Artikler, rapporter og annet (matematikk og statistikk)
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Laplace transformation of Lie class ω = 1 overdetermined systems
(Journal article; Tidsskriftartikkel; Peer reviewed, 20210120)In this paper, we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on one function of one variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs. 
Is there a break in scaling on centennial time scales in Holocene temperature records?
(Conference object; Konferansebidrag, 2017) 
Secondorder PDEs in four dimensions with halfflat conformal structure
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200129)We study secondorder partial differential equations (PDEs) in four dimensions for which the conformal structure defined by the characteristic variety of the equation is halfflat (selfdual or antiselfdual) on every solution. We prove that this requirement implies the Monge–Ampère property. Since halfflatness of the conformal structure is equivalent to the existence of a nontrivial dispersionless ... 
Real Root Finding for Equivariant Semialgebraic Systems
(Conference object; Konferansebidrag, 2018)Let <i><b>R</b></i> be a real closed field. We consider basic semialgebraic sets defined by <i>n</i>variate equations/inequalities of s symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by 2<i>d</i> < <i>n</i>. Such a semialgebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point ... 
Extreme Event Statistics in Dst, SYMH, and SMR Geomagnetic Indices
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230320)Extreme space weather events are rare, and quantifying their likelihood is challenging, often relying on geomagnetic indices obtained from groundbased magnetometer observations that span multiple solar cycles. The Dst index ringcurrent monitor, derived from an hourly average over four lowlatitude stations, is a benchmark for extreme space weather events, and has been extensively studied ... 
Temporal evolution of underice meltwater layers and false bottoms and their impact on summer Arctic sea ice mass balance
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230331)Lowsalinity meltwater from Arctic sea ice and its snow cover accumulates and creates underice meltwater layers below sea ice.These meltwater layers can result in the formation of new ice layers, or false bottoms, at the interface of this lowsalinity meltwater and colder seawater. As part of the Multidisciplinary drifting Observatory for the Study of the Arctic Climate (MOSAiC), we used a ... 
Seafood production in Northern Norway: Analyzing variation and codevelopment in aquaculture and coastal fisheries
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230727)Norway is one of the leading oceanbased food production nations. Its seafood industry comprises wildcapture fisheries and farmed fish production. Both industries play a provisional role but also contribute to economic development of the country and help sustain coastal communities, particularly, in Northern Norway. Coastal fishery has been the staple industry in Northern Norway for centuries, while ... 
Mapping the shape and dimension of threedimensional Lagrangian coherent structures and invariant manifolds
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230310)We introduce maps of Cauchy–Green strain tensor eigenvalues to barycentric coordinates to quantify and visualize the full geometry of threedimensional deformation in stationary and nonstationary fluid flows. As a natural extension of Lagrangian coherent structure diagnostics, which provide separate scalar fields and a onedimensional quantification of fluid deformation, our barycentric mapping ... 
Students’ mathematical beliefs and motivation in the context of inquirybased mathematics teaching
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230329)In this paper, we investigate the learning experiences, beliefs and motivations of students in classes where the mathematics teachers have received support for using inquirybased learning activities. Data were collected from 248 students in the agerange 11–16 using electronic questionnaires. Our results show that key features of inquirybased mathematics were only moderately reflected in these ... 
A quasiobjective single buoy approach for un derstanding Lagrangian coherent structures and sea ice dynamics
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230411)Sea ice drift and deformation, namely sea ice dynamics, play a significant role in atmosphere–ice–ocean coupling. Deformation patterns in sea ice can be observed over a wide range of spatial and temporal scales, though highresolution objective quantification of these features remains difficult. In an effort to better understand local deformation of sea ice, we adapt the trajectorystretching exponents ... 
Charting the solar cycle
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230209)Sunspot records reveal that whilst the Sun has an approximately 11 year cycle of activity, no two cycles are of the same duration. Since this activity is a direct driver of space weather at Earth, this presents an operational challenge to quantifying space weather risk. We recently showed that the Hilbert transform of the sunspot record can be used to map the variable cycle length onto a regular ... 
