Center manifolds for impulsive equations under nonuniform hyperbolicity

We establish the existence of smooth center manifolds under sufficiently small perturbations of an impulsive linear equation. In particular, we obtain the C¹ smoothness of the manifolds outside the jumping times. We emphasize that we consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential trichotomy.     

Reversibility of Conjugacies for Nonautonomous Equations

We establish a reversible version of the Grobman–Hartman theorem for nonautonomous differential equations in Banach spaces. Namely, we show that if the differential equation is reversible, then the topological conjugacies in the Grobman–Hartman theorem also commute with the symmetries. The result is illustrated with an example.     

Insertion of Continuous Real Functions on Spaces,Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.     

Ionic azo-codendrimers: Influence of the acids contents in the liquid crystalline properties and the photoinduced optical anisotropy

A series of codendrimers has been prepared by the grafting of poly(propylene imine) PPI-(NH₂)₁₆ (G = 3) with two different carboxylic acids: the aromatic-based 5-[4′-(4-cyanophenylazo)phenyloxy]pentanoic acid (AZO) and the aliphatic 2,2-bis(undecanoyloxymethylene)propionic acid (BUPA) in different proportions. Their thermal properties, liquid crystalline behavior and photoinduced optical anisotropy have been investigated. The formation of the ionic compounds was confirmed by nuclear magnetic resonance (NMR) spectroscopy, and Fourier transform infrared (FT-IR) spectroscopy. The influence of the acid percentage in the liquid crystalline behavior was investigated by means of differential scanning calorimetry (DSC), polarizing optical microscopy (POM) and X-ray diffractometry (XRD). All the resulting co-dendrimers present liquid crystalline properties displaying an evolution from nematic mesophase for the azo-richer dendrimers to smectic A mesophase for the BUPA-richer dendrimers. Only materials with low azobenzene contents up to four AZO units per dendrimer on average were processable by casting from dichloromethane solutions and resulted in transparent thin films appropriate for optical studies. The photoinduced dichroism reached was higher in the dendrimer with higher azo content (four units per dendrimer) being this material a good compromise between processability and optical response.     

New Triterpenoid and Ergostane Glycosides from the Leaves of Hydrocotyle umbellata L.

Two new triterpenoid glycosides, together with two new ergostane glycosides, umbellatosides A–D ( 1 – 4 , resp.), have been isolated from the leaves of Hydrocotyle umbellata L. Their structures were established by 2D‐NMR spectroscopic techniques (¹H,¹H‐COSY, TOCSY, NOESY, HSQC, and HMBC) and mass spectrometry as 3β,22β‐dihydroxy‐3‐O‐[α‐L ‐rhamnopyranosyl‐(1→2)‐β‐D ‐glucuronopyranosyl]olean‐12‐en‐28‐oic acid 28‐O‐β‐D ‐glucopyranosyl ester ( 1 ), 3‐O‐[α‐L ‐rhamnopyranosyl‐(1→2)‐β‐D ‐glucuronopyranosyl]oleanolic acid 28‐O‐β‐D ‐glucopyranosyl ester ( 2 ), (3β,11α,26)‐ergosta‐5,24(28)‐diene‐3,11,26‐triol 3‐O‐(β‐D ‐glucopyranosyl)‐11‐O‐(α‐L ‐rhamnopyranosyl)‐26‐O‐β‐D ‐glucopyranoside ( 3 ), and (3β,11α,21,26)‐ergosta‐5,24(28)‐diene‐3,11,21,26‐tetrol 3‐O‐(β‐D ‐glucopyranosyl)‐11‐O‐(α‐L ‐rhamnopyranosyl)‐26‐O‐β‐D ‐glucopyranoside ( 4 ).     

Synthesis of caffeic acid molecularly imprinted polymer microspheres and high-performance liquid chromatography evaluation of their sorption properties

In the current work, a molecularly imprinted polymer (MIP) has been synthesised and used to enable the extraction of a naturally-occurring antioxidant from complex media. More specifically, we describe the first example of a caffeic acid (CA) MIP which has been synthesised in the form of well-defined polymer microspheres, and its use for the extraction of CA from fruit juice sample. The CA MIP was synthesised by precipitation polymerisation using 4-vinylpyridine as functional monomer, divinylbenzene-80 as crosslinker and acetonitrile:toluene (75/25, v/v) as porogen. The particle sizing and morphological characterisation of the polymers was carried out by means of scanning electron microscopy (narrow particle size distribution; ～5 and 1.5 μm particle diameters for the MIP and NIP [non-imprinted polymer], respectively) and nitrogen sorption porosimetry (specific surface areas of 340 and 350 m(2)g(-1), and specific pore volumes of 0.17 and 0.19 cm(3)g(-1) for the MIP and NIP, respectively). The polymers were evaluated further by batch rebinding experiments, and from the derived isotherms their binding capacity and binding strength were determined (number of binding sites (N(K))=0.6 and 0.3 mmol g(-1) for the MIP and NIP, respectively, and apparent average adsorption constant (K(N))=10.0 and 1.6L mmol(-1) for the MIP and NIP, respectively). To evaluate the molecular recognition character of the MIP it was packed into a stainless steel column (50 mm × 4.6 mm i.d.) and evaluated as an HPLC-stationary phase. The mobile phase composition, flow rate, and the elution profile were then optimised in order to improve the peak shape without negatively affecting the imprinting factor (IF). Very interesting, promising properties were revealed. The imprinting factor (IF) under the optimised conditions was 11.9. Finally, when the imprinted LC column was used for the selective recognition of CA over eight related compounds, very good selectivity was obtained. This outcome enabled the direct extraction of CA in commercial apple juice samples with recoveries in excess of 81% and, rather significantly, without any need for a clean-up step prior to the extraction.     

