Recent additions

  • 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.
  • 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 ...
  • Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media 

    Amaziane, Brahim; Jurak, Murat; Pankratov, Leonid; Piatnitski, Andrey (Journal article; Peer reviewed, 2018-03-15)
    In this paper, we consider nonisothermal two-phase flows through heterogeneous porous media with periodic microstructure. Examples of such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste, thermally enhanced oil recovery and geothermal systems. The mathematical model is given by a coupled system of two-phase flow equations, and an ...
  • Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime 

    Braides, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita (Journal article; Peer reviewed, 2018-04-30)
    We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability 1−p 1−p and p, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in Z 2 Z2 . We prove that there exists p 0 p0 such that for p≤ p 0 p≤p0 such ...
  • Steady States, Fluctuation-Dissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment 

    Mathieu, P; Piatnitski, A (Journal article; Peer reviewed; Tidsskriftartikkel, 2018-04-02)
    Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle, we introduce the notions of steady state and weak steady state. We establish the continuity of weak steady states for an ergodic and uniformly elliptic environment. ...
  • 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 ...
  • Dynamic plastic response of beams subjected to localised pulse loads 

    Thil, Nicolas; Mehreganian, Navid; Moatamedi, Mojtaba; Louca, Luke A.; Soleiman Fallah, Arash (Journal article; Peer reviewed, 2018-10-31)
    Localised blast loads give rise to high gradients of overpressure detrimental to structural elements as beams and plates. This article presents an analytical study on the dynamic plastic response of beams made of a ductile metallic material due to close-in pulse pressure loading. The close-in pressure load is characterised by a spatially varying function constant over a central region and exponentially ...
  • Hardy-type inequalities in fractional h-discrete calculus 

    Persson, Lars Erik; Oinarov, Ryskul; Shaimardan, Serikbol (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-04)
    The first power weighted version of Hardy’s inequality can be rewritten as [<i>mathematical formula</i>] where the constant <i>C</i> =[<i>p</i> / <i>p</i> - <i><b>a</b></i> - 1]<sup><i>p</i></sup> is sharp. This inequality holds in the reversed direction when<math xmlns=""> <mn>0</mn> <mo>&#x2264;<!-- ≤ --></mo> <mi><i>p</i></mi> <mo>&lt;</mo> <mn>1</mn> ...
  • Geometric Construction of Some Lehmer Means 

    Høibakk, Ralph; Lukkassen, Dag; Meidell, Annette; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-11-14)
    The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0,1 and 2 can be geometrically ...

    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
  • Two-sided estimates of the Lebesgue constants with respect to Vilenkin systems and applications 

    Blahota, Istvan; Persson, Lars Erik; Tephnadze, G (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-03-13)
    In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H 1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.
  • Some inequalities for Cesàro means of double Vilenkin-Fourier series 

    Tephnadze, G; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 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.
  • 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 ...
  • Local Flexibility Market Design for Aggregators Providing Multiple Flexibility Services at Distribution Network Level 

    Olivella-Rosell, Pol; Lloret-Gallego, Pau; Munne-Collado, Ingrid; Villafafila-Robles, Roberto; Sumper, Andreas; Ottesen, Stig Ødegaard; Rajasekharan, Jayaprakash; Bremdal, Bernt Arild (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-02)
    This paper presents a general description of local flexibility markets as a market-based management mechanism for aggregators. The high penetration of distributed energy resources introduces new flexibility services like prosumer or community self-balancing, congestion management and time-of-use optimization. This work is focused on the flexibility framework to enable multiple participants to compete ...
  • 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.
  • 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.
  • 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).
  • 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 ...
  • Fejér and Hermite-Hadamard Type Inequalities for N-Quasiconvex Functions 

    Abramovich, S; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-12-28)
    Some new extensions and re finements of Hermite – Hadamard and Fejer type inequalities for functions which are N -quasiconvex are derived and discussed.
  • Economic evaluation of the Power grid tariff for households With solar Power installed 

    Sæle, Hanne; Bremdal, Bernt Arild (Journal article; Peer reviewed; Tidsskriftartikkel, 2017)
    This paper focuses on alternative grid tariffs for household customers with roof top PV-panels ("prosumers"), and evaluates how alternative grid tariffs might affect the benefit from investing in a roof top PV-panel. The paper further shows how different orientations of the PV-panels can affect the benefits for the prosumers subjected to different grid tariffs (for example a power grid tariff), where ...

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