Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators

In many works, the linearized non-cutoff Boltzmann operator is considered to behave essentially as a fractional Laplacian. In the present work, we prove that the linearized non-cutoff Boltzmann operator with Maxwellian molecules is exactly equal to a fractional power of the linearized Landau operator which is the sum of the harmonic oscillator and the spherical Laplacian. This result allows to display explicit sharp coercive estimates satisfied by the linearized non-cutoff Boltzmann operator for both Maxwellian and non-Maxwellian molecules.Comment: arXiv admin note: text overlap with arXiv:1111.042

The gut microbiota of Colombians differs from that of Americans, Europeans and Asians

ABSTRACT: The composition of the gut microbiota has recently been associated with health and disease, particularly with obesity. Some studies suggested a higher proportion of Firmicutes and a lower proportion of Bacteroidetes in obese compared to lean people; others found discordant patterns. Most studies, however, focused on Americans or Europeans, giving a limited picture of the gut microbiome. To determine the generality of previous observations and expand our knowledge of the human gut microbiota, it is important to replicate studies in overlooked populations. Thus, we describe here, for the first time, the gut microbiota of Colombian adults via the pyrosequencing of the 16S ribosomal DNA (rDNA), comparing it with results obtained in Americans, Europeans, Japanese and South Koreans, and testing the generality of previous observations concerning changes in Firmicutes and Bacteroidetes with increasing body mass index (BMI). Results: We found that the composition of the gut microbiota of Colombians was significantly different from that of Americans, Europeans and Asians. The geographic origin of the population explained more variance in the composition of this bacterial community than BMI or gender. Concerning changes in Firmicutes and Bacteroidetes with obesity, in Colombians we found a tendency in Firmicutes to diminish with increasing BMI, whereas no change was observed in Bacteroidetes. A similar result was found in Americans. A more detailed inspection of the Colombian dataset revealed that five fiber-degrading bacteria, including Akkermansia, Dialister, Oscillospira, Ruminococcaceae and Clostridiales, became less abundant in obese subjects. Conclusion: We contributed data from unstudied Colombians that showed that the geographic origin of the studied population had a greater impact on the composition of the gut microbiota than BMI or gender. Any strategy aiming to modulate or control obesity via manipulation of this bacterial community should consider this effect

Effect of autoclave sterilisation and heat activated sodium hypochlorite irrigation on the performance of nickel-titanium rotary files against cyclic fatigue

The present study aims to assess the impact of heat-activated sodium hypochlorite (NaOCl) and/or autoclave sterilisation on the cyclic fatigue resistance (CFR) of heat-treated nickel-titanium rotary files used in root canal treatment. The CFR of One Curve (OC) files was evaluated under the following conditions: as received (Group 1; control), immersion in NaOCl at 23 ± 1ºC (Group 2), immersion in NaOCl at 60 ± 1ºC (Group 3), autoclave sterilisation at 135 1ºC (Group 4), combined treatment of autoclave sterilisation and immersion in NaOCl at 23 ± 1ºC (Group 5), and combined treatment of autoclave sterilisation and immersion in NaOCl at 60 ± 1ºC (Group 6). A simulated root canal in a zirconia block was utilised to test the performance of the files. All the types of treatments resulted in significant reductions in fracture resistance of the OC files. Immersion of the files in NaOCl at 23ºC revealed the smallest reduction, while combined treatment of autoclaving and immersion in NaOCl at 60ºC caused the greatest reduction. Autoclave sterilisation or exposure of OC files to 2.5% NaOCl adversely affect the cyclic fatigue life and increasing solution temperature or combined treatment caused additionally significant reduction in CFR