Global Dynamical Network of the Spatially Correlated Pc2 Wave Response for the 2015 St. Patrick's Day Storm
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230426)We show the global dynamics of spatial correlation of Pc2 wave activity can track the evolution of the 2015 St. Patrick's Day geomagnetic storm for an 8 hr time window around onset. The global spatially coherent response is tracked by forming a dynamical network from 1 s data using the full set of 100+ groundbased magnetometer stations collated by SuperMAG and Intermagnet. The pattern of spatial ... 
A frame based approach to computing symmetries with nontrivial isotropy groups
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230324)A frame approach to determining the most general solution admitting a desired symmetry group has previously been examined in Riemannian and teleparallel geometries with some success. In teleparallel geometries, one must determine the general form of the frame and spin connection to generate a general solution admitting the desired symmetry group. Current approaches often rely on the use of the ... 
The three missing terms in Ramanujan’s septic theta function identity
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230223)On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for his theta function φ(q): φ(e^{−7π√7}) = 7^{−3/4}φ(e^{−π√7}){1 + ( )^{2/7} + ( )^{2/7} + ( )^{2/7}}. We give the three missing terms. In addition, we calculate the class invariant G_{343} and further special values of φ(e^{−nπ}), for n = 7, 21, 35, and 49. 
Real gas ﬂows issued from a source
(Journal article; Tidsskriftartikkel; Peer reviewed, 20191223)Stationary adiabatic flows of real gases issued from a source of given intensity are studied. Thermodynamic states of gases are described by Legendrian or Lagrangian manifolds. Solutions of Euler equations are given implicitly for any equation of state and the behavior of solutions of the Navier–Stokes equations with the viscosity considered as a small parameter is discussed. For different intensities ... 
Density ridge manifold traversal
(Chapter; Bokkapittel, 20170619)The density ridge framework for estimating principal curves and surfaces has in a number of recent works been shown to capture manifold structure in data in an intuitive and effective manner. However, to date there exists no efficient way to traverse these manifolds as defined by density ridges. This is unfortunate, as manifold traversal is an important problem for example for shape estimation in ... 
Kontinuitet i overgangen fra skole til universitet  Implikasjoner av Fagfornyelsen for MNTfagene
(Conference object; Konferansebidrag, 202303)Med LK20 Fagfornyelsen innføres det nye læreplaner i skolen, der antall kompetansemål i de ulike fagene er noe redusert for å gi mer rom til dybdelæring, samt at læreplanene i matematikk og fysikk har et større fokus på utforsking, modellering og bruk av numeriske metoder enn tidligere (Ludvigsen et al., 2015; Utdanningsdirektoratet, 2020, 2021). I dette bidraget presenterer vi hvordan en gruppe ... 
Selfassessment of written exercises in STEM courses
(Conference object; Konferansebidrag, 202303)Students of physics in Norway typically spend a lot of time on mandatory problemsolving exercises that they must get a passing grade on to be allowed to take the exam. This is often a primarily summative assessment, which can limit the learning potential. <p> <p>In this contribution, we present an intervention in which traditional mandatory assignments are modified to put more emphasis on ... 
En analyse av vindkraftens og kraftutvekslingens betydning for effektkjøring av norske magasinkraftverk
(Research report; Forskningsrapport, 2023)Effektkjøring av magasinkraftverk er hurtige og store variasjoner i vannføring og produsert effekt. Spesielt kan store variasjoner innenfor et tidsrom på et døgn føre til tilsvarende variasjoner i vannstand i nedstrøm vassdrag og som kan føre til skader på livet i elva. Det er en gjengs oppfatning at et stort innslag av intermitterende, ikkeregulerbare kraftkilder som vindkraft, vil føre til hardere ... 
Objective Momentum Barriers in Wall Turbulence
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220428)We use the recent frameindifferent theory of diffusive momentum transport to identify internal barriers in wallbounded turbulence. Formed by the invariant manifolds of the Laplacian of the velocity field, the barriers block the viscous part of the instantaneous momentum flux in the flow. We employ the level sets of singletrajectory Lagrangian diagnostic tools, the trajectory rotation average ...