On the Propagation of Regularity and Decay of Solutions to the k-Generalized Korteweg-de Vries Equation

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u ₀ ∈ H ^3/4+ (?) whose restriction belongs to H ^l ((b, ∞)) for some l ∈ ?⁺ and b ∈ ? we prove that the restriction of the corresponding solution u(·, t) belongs to H ^l ((β, ∞)) for any β ∈ ? and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves.     

Impact of Positional Isomerism on Pathway Complexity in Aqueous Media

Pathway complexity has become an important topic in recent years due to its relevance in the optimization of molecular assembly processes, which typically require precise sample preparation protocols. Alternatively, competing aggregation pathways can be controlled by molecular design, which primarily rely on geometrical changes of the building blocks. However, understanding how to control pathway complexity by molecular design remains elusive and new approaches are needed. Herein, we exploit positional isomerism as a new molecular design strategy for pathway control in aqueous self‐assembly. We compare the self‐assembly of two carboxyl‐functionalized amphiphilic BODIPY dyes that solely differ in the relative position of functional groups. Placement of the carboxyl group at the 2‐position enables efficient pairwise H‐bonding interactions into a single thermodynamic species, whereas meso‐substitution induces pathway complexity due to competing hydrophobic and hydrogen bonding interactions. Our results show the importance of positional engineering for pathway control in aqueous self‐assembly.     

Polyphenolic Composition and Antioxidant Activity (ORAC,EPR and Cellular) of Different Extracts of Argylia radiata Vitroplants and Natural Roots

Plant biochemistry studies have increased in recent years due to their potential to improve human health. Argylia radiata is an extremophile plant with an interesting polyphenolic profile. However, its biomass is scarce and occasionally available. Argylia in vitro biomass was obtained from tissue culture and compared with in vivo roots regarding its polyphenolic and flavonoid content. Different solvents were used to prepare extracts from the in vitro tissue of callus and aerial plant organs and in vivo roots. UPLC-MS/MS was used to assess the chemical composition of each extract. ORAC-FL and scavenging of free radicals (DPPH and OH) methods were used to determine the antioxidant capacity of extracts. Furthermore, the biological activity of the extracts was established using the cellular antioxidant activity method. The vitroplants were a good source of polyphenols (25–68 mg GAE/100 g tissue FW), and methanol was the most efficient solvent. Eight polyphenolic compounds were identified, and their antioxidant properties were investigated by different chemical methods with EPR demonstrating its specific scavenging activity against free radicals. All extracts showed cellular dose-dependent antioxidant activity. The methanolic extract of vitroplants showed the highest cellular antioxidant activity (44.6% and 51%) at 1 and 10 µg/mL of extract, respectively. Vitroplants of A. radiata are proposed as a biotechnological product as a source of antioxidant compounds with multiple applications.     

Iboga Inspired N-Indolylethyl-Substituted Isoquinuclidines as a Bioactive Scaffold: Chemoenzymatic Synthesis and Characterization as GDNF Releasers and Antitrypanosoma Agents

The first stage of the drug discovery process involves the identification of small compounds with biological activity. Iboga alkaloids are monoterpene indole alkaloids (MIAs) containing a fused isoquinuclidine-tetrahydroazepine ring. Both the natural products and the iboga-inspired synthetic analogs have shown a wide variety of biological activities. Herein, we describe the chemoenzymatic preparation of a small library of novel N-indolylethyl-substituted isoquinuclidines as iboga-inspired compounds, using toluene as a starting material and an imine Diels–Alder reaction as the key step in the synthesis. The new iboga series was investigated for its potential to promote the release of glial cell line-derived neurotrophic factor (GDNF) by C6 glioma cells, and to inhibit the growth of infective trypanosomes. GDNF is a neurotrophic factor widely recognized by its crucial role in development, survival, maintenance, and protection of dopaminergic neuronal circuitries affected in several neurological and psychiatric pathologies. Four compounds of the series showed promising activity as GDNF releasers, and a leading structure (compound 11) was identified for further studies. The same four compounds impaired the growth of bloodstream Trypanosoma brucei brucei (EC₅₀ 1–8 μM) and two of them (compounds 6 and 14) showed a good selectivity index.     

Self-assembling and phase coexistence of SW trimers as complex amphiphile analogues. I. Simulations

We analyse by discrete molecular dynamics the self-assembly of SW trimer particles that contain a different number of attractive and repulsive spheres. They also have different geometries: linear, obtuse, rectangular and equilateral. We identify that some of these molecules exhibit liquid–vapour equilibria while others do not. For all of them, we show the morphological phase diagram built up from the different supra-molecular structures formed by each type of trimer. We simulated 14 different systems with a total of 321 states. The main features of the supra-molecular structures depend only on the composition and geometry of the trimer: triple SW trimers do not form supra-structures, double SW trimers and single SW trimers form monolayers, bilayers and worm-like micelles. The liquid–vapour coexistence properties are also exhibited. These trimers can be used to model complex amphiphiles beyond the standard ones, such as the Gemini and the Bola surfactants as well as colloidal particles.     

