Removal of the indigo color by laser beam–denim interaction

Our experiments show that the laser fading process removes efficiently indigo-dye from denim support. We use the beams from Nd : YAG laser (1064 nm and its second harmonic 532 nm) and CO₂ (10.6 μm) lasers. Different laser pulse parameters were used in order to obtain laser power density and fluency to start the ablation process. The purpose of this work is to determine the change of denim diffuse reflectivity spectra after laser irradiation with different wavelength and different power density. The change of diffuse reflectivity coefficient was up to 17% at 450 nm wavelength (from 8% reflectivity for unirradiated denim).     

Three cocrystals and a cocrystal salt of pyrimidin‐2‐amine and glutaric acid

Four new cocrystals of pyrimidin‐2‐amine and propane‐1,3‐dicarboxylic (glutaric) acid were crystallized from three different solvents (acetonitrile, methanol and a 50:50 wt% mixture of methanol and chloroform) and their crystal structures determined. Two of the cocrystals, namely pyrimidin‐2‐amine–glutaric acid (1/1), C₄H₅N₃·C₆H₈O₄, (I) and (II), are polymorphs. The glutaric acid molecule in (I) has a linear conformation, whereas it is twisted in (II). The pyrimidin‐2‐amine–glutaric acid (2/1) cocrystal, 2C₄H₅N₃·C₆H₈O₄, (III), contains glutaric acid in its linear form. Cocrystal–salt bis(2‐aminopyrimidinium) glutarate–glutaric acid (1/2), 2C₄H₆N₃⁺·C₆H₆O₄²⁻·2C₆H₈O₄, (IV), was crystallized from the same solvent as cocrystal (II), supporting the idea of a cocrystal–salt continuum when both the neutral and ionic forms are present in appreciable concentrations in solution. The diversity of the packing motifs in (I)–(IV) is mainly caused by the conformational flexibility of glutaric acid, while the hydrogen‐bond patterns show certain similarities in all four structures.     

Headspace solid-phase microextraction followed by gas chromatography tandem mass spectrometry for the sensitive determination of benzotriazole UV stabilizers in water samples

A sensitive procedure for the determination of five ultraviolet (UV) absorbers, belonging to the benzotriazole class, in environmental water samples is proposed. Analytes were first extracted and concentrated from the matrix and then selectively determined by gas chromatography in combination with tandem mass spectrometry detection. The high lipophilic character of some of the investigated species resulted in a strong trend to remain sorbed on solid surfaces, even after addition of considerable percentages of methanol (up to 30%) to water. Thus, minimizing sample handling during the enrichment step is mandatory in order to obtain acceptable accuracy and precision. Solid-phase microextraction (SPME), as sample preparation approach, fulfilled the above requirement and provided acceptable figures of merit for the determination of target species in environmental water samples, including raw wastewater. Optimization of SPME conditions showed that the combination of headspace extraction, with a sample temperature of 100 °C and addition of 15 mg of NaCl per milliliter of sample rendered the best compromise in terms of extraction efficiency for all species. Considering a sampling time of 30 min with a poly(dimethylsiloxane)–divinylbenzene-coated SPME fiber, limits of quantification below 2 ng l⁻¹ and relative standard deviations between 5% and 12% were achieved. Three of the five species included in this research were determined in raw wastewater with a maximum concentration of 57 ng l⁻¹ for the Tinuvin 326 UV absorber.     

Paley-Wiener Approximations and Multiscale Approximations in Sobolev and Besov Spaces on Manifolds

An approximation theory by bandlimited functions (≡ Paley-Wiener functions) on Riemannian manifolds of bounded geometry is developed. Based on this theory multiscale approximations to smooth functions in Sobolev and Besov spaces on manifolds are obtained. The results have immediate applications to the filtering, denoising and approximation and compression of functions on manifolds. There exists applications to problems arising in data dimension reduction, image processing, computer graphics, visualization and learning theory.      

