Now showing items 18-37 of 60

    • Matrix factorization of multivariate Bernstein polynomials 

      Dalmo, Rune (Journal article; Peer reviewed; Tidsskriftartikkel, 2015)
      Ordinary univariate Bernstein polynomials can be represented in matrix form using factor matrices. In this paper we present the definition and basic properties of such factor matrices extended from the univariate case to the general case of arbitrary number of variables by using barycentric coordinates in the hyper-simplices of respective dimension. The main results in the paper are related to the ...
    • Multi-source data collection for state-of-the-art data analysis from ground-proximate images in sea ice classification 

      Woltmann, Lucas; Dalmo, Rune; Kristiansen, Raymond (Peer reviewed; Bok; Konferansebidrag; Conference object; Book, 2017-08-08)
      In modern data analysis it is imperative to use well maintained data sources with curated content. This publication gives an approach for research areas, where there is no such central facility. The specific area used here is sea ice classification from images. The publication is split into two parts. The first part describes the integration of discontinuous sources for different aspects of data ...
    • A new discrete Hardy-type inequality with kernels and monotone functions 

      Kalybay, Aigerim; Persson, Lars Erik; Temirkhanova, Ainur (Peer reviewed, 2015-10-06)
      A new discrete Hardy-type inequality with kernels and monotone functions is proved for the case 1<q<p<∞1<q<p<∞. This result is discussed in a general framework and some applications related to Hölder’s summation method are pointed out.

      Kopezhanova, Aigerim; Nursultanov, Erlan; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2018)
      Let Λq( ω ), q > 0, denote the Lorentz space equipped with the (quasi) norm [<i>MATHEMATICAL FORMULA</I>] for a function f on [0,1] and with ω positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system [<i>MATHEMATICAL FORMULA</I>] and generalized Lorentz Λq( ω ) spaces
    • A new look at classical inequalities involving Banach lattice norms 

      Nikolova, Ludmila; Persson, Lars Erik; Varosanec, Sanja (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-12-08)
      Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of ...
    • A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients 

      Memić, Nacima; Persson, Lars Erik; Tephnadze, George; Kroo, A (Peer reviewed, 2016)
      In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so ...
    • Numerical simulation of the dynamic response in pulse-loaded fibre–metal-laminated plates 

      Nwankwo, Ebuka; Fallah, Arash Soleiman; Moatamedi, Mojtaba; Louca, Luke A. (Journal article; Tidsskriftartikkel; Peer reviewed, 2016-07-27)
      This article presents a three-dimensional constitutive model to replicate the dynamic response of blast-loaded fibre–metal laminates made of 2024-0 aluminium alloy and woven composite (glass fibre–reinforced polypropylene). Simulation of the dynamic response is challenging when extreme localised loads are of concern and requires reliable material constitutive models as well as accurate modelling ...
    • On heat conduction in domains containing noncoaxial cylinders 

      Lukkassen, Dag; Meidell, Annette (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)
      We consider heat conduction in domains containing noncoaxial cylinders. In particular, we present some regularity results for the solution and consider criteria which ensure the single valueness of the corresponding complex potential. Examples are discussed. In addition, we present some classes of cases where the parameters describing the solution are rational. Alternative ways of calculating the ...
    • On Some Power Means and Their Geometric Constructions 

      Høibakk, Ralph; Lukkassen, Dag; Meidell, Annette; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2018)
      The main aim of this paper is to further develop the recently initiatedresearch concerning geometric construction of some power means wherethe variables are appearing as line segments. It will be demonstratedthat the arithmetic mean, the harmonic mean and the quadratic meancan be constructed for any number of variables and that all power meanswhere the number of variables are n = 2m, m 1 2 N for all ...
    • Osmosis for non-electrolyte solvents in permeable periodic porous media 

      Heintz, Alexei; Piatnitski, Andrey (Peer reviewed, 2016-08)
      The paper gives a rigorous description, based on mathematical homogenization theory, for flows of solvents with not charged solute particles under osmotic pressure for periodic porous media permeable for solute particles. The effective Darcy type equations for the flow under osmotic pressure distributed within the porous media are derived. The effective Darcy law contains an additional flux term ...
    • Periodic homogenization of nonlocal operators with a convolution-type kernel 

