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  • 1. Abatangelo, Laura
    et al.
    Felli, Veronica
    Hillairet, Luc
    Léna, Corentin
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators2019Inngår i: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 9, nr 2, s. 379-427Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov–Bohm operators with two colliding poles moving on an axis of symmetry of the domain.

  • 2. Abatangelo, Laura
    et al.
    Felli, Veronica
    Léna, Corentin
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications2020Inngår i: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 26, artikkel-id 39Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.

    Fulltekst (pdf)
    fulltext
  • 3.
    Abathun, Addisalem
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Asymptotic distribution of zeros of a certain class of hypergeometric polynomials2014Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The thesis consists of two papers, both treating hypergeometric polynomials, and a short introduction. The main results are as follows.In the first paper,we study the asymptotic zero distribution of a family of hypergeometric polynomials in one complex variable as their degree goes to infinity,using the associated differential equations that hypergeometric polynomials satisfy.   We describe in particular the curve complex on which the zeros cluster, as level curves associated to integrals on an algebraic curve derived from the equation.   The new result is first of all that we are able to formulate results on the location of zeros of generalized hypergeometric polynomials in greater generality than before (earlier results are mainly concerned with the Gauss hypergeometric case.) Secondly, we are able to formulate a precise conjucture giving the asymptotic behaviour of zeros in the generalized case of our polynomials, which covers previous results.In the second paper we partly prove one of the  conjectures in the first paper by using Euler integral representation of the Gauss hypergeometric functions together with the Saddle point method.

  • 4.
    Abathun, Addisalem
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Addis Ababa University, Ethiopia.
    Bøgvad, Rikard
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Asymptotic Distribution of Zeros of a Certain Class of Hypergeometric Polynomialsd2016Inngår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 16, nr 2, s. 167-185Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the asymptotic behavior of the zeros of a family of a certain class of hypergeometric polynomials [GRAPHICS] , using the associated hypergeometric differential equation, as the parameters go to infinity. The curve configuration on which the zeros cluster is characterized as level curves associated with integrals on an algebraic curve. The algebraic curve is the hypergeometrc differential equation, using a similar approach to the method used in Borcea et al. (Publ Res Inst Math Sci 45(2):525-568, 2009). In a specific degenerate case, we make a conjecture that generalizes work in Boggs and Duren (Comput Methods Funct Theory 1(1):275-287, 2001), Driver and Duren (Algorithms 21(1-4):147-156, 1999), and Duren and Guillou (J Approx Theory 111(2):329-343, 2001), and present experimental evidence to substantiate it.

  • 5.
    Abathun, Addisalem
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Addis Ababa University, Ethiopia.
    Bøgvad, Rikard
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    ZEROS OF A CERTAIN CLASS OF GAUSS HYPERGEOMETRIC POLYNOMIALS2018Inngår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 68, nr 4, s. 1021-1031Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that as n -> infinity, the zeros of the polynomial F-2(1) 9-n, (an + 2) (an + 1) ; z] cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999-2001) to the case of a complex parameter alpha and partially proves a conjecture made by the authors in an earlier work.

  • 6. Abbadini, Marco
    et al.
    Di Liberti, Ivan
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    DUALITY FOR COALGEBRAS FOR VIETORIS AND MONADICITY2024Inngår i: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that the opposite of the category of coalgebras for the Vietoris endofunctor on the category of compact Hausdorff spaces is monadic over $\mathsf {Set}$ . We deliver an analogous result for the upper, lower, and convex Vietoris endofunctors acting on the category of stably compact spaces. We provide axiomatizations of the associated (infinitary) varieties. This can be seen as a version of Jonsson-Tarski duality for modal algebras beyond the zero-dimensional setting.

  • 7.
    Abdalla, Mahmoud
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Claesson, Malin
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Stationshöjdens inverkan på resmönster i offentliga lånecykelsystem2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    The focus of this essay is to study the relationship between the usage pattern of public bike-sharing system subscribers and the location of the individual bike station in terms of height. Our hypothesis is that stations at higher elevations are more likely to be used as points of departure rather than arrival, and the opposite for stations with lower elevations.

    Based on data gathered in Chicago and the Greater Boston Area we apply a multiple linear regression analysis with relative elevation, gender and age as regressors, and the proportion of departures of the total activity at each station as the regressand. As an estimator, Weighted Least Squares (WLS) is used. The bike stations activity is varying, and this might cause skewness in the data, something that WLS can reduce. The result from the regression analysis shows that the relative elevation of the station does influence the stations usage pattern, but the parameter value for this regressor is small. The age and gender parameters are not statistically significant, so we end up with a simple linear regression with relative elevation as the only regressor.

