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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 operators2019Ingår i: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 9, nr 2, s. 379-427Artikel i tidskrift (Refereegranskat)
    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 applications2020Ingår i: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 26, artikel-id 39Artikel i tidskrift (Refereegranskat)
    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.

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  • 3.
    Abathun, Addisalem
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Asymptotic distribution of zeros of a certain class of hypergeometric polynomials2014Licentiatavhandling, monografi (Övrigt vetenskapligt)
    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 Polynomialsd2016Ingår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 16, nr 2, s. 167-185Artikel i tidskrift (Refereegranskat)
    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 POLYNOMIALS2018Ingår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 68, nr 4, s. 1021-1031Artikel i tidskrift (Refereegranskat)
    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.
    Abebaw, Tilahun
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematik.
    On the decomposition of D-modules over a hyperplane arrangement2007Licentiatavhandling, monografi (Övrigt vetenskapligt)
  • 7.
    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 plane2010Ingår i: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 48, nr 2, s. 211-229Artikel i tidskrift (Refereegranskat)
    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.

  • 8.
    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 position2012Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, nr 8, s. 2699-2711Artikel i tidskrift (Refereegranskat)
    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).

  • 9. Ackermann, Nils
    et al.
    Szulkin, Andrzej
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A concentration phenomenon for semilinear elliptic equations2013Ingår i: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 207, nr 3, s. 1075-1089Artikel i tidskrift (Refereegranskat)
    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.

  • 10. Adamyan, V.
    et al.
    Langer, H.
    Tretter, Christiane
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Universität Bern, Switzerland.
    Winklmeier, M.
    Dirac-Krein Systems on Star Graphs2016Ingår i: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 86, nr 1, s. 121-150Artikel i tidskrift (Refereegranskat)
    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.

  • 11. Addario-Berry, Louigi
    et al.
    Broutin, Nicolas
    Holmgren, Cecilia
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    CUTTING DOWN TREES WITH A MARKOV CHAINSAW2014Ingår i: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 24, nr 6, s. 2297-2339Artikel i tidskrift (Refereegranskat)
    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.

  • 12.
    Aermark, Lior Alexandra
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hardy and spectral inequalities for a class of partial differential operators2014Doktorsavhandling, monografi (Övrigt vetenskapligt)
    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.

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  • 13.
    Aermark, Lior
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Laptev, A.
    Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field2012Ingår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 23, nr 2, s. 203-208Artikel i tidskrift (Refereegranskat)
    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.

  • 14. Agbor, Dieudonné
    et al.
    Boman, Jan
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the Modulus of Continuity of Mappings Between Euclidean Spaces2013Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 112, nr 1, s. 147-160Artikel i tidskrift (Refereegranskat)
    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.

  • 15. Agmon, Shmuel
    et al.
    Herbst, Ira
    Maad Sasane, Sara
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Persistence of embedded eigenvalues2011Ingår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 261, nr 2, s. 451-477Artikel i tidskrift (Refereegranskat)
    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.

  • 16. 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 Quinto2022Ingår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 30, nr 4, s. 613-617Artikel i tidskrift (Refereegranskat)
    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. 

  • 17.
    Ahlberg, Daniel
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A temporal perspective on the rate of convergence in first-passage percolation under a moment condition2019Ingår i: Brazilian Journal of Probability and Statistics, ISSN 0103-0752, E-ISSN 2317-6199, Vol. 33, nr 2, s. 397-401Artikel i tidskrift (Refereegranskat)
    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.

  • 18.
    Ahlberg, Daniel
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tertiles and the time constant2020Ingår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 57, nr 2, s. 407-408Artikel i tidskrift (Refereegranskat)
    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).

  • 19.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Baldasso, Rangel
    Noise sensitivity and Voronoi percolation2018Ingår i: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 23, artikel-id 108Artikel i tidskrift (Refereegranskat)
    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.

  • 20.
    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-PLANE2020Ingår i: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 30, nr 5, s. 2261-2273Artikel i tidskrift (Refereegranskat)
    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.

  • 21.
    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 degrees2019Ingår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, nr 3, s. 545-559Artikel i tidskrift (Refereegranskat)
    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.

  • 22.
    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 percolation2024Ingår i: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 56, nr 1, s. 411-422Artikel i tidskrift (Refereegranskat)
    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.

  • 23.
    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 walks2021Ingår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 49, nr 5, s. 2637-2667Artikel i tidskrift (Refereegranskat)
    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.

  • 24.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Griffiths, Simon
    Janson, Svante
    Morris, Robert
    Competition in growth and urns2019Ingår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 54, nr 2, s. 211-227Artikel i tidskrift (Refereegranskat)
    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.