Determination of nitrogen mustard hydrolysis products, ethanolamines by gas chromatography-mass spectrometry after tert-butyldimethylsilyl derivatization

A method for determining N-ethyldiethanolamine (EDEA), N-methyldiethanolamine (MDEA) and triethanolamine (TEA), hydrolysis products of nitrogen mustards, in water, urine and blood samples using gas chromatography-mass spectrometry (GC-MS) after derivatization by tert-butyldimethylsilylation (TBDMS) is described. The sample solution was evaporated to dryness, and reacted with N-methyl-N-(tert-butyldimethylsilyl)trifluoroacetamide (MTBSTFA) at 60 degrees C for 1h. The TBDMS derivatives were separated on a DB-5 column and detected by electron-ionization MS. The quantitation of EDEA, MDEA and TEA was performed by measuring the respective peak areas on the extracted ion chromatograms of m/z 216, m/z 202 and m/z 346, respectively, using nonadecane (C19), the peak area of which was measured at m/z 268, as an internal standard. When the water sample was initially analyzed, considerable loss of EDEA, MDEA and TEA occurred by evaporation. The addition of hydrochloric acid (HCl) to the water sample (final 1 mM), however, permitted quantitative recoveries to be achieved (88%, 88% and 79% for EDEA-(TBDMS)2, MDEA-(TBDMS)2 and TEA-(TBDMS)3, respectively). The limits of detections (LODs, scan mode, S/N = 3) were 2.5, 2.5 and 10 ng/ml for EDEA, MDEA and TEA, respectively. Ethanolamines could be also determined in urine samples (volume 0.1 ml), with reasonable recoveries of 72-100% by the addition of HCl (final 1 mM). For the analysis of serum samples, the sample was precipitated by the addition of perchloric acid (final 3.2%), and the resulting supernatant was neutralized with potassium carbonate, and then acidified by the addition of HCl. The recovery of TBDMS derivatives of ethanolamines was found to rather low (7-31%).     

On Birman's sequence of Hardy–Rellich-type inequalities

In 1961, Birman proved a sequence of inequalities $\{I_n\}$, for $n\in \mathbb{N}$, valid for functions in $C_0^n((0,\infty ))?L^2((0,\infty ))$. In particular, $I_1$ is the classical (integral) Hardy inequality and $I_2$ is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space $H_n([0,\infty ))$ of functions defined on $[0,\infty )$. Moreover, $f\in H_n([0,\infty ))$ implies $f^{\prime }\in H_{n?1}([0,\infty ))$; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite $b>0$, these inequalities hold on the standard Sobolev space $H_0^n((0,b))$. Furthermore, in all cases, the Birman constants ${[(2n?1)!!]}^2/2^{2n}$ in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in $L^2((0,\infty ))$ (resp., $L^2((0,b))$). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail.     

The center problem via averaging method

The averaging method has been used to study the problem of the determination of the number of hyperbolic limit cycles that can bifurcate from the period annulus of a center. In this paper we use the averaging method up to any order in the perturbation parameter to determine the center conditions of monodromic singular points of analytic planar vector fields.     

Nonequilibrium molecular dynamics of the rheological and structural properties of linear and branched molecules. Simple shear and poiseuille flows; instabilities and slip

Nonequilibrium molecular-dynamics simulations are performed for linear and branched chain molecules to study their rheological and structural properties under simple shear and Poiseuille flows. Molecules are described by a spring-monomer model with a given intermolecular potential. The equations of motion are solved for shear and Poiseuille flows with Lees and Edward's [A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972)] periodic boundary conditions. A multiple time-scale algorithm extended to nonequilibrium situations is used as the integration method, and the simulations are performed at constant temperature using Nose-Hoover [S. Nose, J. Chem. Phys. 81, 511 (1984)] dynamics. In simple shear, molecules with flow-induced ellipsoidal shape, having significant segment concentrations along the gradient and neutral directions, exhibit substantial flow resistance. Linear molecules have larger zero-shear-rate viscosity than that of branched molecules, however, this behavior reverses as the shear rate is increased. The relaxation time of the molecules is associated with segment concentrations directed along the gradient and neutral directions, and hence it depends on structure and molecular weight. The results of this study are in qualitative agreement with other simulation studies and with experimental data. The pressure (Poiseuille) flow is induced by an external force F(e) simulated by confining the molecules in the region between surfaces which have attractive forces. Conditions at the boundary strongly influence the type of the slip flow predicted. A parabolic velocity profile with apparent slip on the wall is predicted under weakly attractive wall conditions, independent of molecular structure. In the case of strongly attractive walls, a layer of adhered molecules to the wall produces an abrupt distortion of the velocity profile which leads to slip between fluid layers with magnitude that depends on the molecular structure. Finally, the molecular deformation under flow depends on the attractive force of the wall, in such a way that molecules are highly deformed in the case of strong attracting walls.