    The conclusion is thus that even though the relative elevation of the bike station do have a statistically significant impact on the usage pattern in both cities. If the study had been undertaken in cities with more varied topography than Boston or Chicago, the result might have been different. We therefore consider this a field that could benefit from research that is more extensive in the future.

  • 8.
    Abdulla, Tavga
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Nyanlända elevers svårigheter i algebra: En studie om nyanlända elevers uppfattningar om undervisning i algebra samt textuppgifter inom algebra i introduktionsprogram2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna studie är att undersöka vilka matematiska och språkliga svårigheter nyanlända gymnasieelever har när de arbetar med algebra, både deras uppfattningar om undervisning i algebra och hur de löser textuppgifter inom algebra. Samtliga elever i studien är nyanlända och går ett introduktionsprogram och de har ett annat modersmål än svenska.

    Flera studier visar på att elever som har ett annat modersmålspråk än svenska har svårare att klara matematik i skolan och därmed presterar sämre i matematikundervisningen än andra elever som har svenska som modersmål (Malmer, 2002). I denna studie undersöks vad detta beror på och hur undervisningen kan anpassas för att bättre gynna den berörda elevgruppen.

    För att besvara frågeställningarna gjordes elevintervjuer med åtta elever samt ett test i algebra med eleverna som deltog i intervjuerna. Resultaten i denna studie visar på att eleverna hade språkliga svårigheter som påverkade deras problemlösningsförmåga i algebra. En orsak till detta är språkliga svårigheter och detta kan delvis bero på bristfälliga svenskkunskaper som leder till svårigheter att förstå textuppgifter och svårigheter att uttrycka sig när man kommunicerar inom matematik.

    Fulltekst (pdf)
    fulltext
  • 9.
    Abebaw, Tilahun
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Bogvad, Rikard
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Decomposition of D-modules over a hyperplane arrangement in the plane2010Inngår i: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 48, nr 2, s. 211-229Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let alpha(1), alpha(2),..., alpha(m) be linear forms defined on C-n and X = C-n\boolean OR(m)(i=1) V(alpha(i)), where V(alpha(i))={p is an element of C-n : alpha(i)(p)=0}. The coordinate ring O-X of X is a holonomic A(n)-module, where A(n) is the nth Weyl algebra and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a "" twisted"" variant of this An- module which is also holonomic. Define M-alpha(beta) to be the free rank-1 C[x](alpha)-module on the generator alpha(beta) (thought of as a multivalued function), where alpha(beta)=alpha(beta 1)(1),..., alpha(beta m)(m) and the multi-index beta=(beta(1),...,beta(m))is an element of C-m. Our main result is the computation of the number of decomposition factors of M-alpha(beta) and their description when n-2.

  • 10.
    Abebaw, Tilahun
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Addis Ababa University, Ethiopia.
    Bøgvad, Rikard
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Decomposition factors of D-modules on hyperplane configurations in general position2012Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, nr 8, s. 2699-2711Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let alpha(1), ... , alpha(m) be linear functions on C-n and X = C-n \ V(alpha), where alpha = Pi(m)(i=1) alpha(i) and V(alpha) = {p is an element of C-n : alpha(p) = 0}. The coordinate ring O-X = C[x](alpha) of X is a holonomic A(n)-module, where A(n) is the n-th Weyl algebra, and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a twisted variant of this A(n)-module which is also holonomic. Define M-alpha(beta) to be the free rank 1 C[x](alpha)-module on the generator alpha(beta) (thought of as a multivalued function), where alpha(beta) = alpha(beta 1)(1) ... alpha(beta m)(m) and the multi-index beta = (beta(1), ... , beta(m)) is an element of C-m. It is straightforward to describe the decomposition factors of M-alpha(beta), when the linear functions alpha(1), ... , alpha(m) define a normal crossing hyperplane configuration, and we use this to give a sufficient criterion on beta for the irreducibility of M-alpha(beta), in terms of numerical data for a resolution of the singularities of V(alpha).

  • 11.
    Abramczuk, Wojciech
    Stockholms universitet.
    Contributions to three problems in systems of differential and convolution equations1984Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    We study three problems:

    PROBLEM A. Let P(D) be a matrix of partial differential operators with constant coefficient and U an open, convex and bounded set in Rn. Consider the system P(D)u = f where f lies in a Sobolev space on Rn and satisfies the compatibility conditions in U. We give conditions for the existence of a solution u which is, roughly speaking, more regular than f by the degree of P(D) in the (global) Sobolev space meaning.

