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  • 301. Berggren, Stein
    et al.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Meidell, Annette
    Wall, Peter
    Homogenization and computational techniques of iterated structures2001Inngår i: Proceedings of the Eight International Conference on Composites Engineering: ICCE/8 / [ed] David Hui, 2001Konferansepaper (Fagfellevurdert)
  • 302.
    Bergh, Jöran
    et al.
    Chalmers University of Technology, Department of Mathematics.
    Burenkov, Victor
    Department of Differential Equations and Functional Analysis, Russian Peoples' Friendship University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Best constants in reversed Hardy's inequalities for quasimonotone functions1994Inngår i: Acta Scientarum Mathematicarum, ISSN 0001-6969, Vol. 59, nr 1-2, s. 221-239Artikkel i tidsskrift (Fagfellevurdert)
  • 303.
    Bergh, Jöran
    et al.
    Chalmers University of Technology, Department of Mathematics.
    Burenkov, Victor
    Department of Differential Equations and Functional Analysis, Russian Peoples' Friendship University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On some sharp reversed Hölder and Hardy type inequalities1994Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, nr 169, s. 19-29Artikkel i tidsskrift (Fagfellevurdert)
  • 304.
    Bergkvist, Tanja
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematik.
    Rullgård, Hans
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematik.
    On polynomial eigenfunctions for a class of differential operators2002Inngår i: Mathematical research letters, Vol. 9, nr 2, s. 153-171Artikkel i tidsskrift (Fagfellevurdert)
  • 305.
    Berglund, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Evaluating ∫0f(x)dx and ∫ab f(x)dx using residue calculus2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this essay we use complex analysis, in particular modern residue calculus, to compute certain Riemann integrals.

  • 306.
    Berglund, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Numerical Simulations of Linear Stochastic Oscillators: driven by Wiener and Poisson processes2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The main component of this essay is the numerical analysis of stochastic differential equations driven by Wiener and Poisson processes. In order to do this, we focus on two model problems, the geometric Brownian motion and the linear stochastic oscillator, studied in the literature for stochastic differential equations only driven by a Wiener process. This essay covers theoretical as well as numerical investigations of jump - or more specifically, Poisson - processes and how they influence the above model problems.

  • 307.
    Berglund, André
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Hellgren, Erik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Bolåneräntor i Sverige: Enanalys av individuella räntor med multipel linjär regression2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

     I denna rapport undersöks hur ett antal kundspecifika faktorer som belåningrad, bank och inkomst påverkar svenska hushålls individuella bolåneräntor. Metoden som används är multipel linjär regression med transformeringar av förklarande variabler. Transformer som används är log-linjär, linjär-log, log-log samt styckvis linjär. Datan innehåller ett stickprov om ca. 7000 rörliga bolån från juli 2013 insamlade av organisationen Villaägarna på frivillig basis. Variablerna belåningsgrad, lånets storlek och bank bidrar mest till att förklara räntan. Vår analys visar att stora lån i kombination med låg belåningsgrad tenderar till att ge lägst ränta samtidigt som det finns signifikanta skillnader i bolåneränta mellan bankerna även om deras listräntor är lika.  

  • 308.
    Berglund, Tomas
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, EISLAB.
    Strömberg, Thomas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Epi-convergence of minimum curvature variation B-splines2003Rapport (Annet vitenskapelig)
    Abstract [en]

    We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.

  • 309.
    Bergman, Ivar
    Karlstads universitet, Institutionen för ingenjörsvetenskap, fysik och matematik.
    Baire category theorem2009Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In this thesis we give an exposition of the notion of category and the Baire category theorem as a set theoretical method for proving existence. The category method was introduced by René Baire to describe the functions that can be represented by a limit of a sequence of continuous real functions. Baire used the term functions of the first class to denote these functions.

    The usage of the Baire category theorem and the category method will be illustrated by some of its numerous applications in real and functional analysis. Since the usefulness, and generality, of the category method becomes fully apparent in Banach spaces, the applications provided have been restricted to these spaces.

    To some extent, basic concepts of metric topology will be revised, as the Baire category theorem is formulated and proved by these concepts. In addition to the Baire category theorem, we will give proof of equivalence between different versions of the theorem.

    Explicit examples, of first class functions will be presented, and we shall state a theorem, due to Baire, providing a necessary condition on the set of points of continuity for any function of the first class.

     

  • 310.
    Bergman, Parik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Sonebäck, Viktor
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Portfolio Optimization: Approaches to determining VaR and CVaR2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    This thesis analyses portfolio optimization using the risk measures VaR and CVaR with two different underlying assumptions of probability distribution of returns; one being that portfolio returns are normal distributed and the other being a discrete distribution comprised of historical data. The models are run through numerous historical simulations on the OMXS30 with varying time period for historical data and rebalance frequencies. The resulting simulated returns as well as the CVaR outcomes are presented, compared and discussed in order to assess which model performs the best and under what circumstances.

