Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies.

Under investigation in this paper is the integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies. The linear dispersion relations, completeness relations, inverse scattering transform, and fractional soliton solutions of the integrable fractional discrete modified Korteweg-de Vries hierarchy will be explored. The inverse scattering problem will be solved accurately by constructing Gel'fand-Levitan-Marchenko equations and Riemann-Hilbert problem.

A cross-sectional study: family communication, anxiety, and depression in adolescents: the mediating role of family violence and problematic internet use.

Objective: The objective of this study is to explore the relationship between family communication, family violence, problematic internet use, anxiety, and depression and validate their potential mediating role.

Methods: The study population consisted of Chinese adolescents aged 12 to 18 years, and a cross-sectional survey was conducted in 2022. Structural equation models were constructed using AMOS 25.

Research Progress of Duodenal-Jejunal Bypass Liner in the Treatment of Obesity and Type 2 Diabetes Mellitus.

With the development of economy and improvement of people's living standards, the incidence of obesity and type 2 diabetes mellitus (T2DM) has increased significantly and obesity has also become one of the most important risk factors of T2DM. In light of these trends, there have been many ways to take effect in losing weight. However, they also have corresponding deficiencies including inapparent curative effect, complex and incomplete reversible procedures and severe complications.