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  • 351.
    Edlund, Ove
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Solution of linear programming and non-linear regression problems using linear M-estimation methods1999Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis is devoted to algorithms for solving two optimization problems, using linear M-estimation methods, and their implementation. First, an algorithm for the non-linear M-estimation problem is considered. The main idea of the algorithm is to linearize the residual function in each iteration and thus calculate the iteration step by solving a linear M- estimation problem. A 2-norm bound on the variables restricts the step size, to guarantee convergence. The other algorithm solves the dual linear programming problem by making a ``smooth'' approximation of edges and inequality constraints using quadratic functions, thus making it possible to use Newton's method to find the optimal solution. The quadratic approximation of the inequality constraint makes it a penalty function algorithm. The implementation uses sparse matrix techniques. Since it is an active set method, it is possible to reuse the old factor when calculating the new step, by up- and downdating the old factor. It is only occasionally, when the downdating fails, that the factor instead has to be found with a sparse multifrontal LQ-factorization.

  • 352.
    Edlund, Ove
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Ekblom, Håkan
    Algorithms for robustified error-in-variables problems1998Inngår i: COMPSTAT [1998]: proceedings in computational statistics ; 13th symposium held in Bristol, Great Britain, 1998 ; with 61 tables / [ed] Roger Payne; Peter Green, Heidelberg: Physica-Verlag Rudolf Liebig GmbH , 1998, s. 293-298Konferansepaper (Fagfellevurdert)
    Abstract [en]

    From the introduction: We consider the problem of fitting a model of the form $y=f(x,\beta)$ to a set of points $(x_i,y_i)$, $i=1,\dots,n$. If there are measurement or observation errors in $x$ as well as in $y$, we have the so-called errors-in-variables-problem with model equation $$y_i=f(x_i+\delta_i,\beta)+\varepsilon_i,\ i=1,\dots,n,\tag 1$$ where $\delta_i\in\bbfR^m$, $i=1,\dots,n$, are the errors in $x_i\in\bbfR^m$. Then the problem is to find a vector of parameters $\beta\in\bbfR^p$ that minimizes the errors $\varepsilon_i$ and $\delta_i$ in some loss function subject to (1). We present algorithms using more robust alternatives to the least squares criterion.\par We will further discuss, from

  • 353.
    Edlund, Ove
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Ekblom, Håkan
    Computing the constrained M-estimates for regression2005Inngår i: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 49, nr 1, s. 19-32Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Constrained M-estimates for regression have been previously proposed as an alternative class of robust regression estimators with high breakdown point and high asymptotic efficiency. These are closely related to S-estimates, and it is shown that in some cases they will necessarily coincide. It has been difficult to use the CM-estimators in practice for two reasons. Adequate computational methods have been lacking and there has also been some confusion concerning the tuning parameters. Both of these problems are addressed; an updated table for choice of suitable parameter value is given, and an algorithm to compute CM-estimates for regression is presented. It can also be used to compute S-estimates. The computational problem to be solved is global optimization with an inequality constraint. The algorithm consists of two phases. The first phase is finding suitable starting values for the local optimization. The second phase, the efficient finding of a local minimum, is described in more detail. There is a MATLAB code generally available from the net. A Monte Carlo simulation is performed, using this code, to test the performance of the estimator as well as the algorithm.

  • 354.
    Edlund, Ove
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Ekblom, Håkan
    Madsen, Kaj
    Institute of Mathematical Modelling, Technical University of Denmark.
    Algorithms for non-linear M-estimation1997Inngår i: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658, Vol. 12, nr 3, s. 373-383Artikkel i tidsskrift (Fagfellevurdert)
  • 355.
    Edrees, Tarek
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Nikolakopoulos, George
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Signaler och system.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Jonasson, Jan-Erik
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Investigation of changes in modal characteristics before and after damage of a railway bridge: A case study2015Inngår i: The IES Journal Part A: Civil & Structural Engineering, ISSN 1937-3260, E-ISSN 1937-3279, Vol. 8, nr 2, s. 131-144Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The linear, time-invariant transfer function Txy has been utilized for the construction of FRF, based on the ambient vibration measurements. The results presented here indicated the possibility to identify and localize damages in steel railway bridges from the variations in the modal characteristics of the structure. The comparison between the modal characteristics for the healthy and collapsed bridge confirmed that damage had been existed. The abnormal percentage of change in modal damping, between the healthy and any other condition for a structure, can be regarded as a serious indicator for early stages of damage, while the high percentage of change in modal damping can clearly indicate the existence of damage in that structure. The average ratio of change in the damping ratio from the healthy to the collapsed bridge was about 206 % and this ration could be regarded as an index for the existence of a serious damage in steel bridges, which needs further evaluation in other test cases.

