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Maxantalet träffar du kan exportera från sökgränssnittet är 250. Vid större uttag använd dig av utsökningar.
• 1.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Asymptotic distribution of zeros of a certain class of hypergeometric polynomials2014Licentiatavhandling, monografi (Annet vitenskapelig)

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.

• 2.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Addis Ababa University, Ethiopia.
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)

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.

• 3.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematik.
On the decomposition of D-modules over a hyperplane arrangement2007Licentiatavhandling, monografi (Annet vitenskapelig)
• 4.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
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)

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.

• 5. Abebaw, Tilahun
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)

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).

• 6. Ackermann, Nils
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)

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.

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)

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.

• 8.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Hardy and spectral inequalities for a class of partial differential operators2014Doktoravhandling, monografi (Annet vitenskapelig)

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.

• 9.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
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)

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.

• 10. Agbor, Dieudonne
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)

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.

• 11. Agmon, Shmuel
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)

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.

• 12.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
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)

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.

• 13.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Existence of an unbounded vacant set for subcritical continuum percolation2018Inngår i: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 23, artikkel-id 63Artikkel i tidsskrift (Fagfellevurdert)

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.

• 14. Ahrens, Benedikt
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
CATEGORICAL STRUCTURES FOR TYPE THEORY IN UNIVALENT FOUNDATIONS2018Inngår i: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 14, nr 3, artikkel-id 18Artikkel i tidsskrift (Fagfellevurdert)

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.

Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. 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)

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.

• 16.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
The inductive wedge product of positive currentsManuskript (preprint) (Annet vitenskapelig)

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).

• 17.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
On the Extension and Wedge Product of Positive Currents2012Doktoravhandling, med artikler (Annet vitenskapelig)

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.

• 18. Albeverio, Sergio
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Singular perturbations of differential operators: solvable Schrödinger type operators2000Bok (Fagfellevurdert)
• 19.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Combinatorial Methods in Complex Analysis2013Doktoravhandling, med artikler (Annet vitenskapelig)

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.

• 20.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
On Eigenvalues of the Schrodinger Operator with an Even Complex-Valued Polynomial Potential2012Inngår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 12, nr 2, s. 465-481Artikkel i tidsskrift (Fagfellevurdert)

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.

• 21.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential2010Licentiatavhandling, med artikler (Annet vitenskapelig)

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.

• 22.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Schur polynomials, banded Toeplitz matrices and Widom's formula2012Inngår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 19, nr 4, s. P22-Artikkel i tidsskrift (Fagfellevurdert)

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.

• 23.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stretched skew Schur polynomials are recurrent2014Inngår i: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 122, s. 1-8Artikkel i tidsskrift (Fagfellevurdert)

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.

• 24.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
On Eigenvalues of the Schrödinger Operator with a Complex-Valued Polynomial Potential2012Inngår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 12, nr 1, s. 119-144Artikkel i tidsskrift (Fagfellevurdert)

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.

• 25.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Around multivariate Schmidt-Spitzer theorem2014Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 446, s. 356-368Artikkel i tidsskrift (Fagfellevurdert)

Given an arbitrary complex-valued infinite matrix $\infmatA=(a_{ij}),$$i=1,\dotsc,\infty;$ $j=1,\dotsc,\infty$  and a positive integer $n$ we introduce anaturally associated  polynomial basis $\polybasis_\infmatA$ of$\C[x_0,\dotsc,x_n]$.We discuss some properties of the locus of  common zeros of all polynomials in $\polybasis_A$ having  a given degree $m$; the latter locus can beinterpreted as the spectrum of the $m\times (m+n)$-submatrix of $\infmatA$ formed by its  $m$ first rows and$(m+n)$ first columns. We initiate the study of the asymptotics of these spectra when $m\to \infty$ inthe case when $\infmatA$ is a banded Toeplitz matrix.In particular, we present and partially prove a conjectural multivariate analogof the well-known Schmidt-Spitzer theorem which describes  the spectral asymptotics for the sequence of principal minors of an arbitrarybanded Toeplitz matrix.Finally, we discuss relations between polynomial bases $\polybasis_\infmatA$ andmultivariate  orthogonal polynomials.

• 26.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Discriminants, Symmetrized Graph monomials and Sums of Squares2012Inngår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 21, nr 4, s. 353-361Artikkel i tidsskrift (Fagfellevurdert)

In 1878, motivated by the requirements of the invariant the-ory of binary forms, J. J. Sylvester constructed, for every graphwith possible multiple edges but without loops, its symmetrizedgraph monomial, which is a polynomial in the vertex labels ofthe original graph. We pose the question for which graphs thispolynomial is nonnegative or a sum of squares. This problem ismotivated by a recent conjecture of F. Sottile and E. Mukhin onthe discriminant of the derivative of a univariate polynomial andby an interesting example of P. and A. Lax of a graph with fouredges whose symmetrized graph monomial is nonnegative butnot a sum of squares. We present detailed information about sym-metrized graph monomials for graphs with four and six edges,obtained by computer calculations.

