Now showing items 28-47 of 60

    • 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; Conference object; Konferansebidrag; 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; Bokkapittel; Chapter, 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; Bokkapittel; Chapter, 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 ...
    • Resolvent bounds for jump generators 

      Kondratiev, Yuri; Molchanov, Stanislav; Piatnitski, Andrey; Zhizhina, Elena (Journal article; Peer reviewed; Tidsskriftartikkel, 2016-12-02)
      The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially, we prove a number of lower and upper bounds for the resolvent of such operators. In particular we focus on sharp estimates of the resolvent kernel for small values of the spectral parameter. We consider two applications of these results. First we obtain pointwise ...
    • A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces 

      Blahota, Istvan; Nagy, Karoly; Persson, Lars Erik; Tephnadze, George (Journal article; Peer reviewed, 2018-09-20)
      The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p to the Lebesgue space L p for all 0<p≤1 . We also prove that the result is sharp in a particular sense.
    • Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications 

      Baramidze, Lasha; Persson, Lars Erik; Tephnadze, G; Wall, P (Peer reviewed, 2016-10-01)
      We prove and discuss some new Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out.
    • Shock Tube. Detail overview of equipment and instruments in the shock tube experimental setup 

      Khawaja, Hassan Abbas; Kapaya, Juma; Moatamedi, Mojtaba (Book; Bok, 2015)
      The shock tube is a device in which a normal shock wave is produced by the interaction of fluids at significantly high-pressure difference. The shock tube is comprised of two sections known as driver and driven sections. These two sections are interacted with the high-speed valve or a bursting disc. When the interaction happens, a shock wave forms almost instantaneously and propagates into the driven ...
    • Singularly perturbed spectral problems with Neumann boundary conditions 

      Piatnitski, Andrey; Rybalko, A; Rybalko, V (Peer reviewed, 2015-09-07)
      The paper deals with the Neumann spectral problem for a singularly perturbed second-order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue and eigenfunction. Using the logarithmic transformation, we reduce the studied problem to an additive eigenvalue problem for a singularly perturbed Hamilton–Jacobi ...
    • Some inequalities for Cesàro means of double Vilenkin-Fourier series 

      Tephnadze, G; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-12-19)
      In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from Lp.
    • Some new estimates of the ‘Jensen gap’ 

      Abramovich, Shoshana; Persson, Lars Erik (Peer reviewed, 2016-02-01)
    • Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator 

      Persson, Lars Erik; Shaimardan, Serikbol (Peer reviewed, 2015-09-24)
      We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n∈Nn∈N. Some new Hardy-type inequalities for this operator are proved and discussed.
    • Some new Hardy-type inequalities in q-analysis 

      Baiarystanov, A.O.; Persson, Lars Erik; Shaimardan, S.; Temirkhanova, A. (Peer reviewed, 2016-09)
      We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q -analogs of (r, p) -weighted Hardy-type inequalities for all possible positive values of the parameters r and p . We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction.
    • Some new Two-Sided Inequalities concerning the Fourier Transform 

      Kopezhanova, Aigerim; Nursultanov, Erlan; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2017)
      The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253).