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| 2. |
- Helenius, Ola, 1970, et al.
(författare)
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Measuring temperature within the didactic space of preschool
- 2016
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 21:4, s. 155-176
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Tidskriftsartikel (refereegranskat)abstract
- The informal character of preschool mathematics, engaged in during children’s play, places complex requirements on preschool teachers. It also leads to challenges in developing appropriate analytical tools for researching teacher work. In this paper a framework, the ”didaktic space”, is described and used to analyse interactions between preschool teachers and children in relationship to mathematical learning situations. An interaction between a preschool teacher and a group of children about how to compare their temperatures is analysed, using this framework. The analysis focuses on how the teacher’s contributions as well as those of the children changed as the role of the mathematics changed. The paper discusses how the didaktic space offers a nuanced understanding of preschool mathematical situations, both to researchers and to teachers.
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| 3. |
- Barza, Sorina, et al.
(författare)
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A Sawyer duality principle for radially monotone functions in Rn
- 2005
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Ingår i: Journal of Inequalities in Pure and Applied Mathematics. - 1443-5756. ; 6:2
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Tidskriftsartikel (refereegranskat)abstract
- Let f be a non-negative function on ℝn, which is radially monotone (0 < f↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup ∫ℝ fg/f↓r(∫ℝn fp v)1/p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given. © 2005 Victoria University
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| 4. |
- Gogatishvili, Amiran, et al.
(författare)
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Characterisation of embeddings in Lorentz spaces
- 2007
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Ingår i: Bulletin of the Australian Mathematical Society. - 0004-9727 .- 1755-1633. ; 76:1, s. 69-92
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Tidskriftsartikel (refereegranskat)abstract
- Some new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embeddingSome new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embedding
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| 5. |
- Johansson, Maria, et al.
(författare)
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A new approach to the Sawyer and Sinnamon characterizations of Hardy's inequality for decreasing functions
- 2008
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Ingår i: Georgian Mathematical Journal. - 1072-947X .- 1572-9176. ; 15:2, s. 295-306
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Tidskriftsartikel (refereegranskat)abstract
- Some Hardy type inequalities for decreasing functions are characterized by one condition (Sinnamon), while others are described by two independent conditions (Sawyer). In this paper we make a new approach to deriving such results and prove a theorem, which covers both the Sinnamon result and the Sawyer result for the case where one weight is increasing. In all cases we point out that the characterizing condition is not unique and can even be chosen among some (infinite) scales of conditions.
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| 6. |
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| 7. |
- Johansson, Maria
(författare)
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Carleman type inequalities and Hardy type inequalities for monotone functions
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This Ph.D. thesis deals with various generalizations of the inequalities by Carleman, Hardy and Polya-Knopp. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In Chapter 2 we consider Carleman's inequality, which may be regarded as a discrete version of Polya-Knopp's inequality and also as a natural limiting inequality of the discrete Hardy inequality. We present several simple proofs of and remarks (e.g. historical) about this inequality. In Chapter 3 we give some sharpenings and generalizations of Carleman's inequality. We discuss and comment on these results and put them into the frame presented in the previous chapter. We also include some new proofs and results. In Chapter 4 we prove a multidimensional Sawyer duality formula for radially decreasing functions and with general weights. We also state the corresponding result for radially increasing functions. In particular, these results imply that we can describe mapping properties of operators defined on cones of such monotone functions. Moreover, we point out that these results can also be used to describe mapping properties of operators between some corresponding general weighted multidimensional Lebesgue spaces. In Chapter 5 we give a weight characterization of the weighted Hardy inequality for decreasing functions and we use this results to give a new weight characterization of the weighted Polya-Knopp inequality for decreasing functions and we also give a new scale of weightconditions for the Hardy inequality for decreasing functions. In Chapter 6 we make a unified approach to Hardy type inequalitits for non-increasing functions and prove a result which covers both the Sinnamon result with one condition and Sawyer's result with two independent conditions for the case when one weight is non-decreasing. In all cases we point out that this condition is not unique and can even be chosen among some (infinte) scales of conditions. In Chapter 7 we obtain the characterization of the general Hardy operator restricted to monotone functions. In Chapter 8 we present some new integral conditions characterizing the embedding between some Lorentz spaces. Only one condition is necessary for each case which means that our conditions are different and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame. In our proof we use a technique of discretization and anti-discretization developed by A. Gogatishvili and L. Pick, where they considered the opposite embedding.
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| 8. |
- Johansson, Maria, et al.
(författare)
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Hardy inequality with three measures on monotone functions
- 2008
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 11:3, s. 393-413
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Tidskriftsartikel (refereegranskat)abstract
- Characterization of Lvp[0, ∞) - L μq[O, ∞) boundedness of the general Hardy operator (Hsf)(x) =(∫[0,x] fsudλ) 1/s restricted to monotone functions f ≥ 0 for 0 < p.q.s < ∞ with positive Borel σ -finite measures λ, μ and v is obtained.
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| 9. |
- Johansson, Maria, et al.
(författare)
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Multidimensional inequalities of Hardy and (limit) Pólya-Knopp types
- 2012
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Ingår i: Analysis for science, engineering and beyond. - Heidelberg : Encyclopedia of Global Archaeology/Springer Verlag. - 9783642202353 - 9783642202360 ; , s. 267-304
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Bokkapitel (refereegranskat)abstract
- In this review paper we complement the classical two-dimensional Hardy-type inequality by E. Sawyer (see MR87f:42052) in various ways. In particular, ideas and results from three recent Ph.D. theses are unified and presented in this frame. Also some complementary new results are proved and some open questions are raised.
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| 10. |
- Johansson, Maria, et al.
(författare)
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Young children’s multimodal mathematical explanations
- 2014
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Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer. - 1863-9690 .- 1863-9704. ; 46:6, s. 895-909
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates how three children provided mathematical explanations whilst playing with a set of glass jars in a Swedish preschool. Using the idea of semiotic bundles combined with the work on multimodal interactions, the different semiotic resources used individually and in combinations by the children are described. Given that the children were developing their verbal fluency, it was not surprising to find that they also included physical arrangements of the jars and actions to support their explanations. Hence, to produce their explanations of different attributes such as thin and sameness, the children drew on each other’s gestures and actions with the jars. This research has implications for how the relationship between verbal language and gestures can be viewed in regard to young children’s explanations.
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