  • 356.
    Elfgren, Lennart
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Ohlsson, Ulf
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Sabourova, Natalia
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Signal processing in modal analysis of bridges2009Konferansepaper (Annet vitenskapelig)
  • 357.
    Elsner, J.
    et al.
    Department of Physics, University of Exeter.
    Jones, R.
    Department of Physics, University of Exeter.
    Haugk, M.
    Technische Universität, Theoretische Physik III, D-09107 Chemnitz.
    Gutierrez, R.
    Technische Universität, Theoretische Physik III, D-09107 Chemnitz.
    Frauenheim, Th.
    Theoretische Physik III, TU Chemnitz.
    Heggie, M.I.
    CPES, University of Sussex, Falmer, Brighton.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Briddon, P.R.
    Department of Physics, University of Newcastle.
    Effect of oxygen on the growth of (101‾0) GaN surfaces: The formation of nanopipes1998Inngår i: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 73, nr 24, s. 3530-3532Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Local density-functional methods are used to examine the behavior of O and O-related defect complexes on the walls of nanopipes in GaN. We find that O has a tendency to segregate to the (10 1̄ 0) surface and identify the gallium vacancy surrounded by three oxygen impurities [VGa-(ON)3] to be a particularly stable and electrically inert complex. We suggest that during Stranski-Krastanow growth, when interisland spaces shrink, these defects reach a critical concentration beyond which further growth is prevented and nanopipes are formed

  • 358.
    Elsner, J
    et al.
    University of Exeter.
    Jones, R
    University of Exeter.
    Heggie, M I
    University of Sussex.
    Sitch, P K
    Technische Universität, Chemnitz.
    Haugk, M
    Technische Universität, Chemnitz.
    Frauenheim, Th
    Technische Universität, Chemnitz.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Briddon, P R
    University of Newcastle Upon Tyne.
    Deep acceptors trapped at threading-edge dislocations in GaN1998Inngår i: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 58, nr 19, s. 12571-12574Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Local-density-functional methods are used to examine the behavior of the oxygen defect, gallium vacancy, and related defect complexes trapped at threading-edge dislocations in GaN. These defects are found to be particularly stable at the core of the dislocation where oxygen sits twofold coordinated in a bridge position. VGa-ON is found to be a deep double acceptor, VGa-(ON)2 is a deep single acceptor, and VGa-(ON)3 at the dislocation core is electrically inactive. We suggest that the first two defects are responsible for a deep acceptor level associated with the midgap yellow luminescence band.

  • 359. Elsner, J.
    et al.
    Jones, R.
    Department of Physics, University of Exeter.
    Sitch, P.K.
    Frauenheim, Th.
    Theoretische Physik III, TU Chemnitz.
    Heggie, M.I.
    CPES, University of Sussex, Falmer, Brighton.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Briddon, P.R.
    Department of Physics, University of Newcastle.
    Structural and electrical properties of threading dislocations in GaN1997Inngår i: Defects in semiconductors: proceedings of the 19th International Conference on Defects in Semiconductors, Aveiro, Portugal, July 1997 / [ed] Gordon Davies, Trans Tech Publications Inc., 1997, s. 1203-1210Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The atomic structures and electrical properties for threading screw and threading edge dislocations of wurtzite GaN are calculated within the local-density approximation. Both dislocations are electrically inactive with a band gap free from deep levels. These results are understood to arise from relaxed core structures which are similar to (1010) surfaces. The threading screw dislocations are found to be stable with an open-core whereas the threading edge dislocations possess filled cores.

  • 360.
    Elsner, J
    et al.
    University of Exeter.
    Jones, R
    University of Exeter.
    Stich, P K
    Technische Universität, Chemnitz.
    Porezag, V D
    Technische Universität, Chemnitz.
    Elstner, M
    Technische Universität, Chemnitz.
    Frauenheim, Th
    Technische Universität, Chemnitz.
    Heggie, M I
    University of Sussex.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Briddon, P R
    University of Newcastle Upon Tyne.
    Theory of threading edge and screw dislocations in GaN1997Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 79, nr 19, s. 3672-3675Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The atomic structures, electrical properties, and line energies for threading screw and threading edge dislocations of wurtzite GaN are calculated within the local-density approximation. Both dislocations are electrically inactive with a band gap free from deep levels. These results are understood to arise from relaxed core structures which are similar to (101̅ 0) surfaces.

