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  • 1.
    Dmytryshyn, Andrii
    Umeå universitet, Institutionen för datavetenskap.
    Miniversal deformations of pairs of skew-symmetric matrices under congruence2016Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 506, s. 506-534Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 2.
    Dmytryshyn, Andrii
    Department of Computing Science, Umeå University, Umeå, Sweden.
    Miniversal deformations of pairs of symmetric matrices under congruence2019Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 568, s. 84-105Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 3.
    Dmytryshyn, Andrii
    et al.
    Department of Computing Science, Umeå University, Umeå, Sweden.
    Futorny, Vyacheslav
    Department of Mathematics, University of São Paulo, São Paulo, Brazil.
    Klymchuk, Tetiana
    Universitat Politècnica de Catalunya, Barcelona, Spain; Taras Shevchenko National University, Kiev, Ukraine.
    Sergeichuk, Vladimir V.
    Institute of Mathematics, Kiev, Ukraine.
    Generalization of Roth's solvability criteria to systems of matrix equations2017Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 527, s. 294-302Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 4.
    Dmytryshyn, Andrii
    et al.
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Futorny, Vyacheslav
    Department of Mathematics, University of São Paulo, São Paulo, Brazil.
    Kågström, Bo
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Klimenko, Lena
    National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kiev, Ukraine.
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence2015Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 469, s. 305-334Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We construct the Hasse diagrams G2 and G3 for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A + λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2 B and G3 B for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.

  • 5.
    Dmytryshyn, Andrii
    et al.
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Futorny, Vyacheslav
    Department of Mathematics, University of São Paulo, São Paulo, Brazil.
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Miniversal deformations of matrices of bilinear forms2012Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, nr 7, s. 2670-2700Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29–43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence.

  • 6.
    Dmytryshyn, Andrii
    et al.
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Futorny, Vyacheslav
    Department of Mathematics, University of São Paulo, São Paulo, Brazil.
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Miniversal deformations of matrices under *congruence and reducing transformations2014Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 446, nr April, s. 388-420Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Arnold (1971) [1] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We give miniversal deformations of matrices of sesquilinear forms; that is, of square complex matrices under *congruence, and construct an analytic reducing transformation to a miniversal deformation. Analogous results for matrices under congruence were obtained by Dmytryshyn, Futorny, and Sergeichuk (2012) [11].

  • 7.
    Dmytryshyn, Andrii
    et al.
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Johansson, Stefan
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Kågström, Bo
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Canonical structure transitions of system pencils2017Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 38, nr 4, s. 1249-1267Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the changes of the canonical structure information under small perturbations for a system pencil associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformations. The results allow us to track possible changes of important linear system characteristics under small perturbations.

  • 8.
    Dmytryshyn, Andrii
    et al.
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Kågström, Bo
    Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
    Coupled Sylvester-type Matrix Equations and Block Diagonalization2015Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 36, nr 2, s. 580-593Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 9.
    Edman, Rickard
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Östberg, Markus
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Γ-funktionenEn kort introduktion2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 10.
    Flodén, L.
    et al.
    Department of Quality technology and management, mechanical engineering and mathematics, Mid Sweden University, Östersund, Sweden.
    Holmbom, A.
    Department of Quality technology and management, mechanical engineering and mathematics, Mid Sweden University, Östersund, Sweden.
    Lobkova, T.
    Department of Quality technology and management, mechanical engineering and mathematics, Mid Sweden University, Östersund, Sweden.
    Olsson Lindberg, M.
    Department of Quality technology and management, mechanical engineering and mathematics, Mid Sweden University, Östersund, Sweden.
    Zhang, Ye
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem2017Inngår i: ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Melville, USA: American Institute of Physics (AIP), 2017, Vol. 1798, nr 1, artikkel-id 020177Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ε → 0.We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ε−1∂tuε as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.

  • 11.
    Jafari, Raheleh
    et al.
    Agder University College, Grimstad, Norway.
    Razvarz, Sina
    National Polytechnic Institute, Mexico City, Mexico.
    Gegov, Alexander
    University of Portsmouth, Portsmouth, UK.
    Paul, Satyam
    National Polytechnic Institute, Mexico City, Mexico.
    Keshtkar, Sajjad
    Universidad Nacional Autonoma de Mexico (UNAM), Mexico City, Mexico.
    Fuzzy Sumudu Transform Approach to Solving Fuzzy Differential Equations With Z-Numbers2019Inngår i: Advanced Fuzzy Logic Approaches in Engineering Science / [ed] Mangey Ram, Hershey, PA, USA: IGI Global , 2019, s. 18-48Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    Uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this book chapter, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of fuzzy numbers and Z-numbers. Important theorems are laid down to illustrate the properties of FST. This new technique is compared with Average Euler method and Max-Min Euler method. The theoretical analysis and simulation results show that the FST method is effective in estimating the solutions of FDEs.

  • 12.
    Yousefnezhad, Mohsen
    et al.
    School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
    Mohammadi, Seyyed Abbas
    Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran.
    Bozorgnia, Farid
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    A free boundary problem for a predator-prey model with nonlinear prey-taxix2018Inngår i: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 63, nr 2, s. 125-147Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary and the stability of the solutions.

  • 13.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Lukyanenko, Dmitry V.
    Department of Mathematics, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russian Federation.
    Yagola, Anatoly G.
    Department of Mathematics, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russian Federation.
    An optimal regularization method for convolution equations on the sourcewise represented set2015Inngår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 23, nr 5, s. 465-475Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article, we consider an inverse problem for the integral equation of the convolution typein a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a prioriinformation (sourcewise representation) based on optimal recovery theory we propose a new method. Theregularization and optimization properties of this method are proved. An optimal minimal a priori error ofthe problem is found. Moreover, a so-called optimal regularized approximate solution and its correspondingerror estimation are considered. Eciency and applicability of this method are demonstrated in a numericalexample of the image deblurring problem with noisy data.

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