    PROBLEM B. Let P(D) and U be as above and let K be a compact convex subset of U. Let u be a function in a quasi-analytic class on U\ K such that P(D)u = 0 there. We give conditions on P(D) which imply that every such u may by continued to U as a solution of the considered homogeneous system and in the same quasi-analytic class. The conditions are also necessary.

    PROBLEM C. Let u be a (ultra-) distribution with compact support on Rn. The condition for u to act surjectively on a class of (ultra-distributions is usually expressed as a condition on the decrease of the Fourier transform of u. We localize this condition for the Gevrey distributions. We also prove that some measures of Cantor type, in particular the tenary measure, do not act surjectively on the usual distributions on R1.

  • 12. Abtahi, Yasmine
    et al.
    Adler, J.
    Guillemette, D.
    Herheim, R.
    Lerman, S.
    Maheux, J-F.
    Valero, Paola
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Otherness in mathematics education2018Inngår i: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] E. Bergqvist, M. Österholm, C. Granberg, L. Sumpter, Umeå, Sweden: PME , 2018, Vol. 1, s. 95-124Konferansepaper (Fagfellevurdert)
  • 13. Aceto, Luca
    et al.
    Della Monica, Dario
    Goranko, Valentin
    Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.
    Ingólfsdóttir, Anna
    Montanari, Angelo
    Sciavicco, Guido
    A complete classification of the expressiveness of interval logics of Allen’s relations: the general and the dense cases2016Inngår i: Acta Informatica, ISSN 0001-5903, E-ISSN 1432-0525, Vol. 53, nr 3, s. 207-246Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Interval temporal logics take time intervals, instead of time points, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments.

  • 14. Ackermann, Nils
    et al.
    Szulkin, Andrzej
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A concentration phenomenon for semilinear elliptic equations2013Inngår i: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 207, nr 3, s. 1075-1089Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    For a domain $\Omega\subset\dR^N$ we consider the equation $ -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $\Omega$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if $u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence $(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain $L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and $u_n$ are ground state solutions, then they concentrate at one of these points.

  • 15. Adamyan, V.
    et al.
    Langer, H.
    Tretter, Christiane
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Universität Bern, Switzerland.
    Winklmeier, M.
    Dirac-Krein Systems on Star Graphs2016Inngår i: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 86, nr 1, s. 121-150Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the spectrum of a self-adjoint Dirac–Krein operator with potential on a compact star graph G with a finite number n of edges. This operator is defined by a Dirac–Krein differential expression with summable matrix potentials on each edge, by self-adjoint boundary conditions at the outer vertices, and by a self-adjoint matching condition at the common central vertex of G. Special attention is paid to Robin matching conditions with parameter τ∈R∪{∞}. Choosing the decoupled operator with Dirichlet condition at the central vertex as a reference operator, we derive Krein’s resolvent formula, introduce corresponding Weyl–Titchmarsh functions, study the multiplicities, dependence on τ, and interlacing properties of the eigenvalues, and prove a trace formula. Moreover, we show that, asymptotically for R→∞, the difference of the number of eigenvalues in the intervals [0,R) and [−R,0) deviates from some integer κ0, which we call dislocation index, at most by n+2.

  • 16. Addario-Berry, Louigi
    et al.
    Broutin, Nicolas
    Holmgren, Cecilia
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    CUTTING DOWN TREES WITH A MARKOV CHAINSAW2014Inngår i: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 24, nr 6, s. 2297-2339Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton-Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny n. Our proof is based on a coupling which yields a precise, nonasymptotic distributional result for the case of uniformly random rooted labeled trees (or, equivalently, Poisson Galton-Watson trees conditioned on their size). Our approach also provides a new, random reversible transformation between Brownian excursion and Brownian bridge.

  • 17. Adolfson, Malin
    et al.
    Laseen, Stefan
    Linde, Jesper
    Villani, Mattias
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Empirical properties of closed- and open-economy DSGE models of the Euro area2008Inngår i: Macroeconomic Dynamics, ISSN 1365-1005, E-ISSN 1469-8056, Vol. 12, s. 2-19Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we compare the empirical proper-ties of closed- and open-economy DSGE models estimated on Euro area data. The comparison is made along several dimensions; we examine the models in terms of their marginal likelihoods, forecasting performance, variance decompositions, and their transmission mechanisms of monetary policy.

