Quasi-linear Schrödinger–Poisson system under an exponential critical nonlinearity: existence and asymptotic behaviour of solutions

We prove the generalized $$L^p$$ -Poincaré inequalities and Sobolev type inequalities on graphs with polynomial volume growth. They are optimal on Vicsek graphs.     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

Bootstrap and permutation tests in ANOVA for directional data

The problem of testing the null hypothesis of a common direction across several populations defined on the hypersphere arises frequently when we deal with directional data. We may consider the Analysis of Variance (ANOVA) for testing such hypotheses. However, for the Watson distribution, a commonly used distribution for modeling axial data, the ANOVA test is only valid for large concentrations. So we suggest to use alternative tests, such as bootstrap and permutation tests in ANOVA. Then, we investigate the performance of these tests for data from Watson populations defined on the hypersphere.     

Laguncularia racemosa Phenolics Profiling by Three-Phase Solvent System Step-Gradient Using High-Performance Countercurrent Chromatography with Off-Line Electrospray Mass-Spectrometry Detection

The detailed metabolite profiling of Laguncularia racemosa was accomplished by high-performance countercurrent chromatography (HPCCC) using the three-phase system n-hexane–tert-butyl methyl ether–acetonitrile–water 2:3:3:2 (v/v/v/v) in step-gradient elution mode. The gradient elution was adjusted to the chemical complexity of the L. racemosa ethyl acetate partition and strongly improved the polarity range of chromatography. The three-phase solvent system was chosen for the gradient to avoid equilibrium problems when changing mobile phase compositions encountered between the gradient steps. The tentative recognition of metabolites including the identification of novel ones was possible due to the off-line injection of fractions to electrospray ionization mass spectrometry (ESI-MS/MS) in the sequence of recovery. The off-line hyphenation profiling experiment of HPCCC and ESI-MS projected the preparative elution by selected single ion traces in the negative ionization mode. Co-elution effects were monitored and MS/MS fragmentation data of more than 100 substances were used for structural characterization and identification. The metabolite profile in the L. racemosa extract comprised flavonoids, hydrolysable tannins, condensed tannins and low molecular weight polyphenols.     

Drying Effects on Chemical Composition and Antioxidant Activity of Lippia thymoides Essential Oil,a Natural Source of Thymol

Leaves of Lippia thymoides (Verbenaceae) were dried in an oven at 40, 50 and 60 °C and the kinetic of drying and the influence of the drying process on the chemical composition, yield, and DPPH radical scavenging activity of the obtained essential oils were evaluated. The composition of the essential oils was determined with gas chromatography-mass spectrometry and gas chromatography-flame ionization detection analyses. The influence of drying on the chemical composition of the essential oils of L. thymoides was evaluated by multivariate analysis, and their antioxidant activity was investigated via the 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay. The Midilli model was the most appropriate to describe the behavior of drying kinetic data of L. thymoides leaves. Thymol was the major compound for all analyzed conditions; the maximum content was obtained from fresh leaves (62.78 ± 0.63%). The essential oils showed DPPH radical scavenging activity with an average of 73.10 ± 12.08%, and the fresh leaves showed higher inhibition (89.97 ± 0.31%). This is the first study to evaluate the influence of drying on the chemical composition and antioxidant activity of L. thymoides essential oils rich in thymol.     

Parkia pendula Seed Lectin: Potential Use to Treat Cutaneous Wounds in Healthy and Immunocompromised Mice

Parkia pendula seed lectin was used to treat cutaneous wounds of normal and immunocompromised mice, inducing cicatrization. Methotrexate (0.8 mg/kg/week) was used as immunosuppressive drug. Wounds were produced in the dorsal region (1 cm²) of female albino Swiss mice (Mus musculus), health and immunocompromised. Wounds were daily topically treated with 100 μL of the following solutions: (1) control (NaCl 0.15 M), (2) control Im (0.15 M NaCl), (3) P. pendula seed lectin (100 μg/mL), and (4) P. pendula seed lectin Im (100 μg/mL). Clinical evaluation was performed during 12 days. Biopsies for histopathology analysis and microbiological examinations were carried out in the second, seventh, and 12th days. The presence of edema and hyperemia was observed in all groups during inflammatory period. The first crust was detected from the second day, only in the groups treated with P. pendula seed lectin. Microbiological analysis of wounds from day 0 to day 2 did not show bacterium at P. pendula seed lectin group; however, Staphylococcus sp. was detected every day in the other groups. The lectin markedly induced a total wound closing at P. pendula seed lectin and P. pendula seed lectin Im groups on 11th day of evolution. The present study suggests that P. pendula seed lectin is a biomaterial potential to show pharmacological effect in the repair process of cutaneous wounds.