| 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. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- de Hoop, Maarten, et al.
(författare)
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Semiclassical analysis of elastic surface waves
- 2017
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable to the wave length. Such a medium can also be thought of as a surficial layer (which can be thick) overlying a half space. The analysis is based on the work of Colin de Verdi\`ere on acoustic surface waves. The description is geometric in the boundary and locally spectral "beneath" it. Effective Hamiltonians of surface waves correspond with eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities. Using these Hamiltonians, we obtain pseudodifferential surface wave equations. We then construct a parametrix. Finally, we discuss Weyl's formulas for counting surface modes, and the decoupling into two classes of surface waves, that is, Rayleigh and Love waves, under appropriate symmetry conditions.
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| 8. |
- de Hoop, Maarten V., et al.
(författare)
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Analysis of wavenumber resonances for the Rayleigh system in a half space
- 2023
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : Royal Society. - 1364-5021 .- 1471-2946. ; 479:2277
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Tidskriftsartikel (refereegranskat)abstract
- We present a comprehensive analysis of wavenumber resonances or leaking modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an appropriate Riemann surface, a boundary matrix and a reflection matrix in analogy to the studies of scattering resonances associated with the Schrödinger operator. We analyse their analytic properties and characterize the distribution of these wavenumber resonances. Furthermore, we show that the resonances appear as poles of the meromorphic continuation of the resolvent to the nonphysical sheets of the Riemann surface as expected.
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| 9. |
- De Hoop, Maarten V, et al.
(författare)
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Inverse problem for Love waves in a layered, elastic half-space
- 2024
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Ingår i: Inverse Problems. - : Institute of Physics Publishing (IOPP). - 0266-5611 .- 1361-6420. ; :045013, s. 1-44
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study Love waves in a layered, elastic half-space. We first address the direct problem and we characterize the existence of Love waves through the dispersion relation. We then address the inverse problem and we show how to recover the parameters of the elastic medium from the empirical knowledge of the frequency–wavenumber couples of the Love waves.
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| 10. |
- de Hoop, Maarten V., et al.
(författare)
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Inverse problem for the Rayleigh system with spectral data
- 2022
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Ingår i: Journal of Mathematical Physics. - : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 63:3, s. 1-33
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Tidskriftsartikel (refereegranskat)abstract
- We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lamé parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution, while the data are captured in a Jost function, and we point out parallels with a corresponding problem for the Schrödinger equation. The Jost function can be identified with spectral data. We derive a Gel’fand-Levitan type equation and obtain uniqueness with two distinct frequencies.
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