  • 18. Adolfson, Malin
    et al.
    Linde, Jesper
    Villani, Mattias
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Forecasting performance of an open economy DSGE model2007Inngår i: Econometric Reviews, ISSN 0747-4938, E-ISSN 1532-4168, Vol. 26, nr 04-feb, s. 289-328Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper analyzes the forecasting performance of an open economy dynamic stochastic general equilibrium (DSGE) model, estimated with Bayesian methods, for the Euro area during 1994Q1-2002Q4. We compare the DSGE model and a few variants of this model to various reduced form forecasting models such as vector autoregressions (VARs) and vector error correction models (VECM), estimated both by maximum likelihood and, two different Bayesian approaches, and traditional benchmark models, e.g., the random. walk. The accuracy of point forecasts, interval forecasts and the predictive distribution as a whole are assessed in, an out-of-sample rolling event evaluation using several univariate and multivariate measures. The results show that the open economy DSGE model compares well with more empirical models and thus that the tension between, rigor and fit in older generations of DSGE models is no longer present. We also critically examine the role of Bayesian model probabilities and other frequently used low-dimensional summaries, e.g., the log determinant statistic, as measures of overall forecasting performance.

  • 19.
    Aermark, Lior Alexandra
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hardy and spectral inequalities for a class of partial differential operators2014Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This thesis is devoted to the study of Hardy and spectral inequalities for the Heisenberg and the Grushin operators. It consists of five chapters. In chapter 1 we present basic notions and summarize the main results of the thesis. In chapters 2-4 we deal with different types of Hardy inequalities for Laplace and Grushin operators with magnetic and non-magnetic fields. It was shown in an article by Laptev and Weidl that for some magnetic forms in two dimensions, the Hardy inequality holds in its classical form. More precisely, by considering the Aharonov-Bohm magnetic potential, we can improve the constant in the respective Hardy inequality. In chapter 2 we establish an Lp - Hardy inequality related to Laplacians with magnetic fields with Aharonov-Bohm vector potentials. In chapter 3 we introduce a suitable notion of a vector field for the Grushin sub-elliptic operator G and obtain an improvement of the Hardy inequality, which was previously obtained in the paper of N. Garofallo and E. Lanconelli. In chapter 4 we find an Lp version of the Hardy inequality obtained in chapter 2. Finally in chapter 5 we aim to find the CLR and Lieb-Thirringbninequalities for harmonic Grushin-type operators. As the Grushin operator is non-elliptic, these inequalities will not take their classical form.

    Fulltekst (pdf)
    fulltext
  • 20.
    Aermark, Lior
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Laptev, A.
    Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field2012Inngår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 23, nr 2, s. 203-208Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A version of the Aharonov-Bohm magnetic field for a Grushin subelliptic operator is introduced; then its quadratic form is shown to satisfy an improved Hardy inequality.

  • 21. Afshari, Bahareh
    et al.
    Enqvist, Sebastian
    Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen.
    Leigh, Graham E.
    Cyclic proofs for the first-order µ-calculus2024Inngår i: Logic journal of the IGPL (Print), ISSN 1367-0751, E-ISSN 1368-9894, Vol. 32, nr 1, s. 1-34Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce a path-based cyclic proof system for first-order μ-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal μ-calculus.

  • 22. Afshari, Bahareh
    et al.
    Enqvist, Sebastian
    Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen.
    Leigh, Graham e.
    Marti, Johannes
    Venema, Yde
    PROOF SYSTEMS FOR TWO-WAY MODAL MU-CALCULUS2023Inngår i: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a class of non-wellfounded proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations.

  • 23. Agbor, Dieudonné
    et al.
    Boman, Jan
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the Modulus of Continuity of Mappings Between Euclidean Spaces2013Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 112, nr 1, s. 147-160Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let f be a function from R-P to R-q and let Lambda be a finite set of pairs (theta, eta) is an element of R-P x R-q. Assume that the real-valued function (eta, f(x)) is Lipschitz continuous in the direction theta for every (theta, eta) is an element of Lambda. Necessary and sufficient conditions on Lambda are given for this assumption to imply each of the following: (1) that f is Lipschitz continuous, and (2) that f is continuous with modulus of continuity <= C epsilon vertical bar log epsilon vertical bar.

  • 24. Aghapour, Sajad
    et al.
    Andersson, Lars
    Rosquist, Kjell
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    The zilch electromagnetic conservation law revisited2020Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 61, nr 12, artikkel-id 122902Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric Lagrangian, while non-vanishing, is a total divergence as required by the Noether theory. The variational nature of the zilch conservation law was previously known only for some of the components of the zilch tensor, notably the optical chirality. By contrast, our analysis is fully covariant and is, therefore, valid for all components of the zilch tensor. The analysis is presented here for both the real and complex versions of duality-symmetric Maxwell Lagrangians.

  • 25. Agmon, Shmuel
    et al.
    Herbst, Ira
    Maad Sasane, Sara
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Persistence of embedded eigenvalues2011Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 261, nr 2, s. 451-477Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider conditions under. which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < infinity we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension in. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.