J-aggregation of a sulfonated amphiphilic porphyrin at the air-water interface as a function of pH

π-A isotherms, ellipsometric measurements, Brewster angle microscopy (BAM) and reflection spectroscopy have been utilized to characterize the films of an amphiphilic porphyrin ((OD)(3)TPPS(3)) at the air-water interface as a function of pH. This porphyrin forms stable mono-molecular layers at such interfaces, and exhibits different J-aggregation as a function of pH. The J-aggregation of (OD)(3)TPPS(3) on neutral pH subphases is notable considering that the nitrogen atoms at the central macrocycle have a pK(a)≈4.9. The type of aggregates at neutral pH is like those detected at pH<4, because the central porphyrin ring is already protonated. However at basic pH the aggregation happens without protonation of the central ring but can be instead controlled by application of the surface pressure. At the air-water interface, (OD)(3)TPPS(3) shows two bands, a red component and a blue component, which have characteristics of non-degenerate linear oscillators being perpendicularly polarized between each other. The spectral behavior observed on subphases at different pHs is qualitatively interpreted by means of exciton coupling theory, assuming that the degenerate transitions attributed to the Soret band are split. Additionally, highly oriented molecular films of these J-aggregates were deposited onto transparent quartz slides.     

Optimization of the derivatization reaction and the solid-phase microextraction conditions using a D-optimal design and three-way calibration in the determination of non-steroidal anti-inflammatory drugs in bovine milk by gas chromatography-mass spectrometry

An experimental design optimization is reported of an analytical procedure used in the simultaneous determination of seven non-steroidal anti-inflammatory drugs (NSAIDs) in bovine milk by gas chromatography with mass spectrometry detection (GC-MS). This analytical procedure involves a solid-phase microextraction (SPME) step and an aqueous derivatization procedure of the NSAIDs to ethyl esters in bovine milk. The following NSAIDs are studied: ibuprofen (IBP), naproxen (NPX), ketoprofen (KPF), diclofenac (DCF), flufenamic acid (FLF), tolfenamic acid (TLF) and meclofenamic acid (MCL). Three kinds of SPME fibers - polyacrylate (PA), polydimethylsiloxane/divinylbenzene (PDMS/DVB) and polydimethylsiloxane (PDMS) - are compared to identify the most suitable one for the extraction process, on the basis of two steps: to determine the equilibrium time of each fiber and to select the fiber that provides the best figures-of-merit values calculated with three-way PARAFAC-based calibration models at the equilibrium time. The best results were obtained with the PDMS fiber. Subsequently, 8 experimental factors (related to the derivatization reaction and the SPME) were optimized by means of a D-optimal design that involves only 14 rather than 512 experiments in the complete factorial design. The responses used in the design are the sample mode loadings of the PARAFAC decomposition which are related to the quantity of each NSAID that is extracted in the experiment. Owing to the fact that each analyte is unequivocally identified in the PARAFAC decomposition, a calibration model is not needed for each experimental condition. The procedure fulfils the performance requirements for a confirmatory method established in European Commission Decision 2002/657/EC.     

Acid natural clinoptilolite: structural properties against adsorption/separation of n-paraffins

The employment of an acid natural clinoptilolite (AZH-1) in the adsorption and separation of n-paraffins has been evaluated. Natural clinoptilolite, NZ, was the raw material used to prepare the sodium-exchanged clinoptilolite (AZ) starting from which the AZH-1 sample was obtained by acid treatment. The structural stability of the samples after the applied treatments was demonstrated. The nitrogen adsorption experiments indicated that the acid sample has a homogeneous porous distribution and a considerable increase in the micropore volume with respect to NZ and AZ. The employment of the inverse gas chromatography at infinite dilution (IGCID) allowed studying the adsorption and separation of n-paraffin mixtures on AZH-1. It was also confirmed that the diffusion on AZH-1 took place in an unblocked structure through the A channel of ten members with minimal interactions. The IGCID results demonstrated the capacities of the acid Cuban natural zeolite in the adsorption and separation of n-paraffin mixtures.