On the systematic approach to the classification of differential equations by group theoretical methods

Complete symmetry groups enable one to characterise fully a given differential equation. By considering the reversal of an approach based upon complete symmetry groups we construct new classes of differential equations which have the equations of Bateman, Monge–Ampère and Born–Infeld as special cases. We develop a symbolic algorithm to decrease the complexity of the calculations involved.     

Lie algebraic treatment of the quadratic invariants for a quantum system

We consider the problem of the time-dependent degenerate parametric amplifier. We obtain the quadratic invariant and use it to derive the wave function via its su(1, 1) algebraic basis and a unitary transformation to the time-dependent Schrödinger equation for the parametric amplifier. We obtain the real and the complex invariants, which we use to solve the time-dependent Cauchy problem. Using different integrability conditions, we find the most general solution, which we analyze extensively, providing details of the calculations.     

Synergistic Anti-Inflammatory Activity of Ginger and Turmeric Extracts in Inhibiting Lipopolysaccharide and Interferon-γ-Induced Proinflammatory Mediators

This study aims to investigate the combined anti-inflammatory activity of ginger and turmeric extracts. By comparing the activities of individual and combined extracts in lipopolysaccharide and interferon-γ-induced murine RAW 264.7 cells, we demonstrated that ginger-turmeric combination was optimal at a specific ratio (5:2, w/w) in inhibiting nitric oxide, tumour necrosis factor and interleukin 6 with synergistic interaction (combination index < 1). The synergistic inhibitory effect on TNF was confirmed in human monocyte THP-1 cells. Ginger-turmeric combination (5:2, w/w) also upregulated nuclear factor erythroid 2–related factor 2 activity and heme oxygenase-1 protein expression. Additionally, 6-shogaol, 8-shogaol, 10-shogaol and curcumin were the leading compounds in reducing major proinflammatory mediators and cytokines, and a simplified compound combination of 6-s, 10-s and curcumin showed the greatest potency in reducing LPS-induced NO production. Our study provides scientific evidence in support of the combined use of ginger and turmeric to alleviate inflammatory processes.