  • 25.
    Ahlberg, Daniel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tassion, Vincent
    Teixeira, Augusto
    Existence of an unbounded vacant set for subcritical continuum percolation2018Ingår i: Electronic Communications in Probability, E-ISSN 1083-589X, Vol. 23, artikel-id 63Artikel i tidskrift (Refereegranskat)
    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.

  • 26.
    Ahlkrona, Josefin
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Uppsala University, Sweden; Kiel University, Germany.
    How much are the greenland and antarctic ice sheets melting?2018Ingår i: XRDS: Crossroads, The ACM Magazine for Students, ISSN 1528-4972, Vol. 25, nr 1, s. 42-47Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
  • 27.
    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 modelling2021Ingår i: Journal of Computational Physics: X, ISSN 2590-0552, Vol. 11, artikel-id 100090Artikel i tidskrift (Refereegranskat)
    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.

  • 28. Ahlqvist, Eric
    et al.
    Carlson, Magnus
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    The etale cohomology ring of the ring of integers of a number field2023Ingår i: Research in Number Theory, ISSN 2522-0160, Vol. 9, nr 3, artikel-id 58Artikel i tidskrift (Refereegranskat)
    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.

  • 29. 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 rings2023Ingår i: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 57, nr 4, s. 1303-1312Artikel i tidskrift (Refereegranskat)
    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.

  • 30. 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 Foundations2021Ingår i: Mathematical Structures in Computer Science, ISSN 0960-1295, E-ISSN 1469-8072, Vol. 31, nr 1, s. 1-2Artikel i tidskrift (Övrigt vetenskapligt)
  • 31. Ahrens, Benedikt
    et al.
    Lumsdaine, Peter Lefanu
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Displayed Categories2019Ingår i: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 15, nr 1, artikel-id 20Artikel i tidskrift (Refereegranskat)
    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.

  • 32. Ahrens, Benedikt
    et al.
    Lumsdaine, Peter Lefanu
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Voevodsky, Vladimir
    CATEGORICAL STRUCTURES FOR TYPE THEORY IN UNIVALENT FOUNDATIONS2018Ingår i: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 14, nr 3, artikel-id 18Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in univalent type theory, where the comparisons between them can be given more elementarily than in set-theoretic foundations. Specifically, we construct maps between the various types of structures, and show that assuming the Univalence axiom, some of the comparisons are equivalences. We then analyze how these structures transfer along (weak and strong) equivalences of categories, and, in particular, show how they descend from a category (not assumed univalent/saturated) to its Rezk completion. To this end, we introduce relative universes, generalizing the preceding notions, and study the transfer of such relative universes along suitable structure. We work throughout in (intensional) dependent type theory; some results, but not all, assume the univalence axiom. All the material of this paper has been formalized in Coq, over the UniMath library.

  • 33. Ahrens, Benedikt
    et al.
    Matthes, Ralph
    Mörtberg, Anders
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Implementing a category-theoretic framework for typed abstract syntax2022Ingår i: CPP '22: Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs / [ed] Andrei Popescu; Steve Zdancewic, New York: Association for Computing Machinery (ACM), 2022, s. 307-323Konferensbidrag (Refereegranskat)
    Abstract [en]

    In previous work ("From signatures to monads in UniMath"),we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant.

    In the present work, we describe what was necessary to generalize that work to account for simply-typed languages. First, some definitions had to be generalized to account for the natural appearance of non-endofunctors in the simply-typed case. As it turns out, in many cases our mechanized results carried over to the generalized definitions without any code change. Second, an existing mechanized library on 𝜔-cocontinuous functors had to be extended by constructions and theorems necessary for constructing multi-sorted syntax. Third, the theoretical framework for the semantical signatures had to be generalized from a monoidal to a bicategorical setting, again to account for non-endofunctors arising in the typed case. This uses actions of endofunctors on functors with given source, and the corresponding notion of strong functors between actions, all formalized in UniMath using a recently developed library of bicategory theory. We explain what needed to be done to plug all of these ingredients together, modularly.

    The main result of our work is a general construction that, when fed with a signature for a simply-typed language, returns an implementation of that language together with suitable boilerplate code, in particular, a certified monadic substitution operation.

  • 34. 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 SURFACES2016Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, nr 2, s. 513-527Artikel i tidskrift (Refereegranskat)
    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.

  • 35.
    Al Abdulaali, Ahmad
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    The inductive wedge product of positive currentsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, we discuss the wedge product of positive pluriharmonic (resp. plurisubharmonic) current of bidimension $(p,p)$ with the Monge-Ampère operator of plurisubharmonic function. In the first part of the paper, we define this product when the locus points of the plurisubharmonic function are located in a (2p-2)-dimensional closed set (resp. (2p-4)-dimensional sets), in the sense of Hartogs. The second part treats the case when these locus points are contained in a compact complete pluripolar sets and p≥ 2 (resp. p≥3).

