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  • 1.
    Adamowicz, Tomasz
    et al.
    Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland.
    Lundström, Niklas L.P.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures2016Ingår i: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, nr 2, s. 623-658Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.

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  • 2.
    Amanuel, Meron
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    ON GENERATING THE PROBABILITY MASS FUNCTION USING FIBONACCI POWER SERIES2022Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    This thesis will focus on generating the probability mass function using Fibonacci sequenceas the coefficient of the power series.

    The discrete probability, named Fibonacci distribution,was formed by taking into consideration the recursive property of the Fibonacci sequence,the radius of convergence of the power series, and additive property of mutually exclusiveevents. This distribution satisfies the requisites of a legitimate probability mass function.

    It's cumulative distribution function and the moment generating function are then derived and the latter are used to generate moments of the distribution, specifically, the mean and the variance.

    The characteristics of some convergent sequences generated from the Fibonacci sequenceare found useful in showing that the limiting form of the Fibonacci distribution is a geometricdistribution. Lastly, the paper showcases applications and simulations of the Fibonacci distribution using MATLAB.

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  • 3.
    Andersson, Henrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Classification of spectral signatures in biological aerosols2013Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    I det här examensarbetet har multivariat dataanalys använts för att utvärdera förbehandlings-metoder, t.ex. normalisering, och klassificeringsmöjligheter för spektralt data insamlat med Laser Induced Breakdown Spectroscopy (LIBS). Systemet som FOI utvecklat under de senaste åren i syfte att analysera enstaka partiklar i luft har använts i laboratoriemiljö för att samla data från tio olika prover. En principalkomponentanalys (PCA) visar att det går att se skillnader mellan proverna utifrån de två datatyperna som erhålls från LIBS, 2D CCD bilder och spektra extraherat från dessa bilder. Vidare så visar resultat från partiell minstakvadrat-diskriminantanalys (PLS-DA) att normalisering av data endast har en visuell effekt i PCA score-plottar och inte har någon inverkan på modellernas prediktionsfömåga. Resultat visar även på möjligheter att beskära och binna pixlar i bilderna i viss utstreckning utan att förlora signifikant prediktionsförmåga.

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    Classification of spectral signatures in biological aerosols
  • 4.
    Bengzon, Fredrik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats G
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Adaptive finite element approximation of multiphysics problems: a fluid structure interaction model problem2010Ingår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, nr 12, s. 1451-1465Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider computation of the displacement of an elastic object immersed into a viscous incompressible flow. For simplicity, we assume that the mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. We derive an a posteriori error estimate for this one way coupled problem using duality techniques. Based on these estimates we develop an adaptive algorithm that automatically constructs a suitable adapted mesh for the fluid and solid domains given goal quantities specified on the solid problem.

  • 5.
    Berglund, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Evaluating ∫0f(x)dx and ∫ab f(x)dx using residue calculus2014Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    I den har uppsatsen använder vi komplex analys, då särskilt modern residykalkyl, for att beräkna vissa Riemann-integraler.

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    Andre_Berglund_Bachelors_Umea
  • 6.
    Berglund, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Numerical Simulations of Linear Stochastic Oscillators: driven by Wiener and Poisson processes2017Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Den huvudsakliga komponenten av uppsatsen är en numerisk analys av stokastiska differentialekvationer drivna av Wiener- och Poisson-processer. För att göra det så fokuserar vi på två modellproblem, den geometriska Brownska rörelsen samt den linjära stokastiska oscillatorn, studerade i litteratur för stokastiska differentialekvationer som bara drivs av en Wiener-process.Den här uppsatsen täcker teoretiska samt numeriska undersökningar av hopp - eller mer specifikt, Poisson - processer och hur de påverkar de ovan nämnda modellproblemen.

