Well-posedness in Sobolev spaces for semi-linear 3-evolution equations

We prove local in time well-posedness of the Cauchy problem in Sobolev spaces for semi-linear 3-evolution equations of the first order. We require real principal part, but complex valued coefficients for the lower order terms. Therefore decay conditions on the imaginary parts are needed, as \(x\rightarrow \infty \) .     

Two Crystal Forms of a Hydrated 2:1 β-Cyclodextrin Fluconazole Complex: Single Crystal X-ray Structures,Dehydration Profiles,and Conditions for Their Individual Isolation

Inclusion complexes between cyclodextrins (CDs) and active pharmaceutical ingredients (APIs) have potential for pharmaceutical formulation. Since crystallization of a given complex may result in the isolation of multiple crystal forms, it is essential to characterize these forms with respect to their structures and physicochemical properties to optimize pharmaceutical candidate selection. Here, we report the preparation and characterization of two crystallographically distinct hydrated forms of an inclusion complex between β-cyclodextrin (β-CD) and the antifungal API fluconazole (FLU) as well as temperature–concentration conditions required for their individual isolation. Determination of crystal water contents was achieved using thermoanalytical methods. X-ray analyses revealed distinct structural differences between the triclinic (TBCDFLU, space group P1) and monoclinic (MBCDFLU, space group C2) crystal forms. Removal of the crystals from their mother liquors led to rapid dehydration of the MBCDFLU crystal, while the TBCDFLU crystal was stable, a result that could be reconciled with the distinct packing arrangements in the respective crystals. This study highlights (a) the importance of identifying possible multiple forms of a cyclodextrin API complex and controlling the crystallization conditions, and (b) the need to characterize such crystal forms to determine the extent to which their physicochemical properties may differ.     

The Renaissance of α‐Methylene‐γ‐butyrolactones: New Synthetic Approaches

The amount of research activity concerning α‐methylene‐γ‐butyrolactones and α‐alkylidene‐γ‐butyrolactones has increased dramatically in recent years. This Review summarizes the structural types, biological activities, and biosynthesis of these compounds, concentrating on publications from the past 10 years. Traditional approaches to α‐methylene‐γ‐butyrolactones and α‐alkylidene‐γ‐butyrolactones are then reviewed together with novel approaches, including those from our own research group, reported more recently.     

Mass Spectrometric and Synchrotron Radiation based techniques for the identification and distribution of painting materials in samples from paints of Josep Maria Sert

ABSTRACT: BACKGROUND: Establishing the distribution of materials in paintings and that of their degradation products by imaging techniques is fundamental to understand the painting technique and can improve our knowledge on the conservation status of the painting. The combined use of chromatographic-mass spectrometric techniques, such as GC/MS or Py/GC/MS, and the chemical mapping of functional groups by imaging SR FTIR in transmission mode on thin sections and SR XRD line scans will be presented as a suitable approach to have a detailed characterisation of the materials in a paint sample, assuring their localisation in the sample build-up. This analytical approach has been used to study samples from Catalan paintings by Josep Maria Sert y Badia (20th century), a muralist achieving international recognition whose canvases adorned international buildings. RESULTS: The pigments used by the painter as well as the organic materials used as binders and varnishes could be identified by means of conventional techniques. The distribution of these materials by means of Synchrotron Radiation based techniques allowed to establish the mixtures used by the painter depending on the purpose. CONCLUSIONS: Results show the suitability of the combined use of SR FTIR and SR XRD mapping and conventional techniques to unequivocally identify all the materials present in the sample and their localization in the sample build-up. This kind of approach becomes indispensable to solve the challenge of micro heterogeneous samples. The complementary interpretation of the data obtained with all the different techniques allowed the characterization of both organic and inorganic materials in the samples layer by layer as well as to establish the painting techniques used by Sert in the works-of-art under study.     

Fabry–Perot effect on dimer nanoantennas

In this work, we investigate the interaction between a single quantum emitter and dimer nanoantennas through a Fabry–Perot structure composed of an appropriate combination of two dielectric layers. This type of dielectric configuration is well known in the microwave region to increase the antenna performance, such as directivity, radiation efficiency, and radiation resistance. Here, the Fabry–Perot concept is transposed to the optical domain. The single emitter couples to the antenna through the dielectric structure, giving rise to a wide aperture field on top of the dielectrics with the same polarization of the emitter. This purely polarized aperture field can be used to excite one or more conveniently spaced nanoantennas. We demonstrate by 3D numerical calculations that the directivity and excitation rate of a single dimer is highly increased. Also, we show that multiple dimers arranged in an array configuration can be enhanced due to the wide aperture field generated by a single emitter.     

Liouville theorems in halfspaces for parabolic hypoelliptic equations

Abstract We prove some one-side Liouville-type theorems in halfspaces for a class of evolution hypoelliptic equations. The operators we deal with are left translation invariant, and homogeneous of degree two, on homogeneous Lie groups on . Keywords: Parabolic operators, Liouville Theorems, Liouville Theorems in halfspaces Mathematics Subject Classification (2000): 35K65, 35H10, 35B99     

Bracciano's Lake waters: an experimental survey on the surface layer pollution

The chemical and trophic conditions of the surface waters of the lake Bracciano, near Roma, have been investigated all through the year 2005. Electrical conductivity, pH, alkalinity, hardness, total nitrogen, phosphorus content, chloride, fluoride and sulphate ions were measured. The results were compared with similar analyses formerly carried out by different authors, to achieve a right evaluation of the actual quality of the surface waters of the lake Bracciano all over the year 2005.     

Taxonomical markers in two endemic plants of Sardinia: Verbascum conocarpum and Scrophularia trifoliata

The monoterpenoid composition of Verbascum conocarpum and Scrophularia trifoliata, both endemic plants of Sardinia, was examined. The main chemotaxonomic markers of Scrophulariaceae, the iridoids aucubin, verbascoside and catalpol, were isolated.     

Revealing the Fine Details of Functionalized Silica Surfaces by Solid‐State NMR and Adsorption Isotherm Measurements: The Case of Fluorinated Stationary Phases for Liquid Chromatography

The structural and chromatographic characterization of two novel fluorinated mesoporous materials prepared by covalent reaction of 3‐(pentafluorophenyl)propyldimethylchlorosilane and perfluorohexylethyltrichlorosilane with 2.5 μm fully porous silica particles is reported. The adsorbents were characterized by solid state ²⁹Si, ¹³C, and ¹⁹F NMR spectroscopy, low‐temperature nitrogen adsorption, elemental analysis (C and F), and various chromatographic measurements, including the determination of adsorption isotherms. The structure and abundance of the different organic surface species, as well as the different silanol types, were determined. In particular, the degree of so‐called horizontal polymerization, that is, Si‐O‐Si bridging parallel to the silica surface due to the reaction, under “quasi‐dry” conditions, of trifunctional silanizing agents with the silica surface was quantified. Significant agreement was found between the information provided by solid‐state NMR, elemental analysis, and excess isotherms regarding the amount of surface residual silanol groups, on the one hand, and the degree of surface functionalization, on the other. Finally, the kinetic performance of the fluorinated materials as separation media for applications in near‐ultrahigh‐performance liquid chromatography was evaluated. At reduced velocities of about 5.5 (ca. 600 bar backpressure at room temperature) with 3 mm diameter columns and toluene as test compound, reduced plate heights on the order of 2 were obtained on columns of both adsorbents.