Classification of finite-dimensional modules over semisimple Lie algebras

Sophus Lie (1842-1899) known as the founder of the theory of transformation groups, originally aimed to study solutions of differential equations via their symmetries. Over the decades this theory has evolved into the theory of Lie groups. These Lie groups are of an analytic and geometric nature, but Sophus Lie's principal discovery was that...

Modelling stability of Avicennia marina mangroves under wave and wind loads: Effect of soil and root system on tree resistance

Mangroves can provide coastal protection by attenuating waves, currents, and trapping sediment (Menéndez et al., 2020; Bao, 2011). The effect of mangroves on the hydrodynamics depends on their size, location, density, distribution and morphology of the vegetation (Mendez and Losada, 2004). Mangrove loss during storm events will therefore impact...

The elementary particles and the root system E8

E8 is a famous root system in mathematics. Lisi claims in his paper “An Exceptionally Simple Theory of Everything” that there is a connection between the standard model of the elementary particles and this root system. He claims that standard model has the same structure as the root system E8. If this is true, there must be a mapping from the...

What Do Plants Leave after Summer on the Ground?: The Effect of Afforested Plants in Arid Environments

The implementation of afforestation programs in arid environments in northern China had modified the natural vegetation patterns. This increases the evaporation flux; however, the influence of these new covers on the soil water conditions is poorly understood. This work aims to describe the effect of Willow bushes (Salix psammophila C. Wang...

Urban Vegetation Modeling 3D Levels of Detail

3D city models are now common planning and analysis tools. Urban vegetation as a feature in these models, however, is neglected overshadowed by the focus on buildings, so its inclusion in 3D city models is often symbolic. On the other hand, urban vegetation improves the comfort and social well being of a city’s inhabitants and is a resource for...

De wortelsystemen in E8

In dit verslag wordt besproken hoe je deelwortelsystemen in het wortelsysteem E8 kan vinden. In het begin wordt er algemene theorie over wortelsystemen gegeven. Vervolgens worden er twee manieren besproken hoe je deelwortelsystemen in wortelsystemen kan vinden. Uiteindelijk worden de twee manieren toegepast op E8 om deelwortelsystemen in E8 te...

Het wortelsysteem van E8: Een model voor elementaire deeltjes?

In dit onderzoek wordt gekeken of het model voor elementaire deeltjes voorgesteld door de Amerikaanse fysicus Antony G. Lisi bevestigd of weerlegd kan worden. In dit model worden elementaire deeltjes gekoppeld aan wortels uit het wortelsysteem van E8 en worden ladingen gekoppeld aan gewichten van dit wortelsysteem. Interacties tussen deeltjes...

A Study on Geometric and Material Properties of the Mangrove Root System in Singapore

Although the effect of wave attenuation by mangrove has been widely observed and studied, the problem pertaining to how to accurately describe the geometrical properties is still remaining unresolved. Also, the material properties of mangrove root have not been comprehensively studied before. This is study is dedicated for the survey on...