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  • 7.
    Bergqvist, Ewa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Positive currents related to polynomial convexity1999Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
  • 8.
    Bergström, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Feature extraction and cluster analysis of oil slicks using optical satellite data2021Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
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  • 9.
    Björnfot, Fredrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    GDP Growth Rate Nowcasting and Forecasting2017Självständigt arbete på avancerad nivå (yrkesexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The main purpose of this project was to help Swedbank get a better understandingof how gross domestic product growth rate develops in the future froma data set of macroeconomic variables. Since GDP values are released long aftera quarter has ended Swedbank would like to have a model that could predictupcoming GDP from these data sets. This was solved by a combination ofgrowth rate predictions from a dynamic factor model, a vector autoregressivemodel and two machine learning models. The predictions were combined usinga weighting method called system averaging model where the model predictionwith least historical error receives the largest weight in the nal future prediction.In previous work a simple moving average model has been implementedto achieve this eect however there are several aws in a simple moving averagemodel. Most of these defects could in theory be avoided by using an exponentialweighting scheme instead. This resulted in the use of an exponentialweighting method that is used to calculate weights for future predictions. Themain conclusions from this project were that some predictions could get betterwhen removing bad performing models which had too large of a weight. Puttingtoo high weight on a single well performing model is also not optimal since thepredictions could get very unstable because of varying model performance. Theexponential weighting scheme worked well for some predictions however whenthe parameter , that controls how the weight is distributed between recent andhistorical errors, got too small a problem arose. Too few values were used toform the nal weights for the prediction and the estimate got unsteady results.

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  • 10.
    Bjørnstad Pedersen, Lars
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    An analysis of a shared mating in V2.2014Självständigt arbete på avancerad nivå (magisterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    I detta examensarbete undersöker vi, från en topologisk synvinkel och utan applicering av Thurstons teorem, varför matchningen av det så kallade basilikapolynomet

     och dendriten  är delad med matchningen av  och dendriten .

    Båda dessa matchningar är lika med den rationella avbildningen

     .

    Definierat i examensarbetet är för båda matchningarna homoemorfa koordinatbyten från mängden till Fatou- och Juliamängden av . Här är  den ifyllda Juliamängden av avbildningen  och  är den -fixerade punkten i .

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    An analysis of a shared mating in V2 - 2014 - Lars Pedersen
  • 11.
    Borgqvist, Johannes G.
    et al.
    Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, United Kingdom.
    Ohlsson, Fredrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Baker, Ruth E.
    Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, United Kingdom.
    Energy translation symmetries and dynamics of separable autonomous two-dimensional ODEs2023Ingår i: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 454, artikel-id 133876Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study symmetries in the phase plane for separable, autonomous two-state systems of ordinary differential equations (ODEs). We prove two main theoretical results concerning the existence and non-triviality of two orthogonal symmetries for such systems. In particular, we show that these symmetries correspond to translations in the internal energy of the system, and describe their action on solution trajectories in the phase plane. In addition, we apply recent results establishing how phase plane symmetries can be extended to incorporate temporal dynamics to these energy translation symmetries. Subsequently, we apply our theoretical results to the analysis of three models from the field of mathematical biology: a canonical biological oscillator model, the Lotka–Volterra (LV) model describing predator–prey dynamics, and the SIR model describing the spread of a disease in a population. We describe the energy translation symmetries in detail, including their action on biological observables of the models, derive analytic expressions for the extensions to the time domain, and discuss their action on solution trajectories.

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  • 12. Brännström, Niklas
    et al.
    Persson, Leif A.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A measure theoretic approach to linear inverse atmospheric dispersion problems2015Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 31, nr 2, artikel-id 025009Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made (other than assuming that it is indeed a source, i.e. not a sink). We investigate the source-sensor relationship and rigorously state solvability conditions for when the inverse problem can be solved using a least-squares optimization method. That is, we derive conditions for when the least-squares problem is well-defined.

  • 13. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Augmented Lagrangian finite element methods for contact problems2019Ingår i: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 53, nr 1, s. 173-195Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.

  • 14.
    Burman, Erik
    et al.
    Department of Mathematics, University College London, Gower Street, London, United Kingdom.
    Hansbo, Peter
    Department of Mechanical Engineering, Jönköping University, 551 11, Jönköping, Sweden.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    CutFEM based on extended finite element spaces2022Ingår i: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 152, nr 2, s. 331-369Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected by the boundary occur and these elements must in general by stabilized in some way. Discrete extension operators provides such a stabilization by modification of the finite element space close to the boundary. More, precisely the finite element space is extended from the stable interior elements over the boundary in a stable way which also guarantees optimal approximation properties. Our framework is applicable to all standard nodal based finite elements of various order and regularity. We develop an abstract theory for elliptic problems and associated parabolic time dependent partial differential equations and derive a priori error estimates. We finally apply this to some examples of partial differential equations of different order including the interface problems, the biharmonic operator and the sixth order triharmonic operator.