  • 36.
    Al Abdulaali, Ahmad Khalid
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the Extension and Wedge Product of Positive Currents2012Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This dissertation is concerned with extensions and wedge products of positive currents. Our study can be considered as a generalization for classical works done earlier in this field.

    Paper I 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.

    In Paper II, we discuss the wedge product of positive pluriharmonic (resp. plurisubharmonic) current of bidimension (p,p) with the Monge-Ampère operator of plurisubharmonic function. In the first part of the paper, we define this product when the locus points of the plurisubharmonic function are located in a (2p-2)-dimensional closed set (resp. (2p-4)-dimensional sets), in the sense of Hartogs. The second part treats the case when these locus points are contained in a compact complete pluripolar sets and p≥2 (resp. p≥3).

    Paper III studies the extendability of negative S-plurisubharmonic current of bidimension (p,p) across a (2p-2)-dimensional closed set. Using only the positivity of S, we show that such extensions exist in the case when these obstacles are complete pluripolar, as well as zero sets of C2-plurisubharmoinc functions.

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  • 37. Albert, Michael
    et al.
    Holmgren, Cecilia
    Johansson, Tony
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Skerman, Fiona
    Embedding Small Digraphs and Permutations in Binary Trees and Split Trees2020Ingår i: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 82, nr 3, s. 589-615Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees (Cai et al. in Combin Probab Comput 28(3):335-364, 2019). We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye (SIAM J Comput 28(2):409-432, 1998. 10.1137/s0097539795283954). Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree, with probability tending to one as the number of balls increases, the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embeddings of digraphs into split trees which may be of independent interest.

  • 38. Albeverio, Sergio
    et al.
    Kurasov, Pavel
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Singular perturbations of differential operators: solvable Schrödinger type operators2000Bok (Refereegranskat)
  • 39.
    Aldeghi, Nausica
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Rohleder, Jonathan
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions2023Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 524, nr 1, artikel-id 127078Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.

  • 40.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Combinatorial Methods in Complex Analysis2013Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The theme of this thesis is combinatorics, complex analysis and algebraic geometry. The thesis consists of six articles divided into four parts.

    Part A: Spectral properties of the Schrödinger equation

    This part consists of Papers I-II, where we study a univariate Schrödinger equation with a complex polynomial potential. We prove that the set of polynomial potentials that admit solutions to the Schrödingerequation is connected, under certain boundary conditions. We also study a similar result for even polynomial potentials, where a similar result is obtained.

    Part B: Graph monomials and sums of squares

    In this part, consisting of Paper III, we study natural bases for the space of homogeneous, symmetric and translation-invariant polynomials in terms of multigraphs. We find all multigraphs with at most six edges that give rise to non-negative polynomials, and which of these that can be expressed as a sum of squares. Such polynomials appear naturally in connection to expressing certain non-negative polynomials as sums of squares.

    Part C: Eigenvalue asymptotics of banded Toeplitz matrices

    This part consists of Papers IV-V. We give a new and generalized proof of a theorem by P. Schmidt and F. Spitzer concerning asymptotics of eigenvalues of Toeplitz matrices. We also generalize the notion of eigenvalues to rectangular matrices, and partially prove the a multivariate analogue of the above.

    Part D: Stretched Schur polynomials

    This part consists of Paper VI, where we give a combinatorial proof that certain sequences of skew Schur polynomials satisfy linear recurrences with polynomial coefficients.

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  • 41.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Free Action and Cyclic Sieving on Skew Semi-standard Young Tableaux2023Ingår i: Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, E-ISSN 1017-060X, Vol. 49, nr 1, artikel-id 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note, we provide a short proof of Theorem 4.3 in the paper titled Crystals, semistandard tableaux and cyclic sieving phenomenon, by Y.-T. Oh and E. Park, which concerns a cyclic sieving phenomenon on semi-standard Young tableaux. We also extend their result to skew shapes.

  • 42.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    LLT polynomials, elementary symmetric functions and melting lollipops2021Ingår i: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 53, nr 2, s. 299-325Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We conjecture an explicit positive combinatorial formula for the expansion of unicellular LLT polynomials in the elementary symmetric basis. This is an analogue of the Shareshian-Wachs conjecture previously studied by Panova and the author in 2018. We show that the conjecture for unicellular LLT polynomials implies a similar formula for vertical-strip LLT polynomials. We prove positivity in the elementary symmetric basis for the class of graphs called melting lollipops previously considered by Huh, Nam and Yoo. This is done by proving a curious relationship between a generalization of charge and orientations of unit-interval graphs. We also provide short bijective proofs of Lee's three-term recurrences for unicellular LLT polynomials, and we show that these recurrences are enough to generate all unicellular LLT polynomials associated with abelian area sequences.

