Search results for "Matematikk"
showing 10 items of 707 documents
Variational principles for fluid dynamics on rough paths
2022
In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynamics (RGFD) models as critical points of rough action functionals. These RGFD models characterize Lagrangian trajectories in fluid dynamics as geometric rough paths (GRP) on the manifold of diffeomorphic maps. Three constrained variational approaches are formulated for the derivation of these models. The first is the Clebsch formulation, in which the constraints are imposed as rough advection laws. The second is the Hamilton-Pontryagin formulation, in which the constraints are imposed as right-invariant rough vector…
Asymptotic geometry and Delta-points
2022
We study Daugavet- and $\Delta$-points in Banach spaces. A norm one element $x$ is a Daugavet-point (respectively a $\Delta$-point) if in every slice of the unit ball (respectively in every slice of the unit ball containing $x$) you can find another element of distance as close to $2$ from $x$ as desired. In this paper we look for criteria and properties ensuring that a norm one element is not a Daugavet- or $\Delta$-point. We show that asymptotically uniformly smooth spaces and reflexive asymptotically uniformly convex spaces do not contain $\Delta$-points. We also show that the same conclusion holds true for the James tree space as well as for its predual. Finally we prove that there exis…
Analysing tensions faced by pre-service mathematics teachers engaging in digital fabrication.
2022
This article analyses tensions pre-service teachers faced during the last workshop of participation in a series of professional development workshops on digital fabrication for creating manipulatives for mathematics education. Using the concept of community of practice and the notion of tension as a theoretical framework and a qualitative research design including video recording with 5 pre-service teachers, we identified three tension categories: technological, pedagogical, and workshop design. The results indicate that tensions are often caused by conflictual decisions between the workshop designers’ and students’ objectives as well as difficulties in digital fabrication and its applicati…
How are proof and proving conceptualized in mathematics curriculum documents in the USA and Japan?
2022
Only a few international comparative studies have reported on proof and proving in curriculum documents. This report proposes a method of comparing the meaning of proof-related words in two specific countries’ curriculum documents (the USA and Japan) through quantitative and interpretative analyses. Using a text mining approach to explore text data, we found that the co-occurrence network of the words “proof” and “prove” in curriculum documents from the two countries is quite different. In the USA, the word “proof” is concerned with justification and “prove” is used as a general process, while in Japan “proof” is more related to discovery and “prove” is more associated with specific theorem…
Isometric factorization of vector measures and applications to spaces of integrable functions
2022
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, t…
Teaching and learning for mathematical literacy
2020
This dissertation reports from research that investigates the nature of teaching and learning for mathematical literacy in three lower secondary schools in Norway. Mathematical literacy is a notion used to denote the competences required to meet the mathematical demands of life in modern society. The importance of education for mathematical literacy is emphasised by The Organisation for Economic Cooperation and Development (OECD), and mathematical literacy has become increasingly prominent in national curricula around the world. In the Norwegian curriculum, mathematical literacy is considered a basic skill that should be developed across school subjects. This study of teaching and learning …
Investigation of temperature coefficients of PV modules through field measured data
2021
Abstract Varying broadband irradiance and temperature are generally known as the major factors influencing the performance of PV modules, but studies have also shown the substantial impact of spectral variations. In this work, a simple and efficient method to calculate the temperature coefficient using long term data is demonstrated. Temperature coefficients of PV modules are estimated from long term performance data following IEC 60891 standard with additional spectral correction, and are compared against the datasheet values. Significant improvement of correlation coefficient from −0.89 to −0.97 is observed during the regression for maximum power temperature coefficient of two poly-crysta…
Gold dipyrrin-bisphenolates: A combined experimental and DFT study of metal-ligand interactions
2020
Given that noninnocent and metalloradical-type electronic structures are ubiquitous among dipyrrin-bisphenolate (DPP) complexes, we synthesized the gold(III) derivatives as potentially innocent paradigms against which the properties of other metallo-DPP derivatives can be evaluated. Electronic absorption spectra, electrochemical studies, a single-crystal X-ray structure, and DFT calculations all suggest that the ground states of the new complexes indeed correspond to an innocent AuIII–DPP3−, paralleling a similar description noted for Au corroles. Interestingly, while DFT calculations indicate purely ligand-centered oxidations, reduction of AuDPP is predicted to occur across both the metal …
Prospective mathematics teachers’ self-referential metaphors as indicators of the emerging professional identity
2019
Ideals play a key role in a student teachers’ identity work. They form targets to strive for and a mirror for reflection. In this paper, we examine Finnish mathematics student teachers’ metaphors for the teacher’s role (N= 188). We classified the metaphors according to a model that identified teachers as subject matter experts, didactical experts, and pedagogical experts, with the addition of another two categories, self-referential and contextual. For the exploration of emerging professional identities, we studied the self-referential metaphors, which formed the most common category in the data. We observed that every third metaphor described either student teachers’ personalities or their…
Detection of Candidatus Neoehrlichia mikurensis in Norway up to the northern limit of Ixodes ricinus distribution using a novel real time PCR test ta…
2019
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Background Candidatus Neoehrlichia mikurensis is an emerging tick-borne pathogen. It is widely distributed in Ixodes ricinus ticks in Europe, but knowledge of its distribution in Norway, where I. ricinus reaches its northern limit, is limited. In this study we have developed a real time PCR test for Ca. N. mikurensis and used it to invest…