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  • 15.
    Burman, Erik
    et al.
    Department of Mathematics, University College London, London, United Kingdom.
    Hansbo, Peter
    Department of Materials and Manufacturing, Jönköping University, Jönköping, Sweden.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions2024Ingår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 93, nr 345, s. 35-54Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution u ∈ Hs with s ∈ (1, 3/2]. For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.

  • 16.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    An equivalence to the Gleason problem2010Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 370, nr 2, s. 373-378Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we study the Gleason problem locally. A new method for solving the Gleason A problem is presented. This is done by showing an equivalent statement to the Gleason A problem. In order to prove this statement, necessary and a sufficient conditions for a bounded domain to have the Gleason A property are found. Also an example of a bounded but not smoothly-bounded domain in C(n) is given, which satisfies the sufficient condition at the origin, and hence has the Gleason A property there.

  • 17.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Analytic properties in the spectrum of certain Banach algebras2009Ingår i: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 261, nr 1, s. 189-200Artikel i tidskrift (Refereegranskat)
  • 18.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nebenhülle and the Gleason problem2010Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, nr 1, s. 267-273Artikel i tidskrift (Refereegranskat)
  • 19.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Spectrum of certain Banach algebras and $\overline\partial$-problems2007Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 90, nr 1, s. 51-58Artikel i tidskrift (Refereegranskat)
  • 20.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Trivial generators for nontrivial fibres2008Ingår i: MATHEMATICA BOHEMICA, ISSN 0862-7959, Vol. 133, nr 2, s. 121-131Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in $\mathbb{C}^n$ where the fibre is nontrivial, has to exceed $n$. This is shown not to be the case.

  • 21.
    Carlsson, Linus
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A note on B-envelope of holomorphy and B-extendable domains2008Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 53, nr 4, s. 307-309Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let B subset of H(infinity)(X) be a Banach Algebra on a Riemann domain X over C(n). We show that under certain conditions on B and X, all functions in B can be extended to functions in B(E(B, X)) where E(B, X) is the B-envelope of holomorphy.

  • 22.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Measures of finite pluricomplex energy2019Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, nr 1, s. 203-213Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study a complex Monge-Ampere type equation of the form (dd(c)u)(n) = ke(-u)dV/integral e(-u)dV.

  • 23.
    Chuaqui, Martin
    et al.
    Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile.
    Hernández, Rodrigo
    Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile.
    Llinares, Adrián
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain.
    Mas, Alejandro
    Departamento de Análisis Matemático, Universidad de Valencia, Burjassot, Spain.
    On the convolution of convex 2-gons2024Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 538, nr 2, artikel-id 128387Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the convolution of functions of the form [Formula presented] which map the open unit disk of the complex plane onto polygons of 2 edges when α∈(0,1). Inspired by a work of Cima, we study the limits of convolutions of finitely many fα and the convolution of arbitrary unbounded convex mappings. The analysis for the latter is based on the notion of angle at infinity, which provides an estimate for the growth at infinity and determines whether the convolution is bounded or not. A generalization to an arbitrary number of factors shows that the convolution of n randomly chosen unbounded convex mappings has a probability of 1/n! of remaining unbounded. We provide the precise asymptotic behavior of the coefficients of the functions fα.

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  • 24. Cinti, Chiara
    et al.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Polidoro, Sergio
    A Note on Harnack Inequalities and Propagation Sets for a Class of Hypoelliptic Operators2010Ingår i: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 33, nr 4, s. 341-354Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we are concerned with Harnack inequalities for non-negative solutions u:Ω→ℝ to a class of second order hypoelliptic ultraparabolic partial differential equations in the form Lu:=∑j=1mX2ju+X0u−∂tu=0 where Ω is any open subset of ℝN + 1, and the vector fields X1, ..., Xm and X0t are invariant with respect to a suitable homogeneous Lie group. Our main goal is the following result: for any fixed (x0, t0) ∈ Ω we give a geometric sufficient condition on the compact sets K⊆Ω for which the Harnack inequality supK u≤CK u(x0, t0) holds for all non-negative solutions u to the equation Lu=0. We also compare our result with an abstract Harnack inequality from potential theory.

