Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method

Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved to be convergent. Then, Tranter's method is discussed. This method was devised in the 1950s to solve certain pairs of dual integral equations. It is shown that this method is also convergent because it leads to the same algebraic system as the spectral method

Increased Intestinal Permeability in Older Subjects Impacts the Beneficial Effects of Dietary Polyphenols by Modulating Their Bioavailability

Polyphenols have great potential in regulating intestinal health and ameliorating pathological conditions related to increased intestinal permeability (IP). However, the efficacy of dietary interventions with these phytochemicals may significantly be influenced by interindividual variability factors affecting their bioavailability and consequent biological activity. In the present study, urine samples collected from older subjects undergoing a crossover intervention trial with polyphenol-rich foods were subjected to metabolomics analysis for investigating the impact of increased IP on the bioavailability of polyphenols. Interestingly, urinary levels of phase II and microbiota-derived metabolites were significantly different between subjects with healthier intestinal barrier integrity and those with increased IP disruption. Our results support that this IP-dependent impaired bioavailability of polyphenols could be attributed to disturbances in the gut microbial metabolism and phase II methylation processes. Furthermore, we also observed that microbiota-derived metabolites could be largely responsible for the biological activity elicited by dietary polyphenols against age-related disrupted IP

Estimated intakes of nutrients and polyphenols in participants completing the maple randomised controlled trial and its relevance for the future development of dietary guidelines for the older subjects

The evaluation of food intake in older subjects is crucial in order to be able to verify adherence to nutritional recommendations. In this context, estimation of the intake of specific dietary bioactives, such as polyphenols, although particularly challenging, is necessary to plan possible intervention strategies to increase their intake. The aims of the present study were to: (i) evaluate the nutritional composition of dietary menus provided in a residential care setting; (ii) estimate the actual intake of nutrients and polyphenols in a group of older subjects participating in the MaPLE study; and (iii) investigate the impact of an eight-week polyphenol-rich dietary pattern, compared to an eight-week control diet, on overall nutrient and polyphenol intake in older participants. The menus served to the participants provided ~770 mg per day of total polyphenols on average with small variations between seasons. The analysis of real consumption, measured using weighed food diaries, demonstrated a lower nutrient (~20%) and polyphenol intake (~15%) compared to that provided by the menus. The feasibility of dietary patterns that enable an increase in polyphenol intake with putative health benefits for age-related conditions is discussed, with a perspective to developing dietary guidelines for this target population