Frequency stabilization of a frequency-doubled 1556-nm source to the 5S(1/2) ? 5D (5/2) two-photon transitions of rubidium

Improvements in the power level of sources near 1550 nm and in the efficiency of waveguide frequency doublers enabled us to lock a frequency-doubled source directly to the 5S(1/2) ? 5D(5/2) two-photon transitions near 778 nm. We obtained a sufficiently powerful second-harmonic signal, exceeding 2 mW, by doubling an external-cavity diode laser that was amplified by an erbium-doped fiber amplifier in a periodically poled LiNbO(3) channel waveguide. Our experimental scheme can be used for realizing compact, high-performance frequency standards near 1550 nm for fiber-optic communication and sensing applications.     

Spectrofluorimetric Determination of Coumarin in Commercial Tablets

A simple, rapid and effective analytical method based on fluorescence spectroscopy for the determination of coumarin in pharmaceutical formulations without pre-treatment or pre-concentration step was development. Coumarin had maximum excitation and emission at 310 nm and 390 nm, respectively. Optimum conditions for the detection of coumarin were investigated. Under optimized conditions, we observed a linear behavior for the sign of coumarin in the concentration range of 2.5 × 10⁻⁶ to 1.0 × 10⁻⁴ mol L⁻¹, with linearity of 0.998 and sensitivity of 2.9 × 10¹⁰ u.a/mol L⁻¹. The proposed method was validated in terms of accuracy, precision and specificity of coumarin using the standard addition and external calibration. It was noted that the results support (P < 0.05), indicating that the matrices were not an interference in the determination of coumarin by fluorescence spectroscopy. The results were favorable compared with those obtained by reference chromatographic methods.     

Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

We consider the class of minimal surfaces given by the graphical strips ${{\mathcal S}}We consider the class of minimal surfaces given by the graphical strips S{{\mathcal S}} in the Heisenberg group \mathbb H¹{{\mathbb {H}}^1} and we prove that for points p along the center of \mathbb H¹{{\mathbb {H}}^1} the quantity \fracs_H(S?B(p,r))r^Q-1{\frac{\sigma_H(\mathcal S\cap B(p,r))}{r^{Q-1}}} is monotone increasing. Here, Q is the homogeneous dimension of \mathbb H¹{{\mathbb {H}}^1} . We also prove that these minimal surfaces have maximum volume growth at infinity.     

Local Behavior of <Emphasis Type="Italic">p</Emphasis>-harmonic Green’s Functions in Metric Spaces

We describe the behavior of p-harmonic Green’s functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality.     

A minimum problem with free boundary for a degenerate quasilinear operator

In this paper we prove regularity (near flat points) of the free boundary 0\}\cap\Omega$" align="middle" border="0"> in the Alt-Caffarelli type minimum problem for the p-Laplace operator: 0\}}\right)dx\rightarrow \min\qquad (1 Received: 3 June 2003, Accepted: 9 June 2004, Published online: 8 February 2005Mathematics Subject Classification (2000): 35R35, 35J60The first author is partially supported by NSF Grant DMS-0202801 and NSF CAREER Grant DMS-0239771     

pH Switchable Water Dispersed Photocatalytic Nanoparticles

Photogeneration of Reactive Oxygen Species (ROS) finds applications in fields as different as nanomedicine, art preservation, air and water depollution and surface decontamination. Here we present photocatalytic nanoparticles (NP) that are active only at acidic pH while they do not show relevant ROS photo-generation at neutral pH. This dual responsivity (to light and pH) is achieved by stabilizing the surface of TiO₂ NP with a specific organic shell during the synthesis and it is peculiar of the achieved core shell-structure, as demonstrated by comparison with commercial photocatalytic TiO₂ NP. For the investigation of the photocatalytic activity, we developed two methods that allow real time detection of the process preventing any kind of artifact arising from post-treatments and delayed analysis. The reversibility of the pH response was also demonstrated as well as the selective photo-killing of cancer cells at acidic pH.     

Hardy–Sobolev Type Inequalities with Sharp Constants in Carnot–Carathéodory Spaces

We prove a generalization with sharp constants of a classical inequality due to Hardy to Carnot groups of arbitrary step, or more general Carnot–Carathéodory spaces associated with a system of vector fields of Hörmander type. Under a suitable additional assumption (see Eq. 1.6 below) we are able to extend such result to the nonlinear case \(p\not= 2\). We also obtain a sharp inequality of Hardy–Sobolev type.     

Pd(OAc)2/M(NO3)n (M = Cu(II), Fe(III); n = 2, 3): Kinetic investigations of an alternative Wacker system for the oxidation of natural olefins

Pd-catalyzed oxidative coupling of camphene by dioxygen afforded mainly a diene, which subsequently underwent oxidation to a ring-expanded β,γ-unsaturated ketone with LiNO₃ as reoxidant. However, the instability of LiNO₃ results to the decomposition of NO₃⁻ ions which subsequently deactivates the catalyst. The present investigation describes the oxidation of terpenes catalyzed by Pd(OAc)₂/M(NO₃)_n (M = Cu(II), Fe(III); n = 2 or 3), using dioxygen as final oxidant. Fe(III) and Cu(II) effectively stabilize the nitrate reoxidant as determined by the significant increase of both catalytic activity and stability of the system. Turnover frequency suggests that Fe(III) is the most efficient co-catalyst. Moreover, it is established that the co-catalysts NO₃⁻, Cu(II) and especially Fe(III) ions, change the product distribution (diene/ketone) remarkably. Their involvement in the rate-determining step was investigated and the results of the kinetic investigations clarified important aspects of Pd(II)-catalyzed oxidation reactions. The described protocol offers an alternative to the traditional Wacker system which uses CuCl₂ as co-catalyst and is not effective in promoting the oxidation of bicycle olefins.     

Development of analytical method for the quality control of the fruit bark of Punica granatum L. (pomegranate) and antichemotatic activity of extract and rich fraction in punicalagins

Pomegranate is of current interest owing to the existing potential for industrial uses of fruit peels. This includes its availability as a raw vegetable material, a byproduct that constitutes residue in the use of the species and is recognized as a functional product, and beneficial health properties, as will be demonstrated in the studies cited. Therefore, it is necessary to ensure its effectiveness and safety. Toward this end, the aim of this study was to develop and validate an analytical method for the separation and quantification of total punicalagin present in the bark of the fruit of Punica granatum by HPLC. Purity tests such as water determination and total ashes were also performed. The ability of the extract and enriched fraction of punicalagin to inhibit leukocyte migration in vitro was determined by the Boyden's chamber method. The developed HPLC method demonstrated good separation and quantification of the punicalagin α and β anomers. The method is efficient and reliable, and can ultimately be used for the analysis of the extract of pomegranate. The crude extract and the fraction of punicalagins significantly inhibited leukocyte migration at concentrations of 1 and 10 μg/mL in relation to the negative control, indicating potential antichemotactic action.