  • 25.
    Daghighi, Abtin
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Gauthier, Paul M.
    Université de Montréal, Montréal, Canada.
    An algebra of polyanalytic functions2021Ingår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 165, nr 2, s. 225-240Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The most important uniform algebra is the family of continuous functions on a compact subset K of the complex plane C which are analytic on the interior int(K). For polyanalytic functions and compact sets K which are regular (i.e. K = int(K)), we introduce analogous spaces, which are Banach spaces with respect to the sup-norm, but are not closed with respect to the usual pointwise multiplication. We introduce a multiplication on these spaces and investigate the resulting algebras.

  • 26.
    Dmytryshyn, Andrii
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Miniversal deformations of pairs of skew-symmetric matrices under congruence2016Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 506, s. 506-534Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair (A, B) we provide a normal form with a minimal number of independent parameters to which all pairs of skew-symmetric matrices ((A) over tilde (,) (B) over tilde), close to (A, B) can be reduced by congruence transformation which smoothly depends on the entries of the matrices in the pair ((A) over tilde (,) (B) over tilde). An upper bound on the distance from such a miniversal deformation to (A, B) is derived too. We also present an example of using miniversal deformations for analyzing changes in the canonical structure information (i.e. eigenvalues and minimal indices) of skew-symmetric matrix pairs under perturbations.

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  • 27.
    Dmytryshyn, Andrii
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Miniversal deformations of pairs of symmetric matrices under congruence2019Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 568, s. 84-105Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For each pair of complex symmetric matrices (A, B) we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices ((A) over tilde (B) over tilde), close to (A, B) can be reduced by congruence transformation that smoothly depends on the entries of (A ) over tilde and (B) over tilde. Such a normal form is called a miniversal deformation of (A, B) under congruence. A number of independent parameters in the miniversal deformation of a symmetric matrix pencil is equal to the codimension of the congruence orbit of this symmetric matrix pencil and is computed too. We also provide an upper bound on the distance from (A, B) to its miniversal deformation.

  • 28.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Futorny, Vyacheslav
    Klymchuk, Tetiana
    Sergeichuk, Vladimir V.
    Generalization of Roth's solvability criteria to systems of matrix equations2017Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 527, s. 294-302Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    W.E. Roth (1952) proved that the matrix equation AX - XB = C has a solution if and only if the matrices [Graphics] and [Graphics] are similar. A. Dmytryshyn and B. Kagstrom (2015) extended Roth's criterion to systems of matrix equations A(i)X(i')M(i) - (NiXi"Bi)-B-sigma i = Ci (i = 1,..., s) with unknown matrices X1,, X-t, in which every X-sigma is X, X-T, or X*. We extend their criterion to systems of complex matrix equations that include the complex conjugation of unknown matrices. We also prove an analogous criterion for systems of quaternion matrix equations. (C) 2017 Elsevier Inc. All rights reserved.

  • 29.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå Univ, HPC2N, SE-90187 Umeå, Sweden.
    Kågstrom, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå Univ, HPC2N, SE-90187 Umeå, Sweden.
    Coupled Sylvester-type Matrix Equations and Block Diagonalization2015Ingår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 36, nr 2, s. 580-593Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and $\star$-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of $2 \times 2$ block matrix representations of the equations are block diagonalizable by (linked) equivalence transformations. Various applications leading to several particular cases have already been investigated in the literature, some recently and some long ago. Solvability of these cases follow immediately from our general consistency theory. We also show how to apply our main result to systems of Stein-type matrix equations.

  • 30.
    Elfverson, Daniel
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Målqvist, Axel
    Multiscale methods for problems with complex geometry2017Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 321, s. 103-123Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in the energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affected by the way the domain boundary cuts the coarse elements in the background mesh. The analytical findings are verified in a series of numerical experiments.

