Uniqueness of limit cycles bounded by two invariant parabolas

In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.     

Local–global multiscale model reduction for flows in high-contrast heterogeneous media

In this paper, we study model reduction for multiscale problems in heterogeneous high-contrast media. Our objective is to combine local model reduction techniques that are based on recently introduced spectral multiscale finite element methods (see [19]) with global model reduction methods such as balanced truncation approaches implemented on a coarse grid. Local multiscale methods considered in this paper use special eigenvalue problems in a local domain to systematically identify important features of the solution. In particular, our local approaches are capable of homogenizing localized features and representing them with one basis function per coarse node that are used in constructing a weight function for the local eigenvalue problem. Global model reduction based on balanced truncation methods is used to identify important global coarse-scale modes. This provides a substantial CPU savings as Lyapunov equations are solved for the coarse system. Typical local multiscale methods are designed to find an approximation of the solution for any given coarse-level inputs. In many practical applications, a goal is to find a reduced basis when the input space belongs to a smaller dimensional subspace of coarse-level inputs. The proposed approaches provide efficient model reduction tools in this direction. Our numerical results show that, only with a careful choice of the number of degrees of freedom for local multiscale spaces and global modes, one can achieve a balanced and optimal result.     

Experimental NMR and MS study of benzoylguanidines. Investigation of E/Z isomerism

Molecules containing the guanidinic nuclei possess several pharmacological applications, and knowing the preferred isomers of a potential drug is important to understand the way it operates pharmacologically. Benzoylguanidines were synthesized in satisfactory to good yields and characterized by NMR, Electrospray Ionization Mass Spectrometry (ESI‐MS) and Fourrier Transform InfraRed Spectroscopy techniques (FTIR). E/Z isomerism of the guanidines was studied and confirmed by NMR analysis in solution (¹H‐¹³C Heteronuclear Single Quantum Coherence (HSQC) and Heteronuclear Multiple‐Bond Correlation (HMBC), ¹H‐¹⁵N HMBC, ¹H‐¹H Correlation Spectroscopy (COSY) and Nuclear Overhauser Effect Spectroscopy (NOESY) experiments) at low temperatures. Compounds with p‐Cl and p‐Br aniline moiety exist mainly as Z isomer with a small proportion of E isomer, whereas compounds with p‐NO2 moiety showed a decrease in proportion of isomer Z. The results are important for the application of these molecules as enzymatic inhibitors. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Synthesis of Polysubstituted Symmetrical BODIPYs via Fischer Carbene Complexes: Theoretical,Photophysical and Electrochemical Evaluation

A series of new symmetrical highly substituted BODIPYs 6 a – l was synthesized through a prefunctionalization approach in 35 %–89 % yields from the pyrrole core. This strategy allowed modulation of the substituents at the different positions based on the choice of Fischer's alkynyl carbenes, oxazolones and aldehydes used as precursors. The substituent variation at positions 2, 6, 3 and 5 had the greatest effect on the modulation of their photophysical properties such as absorption (λ_abs) and emission (λ_em) wavelengths, extinction coefficient (ϵ), quantum yields (ϕ), Stokes shifts (Δν), fluorescence decay, radiative (k_rad) and non-radiative (k_nr) constants and the CIE 1931 coordinates. Theoretical calculations allowed to corroborate the effect of the substituents of meso-position on the modification of the dihedral angles. Cyclic voltammetry studies revealed that the BODIPY series presents similar redox potential behavior, being electrochemically active even in successive cycles, which suggests that transport by diffusion is the dominant process.