    Our key findings is that using a discrete, historical probability distribution for optimizing a portfolio with respect to CVaR, comprised of around 320 days worth of data and using a rebalancing frequency of 20 days performs the best with respect to total return and actual CVaR. This method manages to take the fat tails of the market return distribution into account and as such successfully avoids the larger market downturns.

    The results of this thesis also indicate that historical VaR optimization is inferior to CVaR optimization. However due to lack of computational power this comparison is inconclusive.

  • 311.
    Bergqvist, Ewa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Positive currents related to polynomial convexity1999Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 312.
    Bergqvist, Göran
    et al.
    Linköpings Universitet, Sweden.
    Lankinen, Paul
    Mälardalens högskola, Institutionen för matematik och fysik.
    Unique characterization of the Bel-Robinson tensor2004Inngår i: Classical and Quantum Graviry, ISSN 0264-9381, Vol. 21, nr 14, s. 3499-3503Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

  • 313.
    Bergström, Jonas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Pricing American Options using Lévy Processes and Monte Carlo Simulations2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 314.
    Bergström, Jonas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Pricing the American Option Using Itô’s Formula and Optimal Stopping Theory2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 315.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Development of three-dimensional disturbances in pipe poiseuille flow1992Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 316.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Evolution of laminar disturbances in pipe Poiseuille flow1993Inngår i: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 12, nr 6, s. 749-768Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An experimental study on the evolution of localized disturbances in pipe Poiseuille flow has been performed. The aim was to investigate the relevance of the theoretical findings on the algebraic transient growth mechanism. For non-axisymmetric disturbances the amplitudes and the propagation velocities were measured in the laminar regime. The initial disturbances were induced radially through the pipe wall and had a distribution in the azimuthal direction corresponding to a periodicity of one and five, respectively. The amplitude of the resulting streamwise velocity perturbation was measured at different radial and axial positions by means of laser doppler velocimetry. In the laminar regime, the results showed that the disturbance peaks are actually amplified but will eventually decay as predicted in the theory. The peak of an initial disturbance of periodicity five showed a rapid amplification to a maximum before the decay sets in. The initial disturbance of periodicity gave a more slowly varying disturbance peak level over the investigated interval. The propagation speed of the front of the disturbances was in the range of 0.86-0.9 times the centreline velocity. The propagation speed of the disturbance peaks was in the range of 0.51 to 0.80 times the centreline velocity and dependent on the azimuthal distribution of the initial disturbance.

  • 317.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Initial algebraic growth of small angular dependent disturbances in pipe Poiseuille flow1992Inngår i: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 87, nr 1, s. 61-79Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The evolution of small, angular dependent velocity disturbances in laminar pipe flow is studied. In particular, streamwise independent perturbations are considered. To fully describe the flow field, two equations are required, one for the radial and the other for the streamwise velocity perturbation. Whereas the former is homogeneous, the latter has the radial velocity component as a forcing term. The normal modes of the system are determined and analytical solutions for eigenfunctions, damping rates and phase velocities are calculated. Then, the initial value problem is treated and the time development of the disturbances is determined.

  • 318.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Interactions of three components and subcritical self-sustained amplification of disturbances in plane Poiseuille flow1999Inngår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 11, nr 3, s. 590-601Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A low-dimensional nonlinear model for the normal velocity (v) and normal vorticity (eta) disturbance development in plane Poiseuille flow is studied. The study is restricted to the interactions of a pair of oblique components of the form e(/(alpha x+/-beta z)) and the component of the form e(/2 beta z) where alpha and beta are streamwise and spanwise wave numbers, respectively. The disturbances considered are also assumed to be highly elongated in the streamwise direction. Owing to the non-normal properties of the basic equations, the eta disturbance is first transiently amplified. Then, if the Reynolds number (R) and the initial disturbance are sufficiently large, the nonlinear interactions lead to a self-sustained process of disturbance amplification at subcritical R. For large R (R greater than or similar to 5000). the threshold disturbance amplitude scales like R-3. The, results also strongly indicate that the nonlinear feedback from eta to v is crucial for the establishment of the self-sustained process.

