| 1. |
- 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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| 2. |
- Lindström, Torsten, 1965-, et al.
(författare)
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A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
- 2016
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Ingår i: Scientific World Journal. - : Hindawi Limited. - 1537-744X .- 2356-6140.
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Tidskriftsartikel (refereegranskat)abstract
- The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too.
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| 3. |
- Lindström, Torsten, et al.
(författare)
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Uniqueness of limit cycles for a limiting case of the chemostat : does it justify the use of logistic growth rates?
- 2015
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Ingår i: Electronic Journal of Qualitative Theory of Differential Equations. - : University of Szeged. - 1417-3875. ; :47, s. 1-14
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Tidskriftsartikel (refereegranskat)abstract
- On infinitesimally short time intervals various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann, The dynamics of physiologically structured populations, 1986, p. 3). This is one of the cornerstones for differential equations modeling in general. Complicated models for processes interacting in a complex manner may be built up, and not only in population dynamics. The principle holds as long as the various contributions are taken into account exactly. In this paper we discuss commonly used approximations that may lead to non-removable dependency terms potentially affecting the long run qualitative behavior of the involved equations. We prove that these terms do not produce such effects in the simplest and most interesting biological case, but the general case is left open. Our main result is a rather complete analysis of an important limiting case. Once complete knowledge of the qualitative properties of simple models is obtained, it greatly facilitates further studies of more complex models. A consequence of our analysis is that standard methods can be applied. However, the application of those methods is far from straightforward and require non-trivial estimates in order to make them valid for all values of the parameters. We focus on making these proofs as elementary as possible.
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| 4. |
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| 5. |
- Argatov, Ivan, et al.
(författare)
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Gravitational settling of a cell on a high-aspect-ratio nanostructured substrate : An asymptotic modeling approach
- 2022
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Ingår i: Applied Mathematical Modelling. - : Elsevier. - 0307-904X .- 1872-8480. ; 108, s. 294-307
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Tidskriftsartikel (refereegranskat)abstract
- The problem of contact deformation of an elastic body loaded by gravitational forces and laying on several small rigid supports is considered in the framework of the linear theory of elasticity. Using the method of matched asymptotic expansions, the limit asymptotic model for determining the support reactions and the kinematic parameters of the body settling is derived. The effect of the body surface reinforcement is discussed. The case of a uniform (symmetric) settling is considered in detail.
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| 6. |
- Argatov, Ivan I
(författare)
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A scalar prototype problem of deep abrasive drilling with an infinite free boundary : an asymptotic modeling study
- 2019
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Ingår i: Journal of Engineering Mathematics. - : Springer. - 0022-0833 .- 1573-2703. ; 118:1, s. 29-41
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Tidskriftsartikel (refereegranskat)abstract
- A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a priori unknown domain with overdetermined boundary conditions, the right-hand sides of which depend on the unit normal to the free boundary. A perturbation analysis of the nonstandard free boundary problem that models deep abrasive drilling has been performed under the assumption that the free boundary is close to the surface of a given semi-infinite cylinder, the longitudinal position of which depends on the boundary data, and the leading-order asymptotic solution has been developed.
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| 7. |
- Baravdish, George, et al.
(författare)
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Extension of p-Laplace Operator for Image Denoising
- 2016
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Ingår i: 27th IFIP TC 7 Conference, CSMO 2015, Sophia Antipolis, France, June 29 - July 3, 2015, Revised Selected Papers. - Cham : Springer. - 9783319557946 - 9783319557953 ; , s. 107-116, s. 107-116
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Bokkapitel (refereegranskat)abstract
- In this work we introduce a novel operator $$\displaystyle \varDelta _(p,q)$$ as an extended family of operators that generalize the p-Laplace operator. The operator is derived with an emphasis on image processing applications, and particularly, with a focus on image denoising applications. We propose a non-linear transition function, coupling p and q, which yields a non-linear filtering scheme analogous to adaptive spatially dependent total variation and linear filtering. Well-posedness of the final parabolic PDE is established via pertubation theory and connection to classical results in functional analysis. Numerical results demonstrates the applicability of the novel operator $$\displaystyle \varDelta _(p,q)$$ .
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| 8. |
- Baravdish, George, 1964-, et al.
(författare)
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Generalizations of p-Laplace operator for image enhancement : Part 2
- 2020
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Ingår i: Communications on Pure and Applied Analysis. - Springfield, MO, United States : American Institute of Mathematical Sciences. - 1534-0392 .- 1553-5258. ; 19:7, s. 3477-3500
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Tidskriftsartikel (refereegranskat)abstract
- We have in a previous study introduced a novel elliptic operator Delta((p,q))u = vertical bar del u vertical bar(q) Delta(1)u + (p - 1) vertical bar del u vertical bar(p-2)Delta(infinity) u, p >= 1, q >= 0, as a generalization of the p-Laplace operator. In this paper, we establish the well-posedness of the parabolic equation u(t) =vertical bar del u vertical bar(1-q) Delta((1+q,q)), where q = q(vertical bar del u vertical bar) is continuous and has range in [0, 1], in the framework of viscosity solutions. We prove the consistency and convergence of the numerical scheme of finite differences of this parabolic equation. Numerical simulations shows the advantage of this operator applied to image enhancement.
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| 9. |
- Baravdish, George, 1964-, et al.
(författare)
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On a new singular and degenerate extension of the p-Laplace operator
- 2024
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Ingår i: Nonlinear Analysis. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0362-546X .- 1873-5215. ; 244
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Tidskriftsartikel (refereegranskat)abstract
- We study a novel degenerate and singular elliptic operator Δ˜(τ,χ) defined by Δ˜(τ,χ)u=τ(x,Du)(|Du|Δ1u+χ(x,Du)Δ∞u), where the singular weights τ(x,s)>0 and χ(x,s)≥0 are continuous functions on Ω×Rn∖{0}. The operator Δ˜(τ,χ) is an extension of Δ(p,q)u=|Du|qΔ1u+(p−1)|Du|p−2Δ∞u,p≥1,q≥0, introduced by the authors in Baravdishet al. (2020), which in turn is an extension of the p-Laplace operator Δp. We establish the well-posedness of the Neumann boundary value problem for the parabolic equation ut=Δ˜(τ,χ)u in the framework of viscosity solutions. For the solution u, the weight χ controls the evolution along the tangential and the normal directions, respectively, on the level surface of u. The weight τ controls the total speed of the evolution of u. We also prove the consistency and the convergence of the numerical scheme for the finite differences method of the parabolic equation above. Numerical simulations show that our novel nonlinear operator Δ˜(τ,χ) gives better results than both the Perona–Malik (Perona and Malik, 1990) and total variation (TV) methods (Chan and Shen, 2005) when applied to image enhancement.
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| 10. |
- Björklund, Camilla, 1977, et al.
(författare)
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Sharpening the Focus on Numbers and Counting: Preschool Educators Differentiating Aspects of Mathematical Knowledge for Teaching
- 2017
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Ingår i: Mathematics Teacher Education and Development. - : Mathematics Education Research Group of Australasia. - 1442-3901. ; 19:3, s. 117-134
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Tidskriftsartikel (refereegranskat)abstract
- This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics education practice. The object of learning for the participants is more specifically how numbers and counting are made content for learning in preschool practice. The educators’ authentic documentations are reflected upon in focus group meetings and further analysed by the researchers to find out what aspects the educators differentiate during the programme. Results show that educators’ learning about content for children’s learning in preschool is a complex process. This process involves several aspects necessary to discern for a professional development to occur, but the collaborative approach seems prosperous in that new aspects are brought to the fore, influencing their reflective practice.
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