In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next approximation. We sharpen his results with a geometric method and give both sharp upper and lower bounds. We also calculate the asymptotic frequency that these bounds occur.

In order to combat the growing problems associated with biological invasions, many researchers have focused on identifying which communities are most vulnerable to invasion by exotic species. However, once established, invasive species can significantly change the composition of the communities that they invade. The first step to disentangling the direction of causality is to discern whether a ...

In a 2-year field study, we quantified lateral root growth patterns and soil water depletion dynamics in the invasive annual Centaurea solstitialis and two native perennials, Elymus glaucus and Grindelia camporum. Centaurea solstitialis produced lateral roots most actively from early April to mid-June, during the late rosette to spiny seedhead stage while both root growth and water depletion we...

BACKGROUND Centaurea aegyptiaca L (Asteraceae), is one of the most attractive plants growing wildly in Sinai, and is not well investigated for its phytochemical constituents. This study represents the first in-depth characterization of the phenolic profile of the aerial parts of C. aegyptiaca methanolic extract utilizing liquid chromatography (LC) combined with electrospray ionization (ESI) tan...

Background and objectives: The genus Centaurea from the Asteraceae family is one of the most widely distributed plant genera worldwide that has been extensively used in folk medicine for hundreds of years. The present study is the first investigation about the principal constituents of Centaurea albonitens Turrill which is native to Iran. Methods: The aerial parts of C. albonitens were extracte...

The blue bottle experiment is a collective term for autoxidation reactions catalysed by redox indicators. The reactions are characterized by their repeatable cycle of colour changes when shaken/left to stand and intricate chemical pattern formation. The blue bottle experiment is studied based on calculated solution-phase half-cell reduction potential of related reactions. Our investigation conf...

The effects of declining plant biodiversity on ecosystem processes are well studied, with most investigations examining the role of species richness declines rather than declines of species abundance. Using grassland mesocosms, we examined how the abundance of a native, resident species, Hemizonia congesta (hayfield tarweed), affected exotic Centaurea solstitialis (yellow starthistle) invasion....

Understanding the role of competition in the organization of communities is limited in part by the difficulty of extrapolating the outcomes of small-scale experiments to how such outcomes might affect the distribution and abundance of species. We modeled the community-level outcomes of competition, using experimentally derived competitive effects and responses between an exotic invasive plant, ...