Some examples for the Poincaré and Painlevé problems

In 1891, Poincaré started a series of three papers in which he tried to answer the following question (cf. [21-23]): “Is it possible to decide if an algebraic differential equation in two variables is algebraically integrable?” (in the sense that it has a rational first integral). More or less at the same time P. Painlevé asked the following question: “Is it possible to recognize the genus of the general solution of an algebraic differential equation in two variables which has a rational first integral?”. In this paper we give examples of one-parameter families which show that both problems have a negative answer. With some of the families we can also answer a question posed by M. Brunella in [5].     

Continuous spectral decompositions of Abelian group actions on -algebras

Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell bundles over the Pontrjagin dual group of G as continuous spectral decompositions of G-actions on C^*-algebras. We classify such spectral decompositions using certain dense subspaces related to Marc Rieffel's theory of square-integrability. There is a unique continuous spectral decomposition if the group acts properly on the primitive ideal space of the C^*-algebra. But there are also examples of group actions without or with several inequivalent spectral decompositions.     

Spot tests for calcium sulphate, lead sulphate, silver, thallium, and formaldehyde based on reactions with selenosulphate

Summary Spot tests have been described for calcium sulphate, lead sulphate, silver, thallium and formaldehyde based on the reaction with selenosulphate. In these reactions either red elemental selenium (CaSO₄, CH₂O) or black metal selenide (PbSO₄ Tl, Ag) is formed. The limits of identification are: 0.2 mg of PbS04 or CaSO₄, 2 g of Ag, 10 g of Tl, 0.2 g of CH₂O.

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Zusammenfassung Für Calciumsulfat, Bleisulfat, Silber, Thallium und Formaldehyd werden Tüpfelproben beschrieben, die auf Umsetzungen mit Selenosulfat beruhen. Hierbei -wird entweder rotes elementares Selen abgeschieden (CaSO₄ CH₂O) oder schwarze Selenide werden gebildet (PbSO₄, Tl, Ag). Die Nachweisgrenzen betragen: 0,2 mg PbSO₄ oder CaSO₄, 2 g Ag, 10 g Tl, 0,2 g CH₂O.

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This paper has been dedicated to Prof. Dr.Fritz Wessely, Vienna, on the occasion of his 70th birthday.     

Simple HPLC‐UV for the quantification of a new leishmanicidal candidate (E)‐1‐4(trifluoromethyl) benzylidene)‐5‐(2‐4‐dichlorozoyl) carbonylhydrazine (LASSBio‐1736) in rat plasma for pharmacokinetics assessment

In this study, a sensitive HPLC‐UV assay was developed and validated for the determination of LASSBio‐1736 in rat plasma with sodium diclofenac as internal standard (IS). Liquid–liquid extraction using acetonitrile was employed to extract LASSBio‐1736 and IS from 100 μL of plasma previously basified with NaOH 0.1 M. Chromatographic separation was carried on Waters Spherisorb^®S5 ODS2 C₁₈ column (150 × 4.6 mm, 5 μm) using an isocratic mobile phase composed by water with triethylamine 0.3% (pH 4), methanol and acetonitrile grade (45:15:40, v/v/v) at a flow rate of 1 mL/min. Both LASSBio‐1736 and IS were eluted at 4.2 and 5 min, respectively, with a total run time of 8 min only. The lower limit of quantification was 0.2 μg/mL and linearity between 0.2 and 4 μg/mL was obtained, with an R² > 0.99. The accuracy of the method was >90.5%. The relative standard deviations intra and interday were <6.19 and <7.83%, respectively. The method showed the sensitivity, linearity, precision, accuracy and selectivity required to quantify LASSBio‐1736 in preclinical pharmacokinetic studies according to the criteria established by the US Food and Drug Administration and European Medicines Agency. Copyright © 2016 John Wiley & Sons, Ltd.     

13C CP/MAS NMR studies of morphological changes in polypropylene: 2. The double melting endotherm of spunbonded fabrics

The double melting endotherm of spunbonded isotactic polypropylene (iPP) fabrics was investigated by monitoring changes in the solid-state NMR spectrum that result from thermal annealing. The DSC melting thermogram was found to change from a double to a single endotherm at anneal temperatures ≥156°C, with a concomitant increase in percent crystallinity. All of the carbon resonances in the CP/MAS NMR spectrum of the purely crystalline phase of iPP were found to be composed of multiple peaks with relative intensities that depend on anneal temperature. By monitoring the changes in the distribution of intensity among the various peaks of a given resonance, a transition temperature of 156°C was identified. Arguments are presented that this redistribution of intensity within a given carbon resonance characterizes the transformation from the α₁ to the α₂ monoclinic crystal form. The exothermicity associated with this transformation is responsible for the observation of a double melting endotherm by DSC. The splitting patterns observed in the NMR spectrum are discussed in terms of interlayer distances between layers of isochiral helices and the density of exposed methyls at the contact faces of these interlayers. © 1996 John Wiley & Sons, Inc.     

Components of Banisteriopsis caapi,a Plant Used in the Preparation of the Psychoactive Ayahuasca,Induce Anti-Inflammatory Effects in Microglial Cells

Banisteriopsis caapi is used to prepare the psychoactive beverage ayahuasca, and both have therapeutic potential for the treatment of many central nervous system (CNS) conditions. This study aimed to isolate new bioactive compounds from B. caapi extract and evaluate their biological activity, and that of the known β-carboline components of the plant (harmine, harmaline, and tetrahydroharmine), in BV-2 microglial cells, the in vivo activation of which is implicated in the physiopathology of CNS disorders. B. caapi extract was fractionated using semipreparative liquid chromatography (HPLC-DAD) and the exact masses ([M + H]⁺ m/z) of the compounds in the 5 isolated fractions were determined by high-resolution LC-MS/MS: F1 (174.0918 and 233.1289), F2 (353.1722), F3 (304.3001), F4 (188.1081), and F5 (205.0785). Harmine (75.5–302 µM) significantly decreased cell viability after 2 h of treatment and increased the number of necrotic cells and production of reactive oxygen species at equal or lower concentrations after 24 h. F4 did not impact viability but was also cytotoxic after 24 h. Most treatments reduced proinflammatory cytokine production (IL-2, IL-6, IL-17, and/or TNF), especially harmaline and F5 at 2.5 µM and higher concentrations, tetrahydroharmine (9.3 µM and higher), and F5 (10.7 µM and higher). The results suggest that the compounds found in B. caapi extract have anti-inflammatory potential that could be explored for the development of treatments for neurodegenerative diseases.     

Collisional effects in the tokamap

Plasmas confined in tokamaks with non-symmetric perturbations are surrounded by a chaotic layer of magnetic field lines that guide charged particles to the tokamak wall. We use an analytical two-dimensional symplectic mapping to study the resulting fractal patterns of field line escape. However, particles may experience several collisions before escaping toward the tokamaks wall. We add a random collisional term to the field line mapping to investigate how the particle collisions modify their escape patterns.     

Tokamak magnetic field lines described by simple maps

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.     

First-principles theory of correlated transport through nanojunctions

We report the inclusion of electron-electron correlation in the calculation of transport properties within an ab initio scheme. A key step is the reformulation of Landauer's approach in terms of an effective transmittance for the interacting electron system. We apply this framework to analyze the effect of short-range interactions on Pt atomic wires and discuss the coherent and incoherent correction to the mean-field approach.