  • 361.
    Englis, Miroslav
    et al.
    MÚ AV ČR, Zitná 25, 11567 Prague.
    Lukkassen, Dag
    Peetr, Jaak
    Centre for Mathematical Sciences, Lund University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions2004Inngår i: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 570, s. 89-129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In an earlier work, J.-L. Lions produced a means for creating reproducing formulas for the space of harmonic functions with Sobolev boundary values on a domain in real Euclidean space. The present authors give a new proof of this result and also generalize the Lions formula to handle spaces of functions that are annihilated by an elliptic operator. The method of constructing the reproducing kernels seems to be based on the old paradigm of Aronszajn and Bergman. It is interesting to note that this model---that the kernel should take the form $$ K(x,y)=\sum_j e_j(x)·e_j(y) $$ for a suitable orthonormal basis $\{e_j\}$---goes back to the thesis of Bochner. That thesis well predates the early work of Bergman and Szegö.

  • 362.
    Engström, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Mouzon, Johanne
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Córdoba, J.M.
    Instituto de Ciencia de Materiales de Sevilla, Código del Centro.
    Tegman, Ragnar
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Antti, Marta-Lena
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Synthesis of a TiCN – SiC polyhedron and elongated crystals nanopowder at low nitrogen concentration2012Inngår i: Materials letters (General ed.), ISSN 0167-577X, E-ISSN 1873-4979, Vol. 81, s. 148-150Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    At room temperature diluted TiCl4 and CCl4 were reduced by sodium particles and mixed with a polycarbomethylsilane (PCS) solution to yield a precursor. It was dried and subsequently annealed at 1300 °C, 1400 °C and 1450 °C in a tube furnace using argon with 10 ppm N2. After the 1450 °C annealing a nanocrystalline powder of TiC0.5 N0.5–SiC polyhedron and elongated crystals was obtained. At the low nitrogen concentration during annealing a gradual nitration is proposed. It is promoted by carbon gaseous species, precursor oxidation, a sufficient temperature and a summarised nitrogen surplus compared to the titanium and carbon amount.

  • 363. Engström, Jonas
    et al.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Piatnitski, Andrey
    Narvik University College, 8505 Narvik, Norway.
    Wall, Peter
    Homogenization of random degenerated nonlinear monotone operators2006Inngår i: Glasnik Matematicki - Serija III, ISSN 0017-095X, E-ISSN 1846-7989, Vol. 41, nr 1, s. 101-114Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper deals with homogenization of random nonlinear monotone operators in divergence form. We assume that the structure conditions (strict monotonicity and continuity conditions) degenerate and are given in terms of a weight function. Under proper integrability assumptions on the weight function we construct the effective operator and prove the homogenization result.

  • 364.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Analysis of two metapopulation models1994Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 365.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Certain reiteration and equivalence results for the Cobos-Peetre polygon interpolation method1999Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 85, nr 2, s. 310-319Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove some reiteration formulas for the Cobos-Peetre polygon method for $n+1$ tuples that consists of spaces $A_i$ where $A_i$ is of class $\theta_i$ with respect to a compatible pair $(X,Y)$. If $\theta_i$ is suitably chosen, the $J$- and $K$-method coincides and is equal to a space $(X,Y)_{\nu,q}$. For arbitrary chosen $\theta_i$ the $J$- and $K$-spaces will not, in general, coincide. In particular, we show that interpolation of Lorentz spaces over the unit square yields that the $K$-space is the sum of two Lorentz spaces whereas the $J$-space is the intersection of the same two Lorentz spaces.

  • 366.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Contributions to real interpolation theory1997Doktoravhandling, med artikler (Annet vitenskapelig)
  • 367.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Descriptions of some K functionals for three spaces and reiteration1999Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 202, s. 29-41Artikkel i tidsskrift (Fagfellevurdert)
  • 368.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Exact descriptions of some K and E functionals1997Inngår i: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 90, nr 1, s. 75-87Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Exact formulas for theKfunctional of some quasi-Banach couples of the type (X,L∞;) are obtained. In particular we can cover the cases whenX=Lp, q(Lorentzspaces), 0

  • 369.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Generalized sampling in shift invariant spaces with frames2012Inngår i: Acta Mathematica Sinica. English series, ISSN 1439-8516, E-ISSN 1439-7617, Vol. 28, nr 9, s. 1823-1844Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Generalized sampling in a shift invariant subspace V of L 2(ℝ) is considered. A function f in V is processed with different filters L m and then one tries to reconstruct f from the samples L mf(j′k). We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question: How to obtain dual frames with compact support?