Self-imaging by a volume grating

The self-image phenomenon by a volume grating is proposed and theoretically analyzed. A theoretical model based on a path integral formulation to describe wave propagation through the grating inhomogeneous medium is applied. A modified version of the scalar diffraction theory Fresnel propagator is obtained which allows calculating the diffracted field amplitude by the grating. The proposed model is applied to amplitude and/or phase volume gratings. Remarkable features appear, in particular at the fractional Talbot distance 0.125z_T. In this case, if an in-phase real and imaginary grating modulation is considered a self-image intensity profile is observed for determined values of the absorptive and refractive parameters. On the other hand, a spatial comb intensity profile for a near half period shift between the real and imaginary grating modulations is found.     

Comparative bioavailability of two zolpidem hemitartrate formulations in healthy human Brazilian volunteers using high-performance liquid chromatography coupled to tandem mass spectrometry

To assess the bioequivalence of two zolpidem hemitartrate formulations in 30 healthy volunteers. Plasma samples were obtained over a 24 h period. Plasma concentrations of zolpidem were analyzed by liquid chromatography coupled to tandem mass spectrometry with positive ion electrospray ionization using multiple reaction monitoring. Values of peak concentration (C_max), area under curve (AUC), half-life, elimination constant, volume of distribution and clearance showed statistically significant differences when comparing women (604.34 ng h/ml, 127.36 ng/ml, 4.4 h, 0.18 1/h, 50.56 L and 8.55 L/h, respectively) and men (276.1 ng h/ml, 70.9 ng/ml, 3.3 h, 0.26 1/h, 91.42 L and 24.34 L/h, respectively), receiving the same dose (5 mg), respectively. The geometric means with corresponding 90% confidence interval for Test/Reference percentage ratios were 99.73% (CI 93.69–106.16) for C_max, 97.44% (90% CI = 91.85–103.37%) for area under curve of plasma concentration until the last concentration observed (AUC_last) and 98.30% (90% CI = 92.48–104.49) for the area under curve between the first sample (pre-dosage) and infinity (AUC_0–inf). Since the 90% CI for AUC_last, AUC_0–inf and C_max ratios were within the 80–125% interval proposed by the US Food and Drug Administration, it was concluded that zolpidem hemitartrate formulation (5 mg orodispersible tablet) is bioequivalent to the zolpidem hemitartrate formulation (Patz SL 5 mg sublingual tablet) with regard to both the rate and the extent of absorption. A new formulation of zolpidem 2.5 mg may be useful in women for the same clinical benefits as the 5 mg formulation in men.     

Kinetics studies of 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol,and 2,4,4-trimethyl-1-pentanol with chlorine atoms: Photooxidation mechanism of 2,4,4-trimethyl-1-pentanol

The rate constants for the reaction between chlorine atoms and either 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, or 2,4,4-trimethyl-1-pentanol at 298 K were determined using the relative method with 2-butanol and 1-pentanol as reference compounds. The values obtained for 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, and 2,4,4-trimethyl-1-pentanol (k × 10¹⁰ cm³ molec⁻¹ s⁻¹) were, respectively, (2.64 ± 0.5), (2.72 ± 0.5), and (2.50 ± 0.4), in agreement with the values of the rate constants reported in bibliography for similar alcohols and the values estimated by structure activity relationship methods. The photooxidation products of 2,4,4-trimethyl-1-pentanol initiated by chlorine atoms were identified (formaldehyde, 2-propanone, 2,2-dimethyl propanal, 4,4,-dimethyl-2-pentanone, and 3,3-dimethylbutanal), and the reaction mechanism was determined.     

Interface‐fitted moving mesh method for axisymmetric two‐phase flow in microchannels

A boundary‐fitted moving mesh scheme is presented for the simulation of two‐phase flow in two‐dimensional and axisymmetric geometries. The incompressible Navier‐Stokes equations are solved using the finite element method, and the mini element is used to satisfy the inf‐sup condition. The interface between the phases is represented explicitly by an interface adapted mesh, thus allowing a sharp transition of the fluid properties. Surface tension is modelled as a volume force and is discretized in a consistent manner, thus allowing to obtain exact equilibrium (up to rounding errors) with the pressure gradient. This is demonstrated for a spherical droplet moving in a constant flow field. The curvature of the interface, required for the surface tension term, is efficiently computed with simple but very accurate geometric formulas. An adaptive moving mesh technique, where smoothing mesh velocities and remeshing are used to preserve the mesh quality, is developed and presented. Mesh refinement strategies, allowing tailoring of the refinement of the computational mesh, are also discussed. Accuracy and robustness of the present method are demonstrated on several validation test cases. The method is developed with the prospect of being applied to microfluidic flows and the simulation of microchannel evaporators used for electronics cooling. Therefore, the simulation results for the flow of a bubble in a microchannel are presented and compared to experimental data.     

Gravitational entropy of Kerr black holes

Classical invariants of General Relativity can be used to approximate the entropy of the gravitational field. In this work, we study two proposed estimators based on scalars constructed out from the Weyl tensor, in Kerr spacetime. In order to evaluate Clifton, Ellis and Tavakol’s proposal, we calculate the gravitational energy density, gravitational temperature, and gravitational entropy of the Kerr spacetime. We find that in the frame we consider, Clifton et al.’s estimator does not reproduce the Bekenstein–Hawking entropy of a Kerr black hole. The results are compared with previous estimates obtained by the authors using the Rudjord–Gr \(\varnothing \) n–Hervik approach. We conclude that the latter represents better the expected behaviour of the gravitational entropy of black holes.