      Piatnitski, Andrey; Zhizhina, Elena (Journal article; Peer reviewed; Tidsskriftartikkel, 2017)
      The paper deals with a homogenization problem for a nonlocal linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behavior of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled operators ...
    • Pointwise estimates for heat kernels of convolution-type operators 

      Grigor'yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena (Journal article; Peer reviewed; Tidsskriftartikkel, 2018-04-16)
      We study the large‐time behaviour of the fundamental solution of parabolic equations with an elliptic part being non‐local convolution‐type operator. We assume that this operator is a generator of a Markov jump process, and that its convolution kernel decays at least exponentially at infinity. The fundamental solution shows rather different asymptotic behaviour depending on whether | x | ≲ t , or t ...
    • Potential type operators in PDEs and their applications 

      Burtseva, Evgeniya; Lundberg, Staffan; Persson, Lars Erik; Samko, Natasha (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-01)
      We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in ℝ<sup>3</sup> with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.
    • Pre-evaluation and interactive editing of B-spline and GERBS curves and surfaces 

      Lakså, Arne (Peer reviewed; Konferansebidrag; Conference object; Bokkapittel; Chapter, 2017-12)
      Interactive computer based geometry editing is very useful for designers and artists. Our goal has been to develop useful tools for geometry editing in a way that increases the ability for creative design. When we interactively editing geometry, we want to see the change happening gradually and smoothly on the screen. Pre-evaluation is a tool for increasing the speed of the graphics when doing ...
    • Predicting Bedside Falls using Current Context 

      Danielsen, Asbjørn; Bremdal, Bernt Arild (Peer reviewed; Chapter; Bokkapittel, 2018-02-05)
      Each year about a third of the elderly aged 65 or older experience a fall. Many of these falls could be avoided if fall risk assessment and prevention tools where available in the daily living situation. Such tools would need to use the current context as input to predict an imminent fall. This paper presents an approach predicting imminent falls using data from a roof-mounted infrared array combined ...
    • Quantitative analysis of accuracy of voidage computations in CFD-DEM Simulations 

      Khawaja, Hassan Abbas; Scott, Stuart A.; Virk, Muhammad Shakeel; Moatamedi, Mojtaba (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)
    • Recognizing Bedside Events Using Thermal and Ultrasonic Readings 

      Danielsen, Asbjørn; Tørresen, Jim (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-06-09)
      Falls in homes of the elderly, in residential care facilities and in hospitals commonly occur in close proximity to the bed. Most approaches for recognizing falls use cameras, which challenge privacy, or sensor devices attached to the bed or the body to recognize bedside events and bedside falls. We use data collected from a ceiling mounted 80 60 thermal array combined with an ultrasonic sensor ...
    • Refinements of some limit hardy-Type Inequalities via Superquadracity 

      Oguntuase, James A; Persson, Lars Erik; Fabelurin, Olanrewaju O; Adeagbo-Sheikh, Abdulaziz G (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-03)
      Refinements of some limit Hardy-type inequalities are derived and discussed using the concept of superquadracity. We also proved that all three constants appearing in the refined inequalities obtained are sharp. The natural turning point of our refined Hardy inequality is p=2 and for this case we have even equality.
    • Regression analysis using a blending type spline construction 

      Kravetc, Tatiana; Bang, Børre; Dalmo, Rune (Peer reviewed; Chapter; Bokkapittel, 2017-10-18)
      Regression analysis allows us to track the dynamics of change in measured data and to investigate their properties. A sufficiently good model allows us to predict the behavior of dependent variables with higher accuracy, and to propose a more precise data generation hypothesis. By using polynomial approximation for big data sets with complex dependencies we get piecewise smooth functions. One way ...
    • Reiterated homogenization of nonlinear monotone operators in a general deterministic setting 

      Lukkassen, Dag; Nguetseng, Gabriel; Nnang, Hubert; Wall, Peter (Journal article; Peer reviewed; Tidsskriftartikkel, 2009)
      We study reiterated homogenization of a nonlinear non-periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated Σ-convergence. A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ...