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51.
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Bill Domoney 《Research in Mathematics Education》2013,15(1):53-67
Previous research has shown that secondary school students’ understanding of fractions is dominated by the part-whole concept to the possible detriment of their understanding of a fraction as a number in its own right. The present paper reports on an investigation into the understanding of intending primary teachers in this area. Four representatives of a cohort of sixty students on a PGCE course specialising in the lower primary age range were asked detailed questions probing their knowledge of fractions. The conclusion was that the part-whole concept dominates. All of the students were familiar with the numerical concept from their work on the PGCE course, but they reverted to the more familiar part-whole ideas in attempting to solve problems. 相似文献
53.
Bill Jackson 《Journal of Geometry》2011,101(1-2):131-135
We describe characterizations of boundedness and rigidity of generic 2-dimensional direction?Clength frameworks, and give partial results for the open problem of characterizing the global rigidity of such frameworks. 相似文献
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A. Bill V. Hizhnyakov D. Nevedrov G. Seibold E. Sigmund 《Zeitschrift für Physik B Condensed Matter》1997,104(4):753-757
The presence of electronic inhomogeneities strongly reduces the screening of the electron-ion interaction in high-temperature superconductors. This implies the existence of an non-totally screened long-range contribution to the electron-lattice coupling and opens an additional channel for the formation of copper pairs. We calculate the superconducting order parameter taking into account a) the longrange and the short-range parts of the electron-lattice interaction and b) the Coulomb repulsion between charge-carriers. We show that whereas the long-range electron-lattice coupling determines the anisotropy of the order parameter, the Coulomb repulsion and the short-range interactions determine its symmetry. Thus, different high-T c superconductors may have s- or d-wave symmetry, depending on the relative strength of the interactions involved in the pairing. 相似文献
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A direction–length framework is a pair (G,p) where G=(V;D,L) is a ‘mixed’ graph whose edges are labelled as ‘direction’ or ‘length’ edges and p is a map from V to ℝ
d
for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G
+ be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show that (G,p) is bounded if and only if (G
+,p) is infinitesimally rigid. This gives a characterization of when (G,p) is bounded in terms of the rank of the rigidity matrix of (G
+,p). We use this to characterize when a mixed graph is generically bounded in ℝ
d
. As an application we deduce that if (G,p) is a globally rigid generic framework with at least two length edges and e is a length edge of G then (G∖e,p) is bounded. 相似文献