  • 319.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Nonlinear behaviour of transiently amplified disturbances in pipe Poiseuille flow1995Inngår i: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 14, nr 6, s. 719-735Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present work is a continuation of previous investigations of the author and deals with the nonlinear behaviour of transiently amplified disturbances in pipe Poiseuille flow. The disturbances are expanded in terms of a small amplitude parameter, and a spectral formulation, based on the eigenfunctions of the linear problem, is used to solve the resulting evolution equations. For the corresponding linear problem, analytical solutions are known. Here the author shows that the nonlinear problem also allows an analytical treatment. The analysis concentrates on the interaction of the dominating azimuthal wave number components of axially independent disturbances, since they exhibit largest growth in linear theory. The analysis is restricted to the first modes of the components, since these are found to dominate the disturbance magnitude at the peak amplification. In particular, the nonlinear correction for the component with an azimuthal wave number equal to one is considered. Including the nonlinear correction, the author reduces the linearly obtained amplification of the streamwise disturbance energy density and finds that the peak position of the disturbance energy density occurs earlier than for linear disturbance. This result is consistent with the experimental findings on transient growth for subcritical disturbances. Moreover, the reduced amplification is in agreement with recent results from direct numerical simulations of axially dependent disturbances.

  • 320.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Nonmodal growth of three-dimensional disturbances on plane Couette-Poiseuille flows2005Inngår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 17, nr 1Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The time development of three-dimensional disturbances superimposed on a variety of mean flow profiles representing plane Couette-Poiseuille flow is investigated numerically. Specifically, with y representing the wall normal coordinate, the mean flow profiles U(y) are represented by U(y) = A(1-y2) + By, where B = 1 ......

  • 321.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Optimal growth of small disturbances in pipe Poiseuille flow1993Inngår i: Physics of Fluids. A, Fluid Dynamics (1989-1993), ISSN 0899-8213, Vol. 5, nr 11, s. 2710-2720Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A theoretical study is made of initial algebraic growth for small angular-dependent disturbances in pipe Poiseuille flow. The analysis is based on the homogeneous equation for the pressure for which the eigenvalue problem is solved numerically. In the limit of small streamwise wave numbers asymptotic results for the eigenvalues are derived. On the basis of the modes of the system, which are all damped, the initial value problem is considered and in particular the largest possible growth of the disturbance energy density is determined following the ideas of Butler and Farrell [Phys. Fluids A 4, 1637 (1992)]. The results show that a large amplification of the disturbance energy is possible. The largest amplification is obtained for disturbances with a small streamwise wave number and with an azimuthal wave number of one. The energy growth is then only due to the growth of the streamwise disturbance component. However, for disturbances of shorter wavelength, the energy growth is also substantial and not only concentrated to the streamwise velocity component. The wall shear corresponding to disturbances with the largest energy growth also shows a large amplification and the dependence of wave numbers and the Reynolds number is the same as for the energy. However, the wall pressure of a long wavelength disturbance of the largest growth just decays from its initial value, but for disturbances of shorter wavelength, it is also amplified

  • 322.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Self-sustained amplification of disturbances in pipe Poiseuille flow1999Inngår i: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 18, nr 4, s. 635-647Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The nonlinear development of disturbances in pipe Poiseuille flow is studied with a low-dimensional model. The basic system from which the model is derived governs disturbances closely related to the radial velocity and radial vorticity disturbances. The analysis is restricted to the interaction of the two first harmonics of streamwise elongated disturbances since they are the most transiently amplified ones in linear theory. In the resulting dynamical system a nonlinear feedback from the normal vorticity disturbance (which is transiently amplified according to linear theory) to the radial velocity disturbance is present. Above a threshold of the initial amplitude, the feedback leads to a self-sustained amplification of the disturbances continuing for all times.

  • 323.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The effect of the Earth's rotation on the transient amplification of disturbances in pipe flow2003Inngår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 15, nr 10, s. 3028-3035Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In pipe flow, for large Reynolds numbers, A. A. Draad and F. T. M. Nieuwstadt \ref[J. Fluid Mech. 361 (1998), 297--308 showed that the small Coriolis force due to the Earth's rotation may affect the mean flow profile of liquids substantially. In this paper, the development of small disturbances superimposed on a laminar mean flow affected by the Coriolis force is investigated analytically. The investigation is focused on the time development and the transient growth of streamwise-independent disturbances since they are the most amplified disturbances without the Coriolis effect included. The results show that the modification of the parabolic mean flow caused by the Coriolis force significantly affects the transient disturbance amplification when the Reynolds number $(R)$ is high. For example, with $R=9000$ and the Ekman number $\rm Ek=5.23$, due to the Coriolis effect, the peak value of the transient disturbance amplification becomes about two-thirds of the peak value obtained in the case where the mean flow is unaffected by the Coriolis force. When the Reynolds number is decreased, the reduction of the transient growth becomes smaller.