  • 370.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Irregular sampling in shift invariant spaces of higher dimensions2008Inngår i: International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, E-ISSN 1793-690X, Vol. 6, nr 1, s. 121-136Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider irregular sampling in shift invariant spaces V of higher dimensions. The problem that we address is: find epsilon so that given perturbations (lambda(k)) satisfying sup vertical bar lambda(k)vertical bar < epsilon, we can reconstruct an arbitrary function f of V as a Riesz basis expansions from its irregular sample values f(k+lambda(k)). A framework for dealing with this problem is outlined and in which one can explicitly calculate sufficient limits epsilon for the reconstruction. We show how it works in two concrete situations.

  • 371.
    Ericsson, Stefan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The E and K functionals for the pair (X(A),l∞ (B))1997Inngår i: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 48, nr 4, s. 479-486Artikkel i tidsskrift (Fagfellevurdert)
  • 372. Ericsson, Stefan
    et al.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    An analysis method for sampling in shift-invariant spaces2005Inngår i: International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, E-ISSN 1793-690X, Vol. 3, nr 3, s. 301-319Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A subspace V of L2(ℝ) is called shift-invariant if it is the closed linear span of integer-shifted copies of a single function.As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method to derive both new results and relatively simple proofs of some previously known results. Among these are some results of rather general nature and some more specialized results for B-spline wavelets. The main problem under study is to find a shift x0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x0 + k + δk))k∈ℤ, either when all δk = 0 or in the irregular sampling case with an upper bound supk|δk| < δ.

  • 373. Ericsson, Stefan
    et al.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Efficient wavelet prefilters with optimal time-shifts2005Inngår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, nr 7, s. 2451-2461Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain postfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.

  • 374.
    Ericsson, Stefan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Grip, Niklas
    Using a natural deconvolution for analysis of perturbed integer sampling in shift-invariant spaces2011Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 373, nr 1, s. 271-286Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An important cornerstone of both wavelet and sampling theory is shift-invariant spaces, that is, spaces V spanned by a Riesz basis of integer-translates of a single function. Under some mild differentiability and decay assumptions on the Fourier transform of this function, we show that V also is generated by a function ϕ with Fourier transform equal to the convolution of g with the characteristic function living on the interval [-pi,pi]. We explain why analysis of this particular generating function can be more likely to provide large jitter bounds ε such that any f ∈ V can be reconstructed from perturbed integer samples f(k + ε_k) whenever the supremum of |ε_k| is smaller than ε. We use this natural deconvolution to further develop analysis techniques from a previous paper. Then we demonstrate the resulting analysis method on the class of spaces for which g has compact support and bounded variation (including all spaces generated by Meyer wavelet scaling functions), on some particular choices of ϕ for which we know of no previously published bounds and finally, we use it to improve some previously known bounds for B-spline shift-invariant spaces.

  • 375. Ericsson, Stefan
    et al.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Johansson, Elin
    Luleå tekniska universitet.
    Persson, Lars-Erik
    Sjöberg, Ronny
    Nåiden Teknik AB.
    Strömberg, Jan-Olov
    Department of Mathematics/NADA, Royal Institute of Technology.
    Towards automatic detection of local bearing defects in rotating machines2005Inngår i: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 19, nr 3, s. 509-535Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we derive and compare several different vibration analysis techniques for automatic detection of local defects in bearings. Based on a signal model and a discussion on to what extent a good bearing monitoring method should trust it, we present several analysis tools for bearing condition monitoring and conclude that wavelets are especially well suited for this task. Then we describe a large-scale evaluation of several different automatic bearing monitoring methods using 103 laboratory and industrial environment test signals for which the true condition of the bearing is known from visual inspection. We describe the four best performing methods in detail (two wavelet-based, and two based on envelope and periodisation techniques). In our basic implementation, without using historical data or adapting the methods to (roughly) known machine or signal parameters, the four best methods had 9–13% error rate and are all good candidates for further fine-tuning and optimisation. Especially for the wavelet-based methods, there are several potentially performance improving additions, which we finally summarise into a guiding list of suggestion.