• 27.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Scan Statistics for Space-Time Cluster Detection2018Licentiatavhandling, med artikler (Annet vitenskapelig)

Scan statistics are used by public health agencies to detect and localize disease outbreaks. This thesis provides an overview of scan statistics in the context of prospective disease surveillance and outbreak detection, presents a novel scan statistic to deal with the type of zero-abundant data that is often encountered in these settings, and—perhaps most importantly—implements this and other scan statistics in a freely available and open source R package. Additionally, Markov processes and time series methods are frequently used in many disease surveillance methods. The last part of this thesis presents some computationally efficient methods for density evaluation and simulation of irregularly sampled AR(1) processes, that may be useful when implementing surveillance methods based on these types of processes.

• 28.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
A Universal A(infinity) Structure on BV Algebras with Multiple Zeta Value Coefficients2016Inngår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, nr 24, s. 7414-7470Artikkel i tidsskrift (Fagfellevurdert)

We construct an explicit and universal A-infinity deformation of Batalin-Vilkovisky algebras, with all coefficients expressed as rational sums of multiple zeta values. If the Batalin-Vilkovisky algebra that we start with is cyclic, then so is the A-infinity deformation. Moreover, the adjoint action of the odd Poisson bracket acts by derivations of the A-infinity structure. The construction conjecturally defines a new presentation of the Grothendieck-Teichmuller Lie algebra.

• 29.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Universal algebraic structures on polyvector fields2014Doktoravhandling, monografi (Annet vitenskapelig)

The theory of operads is a conceptual framework that has become a kind of universal language, relating branches of topology and algebra. This thesis uses the operadic framework to study the derived algebraic properties of polyvector fields on manifolds.The thesis is divided into eight chapters. The first is an introduction to the thesis and the research field to which it belongs, while the second chapter surveys the basic mathematical results of the field.The third chapter is devoted to a novel construction of differential graded operads, generalizing an earlier construction due to Thomas Willwacher. The construction highlights and explains several categorical properties of differential graded algebras (of some kind) that come equipped with an action by a differential graded Lie algebra. In particular, the construction clarifies the deformation theory of such algebras and explains how such algebras can be twisted by Maurer-Cartan elements.The fourth chapter constructs an explicit strong homotopy deformation of polynomial polyvector fields on affine space, regarded as a two-colored noncommutative Gerstenhaber algebra. It also constructs an explicit strong homotopy quasi-isomorphism from this deformation to the canonical two-colored noncommmutative Gerstenhaber algebra of polydifferential operators on the affine space. This explicit construction generalizes Maxim Kontsevich's formality morphism.The main result of the fifth chapter is that the deformation of polyvector fields constructed in the fourth chapter is (generically) nontrivial and, in a sense, the unique such deformation. The proof is based on some cohomology computations involving Kontsevich's graph complex and related complexes. The chapter ends with an application of the results to properties of a derived version of the Duflo isomorphism.The sixth chapter develops a general mathematical framework for how and when an algebraic structure on the germs at the origin of a sheaf on Cartesian space can be "globalized" to a corresponding algebraic structure on the global sections over an arbitrary smooth manifold. The results are applied to the construction of the fourth chapter, and it is shown that the construction globalizes to polyvector fields and polydifferential operators on an arbitrary smooth manifold.The seventh chapter combines the relations to graph complexes, explained in chapter five, and the globalization theory of chapter six, to uncover a representation of the Grothendieck-Teichmüller group in terms of A-infinity morphisms between Poisson cohomology cochain complexes on a manifold.Chapter eight gives a simplified version of a construction of a family of Drinfel'd associators due to Carlo Rossi and Thomas Willwacher. Our simplified construction makes the connections to multiple zeta values more transparent--in particular, one obtains a fairly explicit family of evaluations on the algebra of formal multiple zeta values, and the chapter proves certain basic properties of this family of evaluations.

• 30.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Grothendieck-Teichmuller group and Poisson cohomologies2015Inngår i: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 9, nr 1, s. 185-214Artikkel i tidsskrift (Fagfellevurdert)

We study actions of the Grothendieck-Teichmuller group GRT on Poisson cohomologies of Poisson manifolds, and prove some go and no-go theorems associated with these actions.