  • 31.
    Enflo, Karin
    Umeå universitet, Humanistiska fakulteten, Institutionen för idé- och samhällsstudier.
    Measuring one-dimensional diversity2022Ingår i: Inquiry, ISSN 0020-174X, E-ISSN 1502-3923Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A large number of diversity measures have been proposed in the literature, almost all of which are designed for sets with elements that differ in multiple aspects. However, these types of measures are not appropriate for sets with elements that differ in a single aspect only, such as duration, value or probability. In this essay I present a new measure of diversity, designed specifically for single aspect diversity. The measure captures the intuitive idea that single aspect diversity is affected by the maximal dissimilarity between the elements, the number of different elements, and the even spacing of the elements’ aspect values, when represented as points in one dimension. I show that the measure satisfies six plausible conditions for a single aspect diversity measure, which concern scale independence, minimal diversity, maximal dissimilarity, restricted function growth, strict monotonicity, and even spacing. The measure is also characterised.

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  • 32.
    Engström, Christian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Torshage, Axel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Accumulation of Complex Eigenvalues of a Class of Analytic Operator FunctionsManuskript (preprint) (Övrigt vetenskapligt)
  • 33.
    Engström, Christian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Torshage, Axel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On equivalence and linearization of operator matrix functions with unbounded entries2017Ingår i: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 89, nr 4, s. 465-492Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of unbounded operator functions. Further, we deduce methods of finding equivalences to operator matrix functions that utilizes equivalences of the entries. Finally, a method of finding equivalences and linearizations to a general case of operator matrix polynomials is presented.

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  • 34.
    Eriksson, Sofia
    et al.
    Department of Mathematics, Linnaeus University, Växjö, Sweden.
    Wang, Siyang
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Summation-by-parts approximations of the second derivative: Pseudoinverse and revisitation of a high order accurate operator2021Ingår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 59, nr 5, s. 2669-2697Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider finite difference approximations of the second derivative, exemplified in Poisson's equation, the heat equation, and the wave equation. The finite difference operators satisfy a summation-by-parts (SBP) property, which mimics the integration-by-parts principle. Since the operators approximate the second derivative, they are singular by construction. When imposing boundary conditions weakly, these operators are modified using simultaneous approximation terms. The modification makes the discretization matrix nonsingular for most choices of boundary conditions. Recently, inverses of such matrices were derived. However, for problems with only Neumann boundary conditions, the modified matrices are still singular. For such matrices, we have derived an explicit expression for the Moore-Penrose inverse, which can be used for solving elliptic problems and some time-dependent problems. For this explicit expression to be valid, it is required that the modified matrix does not have more than one zero eigenvalue. This condition holds for the SBP operators with second and fourth order accurate interior stencil. For the sixth order accurate case, we have reconstructed the operator with a free parameter and show that there can be more than one zero eigenvalue. We have performed a detailed analysis on the free parameter to improve the properties of the second derivative SBP operator. We complement the derivations by numerical experiments to demonstrate the improvements.

  • 35.
    Eskandari, Setareh
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
    Abkar, Ali
    Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
    Åhag, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Perälä, Antti
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sub-Hilbert relation for Fock-Sobolev type spaces2022Ingår i: New York Journal of Mathematics, E-ISSN 1076-9803, Vol. 28, s. 958-969Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, two specific sub-Hilbert spaces are studied. They arise from the action of a Toeplitz operator on Fock–Sobolev type spaces, in-duced by a general Gaussian type weight. The argument is based on analysing the reproducing kernel of the corresponding sub-Hilbert space.

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  • 36.
    Fontes, Magnus
    et al.
    Centre for Mathematical Science, Lund, Sweden.
    Verdier, Olivier
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Simplified a priori Estimate for the Time Periodic Burgers' Equation2010Ingår i: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, nr 1, s. 34-41Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present here a version of the existence and uniqueness result of time periodic solutions to the viscous Burgers’ equation with irregular forcing terms (with Sobolev regularity –1 in space). The key result here is an a priori estimate which is simpler than the previously treated case of forcing terms with regularity –½ in time.

  • 37. Fontes, Magnus
    et al.
    Verdier, Olivier
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Time-Periodic Solutions of the Burgers Equation2009Ingår i: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 11, nr 2, s. 303-323Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract: We investigate the time periodic solutions to the viscous Burgers equation u(t) - mu u(xx) + uu(x) = f for irregular forcing terms. We prove that the corresponding Burgers operator is a diffeomorphism between appropriate function spaces.

