On an inequality by N. Trudinger and J. Moser and related elliptic equations

It has been shown by Trudinger and Moser that for normalized functions u of the Sobolev space ??^{1, N} (Ω), where Ω is a bounded domain in ?^N, one has ∫_Ω exp(α_N|u|^{N/(N ? 1)})dx ≤ C_N, where α_N is an explicit constant depending only on N, and C_N is a constant depending only on N and Ω. Carleson and Chang proved that there exists a corresponding extremal function in the case that Ω is the unit ball in ?^N. In this paper we give a new proof, a generalization, and a new interpretation of this result. In particular, we give an explicit sequence that is maximizing for the above integral among all normalized “concentrating sequences.” As an application, the existence of a nontrivial solution for a related elliptic equation with “Trudinger‐Moser” growth is proved. © 2002 John Wiley & Sons, Inc.     

Investigating the formation and the properties of monoalkyl carbonates in aqueous medium using capillary electrophoresis with capacitively coupled contactless conductivity detection

Although alkyl carbonic acids (ACAs) and their salts are referred to as instable species in aqueous medium, we demonstrate that a monoalkyl carbonate (MAC) can in fact be easily formed from bicarbonate and an alcohol even in the presence of a high amount of water. A CE system with two capacitively coupled contactless conductivity detectors (C?Ds) was used to obtain different parameters about these species and their reactions. Based on the mobilities obtained for a series of alcohols ranging from 1 to 5 carbons, the coefficients of diffusion and the hydrodynamic radii were calculated. When compared with the equivalent carboxylates, MACs have radii systematically smaller. Although the precise pK(a) values of the ACAs could not be obtained, because of the fast decomposition in acid medium, it was possible, for the first time, to show that they are below 4.0. This result suggests that the acidity of an ACA is quite similar to the first hydrogen of H?CO?. Using a new approach to indirectly calibrate the C?D, the kinetic constants and the equilibrium constants of formation were also obtained. The results suggest that the increase in the chain length makes the MACs less stable and more inert.     

Nanostructure of polysaccharide complexes

The interaction of gum arabic (GA) with chitosan (Ch) of different degree of deacetylation was studied by turbidity measurements, dynamic light scattering and atomic force microscopy. The structure of the complexes was found to be directly related to the charge density of chitosan molecules. Gum arabic and chitosan with a degree of deacetylation of 75% form soluble complexes with a loosely globular structure of about 250 nm, at weight ratios up to 1.2, if the concentrations are kept low (total biopolymer concentration up to 0.06%). If chitosan has a higher charge density (degree of deacetylation of 93%), colloidal particles are formed, independently of the polymer concentration or ratio. At low concentrations and GA/Ch ratios of 1 or 1.2, the particles have diameters of 200-250 nm. The formation of soluble complexes is attributed to a chitosan lower charge density and the presence of non-charged monomers, which prevent the efficient self-assembly of the macromolecules.     

Evaluation of Genotoxicity and Toxicity of Annona muricata L. Seeds and In Silico Studies

Cancer is a multifactorial organic dysfunction for which great efforts are being devoted in searching for new treatments and therapeutic adjuvants. Annona muricata is a fruit that has promising activity against several types of cancer, as it contains acetogenins, the metabolite group associated with this action. Thus, the objective of this study was to evaluate, in experimental models, the toxic behavior of an extract and fraction rich in acetogenins from A. muricata seeds and study the acetogenin, Annonacin, in silico. Phytochemical characterization was made by thin layer chromatography, spectroscopy in the infrared region and nuclear magnetic resonance. Toxicity was evaluated by tests of Allium cepa and Artemia salina, and in silico studies using the SwissDock servers DockThor, PharmMapper, ADMETLab, PreADME, Osiris and ProTox. The extract and fraction showed genotoxic activity against meristematic cells of A. cepa, reducing the mitotic index; however, the extract produced great deleterious effects on the system, even causing cell necrosis. In A. Saline, the extract was more toxic than the fraction, but both samples were considered toxic. Annonacin was effectively linked to complex I, and presented different activities regarding toxicity. Thus, the results of this study are promising, highlighting the anticancer potential of acetogenins.     

GC-MS Chemical Characterization and Antibacterial Effect of the Essential oil of Piper mosenii

Commercialized mouthwashes are generally expensive for the most financially vulnerable populations. Thus, several studies evaluate the antimicrobial potential of herbal products, such as essential oils, to reduce the activity of microorganisms in the mouth. The objective of this research was to carry out the chemical characterization and antibacterial activity of the essential oil of Piper mosenii (EOPm), providing data that enable the development of a low-cost mouthwash formulation aimed at vulnerable communities. The analysis of the antibacterial potential and modulator of bacterial resistance was verified by the microdilution method to determine the minimum inhibitory concentration-MIC. The chemical components were characterized by gas chromatography coupled to mass spectrometry, where 23 chemical constituents were detected, with α-pinene, being the major compound. The EOPm showed a MIC ≥ 1024 µg/mL for all bacterial strains used in the tests. When the EOPm modulating activity was evaluated together with chlorhexidine, mouthwash and antibiotics against bacterial resistance, the oil showed a significant synergistic effect, reducing the MIC of the products tested in combination, in percentages between 20.6% to 96.3%. Therefore, it is recommended to expand the tests with greater variation of EOPm concentration and the products used in this research, in addition to the evaluation of toxicity and in vivo tests, seeking the development of a possible formulation of mouthwash accessible to the vulnerable population.     

Non embedding in sphere bundles

In order to get results of non-embedding of flag-manifolds in the total space of sphere bundles we consider algebraic properties of these two families of manifolds. The main theorem (2.3) gives a general a non-embedding result in terms of algebraic invariants and this theorem is applied to the case of the flag-manifolds.