3 resultados para Geometry of numbers


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Recent proxy measurements reveal that subglacial lakes beneath modern ice sheets periodically store and release large volumes of water, providing an important but poorly understood influence on contemporary ice dynamics and mass balance. This is because direct observations of how lake drainage initiates and proceeds are lacking. Here we present physical evidence of the mechanism and geometry of lake drainage from the discovery of relict subglacial lakes formed during the last glaciation in Canada. These palaeo-subglacial lakes comprised shallow (<10 m) lenses of water perched behind ridges orientated transverse to ice flow. We show that lakes periodically drained through channels incised into bed substrate (canals). Canals sometimes trend into eskers that represent the depositional imprint of the last high-magnitude lake outburst. The subglacial lakes and channels are preserved on top of glacial lineations, indicating long-term re-organization of the subglacial drainage system and coupling to ice flow.

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Recent evidence has highlighted the important role that number ordering skills play in arithmetic abilities (e.g., Lyons & Beilock, 2011). In fact, Lyons et al. (2014) demonstrated that although at the start of formal mathematics education number comparison skills are the best predictors of arithmetic performance, from around the age of 10, number ordering skills become the strongest numerical predictors of arithmetic abilities. In the current study we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was partially mediated by number ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor which included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

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The local solvation environment of uracil dissolved in the ionic liquid 1-ethyl-3-methylimidazolium acetate has been studied using neutron diffraction techniques. At solvent:solute ratios of 3:1 and 2:1 ionic liquid:uracil, little perturbation of the ion-ion correlations compared to those of the neat ionic liquid are observed. We find that solvation of the uracil is driven predominantly by the acetate anion of the solvent. While short distance correlations exist between uracil and the imidazolium cation, the geometry of these contacts suggest that they cannot be considered as hydrogen bonds, in contrast to other studies by Araújo et al. (J. M. Araújo, A. B. Pereiro, J. N. Canongia-Lopes, L. P. Rebelo, I. M. Marrucho, J. Phys. Chem. B 2013, 117, 4109-4120). Nevertheless, this combination of interactions of the solute with both the cation and anion components of the solvents helps explain the high solubility of the nucleobase in this media. In addition, favorable uracil-uracil contacts are observed, of similar magnitude to those between cation and uracil, and are also likely to aid dissolution