High performance parallel numerical methods for Volterra equations with weakly singular kernels

Non-stationary discrete time waveform relaxation methods for Abel systems of Volterra integral equations using fractional linear multistep formulae are introduced. Fully parallel discrete waveform relaxation methods having an optimal convergence rate are constructed. A significant expression of the error is proved, which allows us to estimate the number of iterations needed to satisfy a prescribed tolerance and allows us to identify the problems where the optimal methods offer the best performance. The numerical experiments confirm the theoretical expectations.     

A closed-form solution in a dynamical system related to Bianchi IX

The Bianchi IX cosmological model in vacuum can be represented by several six-dimensional dynamical systems. In one of them we present a new closed form solution expressed by a third Painlevé function.     

Differentiation among dairy products by combination of fast field cycling NMR relaxometry data and chemometrics

A set of commercial milk and Sicilian cheeses was analysed by a combination of fast field cycling (FFC) nuclear magnetic resonance (NMR) relaxometry and chemometrics. The NMR dispersion (NMRD) curves were successfully analysed with a mathematical model applied on Parmigiano–Reggiano (PR) cheese. Regression parameters were led back to the molecular components of cheeses (water trapped in casein micelles, proteins and fats) and milk samples (water belonging to hydration shells around dispersed colloidal particles of different sizes and bulk water). The application of chemometric analysis on relaxometric data enabled differentiating milk from cheeses and revealing differences within the two sample groups of either cheeses or milk samples. Marked differences among cheeses were evidenced by statistical analysis of the sole quadrupolar peaks parameters, suggesting that these contain information on the nature of the milk used during cheese production. Hence, combination of FFC NMR and chemometrics represents a powerful tool to investigate alterations in dairy products.     

Fabrication of zinc oxide nanowires/polymer composites by two‐photon polymerization

We present an approach to fabricate ZnO nanowires/polymer composite into three‐dimensional microstructures, based on two‐photon polymerization direct laser writing, a fabrication method that allows submicrometric spatial resolution. The structural integrity of the structures was inferred by scanning electron microscopy, while the presence and distribution of ZnO nanowires was investigated by energy dispersive X‐ray, Raman spectroscopy, and X‐ray diffraction. The optical properties of the produced composite microstructures were verified by imaging the characteristic ZnO emission using a fluorescence microscope. Hence, such approach can be used to develop composite microstructures containing ZnO nanowires aiming at technological applications. © 2013 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014 , 52, 333–337     

Dynamics of hyaluronan aqueous solutions as assessed by fast field cycling NMR relaxometry

Fast field cycling (FFC) NMR relaxometry has been used to study the conformational properties of aqueous solutions of hyaluronan (HYA) at three concentrations in the range 10 to 25 mg mL^–1. Results revealed that, irrespective of the solution concentration, three different hydration layers surround hyaluronan. The inner layer consists of water molecules strongly retained in the proximity of the HYA surface. Because of their strong interactions with HYA, water molecules in this inner hydration layer are subject to very slow dynamics and have the largest correlation times. The other two hydration layers are made of water molecules which are located progressively further from the HYA surface. As a result, decreasing correlation times caused by faster molecular motion were measured. The NMRD profiles obtained by FFC-NMR relaxometry also showed peaks attributable to ¹H–¹⁴N quadrupole interactions. Changes in intensity and position of the quadrupolar peaks in the NMRD profiles suggested that with increasing concentration the amido group is progressively involved in the formation of weak and transient intramolecular water bridging adjacent hyaluronan chains. In this work, FFC-NMR was used for the first time to obtain deeper insight into HYA–water interactions and proved itself a powerful and promising tool in hyaluronan chemistry.     

Modulation of the Physicochemical Properties of Heteropolynuclear Assemblies Containing Lanthanide Ions and 2,2′-oxydiacetate

Summary: This work focuses on the polynuclear complexes formed by a lanthanide ion (Ln), a bivalent cation (M) and oxydiacetate (oda) as bridging ligand, with general formula [Ln₂M₃(oda)₆(H₂O)₆] · xH₂O. The complexes can adopt more than one polymorphic structure, being the hexagonal (P6/mcc) and cubic (Fd3c) the most noticeable, as determined by x-ray powder diffraction. The influence of Ln and M on the solid-state structure is discussed. In addition, potentiometric studies are performed to support the existence of polynuclear species in solution.     

Analysis of sterols by high-performance liquid chromatography/mass spectrometry combined with chemometrics

A newly developed high-performance liquid chromatography/mass spectrometry (HPLC/MS) method has been successfully used to analyze plasma concentrations of various phytosterols (cholestanol and beta-sitosterol) and cholesterol metabolites (desmosterol and lathosterol). This was based on an unusual solvent combination of water/methanol vs. methanol/acetone/n-hexane applied on a Purospher Star RP-18e (125 x 2 mm, 3 microm) column, which proved excellent for the separation, identification and quantification of plasma sterols. Simple solid-phase extraction preparation of plasma samples was performed, followed by the developed fast and robust HPLC separation. Results on four groups of people were compared, those with low, normal and high plasma cholesterol levels and those with high cholesterol levels on statin therapy, and the results were evaluated using linear discriminant analysis (LDA). Variable selection for LDA was achieved using backward removal selection. Highly discriminatory variables were the ratios of desmosterol to sitosterol and of lathosterol to total plasma cholesterol. The latter ratio was also excellent for distinguishing subjects on statin therapy. The success rate of classification was 100%. The present pilot study shows the potential of HPLC/MS analysis and chemometrics for studying cholesterol-related disorders and warrants future full-scale medical study.     

Lifshitz-Safran coarsening dynamics in a 2D hexagonal system

The coarsening process in a two-dimensional hexagonal system in the region close to both spinodal and order-order transitions was investigated through the Cahn-Hilliard model. We found a distinctive region of the phase diagram where the pinning of dislocations plays only a minor role and the dynamics is led by the triple points. In this region, we found configurations of domains with the same features as those proposed by Lifshitz. As a consequence, different correlation lengths grow logarithmically in time, in good agreement with the predictions of coarsening at low temperatures proposed by Safran.