  • 376.
    Eriksson, J.
    et al.
    Department of Computing Science, Umeå University.
    Wedin, P. A.
    Department of Computing Science, Umeå University.
    Gulliksson, M. E.
    Department of Engineering, Physics, and Mathematics, Mid-Sweden University, Sundsvall.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Regularization methods for uniformly rank-deficient nonlinear least-squares problems2005Inngår i: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 127, nr 1, s. 1-26Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In solving the nonlinear least-squares problem of minimizing ||f(x)||22, difficulties arise with standard approaches, such as the Levenberg-Marquardt approach, when the Jacobian of f is rank-deficient or very ill-conditioned at the solution. To handle this difficulty, we study a special class of least-squares problems that are uniformly rank-deficient, i.e., the Jacobian of f has the same deficient rank in the neighborhood of a solution. For such problems, the solution is not locally unique. We present two solution tecniques: (i) finding a minimum-norm solution to the basic problem, (ii) using a Tikhonov regularization. Optimality conditions and algorithms are given for both of these strategies. Asymptotical convergence properties of the algorithms are derived and confirmed by numerical experiments. Extensions of the presented ideas make it possible to solve more general nonlinear least-squares problems in which the Jacobian of f at the solution is rank-deficient or ill-conditioned.

  • 377.
    Erlandsson, Ove
    et al.
    Luleå tekniska universitet.
    Lagerkrans, Stefan
    Näslund, Reinhold
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Vuorinen, Esa
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Maskinhandboken2000Bok (Annet vitenskapelig)
  • 378.
    Essel, Emmanuel Kwame
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of Reynolds equations2007Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This Licentiate thesis is focussed on some new questions in homogenization theory, which have been motivated by some concrete problems in tribology. From the mathematical point of view, these questions are equipped with scales of Reynolds equations with rapidly oscillating coefficients. In particular, in this Licentiate thesis we derive the corresponding homogenized (averaged) equation. We consider the Reynolds equations in both the stationary and unstationary forms to analyze the effect of surface roughness on the hydrodynamic performance of bearings when a lubricant is flowing through it. In Chapter 1 we describe the possible types of surfaces a bearing can take. Out of these, we select two types and derive the appropriate Reynolds equations needed for their analysis. Chapter 2 is devoted to the derivation of the homogenized equations, associated with the stationary forms of the compressible and incompressible Reynolds equations. We derive these homogenized equations by using the multiple scales expansion technique. In Chapter 3 the homogenized equations for the unstationary forms of the Reynolds equations are considered and some numerical results based on the homogenized equations are presented. In chapter 4 we consider the equivalent minimization problem for the unstationary Reynolds equation and use it to derive a homogenized minimization problem. Finally, we obtain both the lower and upper bounds for the derived homogenized problem.

  • 379.
    Essel, Emmanuel Kwame
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of Reynolds equations and of some parabolic problems via Rothe's method2008Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This PhD thesis is focussed on some problems of great interest in applied mathematics. More precisely, we investigate some new questions in homogenization theory, which have been motivated by some concrete problems in tribology. From the mathematical point of view these questions are euqipped with scales of Reynolds equations with rapidly oscillating coefficients. In particular, in this PhD thesis we derive the corresponding homogenized (averaged) equations. We consider the Reynolds equations in both the stationary and unstationary forms to analyze the effect of surface roughness on the hydrodynamic performance of bearings when a lubricant is flowing through it. In addition we have successfully developed a reiterated homogenization (with three scales) procedure which makes it possible to efficiently study problems connected to hydrodynamic lubrication including shape, texture and roughness. Furthermore, we solve a linear parabolic initial-boundary value problem with singular coefficients in non-cylindrical domains. We accomplish this feat by developing a variant of Rothe's method to prove the existence and uniqueness of a weak solution to the parabolic problem. By combining the Rothe's method and the technique of two scale convergence we derive a homogenized equation for a linear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution. In Chapter 1 we describe some possible types of surfaces a bearing can take. Out of these we select two types and derive the appropriate Reynolds equations needed for their analysis. Chapter 2 is devoted to the derivation of the homogenized equations associated with the stationary forms of the compressible and incompressible Reynolds equations. We derive these homogenized equations by using the multiple scales expansion technique. In Chapter 3 the homogenized equations for the unstationary forms of the Reynolds equations are considered and some numerical results based on the homogenized equations are presented. In Chapter 4 we consider the equivalent minimization problem (varia- tional principle) for the unstationary Reynolds equation and use it to derive a homogenized minimization problem. Moreover, we obtain both the lower and upper bounds for the derived homogenized problem. Chapter 5 is devoted to studying the combined effect that arises due to shape, texture and surface roughness in hydrodynamic lubrication. This is accomplished by first studying a general class of problems that includes the incompressible Reynolds problem in both cartesian and cylindrical coordi- nate forms. In Chapter 6 we prove a homogenization result for the nonlinear equation $\mathrm{div}\,a(x,x/\varpeilson,x/\varepsilon^2,\nabla u_{\varepsilon})=\mathrm{div}\,b(x,x/\varpeilson,x/\varepsilon^2)$, where the coefficients are assumed to be periodic and a is monotone and continuous. This kind of problem has applications in hydrodynamic lubrication of surfaces with roughness on different length scales. In Chapter 7 a variant of Rothe's method is developed, discussed and used to prove existence and uniqueness result for linear parabolic problem with singular coefficients in non-cylindrical domains. In Chapter 8 we combine the Rothe method with a homogenization technique (two-scale convergence) to handle a general time-dependent lin- ear parabolic problem. In particular we prove that both the approximating sequence and the final approximate solution are unique. Finally, we derive a concrete homogenization algorithm on how to compute this homogenized solution.

