Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling

Integrable couplings are associated with non-semisimple Lie algebras. In this paper, we propose a new method to generate new integrable systems through making perturbation in matrix spectral problems for integrable couplings, which is called the `completion process of integrable couplings'. As an example, the idea of construction is applied to the Ablowitz-Kaup-Newell-Segur integrable coupling. Each equation in the resulting hierarchy has a bi-Hamiltonian structure furnished by the component-trace identity

Schwarz Lemma and Schwarz-Pick Lemma for solutions of the α\alpha-harmonic equation

In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of $\alpha$-harmonic equation for $\alpha>-1$ are investigated. By making use of the integral of trigonometric functions, we obtain the two types of inequalities in terms of hypergeometric functions which improve the corresponding results due to Khalfallah et al. (Complex Var. Elliptic Equ., 2023) and Li et al. (Bull. Malays. Math. Sci. Soc., 2022).Comment: 14 pages, 1 figur

Porous amorphous Ge/C composites with excellent electrochemical properties

Porous amorphous germanium/carbon (Ge/C) composites, which were synthesized through the reduction/carbonization of germanium oxide/oleic acid precursors, could exhibit a high-capacity, high-rate and long-life performance due to the synergistic effect of the porous structure and carbon

Molecular docking studies on rocaglamide, a traditional Chinese medicine for periodontitis

Purpose: To undertake an in silico assessment of rocaglamide as a potential drug therapy forperiodontitis (dental arthritis).Method: Lamarckian algorithm-based automated docking approach using AutoDock4.2 tool wasapplied for calculating the best possible binding mode of rocaglamide to IL-23p19 and IL-17, the targets of anti-inflammatory drugs in periodontal disease.Results: The top two interactions of rocaglamide with IL-17 (ΔG = -5.45 and -4.83 kcal/mol) were more spontaneous, and the physical interactions (two hydrogen bonds and one π-πbond) generated in the two IL-17- rocaglamide complexes were higher in number than in IL-23p14-rocaglamide complexes.Conclusion: In silico analysis of rocaglamide, a known antimicrobial and anti-inflammatory agent, is a promising natural candidate for periodontitis therapy, and should be further subjected to in vitro and in vivo anti-periodontitis investigations.Keywords: Periodontitis, Inflammation, Rocaglamide, Molecular docking, Lamarckian algorithm, IL- 23p19, IL-1