From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity. Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24 November, 2006), part of the "General Relativity Trimester" at the Institut Henri Poincare (Fall 2006). Comments and references added. Typos corrected. Submitted to Classical and Quantum Gravit

Optimisation of microwave effect on bioactives contents and colour attributes of aqueous green tea extracts by central composite design

The aim of the present study was to investigate the effects of microwave-assisted extraction parameters on total phenolic content (TPC), total flavonoid content (TFC), condensed tannins content (CTC), DPPH-scavenging activity, and colour attributes of aqueous green tea extracts and to optimise the microwaving conditions using response surface methodology. Microwave power (120–360–600 W) and irradiation time (1–3–5 min) were selected as independent variables. Statistical analysis revealed that all responses were significantly affected by extraction parameters. The optimum microwave-assisted extraction conditions were 350.65 W microwave power and 5 min irradiation time to maximise TPC, TFC, CTC, DPPH-scavenging activity, and L* values and to minimise a* and b* values of aqueous green tea extracts. The predicted TPC was 116.58 mg gallic acid equivalents/g (GAE/g), TFC was 49.33 mg catechin equivalents/g (CE/g), CTC was 9.89 mg catechin equivalents/g (CE/g), DPPH-scavenging activity (IC50) was 294.46 µg/mL, L* value was 12.31, a* value was 2.61 and b* value was 7.02 under optimum microwave-assisted extraction conditions. This study revealed that microwave extraction conditions should be controlled to obtain aqueous green tea extracts with both high bioactivity and acceptable colour quality. © 2020, Springer Science+Business Media, LLC, part of Springer Nature