• 31. Alm, Jonas
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Valuation of Index-Linked Cash Flows in a Heath-Jarrow-Morton Framework2015Inngår i: Risks, ISSN 1670-0139, E-ISSN 2227-9091, Vol. 3, nr 3, s. 338-364Artikkel i tidsskrift (Fagfellevurdert)

In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath-Jarrow-Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.

• 32. Alm, Sven Erick
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stokastik2008Bok (Annet (populærvitenskap, debatt, mm))
• 33. Alm, Sven Erick
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
First Passage Percolation on $$\mathbb {Z}^2$$: A Simulation Study2015Inngår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, nr 3, s. 657-678Artikkel i tidsskrift (Fagfellevurdert)

First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.

• 34. Almqvist, Catarina
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
LifeGene-a large prospective population-based study of global relevance2011Inngår i: European Journal of Epidemiology, ISSN 0393-2990, E-ISSN 1573-7284, Vol. 26, nr 1, s. 67-77Artikkel i tidsskrift (Fagfellevurdert)

Studying gene-environment interactions requires that the amount and quality of the lifestyle data is comparable to what is available for the corresponding genomic data. Sweden has several crucial prerequisites for comprehensive longitudinal biomedical research, such as the personal identity number, the universally available national health care system, continuously updated population and health registries and a scientifically motivated population. LifeGene builds on these strengths to bridge the gap between basic research and clinical applications with particular attention to populations, through a unique design in a research-friendly setting. LifeGene is designed both as a prospective cohort study and an infrastructure with repeated contacts of study participants approximately every 5 years. Index persons aged 18-45 years old will be recruited and invited to include their household members (partner and any children). A comprehensive questionnaire addressing cutting-edge research questions will be administered through the web with short follow-ups annually. Biosamples and physical measurements will also be collected at baseline, and re-administered every 5 years thereafter. Event-based sampling will be a key feature of LifeGene. The household-based design will give the opportunity to involve young couples prior to and during pregnancy, allowing for the first study of children born into cohort with complete pre-and perinatal data from both the mother and father. Questions and sampling schemes will be tailored to the participants' age and life events. The target of LifeGene is to enrol 500,000 Swedes and follow them longitudinally for at least 20 years.

• 35. Alpcan, Tansu
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Can we measure the difficulty of an optimization problem?2014Konferansepaper (Annet vitenskapelig)

Can we measure the difficulty of an optimization problem? Although optimization plays a crucial role in modernscience and technology, a formal framework that puts problemsand solution algorithms into a broader context has not beenestablished. This paper presents a conceptual approach which gives a positive answer to the question for a broad class of optimization problems. Adopting an information and computational perspective, the proposed framework builds upon Shannon and algorithmic information theories. As a starting point, a concrete model and definition of optimization problems is provided. Then, a formal definition of optimization difficulty is introduced which builds upon algorithmic information theory. Following an initial analysis, lower and upper bounds on optimization difficulty are established. One of the upper-bounds is closely related to Shannon information theory and black-box optimization. Finally, various computational issues and future research directions are discussed.

• 36. Alström, Per
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Non-monophyly and intricate morphological evolution within the avian family Cettiidae revealed by multilocus analysis of a taxonomically densely sampled dataset2011Inngår i: BMC Evolutionary Biology, ISSN 1471-2148, E-ISSN 1471-2148, Vol. 11, s. 352-Artikkel i tidsskrift (Fagfellevurdert)

Background: The avian family Cettiidae, including the genera Cettia, Urosphena, Tesia, Abroscopus and Tickellia and Orthotomus cucullatus, has recently been proposed based on analysis of a small number of loci and species. The close relationship of most of these taxa was unexpected, and called for a comprehensive study based on multiple loci and dense taxon sampling. In the present study, we infer the relationships of all except one of the species in this family using one mitochondrial and three nuclear loci. We use traditional gene tree methods (Bayesian inference, maximum likelihood bootstrapping, parsimony bootstrapping), as well as a recently developed Bayesian species tree approach (*BEAST) that accounts for lineage sorting processes that might produce discordance between gene trees. We also analyse mitochondrial DNA for a larger sample, comprising multiple individuals and a large number of subspecies of polytypic species. Results: There are many topological incongruences among the single-locus trees, although none of these is strongly supported. The multi-locus tree inferred using concatenated sequences and the species tree agree well with each other, and are overall well resolved and well supported by the data. The main discrepancy between these trees concerns the most basal split. Both methods infer the genus Cettia to be highly non-monophyletic, as it is scattered across the entire family tree. Deep intraspecific divergences are revealed, and one or two species and one subspecies are inferred to be non-monophyletic (differences between methods). Conclusions: The molecular phylogeny presented here is strongly inconsistent with the traditional, morphology-based classification. The remarkably high degree of non-monophyly in the genus Cettia is likely to be one of the most extraordinary examples of misconceived relationships in an avian genus. The phylogeny suggests instances of parallel evolution, as well as highly unequal rates of morphological divergence in different lineages. This complex morphological evolution apparently misled earlier taxonomists. These results underscore the well-known but still often neglected problem of basing classifications on overall morphological similarity. Based on the molecular data, a revised taxonomy is proposed. Although the traditional and species tree methods inferred much the same tree in the present study, the assumption by species tree methods that all species are monophyletic is a limitation in these methods, as some currently recognized species might have more complex histories.

