共查询到20条相似文献,搜索用时 15 毫秒
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Ian Jones Dave Pratt 《International Journal of Computers for Mathematical Learning》2006,11(3):301-325
Children tend to view the equals sign as an operator symbol bereft of the rich relational properties of equality statements.
It has been argued by some that this restricted view of the equals sign is due to cultural or cognitive factors. We suggest
a significant factor is that rich relational meanings lack relevance within the context of paper-based arithmetic. One possible
way to allow learners access to relational meanings is through interaction with technologically supported utilities for the
equals sign. We report upon a trial in which two students draw on existing and emerging notions of mathematical equivalence
in order to connect an onscreen = object with other arithmetical objects.
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Ian JonesEmail: |
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This paper deals with the length of a Robertson-Seymour's tree-decomposition. The tree-length of a graph is the largest distance between two vertices of a bag of a tree-decomposition, minimized over all tree-decompositions of the graph. The study of this invariant may be interesting in its own right because the class of bounded tree-length graphs includes (but is not reduced to) bounded chordality graphs (like interval graphs, permutation graphs, AT-free graphs, etc.). For instance, we show that the tree-length of any outerplanar graph is ⌈k/3⌉, where k is the chordality of the graph, and we compute the tree-length of meshes.More fundamentally we show that any algorithm computing a tree-decomposition approximating the tree-width (or the tree-length) of an n-vertex graph by a factor α or less does not give an α-approximation of the tree-length (resp. the tree-width) unless if α=Ω(n1/5). We complete these results presenting several polynomial time constant approximate algorithms for the tree-length.The introduction of this parameter is motivated by the design of compact distance labeling, compact routing tables with near-optimal route length, and by the construction of sparse additive spanners. 相似文献
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Ian Jones Matthew Inglis Camilla Gilmore Rhys Evans 《Research in Mathematics Education》2013,15(1):34-49
A cumulative body of research has shown that children typically shift from an operational to a relational conception of the equals sign as they move through schooling. Jones (2008) argued that a truly relational conception of the equals sign comprises a substitutive component and a sameness component. Here we present two studies that build on this argument. The first investigated how the equals sign is typically presented to primary children in England, and we report that in the main an operational conception seems to be promoted. The second study measured the impact of a specially designed intervention on early secondary children's conceptions of the equals sign. Pre- and post-test data revealed that the intervention promoted substitutive and sameness components of symbolic equivalence. We consider the theoretical and pedagogical implications of the results. 相似文献
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Stephan Brandt 《Discrete Mathematics》2010,310(3):662-669
In a triangle-free graph, the neighbourhood of every vertex is an independent set. We investigate the class S of triangle-free graphs where the neighbourhoods of vertices are maximum independent sets. Such a graph G must be regular of degree d=α(G) and the fractional chromatic number must satisfy χf(G)=|G|/α(G). We indicate that S is a rich family of graphs by determining the rational numbers c for which there is a graph G∈S with χf(G)=c except for a small gap, where we cannot prove the full statement. The statements for c≥3 are obtained by using, modifying, and re-analysing constructions of Sidorenko, Mycielski, and Bauer, van den Heuvel and Schmeichel, while the case c<3 is settled by a recent result of Brandt and Thomassé. We will also investigate the relation between other parameters of certain graphs in S like chromatic number and toughness. 相似文献
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Nechemia Burshtein 《Discrete Mathematics》2005,300(1-3):213-217
Questions, partial and complete answers about the diophantine equation in distinct positive integers are given when additional requirements are asked on the xi's such as: being large, odd, even or xixj for i≠j. Various combinations of the above conditions are also considered. 相似文献
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Munir Mahmood Ibtihal Mahmood 《International Journal of Mathematical Education in Science & Technology》2016,47(6):959-960
When asked, a number of students answer zero factorial to be zero as a continuation to the answer of one factorial to be one. Any instructor would then seek a justification of zero factorial to be one from computing nCn via the well- known combination formula. This article conveys a simple presentation of zero factorial to be one based on lower and upper bounds of n factorial. We have not seen this explanation covered in any algebra textbook. 相似文献
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R. Bordley 《Journal of Optimization Theory and Applications》1988,57(3):511-512
Many companies maximize the present value of profit over some time horizon. If the company's problem is an autonomous control
problem, then present value equals the Hamiltonian's decrease over the time horizon divided by the discount factor. 相似文献
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Archiv der Mathematik - qaaa We provide a simple proof for the equality between the normalized volume of a convex polytope with m vertices and the mixed volume of m simplices and thus show the... 相似文献
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The golden mean numerical value φ = 0.5(√5 − 1) has been given a physical manifestation through E infinity theory.This short paper relates the golden mean energy 0.618034 MeV to atomic electron orbitals. 相似文献
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Tobias Müller 《Random Structures and Algorithms》2017,50(4):679-697
In the confetti percolation model, or two‐coloured dead leaves model, radius one disks arrive on the plane according to a space‐time Poisson process. Each disk is coloured black with probability p and white with probability . In this paper we show that the critical probability for confetti percolation equals 1/2. That is, if p > 1/2 then a.s. there is an unbounded curve in the plane all of whose points are black; while if then a.s. all connected components of the set of black points are bounded. This answers a question of Benjamini and Schramm [1]. The proof builds on earlier work by Hirsch [7] and makes use of an adaptation of a sharp thresholds result of Bourgain. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 679–697, 2017 相似文献
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We study the dual problems associated with the robust counterparts of uncertain convex programs. We show that while the primal robust problem corresponds to a decision maker operating under the worst possible data, the dual problem corresponds to a decision maker operating under the best possible data. 相似文献
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Francesco Barioli Shaun M. Fallat Ronald L. Smith 《Linear algebra and its applications》2008,429(7):1568-1578
The minimum rank of a graph G is defined as the smallest possible rank over all symmetric matrices governed by G. It is well known that the minimum rank of a connected graph is at least the diameter of that graph. In this paper, we investigate the graphs for which equality holds between minimum rank and diameter, and completely describe the acyclic and unicyclic graphs for which this equality holds. 相似文献
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Sergio Conti Camillo De Lellis Stefan Müller Mario Romeo 《Comptes Rendus Mathematique》2003,337(4):233-238
We give a short, self-contained argument showing that, for compact connected sets in which are invariant under the left and right action of SO(2), polyconvexity is equivalent to rank-one convexity (and even to lamination convexity). As a corollary, the same holds for O(2)-invariant compact sets. These results were first proved by Cardaliaguet and Tahraoui. We also give an example showing that the assumption of connectedness is necessary in the SO(2) case. To cite this article: S. Conti et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
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