  • 324.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The initial-value problem for three-dimensional disturbances in plane Poiseuille flow of helium II2008Inngår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 598, s. 227-244Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The time development of small three-dimensional disturbances in plane Poiseuille flow of helium II is considered. The study is conducted by considering the interaction of a normal fluid field and a superfluid field. The interaction is caused by a mutual friction forcing between the two flow fields. Specifically, the stability of the normal fluid affected by the mutual forcing is considered. Compared to the ordinary fluid case where the mutual forcing is not present, the presence of the mutual forcing implies a substantial increase of the transient growth of the disturbances. The increase of the transient growth occurs because the mutual forcing reduces the damping of the disturbances. The phase of transient growth becomes thereby more prolonged and higher levels of amplification are reached. There is also a minor effect on the transient growth caused by the modification of the mean flow owing to the mutual forcing. The strongest transient growth occurs for streamwise elongated disturbances, i.e. disturbances with streamwise wavenumber α = 0. When α increases beyond zero, the transient amplification quickly becomes reduced. Striking differences compared to the ordinary fluid case are that the largest transient amplification does not occur when the spanwise wavenumber (β) is close to two and that the peak level of the disturbance energy density amplification does not depend on the square of the Reynolds number.

  • 325.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Transient growth of disturbances in laminar pipe flow1994Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Transient growth of disturbances is studied theoretically in pipe Poiseuille flow and experimentally both in pipe and plane Poiseuille flow. The theoretical results, based on the initial value problem, show that a large transient amplification occurs for small, angular dependent disturbances in pipe Poiseuille flow although all modes are damped. The largest growth is obtained for disturbances with zero streamwise wave number and with an azimuthal periodicity of one. Only the streamwise disturbance component is then amplified and the energy density growth is proportional to the Reynolds number squared. For disturbances of finite axial wave number, also the radial and azimuthal disturbance components are amplified from their initial values but the growth is still dominated by the streamwise disturbance. When the azimuthal wave number increases the disturbance peak occurs at shorter times and the amplification decreases. However, for small times, larger azimuthal wave numbers dominate the growth. Asymptotic results for the most amplified disturbances show that two classes of modes can be distinguished and it is necessary to include modes from both classes to get amplification. The asymptotically derived propagation speeds of the two classes are in the ranges <2/3 times the centerline velocity (Ucl) and <0.818Ucl, respectively. If the nonlinear interaction of axially independent disturbances is considered, the results indicate that the amplification of the most linearly amplified disturbance is reduced. Laser Doppler measurements of the streamwise disturbance velocity due to radially induced initial disturbances of azimuthal periodicities (n) of one and five have also been conducted. The results show that the disturbance velocity in fact exhibits a transient growth. The disturbance with n=1 gives a slowly varying peak-value while the peak owing to an initial disturbance with n=5 shows a more rapid amplification to a maximum before it decays. The propagation speeds of the disturbance peaks are in the range theoretically expected for transiently amplified disturbances. By hot-wire measurements of the streamwise disturbance velocity due to two radially induced jet-like disturbances, the spatial structure of an evolving disturbance is investigated in detail. Especially the positive disturbance velocity exhibits an amplification followed by a decay. The disturbance also spreads and becomes streak-like and elongated in the streamwise direction. The spread implies that an integrated disturbance quantity grows to a peak and eventually decays. The propagation speed and the radial location of the disturbances agree with the theoretical findings for algebraically growing disturbances. In plane Poiseuille flow the symmetry properties of an evolving disturbance are investigated by means of hot-wire anemometry. The initial streamwise disturbance is designed to be symmetric with respect to the normal direction. Despite this, an antisymmetric structure develops in the region where the main amplification occurs as indicated by the theory.

  • 326.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Transient growth of small disturbances in a Jeffrey fluid flowing through a pipe2003Inngår i: Fluid Dynamics Research, ISSN 0169-5983, E-ISSN 1873-7005, Vol. 32, nr 1-2, s. 29-44Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The hydrodynamic stability of small disturbances in a non-Newtonian fluid flowing through a circular pipe is studied analytically. Specifically, the time development of the disturbances and the transient disturbance amplification are studied. The non-Newtonian fluid is modelled by a two-constant Jeffrey model characterized by the relaxation time $\lambda$ and a constant $K$ representing the ratio of relaxation to retardation times. All the investigations are carried out for streamwise-independent disturbances since they are the most amplified ones in a Newtonian fluid and can be treated analytically. The eigenvalue problem and the initial value problem for the disturbances are studied. Compared to the Newtonian case, the results show that, dependent on $K$ and $\lambda$, a reduction or an increase in the disturbance transient growth may occur.

  • 327.
    Bergström, Lars
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Transient properties of a developing laminar disturbance in pipe Poiseuille flow1995Inngår i: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 14, nr 5, s. 601-615Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hot-wire measurements of the velocity disturbance from point-like disturbances in a fully developed laminar pipe Poiseuille flow are performed. Two jets are induced radially into the pipe by diametrically opposed loud speakers. The resulting streamwise disturbance velocity component is investigated over the Reynolds number range 1550-2000. Close to the position of the initial disturbance, the disturbance amplitudes and gradients are large. After a few pipe radii the disturbance is reduced and consists of two small regions of positive disturbance with a larger region of negative disturbance in between. A downstream interval then follows in which the amplitudes of the regions with positive disturbance exhibit an amplification followed by a decay. The peaks of the two amplified regions are located at 0.6 radii and 0.4 radii, respectively, and propagate with velocities of 0.65 times the centreline velocity (Ucl) and 0.88 Ucl, respectively. Subsequently, the disturbance obtains an almost constant level, while it becomes elongated in the streamwise direction. The dominating part of the disturbance is then confined to a region around 0.5 radii from the centerline and the propagation velocity of the region with largest amplitude is in the range 0.7-0.8 Ucl. An integrated disturbance quantity is defined by integrating the square of the disturbance amplitude over the radius and time in a downstream position. In a position a few radii downstream, this quantity has decayed to about 10-20 per cent of the value obtained one pipe radius downstream. It is then amplified by a factor of about five before it finally decays

  • 328.
    Bergström, Lars
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Alfredsson, P. Henrik
    Royal Institute of Technology, Stockholm.
    Symmetry properties of developing three-dimensional laminar disturbances in plane Poiseuille flow1994Inngår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 6, nr 4, s. 1618-1620Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The evolution of a finite-amplitude point-like laminar disturbance in plane Poiseuille flow is investigated using hot-wire anemometry. In contrast to earlier experiments, the initial disturbance was introduced simultaneously through both the upper and lower wall of the channel, resulting in an antisymmetric disturbance in the normal velocity. Although the initial disturbance mainly generated symmetrical streamwise velocity modes, the subsequent development of the perturbation showed a marked tendency for antisymmetry.

  • 329.
    Bergström, Per
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Activity: SIAM Conference on Geometric Design and Computing2007Konferansepaper (Annet (populærvitenskap, debatt, mm))
  • 330.
    Bergström, Per
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Strömningslära och experimentell mekanik.
    Edlund, Ove
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Robust registration of surfaces using a refined iterative closest point algorithm with a trust region approach2017Inngår i: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 74, nr 3, s. 755-779Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of finding a rigid body transformation, which aligns a set of data points with a given surface, using a robust M-estimation technique is considered. A refined iterative closest point (ICP) algorithm is described where a minimization problem of point-to-plane distances with a proposed constraint is solved in each iteration to find an updating transformation. The constraint is derived from a sum of weighted squared point-to-point distances and forms a natural trust region, which ensures convergence. Only a minor number of additional computations are required to use it. Two alternative trust regions are introduced and analyzed. Finally, numerical results for some test problems are presented. It is obvious from these results that there is a significant advantage, with respect to convergence rate of accuracy, to use the proposed trust region approach in comparison with using point-to-point distance minimization as well as using point-to-plane distance minimization and a Newton- type update without any step size control.

  • 331.
    Bergström, Per
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Fergusson, Michael
    Xtura AB, Kungsbacka.
    Folkesson, Patrik
    Xtura AB, Kungsbacka.
    Runnemalm, Anna
    University West, Department of Engineering Sciences, Trollhättan.
    Ottosson, Mattias
    University West, Department of Engineering Sciences, Trollhättan.
    Andersson, Alf
    Chalmers University of Technology, Department of Product and Production Development.
    Sjödahl, Mikael
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Strömningslära och experimentell mekanik.
    Automatic in-line inspection of shape based on photogrammetry2016Inngår i: SPS16, Lund: SPS16 , 2016, , s. 9Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We are describing a fully automatic in-line shape inspection system for controlling the shape of moving objects on a conveyor belt. The shapes of the objects are measured using a full-field optical shape measurement method based on photogrammetry. The photogrammetry system consists of four cameras, a flash, and a triggering device. When an object to be measured arrives at a given position relative to the system, the flash and cameras are synchronously triggered to capture images of the moving object. From the captured images a point-cloud representing the measured shape is created. The point-cloud is then aligned to a CAD-model, which defines the nominal shape of the measured object, using a best-fit method and a feature-based alignment method. Deviations between the point-cloud and the CAD-model are computed giving the output of the inspection process. The computational time to create a point-cloud from the captured images is about 30 seconds and the computational time for the comparison with the CAD-model is about ten milliseconds. We report on recent progress with the shape inspection system.