  • 26. Agranovsky, Mark
    et al.
    Boman, Jan
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hasanov, Alemdar
    Felea, Raluca
    Frikel, Jürgen
    Krishnan, Venky
    Novikov, Roman
    Ramlau, Ronny
    Sebu, Cristiana
    Research biography of a distinguished expert in the field of inverse problems: Professor Eric Todd Quinto2022Inngår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 30, nr 4, s. 613-617Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article gives a brief overview of the research in microlocal analysis, tomography, and integral geometry of Professor Eric Todd Quinto, Robinson Professor of Mathematics at Tufts University, along with the collaborators and colleagues who influenced his work. 

  • 27.
    Agrawal, Vipin
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Mitra, Dhrubaditya
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Chaos and irreversibility of a flexible filament in periodically driven Stokes flow2022Inngår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 106, nr 2, artikkel-id 025103Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The flow of Newtonian fluid at low Reynolds number is, in general, regular and time-reversible due to absence of nonlinear effects. For example, if the fluid is sheared by its boundary motion that is subsequently reversed, then all the fluid elements return to their initial positions. Consequently, mixing in microchannels happens solely due to molecular diffusion and is very slow. Here, we show, numerically, that the introduction of a single, freely floating, flexible filament in a time-periodic linear shear flow can break reversibility and give rise to chaos due to elastic nonlinearities, if the bending rigidity of the filament is within a carefully chosen range. Within this range, not only the shape of the filament is spatiotemporally chaotic, but also the flow is an efficient mixer. Overall, we find five dynamical phases: the shape of a stiff filament is time-invariant-either straight or buckled; it undergoes a period-two bifurcation as the filament is made softer; becomes spatiotemporally chaotic for even softer filaments but, surprisingly, the chaos is suppressed if bending rigidity is decreased further.

  • 28.
    Ahlberg, Daniel
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A temporal perspective on the rate of convergence in first-passage percolation under a moment condition2019Inngår i: Brazilian Journal of Probability and Statistics, ISSN 0103-0752, E-ISSN 2317-6199, Vol. 33, nr 2, s. 397-401Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the rate of convergence in the celebrated Shape Theorem in first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are presented from a temporal perspective and complement previous work by the same author, in which the rate of convergence was studied from the standard spatial perspective.

  • 29.
    Ahlberg, Daniel
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tertiles and the time constant2020Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 57, nr 2, s. 407-408Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequence, we obtain a counter-example to a problem proposed by Alm and Deijfen (2015).

  • 30.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Angel, Omer
    Kolesnik, Brett
    Annihilating Branching Brownian Motion2024Inngår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.

  • 31.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Baldasso, Rangel
    Noise sensitivity and Voronoi percolation2018Inngår i: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 23, artikkel-id 108Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study noise sensitivity and threshold phenomena for Poisson Voronoi percolation on R-2. In the setting of Boolean functions, both threshold phenomena and noise sensitivity can be understood via the study of randomized algorithms. Together with a simple discretization argument, such techniques apply also to the continuum setting. Via the study of a suitable algorithm we show that box-crossing events in Voronoi percolation are noise sensitive and present a threshold phenomenon with polynomial window. We also study the effect of other kinds of perturbations, and emphasize the fact that the techniques we use apply for a broad range of models.

  • 32.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Deijfen, Maria
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hoffman, Christopher
    THE TWO-TYPE RICHARDSON MODEL IN THE HALF-PLANE2020Inngår i: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 30, nr 5, s. 2261-2273Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for infinite coexistence, while for types with different intensities, it is conjectured that infinite coexistence is not possible. In this paper we study the two-type Richardson model in the upper half-plane Z x Z(+), and prove that coexistence of two types starting on the horizontal axis has positive probability if and only if the types have the same intensity.

  • 33.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Deijfen, Maria
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Janson, Svante
    Competing first passage percolation on random graphs with finite variance degrees2019Inngår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, nr 3, s. 545-559Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph in that an uninfected vertex becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of nearest neighbors of type 1 (2). Assuming (essentially) that the degree of a randomly chosen vertex has finite second moment, we show that if lambda(1) = lambda(2), then the fraction of vertices that are ultimately infected by type 1 converges to a continuous random variable V is an element of (0,1), as the number of vertices tends to infinity. Both infection types hence occupy a positive (random) fraction of the vertices. If lambda(1) not equal lambda(2), on the other hand, then the type with the larger intensity occupies all but a vanishing fraction of the vertices. Our results apply also to a uniformly chosen simple graph with the given degree sequence.

