Institutt for matematikk og statistikk: Nye registreringer
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Exact semidefinite programming bounds for packing problems
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-05-25)In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. This algorithm does not require the solution to be strictly feasible and works for large problems. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal ... -
Lightboard – a new teaching tool at the Faculty of Science and Technology at UiT
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-05-05)We would like to present a new tool that was built by three lecturers at UiT last semester – Lightboard. This tool was used before in other countries and other universities, but never at UiT. The COVID-19 pandemic situation motivated the lecturers to find a way to do online lectures differently. Blackboard and chalk work well for natural sciences as long as the lecture is physical and the teacher ... -
Symmetries and Differential Invariants for Inviscid Flows on a Curve
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-02-04)Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given. -
Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06-10)Let V be the weighted projective variety defined by a weighted homogeneous ideal J and C a maximal cone in the Gröbner fan of J with m rays. We construct a flat family over A<sup>m</sup> that assembles the Gröbner degenerations of V associated with all faces of C. This is a multi-parameter generalization of the classical one-parameter Gröbner degeneration associated to a weight. We explain how our ... -
Cosheaves
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-10-21)The categories pCS(X,Pro(k)) of precosheaves and CS(X,Pro(k)) of cosheaves on a small Grothendieck site X, with values in the category Pro(k) of prok-modules, are constructed. It is proved that pCS(X,Pro(k)) satisfies the AB4 and AB5* axioms, while CS(X,Pro(k)) satisfies AB3 and AB5*. Homology theories for cosheaves and precosheaves, based on quasi-projective resolutions, are constructed and investigated. -
Explicit values for Ramanujan's theta function φ(q)
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-01-09)This paper provides a survey of particular values of Ramanujan's theta function φ(q) = ∑ q^(n^2), n = −∞ ... ∞, when q = e^(−π√n), where n is a positive rational number. First, descriptions of the tools used to evaluate theta functions are given. Second, classical values are briefly discussed. Third, certain values due to Ramanujan and later authors are given. Fourth, the methods that are used to ... -
Coloring the Voronoi tessellation of lattices
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-05-03)In this paper we define the chromatic number of a lattice: It is the least number of colors one needs to color the interiors of the cells of the Voronoi tessellation of a lattice so that no two cells sharing a facet are of the same color. We compute the chromatic number of the root lattices, their duals, and of the Leech lattice, we consider the chromatic number of lattices of Voronoi’s first ... -
Finite-sample properties of estimators for first and second order autoregressive processes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-12-05)The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the ... -
On uniqueness of submaximally symmetric parabolic geometries
(Journal article; Tidsskriftartikkel, 2021)Among (regular, normal) parabolic geometries of type (G,P), there is a locally unique maximally symmetric structure and it has symmetry dimension dim(G). The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When G is a complex or split-real simple Lie group of rank at least three or when (G,P)=(G2,P2), we establish a local classification result ... -
Symmetry gaps for higher order ordinary differential equations
(Journal article; Tidsskriftartikkel, 2021)The maximal contact symmetry dimensions for scalar ODEs of order ≥4 and vector ODEs of order ≥3 are well known. Using a Cartan-geometric approach, we determine for these ODE the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvature-constrained submaximal symmetry dimensions are also classified. -
Second-Order PDEs in 3D with Einstein–Weyl Conformal Structure
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-12-07)Einstein–Weyl geometry is a triple (D,g,ω) where D is a symmetric connection, [g] is a conformal structure and ω is a covector such that ∙ connection D preserves the conformal class [g], that is, Dg=ωg; ∙ trace-free part of the symmetrised Ricci tensor of D vanishes. Three-dimensional Einstein–Weyl structures naturally arise on solutions of second-order dispersionless integrable PDEs in 3D. In this ... -
Differential invariants of Kundt spacetimes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-09-07)We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to dimensions three and four. -
Spatiotemporal Analysis of COVID-19 Incidence Data
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-03-11)High-density lipoproteins (HDL) are a heterogenous group of plasma molecules with a large variety in composition. There is a wide specter in lipid content and the number of different proteins that has been associated with HDL is approaching 100. Given this heterogeneity and the fact that the total amount of HDL is inversely related to the risk of coronary heart disease (CHD), there has been ... -
Möbius and coboundary polynomials for matroids
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06-28)We study how some coefficients of two-variable coboundary polynomials can be derived from Betti numbers of Stanley–Reisner rings. We also explain how the connection with these Stanley–Reisner rings forces the coefficients of the two-variable coboundary polynomials and Möbius polynomials to satisfy certain universal equations. -
A Parsimonious Description and Cross-Country Analysis of COVID-19 Epidemic Curves
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-09-06)In a given country, the cumulative death toll of the first wave of the COVID-19 epidemic follows a sigmoid curve as a function of time. In most cases, the curve is well described by the Gompertz function, which is characterized by two essential parameters, the initial growth rate and the decay rate as the first epidemic wave subsides. These parameters are determined by socioeconomic factors and ... -
Estimating Remaining Carbon Budgets Using Temperature Responses Informed by CMIP6
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-07-12)A remaining carbon budget (RCB) estimates how much CO2 we can emit and still reach a specific temperature target. The RCB concept is attractive since it easily communicates to the public and policymakers, but RCBs are also subject to uncertainties. The expected warming levels for a given carbon budget has a wide uncertainty range, which increases with less ambitious targets, i.e., with higher CO2 ... -
On Jordan classes for Vinberg's theta-groups
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-10-23)V. L. Popov has recently introduced an analogue of Jordan classes (packets or decomposition classes) for the action of a θ-group (G0, V), showing that they are finitely-many, locally-closed, irreducible unions of G0-orbits of constant dimension partitioning V. We carry out a local study of their closures showing that Jordan classes are smooth and that their closure is a union of Jordan classes. We ... -
Algebraforståelse blant studentene i brukerkurs i matematikk ved UiT
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-02-24)Ved Institutt for matematikk og statistikk UiT – Norges arktiske universitet ble Brukerkurset i matematikk høsten 2020 lagt om til et prosjektbasert emne og ny eksamensform med avsluttende muntlig gruppeeksamen. Et av målene for vår studie er å kartlegge ferdigheter og forståelse i algebra i begynnelsen av semesteret og hvordan studentene videre møter de algebraiske aktivitetene i prosjektene. I ... -
The Tipping Effect of Delayed Interventions on the Evolution of COVID-19 Incidence
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-04-23)We combine infectious disease transmission and the non-pharmaceutical (NPI) intervention response to disease incidence into one closed model consisting of two coupled delay differential equations for the incidence rate and the time-dependent reproduction number. The model contains three parameters, the initial reproduction number, the intervention strength, and the response delay. The response is ... -
Convergence and completeness for square-well Stark resonant state expansions
(Journal article; Tidsskriftartikkel; Peer reviewed, 2018-11-02)In this paper, we investigate the completeness of the Stark resonant states for a particle in a square-well potential. We find that the resonant state expansions for target functions converge inside the potential well and that the existence of this convergence does not depend on the depth of the potential well, <i>V</i><sub>0</sub>. By analyzing the asymptotic form of the terms in these expansions, ...