  • 38.
    Forsberg, Joel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Swaptions from a Clearinghouse perspective: Hedging swaptions, an option on interest rate swaps, using compression2022Självständigt arbete på avancerad nivå (yrkesexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Med den ökande användningen av ränteswappar är det av stor vikt att förståswaptioner, vilket är en option på en ränteswapp. En swaption kan användasbåde för spekulativa syften och för att hedgea mot risker i ränteförändringar.Det viktigaste att förstå är hur man prissätter en swaption. Eftersom swap-tioner baseras på underliggande tillgångar så kommer vi börja med det mestgrundläggande, obligationer, och arbeta oss fram till modellen vi kommer an-vända, Black76. Black76-modellen är en variant av den nobelprisvinnandemodellen Black-Scholes-Merton. Med denna modell kan vi börja undersökadet huvudsakliga syftet med avhandlingen, en hedgningsstrategi för swap-tioner från perspektivet av ett clearingshus.Clearinghus är en central del av den moderna finansmarknaden. De agerarsom en mellanhand för att hantera affärer mellan clearingmedlemmar ochhar en översikt över marknaden. Ifall en clearingmedlem går i konkurs,kommer clearinghuset att ta över portföljen med tillgångar. Clearinghusetkommer att hålla en auktion för att sälja av portföljen. De strävar efteratt hålla auktionen så snabbt som möjligt och det sker generellt efter 5 till15 dagar. Medan de har portföljen så är de exponerade mot riskerna i till-gångarna och därför är det av största vikt att kunna hedga tillgångarna. Iden här avhandlingen har en strategi och en algorithm tagits fram för attanvända delta-hedging för att uppnå delta-neutralitet under normala mark-nadsrörelser.Vi kommer att undersöka två olika fall. Det första fallet är när portföljen tasöver när det är lång tid kvar till swaptionens förfallodatum. Då kommer viatt använda forward swaps för att hedgea och för att minska antalet swapparkommer vi att använda kompression. Det andra fallet är när förfallodatumetuppnås under tiden som clearinghuset håller i portföljen. Dagarna innan för-fallodatumet kommer vi hedgea med forward swaps med kompression. Närdatumet är nått så kommer vi istället att använda ränteswappar.I båda fallen är resultaten nära att uppnå delta-neutralitet. Med normalis-erade deltan med avsenende på det nominella beloppet är medelvärdet avdelta-exponeringen av magnituden 10−4 för det första fallet och 10−6 för detandra. Men, det är värt att komma ihåg att allting är baserat på simuler-ade värden under förenklade antaganden. Denna avhandling bör utgöra enbra grund för vidare studier där man kan undersöka mer extrema mark-nadsrörelser. Med extremare rörelser skulle man kunna undersöka hedgn-ingsstrategier med andra Greker som till exempel Gamma och Vega.

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  • 39.
    Frentz, Marie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Regularity in the obstacle problem for parabolic non-divergence operators of Hörmander typeManuskript (preprint) (Övrigt vetenskapligt)
  • 40.
    Frentz, Marie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Topics on subelliptic parabolic equations structured on Hörmander vector fields2012Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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  • 41.
    Frentz, Marie
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garofalo, Nicola
    Department of Mathematics, Purdue University, West Lafayette IN 47907-1968.
    Götmark, Elin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Munive, Isidro
    Department of Mathematics, Purdue University, West Lafayette IN 47907-1968.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Non-divergence form parabolic equations associated with non-commuting vector fields: Boundary behavior of nonnegative solutions2012Ingår i: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 11, nr 2, s. 437-474Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In a cylinder Omega(T) = Omega x (0, T) subset of R-+(n+1) we study the boundary behavior of nonnegative solutions of second order parabolic equations of the form

