole and 2‐methyl‐5‐nitroimidazole, respectively, but the analysis was not discriminative between the two compounds. When reverse phase high performance liquid chromatography was applied previous to the electrochemical detection both analytes could be analysed simultaneously. However, the limits of detection slightly increased (10 μM) as a consequence of the use of an organic solvent and a lower sample volume. The relative standard deviation of analytical repeatability was <4.0 % in both techniques. The methods were validated by comparing the results obtained from the analysis of commercial samples with those provided by HPLC‐DAD and no significant differences were detected. Results probed that the modified electrode was a successful tool in the FIA and HPLC analysis of nitro compounds.     

Monitoring the non-radiative relaxation time of PpIX solution with Au nanoparticles using Photoacoustic Spectroscopy

In this work we have used the Photoacoustic Spectroscopy (PAS) to determine in vitro the non-radiative relaxation time (NRRT) of a protoporphyrin IX (PpIX) standard solution and samples of PpIX(1), PpIX(2) and PpIX(3) with Au nanoparticle concentrations of 0.001008, 0.00504 and 0.01008 mmol in 25 mL of water respectively. We have used PpIX disodium salt (DS) solution of 25% HCl. The results show that the NRRT average values, obtained for each one of the solution were: τ = 29 ± 0.001, 84 ± 0.001 and 62 ± 0.009 ms for PpIX(1), PpIX(2) and PpIX(3), respectively. These values were compared with some NRRT of triplet states reported in the literature for molecules with tetrapyrrolic structure, increasing the NRRT considerably. From each solution it was obtained its PAS signal phase as a function of the light modulation frequency from 17 to 80 Hz. UV-vis spectrophotometer, photoluminescence spectroscopy and Transmission Electron Microscopy (TEM) were used in order to obtain the optical absorption spectra, the photoluminescence intensities, and the gold nanoparticle sizes respectively. Our investigations are devoted to improve the thermal treatments of drugs the porphyrins as photosensitizers used in image photodynamic therapy.     

Spacecraft motion around artificial equilibrium points

The main goal of this paper is to describe the motion of a spacecraft around an artificial equilibrium point in the circular restricted three-body problem. The spacecraft is under the gravitational influence of the Sun and the Earth, as primary and secondary bodies, subjected to the force due to the solar radiation pressure and some extra perturbations. Analytical solutions for the equations of motion of the spacecraft are found using several methods and for different extra perturbations. These solutions are strictly valid at the artificial equilibrium point, but they are used as approximations to describe the motion around this artificial equilibrium point. As an application of the method, the perturbation due to the gravitational influence of Jupiter and Venus is added to a spacecraft located at a chosen artificial equilibrium point, near the \(L_3\) Lagrangian point of the Sun–Earth system. The system is propagated starting from this point using analytical and numerical solutions. Comparisons between analytical–analytical and analytical–numerical solutions for several kinds of perturbations are made to guide the choice of the best analytical solution, with the best accuracy.