  • 332.
    Bergvall, Anders
    KTH, Skolan för industriell teknik och management (ITM), Industriell ekonomi och organisation (Inst.).
    The Risk-Return Tradeoff in a Hedged, Client Driven Trading Portfolio2013Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In post-financial crisis times, new legislation in combination with banks’ changed risk aversion has to a great extent changed the proprietary trading to client driven trading, i.e. market making or client facilitation. This type of trading complicates the risk-return dynamics, as the goal is often to minimize risk and achieve profitable commission revenues. This thesis aims to disclose the risk-return tradeoff in a client driven trading environment. This is done by investigating the conditional relation between risk and realized return. As opposed from many studies which proxy the risk with beta or variance, I use a delta-gamma Value at Risk model as the risk proxy, which I also backtest. For the return proxy, I use three different measures; P&L, commission revenues and the sum of these two. A positive tradeoff exists if (i) the return is equally negatively dependent on the risk if the ex post return is negative, as it is positively dependent on the risk if the ex post return is positive and (ii) the average return is significantly positive. For three different client driven trading portfolios tested, I found a positive risk-return tradeoff in one portfolio, between the P&L plus commission revenues and the Value at Risk. However, since a symmetrical conditional relationship between risk and P&L plus commission revenues was found in all portfolios, and the average return was positive, the positive tradeoff would have existed if the average return would have been significantly positive. On the other hand, one could argue that the tradeoff exists, but is not significant. No relation between risk and commission revenues was found. A probable cause to this is the hedging strategies, which would be an interesting topic for further research. 

  • 333.
    Bernhoff, Niclas
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
    Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants2018Inngår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, nr 3, s. 742-761Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.

  • 334.
    Bernhoff, Niclas
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
    Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation2015Inngår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 159, nr 2, s. 358-379Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for a general discrete model of a quantum kinetic equation for excitations in a Bose gas. In the discrete case the plane stationary quantum kinetic equation reduces to a system of ordinary differential equations. These systems are studied close to equilibrium and are proved to have the same structure as corresponding systems for the discrete Boltzmann equation. Then a classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete kinetic equation can be made. The number of additional conditions that need to be imposed for well-posedness is given by some characteristic numbers. These characteristic numbers are calculated for discrete models axially symmetric with respect to the x-axis. When the characteristic numbers change is found in the discrete as well as the continuous case. As an illustration explicit solutions are found for a small-sized model.

  • 335.
    Berntsson, Fredrik
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Orlof, Anna
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Thim, Johan
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Error Estimation for Eigenvalues of Unbounded Linear Operators and an Application to Energy Levels in Graphene Quantum Dots2017Inngår i: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 38, nr 3, s. 293-305Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The eigenvalue problem for linear differential operators is important since eigenvalues correspond to the possible energy levels of a physical system. It is also important to have good estimates of the error in the computed eigenvalues. In this work, we use spline interpolation to construct approximate eigenfunctions of a linear operator using the corresponding eigenvectors of a discretized approximation of the operator. We show that an error estimate for the approximate eigenvalues can be obtained by evaluating the residual for an approximate eigenpair. The interpolation scheme is selected in such a way that the residual can be evaluated analytically. To demonstrate that the method gives useful error bounds, we apply it to a problem originating from the study of graphene quantum dots where the goal was to investigate the change in the spectrum from incorporating electron–electron interactions in the potential.

  • 336. Betancor, Jorge J.
    et al.
    Castro, Alejandro J.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Farina, Juan C.
    Rodriguez-Mesa, L.
    Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions2015Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 431, nr 1, s. 440-470Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the Weinstein type equation L(lambda)u = 0 on (0, infinity) X (0, infinity), where L-lambda= delta(2)(t) + delta-lambda(lambda-1)/x(2), In this paper we characterize the solutions of L(lambda)u = = 0 on (0, infinity) x (0, infinity) representable by Bessel-Poisson integrals of BMO-functions as the ones satisfying certain Carleson properties.

  • 337. Beyersdorff, O.
    et al.
    Bonacina, Ilario
    KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.
    Chew, L.
    Lower bounds: From circuits to QBF Proof Systems2016Inngår i: ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, Association for Computing Machinery (ACM), 2016, s. 249-260Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A general and long-standing belief in the proof complexity community asserts that there is a close connection between progress in lower bounds for Boolean circuits and progress in proof size lower bounds for strong propositional proof systems. Although there are famous examples where a transfer from ideas and techniques from circuit complexity to proof complexity has been effective, a formal connection between the two areas has never been established so far. Here we provide such a formal relation between lower bounds for circuit classes and lower bounds for Frege systems for quantified Boolean formulas (QBF). Starting from a propositional proof system P we exhibit a general method how to obtain a QBF proof system P + 8red, which is inspired by the transition from resolution to Qresolution. For us the most important case is a new and natural hierarchy of QBF Frege systems C-Frege + 8red that parallels the well-studied propositional hierarchy of C-Frege systems, where lines in proofs are restricted to belong to a circuit class C. Building on earlier work for resolution [Beyersdorff, Chew, and Janota, 2015a] we establish a lower bound technique via strategy extraction that transfers arbitrary lower bounds for the circuit class C to lower bounds in C-Frege + 8red. By using the full spectrum of state-of-The-Art circuit lower bounds, our new lower bound method leads to very strong lower bounds for QBF Frege systems: (i) exponential lower bounds and separations for the QBF proof system AC0[p]-Frege + 8red for all primes p; (ii) an exponential separation of AC0[p]-Frege + 8red from TC0-Frege + 8red; (iii) an exponential separation of the hierarchy of constantdepth systems AC0 d-Frege + 8red by formulas of depth independent of d. In the propositional case, all these results correspond to major open problems.