    H u = Sigma(m)(i,j=1) a(ij)(x, t)XiX (j)u - partial derivative(t)u = 0, (x, t) is an element of R-+(n+1),

    where X = {X-l, . . . , X-m} is a system of C-infinity vector fields inR(n) satisfying Hormander's rank condition (1.2), and Omega is a non-tangentially accessible domain with respect to the Carnot-Caratheodory distance d induced by X. Concerning the matrix-valued function A = {a(ij)}, we assume that it is real, symmetric and uniformly positive definite. Furthermore, we suppose that its entries a(ij) are Holder continuous with respect to the parabolic distance associated with d. Our main results are: I) a backward Harnack inequality for nonnegative solutions vanishing on the lateral boundary (Theorem 1.1); 2) the Holder continuity up to the boundary of the quotient of two nonnegative solutions which vanish continuously on a portion of the lateral boundary (Theorem 1.2); 3) the doubling property for the parabolic measure associated with the operator H (Theorem 1.3). These results generalize to the subelliptic setting of the present paper, those in Lipschitz cylinders by Fabes, Safonov and Yuan in [20, 39]. With one proviso: in those papers the authors assume that the coefficients a(ij) be only bounded and measurable, whereas we assume Holder continuity with respect to the intrinsic parabolic distance.

  • 42.
    Frentz, Marie
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Götmark, Elin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The obstacle problem for parabolic non-divergence form operators of Hörmander type2012Ingår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 252, nr 9, s. 5002-2041Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we establish the existence and uniqueness of strong solutions to the obstacle problem for a class of parabolic sub-elliptic operators in non-divergence form structured on a set of smooth vector fields in Rn, X={X1,…,Xq}X={X1,…,Xq}, q⩽n, satisfying Hörmanderʼs finite rank condition. We furthermore prove that any strong solution belongs to a suitable class of Hölder continuous functions. As part of our argument, and this is of independent interest, we prove a Sobolev type embedding theorem, as well as certain a priori interior estimates, valid in the context of Sobolev spaces defined in terms of the system of vector fields.

  • 43.
    Frentz, Marie
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Adaptive stochastic weak approximation of degenerate parabolic equations of Kolmogorov type2010Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 234, nr 1, s. 146-164Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equations of Kolmogorov type have also turned out to be relevant in option pricing in the setting of certain models for stochastic volatility and in the pricing of Asian options. The purpose of this paper is to numerically solve the Cauchy problem, for a general class of second order degenerate parabolic differential operators of Kolmogorov type with variable coefficients, using a posteriori error estimates and an algorithm for adaptive weak approximation of stochastic differential equations. Furthermore, we show how to apply these results in the context of mathematical finance and option pricing. The approach outlined in this paper circumvents many of the problems confronted by any deterministic approach based on, for example, a finite-difference discretization of the partial differential equation in itself. These problems are caused by the fact that the natural setting for degenerate parabolic differential operators of Kolmogorov type is that of a Lie group much more involved than the standard Euclidean Lie group of translations, the latter being relevant in the case of uniformly elliptic parabolic operators.

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  • 44.
    Frentz, Marie
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Pascucci, Andrea
    Polidoro, Sergio
    Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options2010Ingår i: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 347, nr 4, s. 805-838Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we prove optimal interior regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstacles as well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. The problem considered arises in financial mathematics, when considering path-dependent derivative contracts with early exercise feature.

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  • 45.
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Maximal idels in A(Omega)1999Ingår i: Conemporary Mathematics, Vol. 222, s. 173-179Artikel i tidskrift (Refereegranskat)
  • 46.
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    The Gleason problem for A(Omega)1995Ingår i: New Zealand J. Math., Vol. 24, nr 1, s. 17-22Artikel i tidskrift (Refereegranskat)
  • 47.
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    The Gleason property for Reinhardt domains1997Ingår i: Mathematische Annalen, Vol. 308, s. 85-91Artikel i tidskrift (Refereegranskat)
  • 48.
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Ändligt-genererade ideal och Gleason-problemet2008Ingår i: Nordan ÅttaArtikel i tidskrift (Övrigt vetenskapligt)
  • 49. Fällström, Anders
    et al.
    Backlund, Ulf
    A pseudoconvex domain with non schlicht H-infinity envelope1991Ingår i: Geometrical and algebraical aspects in several complex variables. Sem. Conf, Vol. 8, s. 13-18Artikel i tidskrift (Refereegranskat)
  • 50.
    Fällström, Anders
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Backlund, Ulf
    Counterexamples to the Gleason Problem1998Ingår i: Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4), Vol. XXVI, s. 595-603Artikel i tidskrift (Refereegranskat)
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