  • 34.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Deijfen, Maria
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Sfragara, Matteo
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    From stability to chaos in last-passage percolation2024Inngår i: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 56, nr 1, s. 411-422Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the transition from stability to chaos in a dynamic last passage percolation model on  with random weights at the vertices. Given an initial weight configuration at time 0, we perturb the model over time in such a way that the weight configuration at time t is obtained by resampling each weight independently with probability t. On the cube [0, n]d, we study geodesics, that is, weight-maximizing up-right paths from (0,0,⋯,0) to (n,n,⋯,n), and their passage time T. Under mild conditions on the weight distribution, we prove a phase transition between stability and chaos at tVar(T). Indeed, as n grows large, for small values of t, the passage times at time 0 and time t are highly correlated, while for large values of t, the geodesics become almost disjoint.

  • 35.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Griffiths, Simon
    Janson, Svante
    To fixate or not to fixate in two-type annihilating branching random walks2021Inngår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 49, nr 5, s. 2637-2667Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a model of competition between two types evolving as branching random walks on Z(d). The two types are represented by red and blue balls, respectively, with the rule that balls of different colour annihilate upon contact. We consider initial configurations in which the sites of Z(d) contain one ball each which are independently coloured red with probability p and blue otherwise. We address the question of fixation, referring to the sites and eventually settling for a given colour or not. Under a mild moment condition on the branching rule, we prove that the process will fixate almost surely for p not equal 1/2 and that every site will change colour infinitely often almost surely for the balanced initial condition p = 1/2.

  • 36.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Griffiths, Simon
    Janson, Svante
    Morris, Robert
    Competition in growth and urns2019Inngår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 54, nr 2, s. 211-227Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study survival among two competing types in two settings: a planar growth model related to two-neighbor bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncolored sites are given a color at rate 0, 1 or infinity, depending on whether they have zero, one, or at least two neighbors of that color. In the urn scheme, each vertex of a graph G has an associated urn containing some number of either blue or red balls ( but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system, a ball of the same color is added to each neighboring urn, and balls in the same urn but of different colors annihilate on a one-for-one basis. We show that, for every connected graph G and every initial configuration, only one color survives almost surely. As a corollary, we deduce that in the two-type growth model on Z(2), one of the colors only infects a finite number of sites with probability one. We also discuss generalizations to higher dimensions and multi-type processes, and list a number of open problems and conjectures.

  • 37.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tassion, Vincent
    Teixeira, Augusto
    Existence of an unbounded vacant set for subcritical continuum percolation2018Inngår i: Electronic Communications in Probability, E-ISSN 1083-589X, Vol. 23, artikkel-id 63Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the Poisson Boolean percolation model in R-2, where the radius of each ball is independently chosen according to some probability measure with finite second moment. For this model, we show that the two thresholds, for the existence of an unbounded occupied and an unbounded vacant component, coincide. This complements a recent study of the sharpness of the phase transition in Poisson Boolean percolation by the same authors. As a corollary it follows that for Poisson Boolean percolation in R-d, for any d >= 2, finite moment of order d is both necessary and sufficient for the existence of a nontrivial phase transition for the vacant set.

  • 38.
    Ahlkrona, Josefin
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Uppsala University, Sweden; Kiel University, Germany.
    How much are the greenland and antarctic ice sheets melting?2018Inngår i: XRDS: Crossroads, The ACM Magazine for Students, ISSN 1528-4972, Vol. 25, nr 1, s. 42-47Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
  • 39.
    Ahlkrona, Josefin
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Swedish e-Science Research Centre (SeRC), Sweden.
    Elfverson, Daniel
    A cut finite element method for non-Newtonian free surface flows in 2D - application to glacier modelling2021Inngår i: Journal of Computational Physics: X, ISSN 2590-0552, Vol. 11, artikkel-id 100090Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce a novel approach to ice dynamics computations based on the unfitted Finite Element Method CutFEM, which lets the domain boundary cut through elements. By employing CutFEM, complex meshing and remeshing is avoided as the glacier can be immersed in a simple background mesh without loss of accuracy. The ice is modelled as a non-Newtonian, shear-thinning fluid obeying the p-Stokes (full Stokes) equations with the ice atmosphere interface as a moving free surface. A Navier slip boundary condition applies at the glacier base allowing both bedrock and subglacial lakes to be represented. Within the CutFEM framework we develop a strategy for handling non-linear viscosities and thin domains and show how glacier deformation can be modelled using a level set function. In numerical experiments we show that the expected order of accuracy is achieved and that the method is robust with respect to penalty parameters. As an application we compute the velocity field of the Swiss mountain glacier Haut Glacier d'Arolla in 2D with and without an underlying subglacial lake, and simulate the glacier deformation from year 1930 to 1932, with and without surface accumulation and basal melt.