  • 338.
    Biase, Fausto Di
    et al.
    Dipartimento di Matematica, Seconda Universita di Roma.
    Stokolos, Alexander
    Institute of Mathematics, Odessa State University.
    Svensson, Olof
    Weiss, Tomasz
    Institute of Mathematics, University of Warsaw.
    Tangential boundary behaviour of bounded harmonic functions in the unit disc1998Inngår i: Seminari di geometria 1996-1997, Bologna: Universita degli studi di Bologna, Dipartimento di Matematica , 1998, s. 63-68Kapittel i bok, del av antologi (Annet vitenskapelig)
  • 339.
    Biswas, Md Abdul Matin
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Exploiting the Direct Communication Link for Enhancing Effective Capacity Performance of Cognitive Radio Relay Networks2014Independent thesis Advanced level (degree of Master (Two Years))Oppgave
    Abstract [en]

    Nowadays, cognitive radio (CR) is a promising concept to improve the radio spectrum exploitation. CR has tremendous ability to enhance spectrum efficiency by allowing secondary users (SUs) to access licensed radio spectrum resource which is currently not being used by primary users (PUs). One basic challenge of that paradigm is securing the quality of service (QoS) of the primary link transmission while increasing the rate of the secondary links transmission. Cooperative relaying is an encouraging technology which offers the opportunity to maximize the transmission diversity gain significantly in the rapid development growth of wireless communication which contains cognitive radio networks. On the other hand, effective capacity (EC) which is designed to provide a maximum constant arrival rate that a statistical wireless channels can support while satisfying statistical QoS requirements. In this thesis, the performance enhancement analysis of cognitive radio relay network (CRRN) by exploiting the direct communication link has been investigated in Rayleigh fading channel where peak interference power constraint is taken into consider. A spectrum sharing technique is considered in this thesis where a restriction of spectrum sharing is applied by the PUs. Here, an SU can coexist simultaneously with the PU for transmitting data as long as a certain threshold on the peak interference power applied on the primary receiver is not overstepped by the SUs transmission. In addition, it is supposed that there are multiple intermediate relay nodes available to transmit their signal to the destination along with a direct communication link for secondary transmission. Moreover, the SU transmission has to meet a random delay QoS constraint. By providing this QoS constraint, the maximum arrival data rate of SUs can be achieved with small error of probability. Specifically, this thesis also acquires closed-form expressions of EC for CRRN. It is evident that if the channel quality and the interference threshold set by the PU are changed, then the capacity of the channel is also to be changed. In addition, it is also verified that the direct communication link together with multiple relay nodes has significantly higher capacity gains compare to non-direct communication link for CRRN. Matlab simulations are presented to find out theoretical results and Monte-Carlo simulations are carried out to support these numerical results. Both the simulation results and the analytical results match very well.

  • 340.
    Björk Friström, Viking
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Mapping of open-answers using machine learning2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    This thesis investigates if a model can be created to map misspelled answers from open-ended questions to a finite set of brands. The data used for the paper comes from the company Nepa that uses open-questions to measure brand-awareness and consists of misspelled answers and brands to be mapped to. A data structure called match candidate was created and consists of a misspelled answer and brand that it poten-tially be mapped to. Features for the match candidates were engineered and based on the edited distances, posterior probability and common misspellings among other. Multiple machine learning models were tested for classifying the match candidates as positive if the mapping was correct and negative otherwise. The model was tested in two scenarios, one when the answers in the training and testing data came from the same questions and secondly when they came from different ones. Among the classifiers tested, the random forest model performed best in terms of PPV as well as sensitivity. The resulting mapping identified on average 92% of the misspelled answers and map then with 98% accuracy in the first scenario. While in the second scenario 70% of the answers were identified with 95% confidence in the mapping on average.

