Background: The gut microbiota is increasingly recognized as playing an important role in the development of obesity, but the influence of gender remains elusive. Using a large cohort of Chinese adults, our study aimed to identify differences in gut microbiota as a function of body mass index (BMI) and investigate gender specific features within these differences.Methods: Five hundred fifty-one participants were categorized as underweight, normal, overweight, or obese, based on their BMI. Fecal microbiome composition was profiled via 16S rRNA gene sequencing. Generalized linear model (GLM), BugBase, PICRUSt, and SPIEC-EASI were employed to assess the variabilities in richness, diversity, structure, organism-level microbiome phenotypes, molecular functions, and ecological networks of the bacterial community that associated with BMI and sex.Results: The bacterial community of the underweight group exhibited significantly higher alpha diversity than other BMI groups. When stratified by gender, the pattern of alpha diversity across BMI was maintained in females, but no significant difference in alpha diversity was detected among the BMI groups of males. An enrichment of Fusobacteria was observed in the fecal microbiota of obese males, while obese females demonstrated an increased relative abundance of Actinobacteria. Analysis of microbial community-level phenotypes revealed that underweight males tend to have more anaerobic and less facultatively anaerobic bacteria, indicating a reduced resistance to oxidative stress. Functionally, butyrate-acetoacetate CoA-transferase was enriched in obese individuals, which might favor energy accumulation. PhoH-like ATPase was found to be increased in male obese subjects, indicating a propensity to harvest energy. The microbial ecological network of the obese group contained more antagonistic microbial interactions as well as high-degree nodes.Conclusion: Using a large Chinese cohort, we demonstrated BMI-associated differences in gut microbiota composition, functions, and ecological networks, which were influenced by gender. Results in this area have shown variability across several independent studies, suggesting that further investigation is needed to understand the role of the microbiota in modulating host energy harvest and storage, and the impact of sex on these functions.

The paper studies the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic potential. After a rotation number function ρ(λ) has been introduced, it is proved that for any non-negative integer n, the endpoints of the interval ρ −1 (n/2) in R yield the corresponding periodic or anti-periodic eigenvalues. However, as in the Dirichlet problem of the higher dimensional p-Laplacian, it remains open if these eigenvalues represent all periodic and anti-periodic eigenvalues. The result obtained is a partial generalization of the spectrum theory of the one-dimensional Schrödinger operators with periodic potentials.

In this paper, we study positive periodic solutions to the repulsive singular perturbations of the Hill equations. It is proved that such a perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray-Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder's fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions. Recent results in the literature are generalized and significantly improved.

In this paper we will use the coincidence degree to give an existence result of periodic solutions for the scalar Lienard equations with singular forces of repulsivé type. The main result of this paper clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution. As an application, we will improve the results of Ding, Ye, and Wang for the Brillouin electron beam focusing system.