  • 40. Ahlkrona, Josefin
    et al.
    Kirchner, Nina
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för naturgeografi och kvartärgeologi (INK).
    Lötstedt, Per
    A numerical study of scaling relations for non-Newtonian thin film flows with applications in ice sheet modelling2013Inngår i: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, nr 4, s. 417-435Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article treats the viscous, non-Newtonian thin-film flow of ice sheets, governed by the Stokes equations, and the modelling of ice sheets with asymptotic expansion of the analytical solutions in terms of the aspect ratio, which is a small parameter measuring the shallowness of an ice sheet. An asymptotic expansion requires scalings of the field variables with the aspect ratio. There are several, conflicting, scalings in the literature used both for deriving simplified models and for analysis. We use numerical solutions of the Stokes equations for varying aspect ratios in order to compute scaling relations. Our numerically obtained results are compared with three known theoretical scaling relations: the classical scalings behind the Shallow Ice Approximation, the scalings originally used to derive the so-called Blatter-Pattyn equations, and a non-uniform scaling which takes into account a high viscosity boundary layer close to the ice surface. We find that the latter of these theories is the most appropriate one since there is indeed a boundary layer close to the ice surface where scaling relations are different than further down in the ice. This boundary layer is thicker than anticipated and there is no distinct border with the inner layer for aspect ratios appropriate for ice sheets. This makes direct application of solutions obtained by matched asymptotic expansion problematic.

  • 41. Ahlkrona, Josefin
    et al.
    Lötstedt, Per
    Kirchner, Nina
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för naturgeografi.
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, s. 1-19Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.

  • 42. Ahlqvist, Eric
    et al.
    Carlson, Magnus
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    The etale cohomology ring of the ring of integers of a number field2023Inngår i: Research in Number Theory, ISSN 2522-0160, Vol. 9, nr 3, artikkel-id 58Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We compute the cohomology ring H*(X, Z/nZ) for X the spectrum of the ring of integers of a number field K. As an application, we give a non-vanishing formula for an invariant defined by Minhyong Kim.

  • 43. Ahmed, Chwas
    et al.
    Fröberg, Ralf
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Rafiq Namiq, Mohammed
    The graded Betti numbers of truncation of ideals in polynomial rings2023Inngår i: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 57, nr 4, s. 1303-1312Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let R=K[x1,…,xn], a graded algebra S=R/I satisfies Nk,p if I is generated in degree k, and the graded minimal resolution is linear the first p steps, and the k-index of S is the largest p such that S satisfies Nk,p. Eisenbud and Goto have shown that for any graded ring R/I, then R/I≥k, where I≥k=I∩Mk and M=(x1,…,xn), has a k-linear resolution (satisfies Nk,p for all p) if k≫0. For a squarefree monomial ideal I, we are here interested in the ideal Ik which is the squarefree part of I≥k. The ideal I is, via Stanley–Reisner correspondence, associated to a simplicial complex ΔI. In this case, all Betti numbers of R/Ik for k>min{deg(u)∣u∈I}, which of course are a much finer invariant than the index, can be determined from the Betti diagram of R/I and the f-vector of ΔI. We compare our results with the corresponding statements for I≥k. (Here I is an arbitrary graded ideal.) In this case, we show that the Betti numbers of R/I≥k can be determined from the Betti numbers of R/I and the Hilbert series of R/I≥k.

  • 44. Ahmed, S. Ejaz
    et al.
    Fallahpour, Saber
    von Rosen, Dietrich
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Estimation of Several Intraclass Correlation Coefficients2015Inngår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 44, nr 9, s. 2315-2328Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An intraclass correlation coefficient observed in several populations is estimated. The basis is a variance-stabilizing transformation. It is shown that the intraclass correlation coefficient from any elliptical distribution should be transformed in the same way. Four estimators are compared. An estimator where the components in a vector consisting of the transformed intraclass correlation coefficients are estimated separately, an estimator based on a weighted average of these components, a pretest estimator where the equality of the components is tested and then the outcome of the test is used in the estimation procedure, and a James-Stein estimator which shrinks toward the mean.