  • 341.
    Björklund, Mickael
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Schnellmann, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Almost sure absolute continuity of Bernoulli convolutions2010Inngår i: Ann. Inst. H. Poincaré Probab. Statist., ISSN 0246-0203, Vol. 46, nr 3, s. 888-893Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove an extension of a result by Peres and Solomyak on almostsure absolute continuity in a class of symmetric Bernoulli convolutions.

  • 342.
    Björn, Anders
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Boundary regularity and barriers for elliptic and parabolic problems, and sharp capacity estimates for annuli2013Konferansepaper (Fagfellevurdert)
  • 343.
    Björn, Anders
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Cluster sets for Sobolev functions and quasiminimizers2010Inngår i: Journal d'Analyse Mathématique, ISSN 0021-7670, Vol. 112, s. 49-77Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we study cluster sets and essential cluster sets for Sobolev functions and quasiharmonic functions (i.e., continuous quasiminimizers). We develop their basic theory with a particular emphasis on when they coincide and when they are connected. As a main result, we obtain that if a Sobolev function u on an open set has boundary values f in Sobolev sense and f |∂is continuous at x0 ∈ ∂, then the essential cluster set C(u, x0, Ω) is connected. We characterize precisely in which metric spaces this result holds. Further, we provide some new boundary regularity results for quasiharmonic functions. Most of the results are new also in the Euclidean case.

     

     

     

  • 344.
    Björn, Anders
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    The Perron method for p-harmonic functions: new resolutivity and invariance results2012Konferansepaper (Fagfellevurdert)
  • 345.
    Björn, Anders
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    The Perron method for p-harmonic functions: Resolutivity and invariance results2012Konferansepaper (Fagfellevurdert)
  • 346.
    Björn, Anders
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    First-order Sobolev spaces on metric spaces2009Inngår i: Function Spaces, Inequalities and Interpolation (Paseky, 2009) / [ed] Jaroslav Lukes, Lubos Pick, Prague: Matfyzpress , 2009, s. 1-29Konferansepaper (Fagfellevurdert)
  • 347.
    Björn, Anders
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Local and semilocal Poincare inequalities on metric spaces2018Inngår i: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, E-ISSN 1776-3371, Vol. 119, s. 158-192Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider several local versions of the doubling condition and Poincare inequalities on metric measure spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding within every ball. We then study various geometrical and analytical consequences of such local assumptions, such as local quasiconvexity, self-improvement of Poincare inequalities, existence of Lebesgue points, density of Lipschitz functions and quasicontinuity of Sobolev functions. It turns out that local versions of these properties hold under local assumptions, even though they are not always straightforward. We also conclude that many qualitative, as well as quantitative, properties of p-harmonic functions on metric spaces can be proved in various forms under such local assumptions, with the main exception being the Liouville theorem, which fails without global assumptions. (C) 2018 Elsevier Masson SAS. All rights reserved.

  • 348.
    Björn, Anders
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Nonlinear Potential Theory on Metric Spaces2011 (oppl. 1)Bok (Fagfellevurdert)
    Abstract [en]

    The p-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories.

    This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for an interested reader and as a reference text for an active researcher. The presentation is rather self-contained, but the reader is assumed to know measure theory and functional analysis.

    The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space.

    Each chapter contains historical notes with relevant references and an extensive index is provided at the end of the book.

  • 349.
    Björn, Anders
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Poincare inequalities and Newtonian Sobolev functions on noncomplete metric spaces2019Inngår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 266, nr 1, s. 44-69Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let X be a noncomplete metric measure space satisfying the usual (local) assumptions of a doubling property and a Poincare inequality. We study extensions of Newtonian Sobolev functions to the completion (X) over cap of X and use them to obtain several results on X itself, in particular concerning minimal weak upper gradients, Lebesgue points, quasicontinuity, regularity properties of the capacity and better Poincare inequalities. We also provide a discussion about possible applications of the completions and extension results to p-harmonic functions on noncomplete spaces and show by examples that this is a rather delicate issue opening for various interpretations and new investigations. (C) 2018 Elsevier Inc. All rights reserved.

  • 350.
    Björn, Anders
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    TENSOR PRODUCTS AND SUMS OF p-HARMONIC FUNCTIONS, QUASIMINIMIZERS AND p-ADMISSIBLE WEIGHTS2018Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, nr 12, s. 5195-5203Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The tensor product of two p-harmonic functions is in general not p-harmonic, but we show that it is a quasiminimizer. More generally, we show that the tensor product of two quasiminimizers is a quasiminimizer. Similar results are also obtained for quasisuperminimizers and for tensor sums. This is done in weighted R-n with p-admissible weights. It is also shown that the tensor product of two p-admissible measures is p-admissible. This last result is generalized to metric spaces.

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