  • 380.
    Essel, Emmanuel Kwame
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of the stationary compressible Reynolds equation by two-scale convergence (constant bulk modulus case)2007Rapport (Annet vitenskapelig)
  • 381. Essel, Emmanuel Kwame
    et al.
    Kuliev, Komil
    Department of Mathematics and Statistics, University of Cape Coast.
    Kulieva, Gulchehra
    Department of Mathematics and Statistics, University of Cape Coast.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of quasilinear parabolic problems by the method of rothe and two scale convergence2008Rapport (Annet vitenskapelig)
  • 382. Essel, Emmanuel Kwame
    et al.
    Kuliev, Komil
    Kuliev, Gulchehra
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On linear parabolic problems with singular coefficients in non-cylindrical domains2006Rapport (Annet vitenskapelig)
  • 383. Essel, Emmanuel Kwame
    et al.
    Kuliev, Komil
    Department of Mathematics and Statistics, University of Cape Coast.
    Kulieva, Gulchehra
    Department of Mathematics and Statistics, University of Cape Coast.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of quasilinear parabolic problems by the method of Rothe and two scale convergence2010Inngår i: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 55, nr 4, s. 305-327Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a quasilinear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. The existence and uniqueness results are proved by using Rothe's method combined with the technique of two-scale convergence. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution.

  • 384.
    Estreicher, S.K.
    et al.
    Physics Department, Texas Tech University, Lubbock.
    Latham, Chris D.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Heggie, M.I.
    Department of Computer Science, University of Exeter.
    Jones, R.
    Department of Physics, University of Exeter.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Stable and metastable states of C60H: buckminsterfullerene monohydride1992Inngår i: Chemical Physics Letters, ISSN 0009-2614, E-ISSN 1873-4448, Vol. 196, nr 3-4, s. 311-316Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Approximate ab initio Hartree-Fock and first-principles density functional calculations of potential energy surfaces and electronic structures of C60H show that the stable state has H attached to one C atom, outside the buckyball. This C atom is displaced radially outward and is close to being sp3 hybridized. The unpaired electron of C60H is delocalized. The calculated Fermi contact density at the proton is in good agreement with recent low-temperature μSR data. A metastable configuration has atomic H at the center of the ball (H@C60). Once trapped there, H must overcome a large barrier to go through the surface of C60. Other configurations we considered include H attached to one C atom but inside the buckyball, and H bridging one of the two inequivalent CC bonds. The barrier for diffusion of H from outside to the center of C60 have also been calculated. The results are compared to recent muon spin rotation studies in solid C60 and to the states of hydrogen in other forms of carbon.

  • 385.
    Euler, Marianna
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Fourth-order recursion operators for third-order evolution equations2008Inngår i: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 15, nr 2, s. 147-151Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We report the recursion operators for a class of symmetry integrable evolution equations of third order which admit fourth-order recursion operators. Under the given assumptions we obtain the complete list of equations, one of which is the well-known Krichever-Novikov equation.