• 37.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Universidade Eduardo Mondlane.
Direct Images Of Locally Constant Sheaves on Complements to Plane Line Arrangements2015Licentiatavhandling, monografi (Annet vitenskapelig)
• 38. Ambarstsoumian, Gaik
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Microlocal Analysis of an Ultrasound Transform with Circular Source and Receiver Trajectories2013Inngår i: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 598, s. 45-58Artikkel i tidsskrift (Fagfellevurdert)
• 39.
Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
Students' choice of post-compulsory science: In search of schools that compensate for the socio-economic background of their students2013Inngår i: International Journal of Science Education, ISSN 0950-0693, E-ISSN 1464-5289, Vol. 35, nr 18, s. 3141-3160Artikkel i tidsskrift (Fagfellevurdert)

It is commonly argued that socio-economic inequalities can explain many of the differences in achievement and participation in science education that have been reported among countries and among schools within a country. We addressed this issue by examining (a) the relationship between variables associated with socio-economic background and application frequencies to the Swedish Natural Science Programme (NSP) in upper secondary school and (b) whether there are lower secondary schools in Sweden that seem to compensate for these variables. Data from Statistics Sweden (SCB) covering the whole population of 106,483 ninth-grade students were used to calculate the probability for each student to apply to the NSP. Our results indicate that the variables, such as parental educational level and grades, have explanatory power, but with varying effect for different subpopulations of students. For example, grades in mathematics have a greater impact than grades in science for females’ choice of the NSP. The opposite holds for male students. Out of 1,342 schools, 158 deviated significantly from predicted, that is, the students in these schools applied to the NSP in greater or lesser extent than expected. The number of deviating schools is greater than predicted by pure random variation. This suggests that variables of socio-economic background are only a partial explanation of the application frequencies, and that the deviation needs to be investigated further. Our findings suggest that in order to understand why schools deviate positively and so compensate for the socio-economic background of their students, we need to study their practices more closely

• 40.
Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för miljövetenskap och analytisk kemi.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för miljövetenskap och analytisk kemi.
Regionally-Varying Combustion Sources of the January 2013 Severe Haze Events over Eastern China2015Inngår i: Environmental Science and Technology, ISSN 0013-936X, E-ISSN 1520-5851, Vol. 49, nr 4, s. 2038-2043Artikkel i tidsskrift (Fagfellevurdert)

Thick haze plagued northeastern China in January 2013, strongly affecting both regional climate and human respiratory health. Here, we present dual carbon isotope constrained (Delta C-14 and delta C-13) source apportionment for combustion-derived black carbon aerosol (BC) for three key hotspot regions (megacities): North China Plain (NCP, Beijing), the Yangtze River Delta (YRD, Shanghai), and the Pearl River Delta (PRD, Guangzhou) for January 2013. BC, here quantified as elemental carbon (EC), is one of the most health-detrimental components of PM2.5 and a strong climate warming agent. The results show that these severe haze events were equally affected (similar to 30%) by biomass combustion in all three regions, whereas the sources of the dominant fossil fuel component was dramatically different between north and south. In the NCP region, coal combustion accounted for 66% (46-74%, 95% C.I.) of the EC, whereas, in the YRD and PRD regions, liquid fossil fuel combustion (e.g., traffic) stood for 46% (18-66%) and 58% (38-68%), respectively. Taken together, these findings suggest the need for a regionally-specific description of BC sources in climate models and regionally-tailored mitigation to combat severe air pollution events in East Asia.