  • 43.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On Eigenvalues of the Schrodinger Operator with an Even Complex-Valued Polynomial Potential2012Ingår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 12, nr 2, s. 465-481Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we generalize several results in the article Analytic continuation of eigenvalues of a quartic oscillator of A. Eremenko and A. Gabrielov [4]. We consider a family of eigenvalue problems for a Schrodinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k < (d + 2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively. In the case with k = (d + 2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components.

  • 44.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential2010Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials.

    In the first paper, we consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.

    In the second paper, we only consider even polynomial potentials, and show that the spectral determinant for the eigenvalue problem consists of two irreducible components. A similar result to that of paper I is proved for k boundary conditions.

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  • 45.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Schur polynomials, banded Toeplitz matrices and Widom's formula2012Ingår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 19, nr 4, s. P22-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that for arbitrary partitions lambda subset of kappa, and integers 0 <= c < r <= n, the sequence of Schur polynomials S(kappa+k.1c)/(lambda+k.1r)(x(1), ... , x(n)) for k sufficiently large, satisfy a linear recurrence. The roots of the characteristic equation are given explicitly. These recurrences are also valid for certain sequences of minors of banded Toeplitz matrices. In addition, we show that Widom's determinant formula from 1958 is a special case of a well-known identity for Schur polynomials.

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  • 46.
    Alexandersson, Per
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Stretched skew Schur polynomials are recurrent2014Ingår i: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 122, s. 1-8Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that sequences of skew Schur polynomials obtained from stretched semi-standard Young tableauxsatisfy a linear recurrence, which we give explicitly.Using this, we apply this to finding certain asymptotic behavior of these Schur polynomials and present conjectures on minimal recurrences for stretched Schur polynomials.

  • 47.
    Alexandersson, Per
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Gabrielov, Andrei
    On Eigenvalues of the Schrödinger Operator with a Complex-Valued Polynomial Potential2012Ingår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 12, nr 1, s. 119-144Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation.

    We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.

    The first results can be derived from H. Habsch, while the case of a disconnected parameter space is new.

  • 48.
    Alexandersson, Per
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Getachew Kebede, Frether
    An involution on derangements preserving excedances and right-to-left minima2023Ingår i: The Australasian Journal of Combinatorics, ISSN 1034-4942, Vol. 86, nr 3, s. 387-413Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We give a bijective proof of a result by Mantaci and Rakotondrajao from 2003, regarding even and odd derangements with a fixed number of excedances. We refine their result by also considering the set of right-to-left minima

  • 49.
    Alexandersson, Per
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    González-Serrano, Luis Angel
    Maximenko, Egor A.
    Moctezuma-Salazar, Mario Alberto
    Symmetric polynomials in the symplectic alphabet and the change of variables z(j) = x(j) + x(j)(-1)2021Ingår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 28, nr 1, artikel-id P1.56Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Given a symmetric polynomial P in 2n variables, there exists a unique symmetric polynomial Q in n variables such that P(x(1), ..., x(n), x(1)(-1), ..., x(n)(-1)) = Q(x(1) + x(1)(-1), ..., x(n) + x(n)(-1)). We denote this polynomial Q by Phi(n)(P) and show that Phi(n) is an epimorphism of algebras. We compute Phi(n)(P) for several families of symmetric polynomials P: symplectic and orthogonal Schur polynomials, elementary symmetric polynomials, complete homogeneous polynomials, and power sums. Some of these formulas were already found by Elouafi (2014) and Lachaud (2016). The polynomials of the form Phi(n)(s(lambda/mu)((2n))), where s(lambda/mu)((2n)) is a skew Schur polynomial in 2n variables, arise naturally in the study of the minors of symmetric banded Toeplitz matrices, when the generating symbol is a palindromic Laurent polynomial, and its roots can be written as x(1), ..., x(n), x(1)(-1), ..., x(n)(-1). Trench (1987) and Elouafi (2014) found efficient formulas for the determinants of symmetric banded Toeplitz matrices. We show that these formulas are equivalent to the result of Ciucu and Krattenthaler (2009) about the factorization of the characters of classical groups.

  • 50.
    Alexandersson, Per
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hemmingsson, Nils
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Novikov, Dmitry
    Shapiro, Boris Z.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tahar, Guillaume
    Linear first order differential operators and their Hutchinson invariant sets2024Ingår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 391, s. 265-320Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in detail in the simplest case of operators of order 1. Namely, assuming that such an operator T has polynomial coefficients, we interpret it as a continuous family of Hutchinson operators acting on the space of positive powers of linear forms. Using this interpretation of T, we introduce its continuously Hutchinson invariant subsets of the complex plane and investigate a variety of their properties. In particular, we prove that for any T with non-constant coefficients, there exists a unique minimal under inclusion invariant set MTCH and find explicitly what operators T have the property that MTCH=C.

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