  • 45. Ahrens, Benedikt
    et al.
    Huber, Simon
    Mörtberg, Anders
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Preface to the MSCS Issue 31.1 (2021) Homotopy Type Theory and Univalent Foundations2021Inngår i: Mathematical Structures in Computer Science, ISSN 0960-1295, E-ISSN 1469-8072, Vol. 31, nr 1, s. 1-2Artikkel i tidsskrift (Annet vitenskapelig)
  • 46. Ahrens, Benedikt
    et al.
    Lumsdaine, Peter Lefanu
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Displayed Categories2019Inngår i: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 15, nr 1, artikkel-id 20Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce and develop the notion of displayed categories. A displayed category over a category C is equivalent to 'a category D and functor F : D -> C', but instead of having a single collection of 'objects of D' with a map to the objects of C, the objects are given as a family indexed by objects of C, and similarly for the morphisms. This encapsulates a common way of building categories in practice, by starting with an existing category and adding extra data/properties to the objects and morphisms. The interest of this seemingly trivial reformulation is that various properties of functors are more naturally defined as properties of the corresponding displayed categories. Grothendieck fibrations, for example, when defined as certain functors, use equality on objects in their definition. When defined instead as certain displayed categories, no reference to equality on objects is required. Moreover, almost all examples of fibrations in nature are, in fact, categories whose standard construction can be seen as going via displayed categories. We therefore propose displayed categories as a basis for the development of fibrations in the type-theoretic setting, and similarly for various other notions whose classical definitions involve equality on objects. Besides giving a conceptual clarification of such issues, displayed categories also provide a powerful tool in computer formalisation, unifying and abstracting common constructions and proof techniques of category theory, and enabling modular reasoning about categories of multi-component structures. As such, most of the material of this article has been formalised in Coq over the UniMath library, with the aim of providing a practical library for use in further developments.

  • 47.
    Ahrnbom, Moa
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Eklund, Maria
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Hur kan elevers kunskapsutveckling i matematik förbättras: Formativ bedömning i matematikundervisning2010Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med examensarbetet är att fördjupa vår kunskap om och förståelse för formativ bedömning i matematik. Vidare vill vi undersöka om den formativa bedömningen kan förbättra eleverna i klassens kunskapsutveckling i matematik. Vi har gjort en fallstudie i en klass som arbetar formativt för att undersöka hur det kan se ut i praktiken. Underlaget för det samlade materialet består av observation och intervju för att besvara våra två frågeställningar som följer. Hur kan en formativ bedömning se ut i praktiken? Hur kan en koppling mellan lärares och elevers uppfattningar om den pedagogiska verksamheten se ut? Vi har kommit fram till att den formativa bedömningen kan förbättra eleverna i klassens kunskapsutveckling i matematik. I den formativa bedömningen har vi sett vikten av mötet mellan lärare och elev. Att arbeta formativt är tidskrävande.

    Fulltekst (pdf)
    FULLTEXT01
  • 48. Akhtar, Mohammad
    et al.
    Coates, Tom
    Corti, Alessio
    Heuberger, Liana
    Kasprzyk, Alexander
    Oneto, Alessandro
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Petracci, Andrea
    Prince, Thomas
    Tveiten, Ketil
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    MIRROR SYMMETRY AND THE CLASSIFICATION OF ORBIFOLD DEL PEZZO SURFACES2016Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, nr 2, s. 513-527Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces.

  • 49.
    Akinyi Lagehäll, Amanda
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Yemane, Elelta
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Multilevel Cox Regression of Transition to Parenthood among Ethiopian Women2021Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    The birth of the first child is a special event for a mother whose life can change dramatically. In Ethiopia women’s timing to enter motherhood vary between the regions. This paper is therefore focusing on how birth cohort, education and residence affect the rate of entering motherhood for Ethiopian women in the different regions and the entire country. The dataset is extracted from the 2016 Ethiopia Demographic and Health Survey (EDHS) and contains 15,019 women from 487 different households. For more accurate estimations and results, the correlation within households is taken into consideration with multilevel survival analysis. The methods used are the Cox proportional hazard model and two frailty models. The results of the paper show that women residing in rural areas have an increased rate of entering motherhood compared to those residing in urban areas, every age group older than those born 1997 to 2001 have a higher intensity to enter parenthood and those with education have a decreased intensity ratio compared to the women with no education. It also shows that there is a regional difference in the effect of the estimated ratios of the covariates. Performing the multilevel analysis only changes the estimated effects of the covariates in the cities and one region. It is concluded that the estimated intensity ratio of multilevel survival analysis only varies from the standard Cox regression when the region is heterogeneous.

    Fulltekst (pdf)
    Lagehall_A_Yemane_E_2021
  • 50.
    Al Abdulaali, Ahmad
    King Faisal University, Saudi Arabia.
    Extension of Positive Currents with Special Properties of Monge-Ampère Operators2013Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 113, nr 1, s. 108-127Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper deals with the extension of positive currents across different types of sets. For closed complete pluripolar obstacles, we show the existence of such extensions. To do so, further Hausdorff dimension conditions are required. Moreover, we study the case when these obstacles are zero sets of strictly $k$-convex functions.

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