  • 386.
    Euler, Marianna
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Group theoretical methods for solving multidimensional nonlinear partial differential equations1998Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    New methods for constructing both exact and approximate solutions of multidimensional nonlinear partial differential equations are developed. The basis of the methods is taken from the classical Lie transformation group theory. New symmetry concepts are investigated for the construction of solutions of important nonlinear partial differential equations. Those concepts are: conditional symmetries, hidden symmetries, and approximate symmetries. Moreover, we propose a method by which a multidimensional wave equation can be related and classified with respect to a compatible system of multidimensional differential equations. The equations under investigation are: nonlinear Schrödinger equations, nonlinear heat equations, a generalized van der Pol equation, and nonlinear d'Alembert equations. The new solutions presented in this thesis could be of fundamental importance in the applications of the physical processes modelled by the above mentioned differential equations.

  • 387.
    Euler, Marianna
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Second-order recursion operators of third-order evolution equations with fourth-order integrating factors2007Inngår i: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 14, s. 313-315Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We report the recursion operators for a class of symmetry integrable evolution equa- tions of third order which admit a fourth-order integrating factor. Under some as- sumptions we obtain the complete list of equations, one of which is a special case of the Schwarzian Korteweg-de Vries equation.

  • 388.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    A class of semilinear fifth-order evolution equations: recursion operators and multipotentialisations2011Inngår i: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 18, nr Suppl. 1, s. 61-75Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We apply a list of criteria which leads to a class of fifth-order symmetry-integrable evolution equations. The recursion operators for this class are given explicitly. Multipotentialisations are then applied to the equations in this class in order to extend this class of integrable equations.

  • 389.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Aufgaben, Theorie und Lösungen zur Linearen Algebra, Teil 1: Der Euklidische Raum2017Bok (Fagfellevurdert)
    Abstract [de]

    Dieses Buch ist der erste Teil einer dreiteiligen Serie mit dem Titel Aufgaben, Theorieund L¨osungen zur Linearen Algebra. Dieser erste Teil behandelt Vektoren des euklidischen Raumes sowie Matrizen, Matrixalgebra und Systeme von linearen Gleichungen. Wir l¨osen lineare System mit Hilfe des Gaußschen Eliminationsverfahrens und auf anderem Wege und untersuchen die Eigenschaften dieser Systeme in Bezug auf Vektoren und Matrizen. Dar¨uber hinaus betrachten wir lineare Abbildungen und berechnendie Standardmatrizen dieser Abbildungen.

  • 390.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Integrating factors and conservation laws for some Camassa-Holm type equations2012Inngår i: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 11, nr 4, s. 1421-1430Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We classify all 1st-order integrating factors and the correspondingconservation laws for a class of Camassa-Holm type equations.

  • 391.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Invariance of the Kaup-Kupershmidt equation and triangular auto-Bäcklund transformations2012Inngår i: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 19, nr 3, s. 1220001/1-1220001/7Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup-Kupershmidt equation derived by E. G. Reyes in his paper titled ``Nonlocal symmetries and the Kaup-Kupershmidt equation'' [ Math. Phys., 46, 073507, 19 pp., 2005]. These auto-Bäcklund transformations can then be applied to generate solutions of the Kaup-Kupershmidt equation. We show that triangular auto-Bäcklund transformations result from a systematic multipotentialisation of the Kupershmidt equation.

  • 392.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    n-Dimensional real wave equations and the D’Alembert-Hamilton system2001Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 47, nr 8, s. 5125-5133Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We reduce the nonlinear wave equation □nu = αF[exp(βu)] to ordinary differential equtions and construct exact solutions, by the use of a compatible d'Alembert-Hamilton system. The solutions of these ordinary differential equations, together with the solutions of the corresponding d'Alembert-Hamilton equations, provide a rich class of exact solutions of the multidimensional wave equations. The wave equations are studied in n-dimensional Minkowski space.

  • 393.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On Möbius‐invariant and symmetry‐integrable evolution equations and the Schwarzian derivative2019Inngår i: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 143, nr 2, s. 139-156Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider symmetry‐integrable evolution equations in 1 + 1 dimensions of order 3 and order 5. We show that there exist only three equations in this class that are invariant under the Möbius transformation, and we name those Schwarzian equations. We report an interesting relation between the recursion operators of the Schwarzian equations and the corresponding adjoint operators that generate hierarchies of Schwarzian systems in terms of the Schwarzian derivative. This indicates a deep relation between the Schwarzian equations and the Schwarzian derivative. A classification of the fully nonlinear third‐order Schwarzian equations is also reported.

