Averaging a transport equation with small diffusion and oscillating velocity

A complete asymptotic expansion is constructed for the transport equation with diffusion term small with respect to the convection. Error estimates are obtained by using matched asymptotic expansion technique and building all the boundary layer terms in time and in space, necessary for obtaining an accurate error estimate. Copyright © 2003 John Wiley & Sons, Ltd.     

Solid-state carbon-13 NMR Studies of vulcanized elastomers. V. Observation of new structures in sulfur-vulcanized natural rubber

The complementary application of the NMR inversion recovery measurements and the computer fitting of the overlapping spectral region is found to be a useful method for structural analysis of vulcanized natural rubber in the solid state. Since the linewidths in ¹³C-NMR spectra of solids are relatively broad compared with the differences between chemical shifts, some weak signals are completely obscured in the resulting spectra. If the resonances have sufficiently different relaxation times, such as methyl and methylene carbons, it is possible to detect neighboring heavily overlapped signals by using the inversion recovery delay τ value at which the interfering strong resonance has null intensity. The 20 resonances observed in the spectra of crosslinked rubbers are tentatively assigned to the structural units formed during the vulcanization process. It is found that vulcanizates containing smaller amounts of sulfur (1 and 3%) show insignificant changes in the NMR spectra for curing times of 30 and 90 min. Structural modifications in rubbers cured with 10% sulfur continuously increase with the increasing curing time up to 120 min, indicating a significant loss in double bonds in the later stages of the reaction.     

Universality of the dispersion to average multiplicity ratios in high-energy proton-nucleus interactions

It is shown that the existing data on the high-energy proton-nuclear emulsion interactions are consistent with the hypothesis that the ratio of the dispersion to the average multiplicity for different target nuclei is an energy independent constant, the same for all nuclei. Its value is found to be a = 0.58 ± 0.03 in agreement with the one found in proton-proton collisions.     

An insight into antimicrobial activity of the freshwater bryozoan Pectinatella magnifica

The antimicrobial activity of five crude extracts of the freshwater bryozoan Pectinatella magnifica (Leidy, 1851) was evaluated in vitro for the first time. P. magnifica acetone extract exhibited the highest antibacterial activity (minimum inhibitory concentrations (MIC) 0.004–0.350 mg/mL and MBC 0.007–0.500 mg/mL), while its methanol extract showed the most promising antifungal activity (MIC 0.03–0.12 mg/mL and MFC 0.06–0.25 mg/mL). Furthermore, at a concentration of 0.25 MIC, the methanol extract reduced biofilm formation of the bacterial strain Pseudomonas aeruginosa PAO1 in a considerable extent (59.14%). FTIR spectra of the most active extracts indicate the presence of carbonyl compounds, long-chain alcohols and/or sterols. According to the experimental data obtained, P. magnifica methanol extract may be considered as a good resource of novel natural products with potent antibiofilm activity against the bacterium well known for its resistance.     

Intermolecular central to axial chirality transfer in the self-assembled biphenyl containing amino acid-oxalamide gelators

Chiral amino acid and biphenyl incorporating oxalamide gelators 4-7 with large, 9 bond distance between chiral centres and biphenyl units have been studied. CD investigation of 4-octanol gel and the crystal structure of rac-4 reveal that efficient central to axial chirality transfer occurs by intermolecular interactions in gel and solid state assemblies.     

Depth‐resolved in vivo micro‐Raman spectroscopy of a murine skin tumor model reveals cancer‐specific spectral biomarkers

We have developed a micro‐Raman spectrometer system for use to differentiate tumor lesions from normal skin using an in vivo animal model. A study of 494 Raman spectra from 24 mice revealed different spectral patterns at different depths and between normal and tumor‐bearing skin sites. A peak at 899 cm⁻¹ (possibly from proline or fatty acids) and one with higher intensity in the 1325–1330 cm⁻¹ range (assigned to nucleic acids) were correlated with the presence of tumors, which can potentially be used as biomarkers for skin cancer detection. Spectral diagnosis performed on the murine tumor model achieved a diagnostic sensitivity of 95.8% and specificity of 93.8%. These results encourage us to develop further the use of confocal Raman spectroscopy as a clinical tool for noninvasive human skin biochemical analysis, particularly in relation to skin cancer. Copyright © 2010 John Wiley & Sons, Ltd.     

Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization

In this note, we state a representation of the Mellin transform of the exponential functional of Lévy processes in terms of generalized Weierstrass products. As by-product, we obtain a multiplicative Wiener–Hopf factorization generalizing previous results obtained by Patie and Savov (2012) [14] as well as smoothness properties of its distribution.     

Variable degree polynomial splines are Chebyshev splines

Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation diminishing, but also constructive algorithms based on knot insertion. We consider variable degree polynomial splines of order $k\geqslant 2$ spanned by $\{ 1,x,\ldots x^{k-3},(x-x_i)^{m_i-1},(x_{i+1}-x)^{n_i-1} \}$ on each subinterval $[x_i,x_{i+1}\rangle\subset [0,1]$ , i?=?0,1, ...l. Most of the paper deals with non-polynomial case m _i ,n _i ?∈?[4,?∞?), and polynomial splines known as VDP–splines are the special case when m _i , n _i are integers. We describe VDP–splines as being piecewisely spanned by a Canonical Complete Chebyshev system of functions whose measure vector is determined by positive rational functions p(x), q(x). These functions are such that variable degree splines belong piecewisely to the kernel of the differential operator $\frac{d}{dx} p \frac{d}{dx} q \frac{d^{k-2}} {dx^{k-2}}$ . Although the space of splines is not based on an Extended Chebyshev system, we argue that total positivity and variation diminishing still holds. Unlike the abstract results, constructive properties, like Marsden identity, recurrences for quasi-Bernstein polynomials and knot insertion algorithms may be more involved and we prove them only for VDP splines of orders 4 and 5.     

On possible dependence structures of a set of random variables

We give a constructive proof of existence of random vectors and discrete-time random processes with arbitrary nonsingular marginal distributions and arbitrary dependence structure. A corollary of this fact regarding Gaussian distributions is also established, as well as some abstract properties of dependence structures.