• 41.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Risk capital stress testing framework and the new capital adequacy rules2007Rapport (Annet vitenskapelig)
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Risk capital stress-testing framework and the new capital adequacy rules2007Inngår i: Journal of Risk Model Validation, Vol. 1, nr 3, s. 3-28Artikkel i tidsskrift (Fagfellevurdert)
• 43.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Risk capital stress-testing framework and the new capital adequacy rules2007Inngår i: Journal of Risk Model Validation, Vol. 1Artikkel i tidsskrift (Fagfellevurdert)
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Risk tolerance concepts and scenario analysis of bank capital2009Inngår i: Stress-testing for Financial Institutions: Applications, Regulations and Techniques, London: Risk Books , 2009, s. 399-422Kapittel i bok, del av antologi (Annet vitenskapelig)
• 45.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Disproof of some conjectures of P. Turan2007Inngår i: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 117, nr 3, s. 245-250Artikkel i tidsskrift (Fagfellevurdert)

We disprove some power sum conjectures of Turan that would have implied the density hypothesis of the Riemann zeta-function if true.

• 46.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stability estimates for the local Radon transform2018Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, nr 3, artikkel-id 034004Artikkel i tidsskrift (Fagfellevurdert)

We consider the inverse problem for the 2-dimensional local Radon transform R[f], where f is supported in y >= x(2) and R[f](xi, eta) = integral f (x, xi x + eta) dx is defined near (xi, eta) = (0, 0). We give logarithmic estimates of f in terms of R[f] for functions f that satisfy an a priori bound. For a certain class of smooth, positive weight functions m we give similar estimates for the weighted Radon transform R-m vertical bar f](xi, eta) = integral f (x, xi x + eta) m(xi, eta, x) dx.

• 47.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Explicit solutions to certain inf max problems from Turan power sum theory2007Inngår i: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 18, nr 2, s. 189-194Artikkel i tidsskrift (Fagfellevurdert)

In a previous paper [1] we proved that [GRAPHICS] when n + 1 is prime. In this paper we prove that [GRAPHICS] when n - 1 is a prime power, and [GRAPHICS] when n >= 3 is a prime power. We give explicit constructions of n-tuples (z(1),..., z(n)) which we prove are global minima for these problems. These are two of the few times in Turan power sum theory where solutions in the inf max problem can be explicitly calculated.

• 48.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Mergelyan's approximation theorem with nonvanishing polynomials and universality of zeta-functions2013Inngår i: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 167, s. 201-210Artikkel i tidsskrift (Fagfellevurdert)

We prove a variant of the Mergelyan approximation theorem that allows us to approximate functions that are analytic and nonvanishing in the interior of a compact set K with connected complement, and whose interior is a Jordan domain, with nonvanishing polynomials. This result was proved earlier by the author in the case of a compact set K without interior points, and independently by Gauthier for this case and the case of strictly starlike compact sets. We apply this result on the Voronin universality theorem for compact sets K, where the usual condition that the function is nonvanishing on the boundary can be removed. We conjecture that this version of Mergelyan's theorem might be true for a general set K with connected complement and show that this conjecture is equivalent to a corresponding conjecture on Voronin Universality.

• 49.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Summation formulae and zeta functions2006Doktoravhandling, med artikler (Annet vitenskapelig)

This thesis in analytic number theory consists of 3 parts and 13 individual papers.

In the first part we prove some results in Turán power sum theory. We solve a problem of Paul Erdös and disprove conjectures of Paul Turán and K. Ramachandra that would have implied important results on the Riemann zeta function.

In the second part we prove some new results on moments of the Hurwitz and Lerch zeta functions (generalized versions of the Riemann zeta function) on the critical line.

In the third and final part we consider the following question: What is the natural generalization of the classical Poisson summation formula from the Fourier analysis of the real line to the matrix group SL(2,R)? There are candidates in the literature such as the pre-trace formula and the Selberg trace formula.

We develop a new summation formula for sums over the matrix group SL(2,Z) which we propose as a candidate for the title "The Poisson summation formula for SL(2,Z)". The summation formula allows us to express a sum over SL(2,Z) of smooth functions f on SL(2,R) with compact support, in terms of spectral theory coming from the full modular group, such as Maass wave forms, holomorphic cusp forms and the Eisenstein series. In contrast, the pre-trace formula allows us to get such a result only if we assume that f is also SO(2) bi-invariant.

We indicate the summation formula's relationship with additive divisor problems and the fourth power moment of the Riemann zeta function as given by Motohashi. We prove some identities on Kloosterman sums, and generalize our main summation formula to a summation formula over integer matrices of fixed determinant D. We then deduce some consequences, such as the Kuznetsov summation formula, the Eichler-Selberg trace formula and the classical Selberg trace formula.

• 50.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Mergelyan's theorem with polynomials non-vanishing on unions of sets2014Inngår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 59, nr 1, s. 99-109Artikkel i tidsskrift (Fagfellevurdert)

We consider the problem of approximating a function having no zeros on the interior of a set by polynomials having no zeros on the entire set.

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