  • 394.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Problemas, Teoria y Soluciones en Algebra Lineal: Parte 1 Espacio Euclideo2016 (oppl. 1)Bok (Fagfellevurdert)
    Abstract [en]

    This book is the first part of a three-part series titled Problems, Theory and Solutions in Linear Algebra. This first part contains over 100 solved problems and 100 exercises on vectors, matrices, linear systems, as well as linear transformations in Euclidean space. It is intended as a supplement to a textbook in Linear Algebra and the aim of the series it to provide the student with a well-structured and carefully selected set of solved problems as well as a thorough revision of the material taught in a course on this subject for undergraduate engineering and science students.

  • 395.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Problems, Theory and Solutions in Linear Algebra: Part 1: Euclidean Space2015 (oppl. 2)Bok (Fagfellevurdert)
    Abstract [en]

    This book is the first part of a three-part series titled Problems, Theory and Solutions in Linear Algebra. This first part contains over 100 solved problems and 100 exercises on vectors, matrices, linear systems, as well as linear transformations in Euclidean space. It is intended as a supplement to a textbook in Linear Algebra and the aim of the series it to provide the student with a well-structured and carefully selected set of solved problems as well as a thorough revision of the material taught in a course on this subject for undergraduate engineering and science students.

  • 396.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Symmetries for a class of explicitly space- and time-dependent (1+1)-dimensional wave equations1997Inngår i: Proceedings of the second international conference: Memorial Prof. W. Fushchych conference, July 7 - 13, 1997, Kyiv, Ukraine / [ed] Mykola Shkil, Kyev: Institute of Mathematics of the National Academy of Sciences of Ukraine , 1997, Vol. 1, s. 70-78Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper the nonlinear wave equation $\partial^2 u/\partial x_0^2-\partial^2 u/\partial x_1^2+f(x_0,x_1,u)=0$, where $f$ is an arbitrary smooth function of its arguments, is considered from the symmetry standpoint. The form of the most general Lie point symmetry generator of this equation is obtained. The classes of functions $f$, for which the equation in question admits a one-parameter Lie point symmetry group, are constructed. Then, the authors investigate the possible form of generators of conformal transformations, assuming the usual form of generators of Lorentz and scaling transformations, and study the wave equations invariant under such operators. The symmetry groups of obtained equations are used for the construction of ansätze and reductions of these equations to ordinary differential equations. $Q$-conditional (nonclassical) symmetries of the wave equation are also considered. Namely, the determining equations for the coefficients of a $Q$-conditional symmetry operator are found and their compatibility is investigated.

  • 397.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Théorie et Problémes Résolus d'Algèbre Linéaire: Volume 1: Espaces Euclidiens2017 (oppl. 1)Bok (Fagfellevurdert)
    Abstract [fr]

    Ce livre est le premier d'une série de trois ouvrages intitulés Théorie et Problèmes Résolus d'algèbre linéaire. Cette première partie contient plus de 100 problèmes résolus et plus de 100 exercices sur les vecteurs en espaces euclidiens, les matrices, les systèmes linéaires ainsi que les applications linéaires entre espaces euclidiens. Le but de cette série est de fournir aux étudiants de filières scientifiques et techniques un ensemble structuré de problèmes soigneusement choisis ainsi qu'une opportunité d'approfondir leurs connaissances acquises en cours d'algèbre linéaire.

  • 398.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Leach, Peter
    University of KwaZulu-Natal.
    Properties of the Calogero-Degasperis-Ibragimov-Shabat differential sequence2011Inngår i: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 32, nr 1, s. 61-70Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a differential sequence based upon the Calogero-Degasperis-Ibragimov-Shabat Equation and determine first integrals and the general solution. Under suitable transformations eachmember of the differential sequence can be recast as a product of two factors and we report some of the properties of the factored form.

  • 399.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Lindblom, Ove
    Luleå tekniska universitet.
    Explicitly space- and time-dependent d'Alembert equations with symmetries1999Inngår i: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 14, nr 26, s. 4189-4200Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The general d'Alembert equation $\square u+ f(x_0, x_1,u)= 0$ is considered, where $\square$ is the two-dimensional d'Alembert operator. We classify the equation for functions $f$ by which it admits several Lie symmetry algebras, which include the Lorentz symmetry generator. The corresponding symmetry reductions are listed.

  • 400.
    Euler, Marianna
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Euler, Norbert
    Lundberg, Staffan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Invertible Bäcklund transformations for autonomous evolution equations2009Inngår i: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 159, nr 3, s. 418-427Artikkel i tidsskrift (Fagfellevurdert)
567891011 351 - 400 of 1368
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