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.     

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.     

Palladium-catalyzed oxyarylation of olefins using silver carbonate as the base. Probing the mechanism by electrospray ionization mass spectrometry

The Pd(OAc)₂-catalyzed oxyarylation of electron-rich (8 and 12) and electron-poor (10) olefins by ortho-iodophenols (3a-d) was studied using Ag₂CO₃ as the base, in acetone, and in the presence and absence of PPh₃. The corresponding adducts of oxyarylation were obtained in moderate yields. The reaction mechanism was examined by electrospray ionization mass spectrometry (ESI-MS). Cationic arylpalladium intermediate (14), formed by the oxidative insertion of Pd(0) into 3a, and the cationic palladacycles (15), obtained by reaction of 14 with olefins 8 and 12, were intercepted by ESI-MS and characterized by ESI-MS/MS.     

Non-Hausdorff symmetries of C*-algebras

Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed products for such actions, and justify these definitions with some basic general results and examples.     

Integrability of dual coactions on Fell bundle C*-algebras

We study integrability for coactions of locally compact groups. For abelian groups, this corresponds to integrability of the associated action of the Pontrjagin dual group. The theory of integrable group actions has been previously studied by Ruy Exel, Ralf Meyer and Marc Rieffel. Our goal is to study the close relationship between integrable group coactions and Fell bundles. As a main result, we prove that dual coactions on C*-algebras of Fell bundles are integrable, generalizing results by Ruy Exel for abelian groups.     

Evaluation of a biosensor based on reduced graphene oxide and glucose oxidase enzyme on the monitoring of second-generation ethanol production

Journal of Solid State Electrochemistry - An easily prepared biosensor based on reduced graphene oxide (rGO) and glucose oxidase (GOx) enzyme was developed to monitor the enzymatic hydrolysis...     

A functionalized renewable carbon-based surface for sensor development

This paper describes the surface modification of glassy carbon (GC) electrodes with a bamboo-based renewable carbon (RC) before and after an acid functionalization procedure with a sulfonitric solution (1:3 HNO₃/H₂SO₄). The morphology and structural characterization indicate an increase of functional groups in the functionalized renewable carbon (RCF) surface. The enhanced electroanalytical properties of RC and RCF were evaluated by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) in two different setups, in the presence of the redox couple ([Fe(CN)₆]^3−/4−) and escitalopram (EST). The results revealed an enhancement for the electrochemical responses of both inorganic and organic compounds in the electrolyte. Therefore, the use of new carbon-based materials such as renewable carbon for development of electrochemical sensors brings a fresh approach to low-cost device development.