• 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 ...
    • Steklov Problems in Perforated Domains with a Coefficient of Indefinite Sign 

      Piatnitski, Andrey L.; Piat, Valeria C.; Nazarov, Sergey S. (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)
    • 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 ...
    • 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)
    • Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem 

      Dechevski, Lubomir T (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)
    • Weighted Hardy Operators in Complementary Morrey Spaces 

      Lukkassen, Dag; Persson, Lars Erik; Samko, Stefan (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)
    • Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces 

      Lukkassen, Dag; Persson, Lars Erik; Samko, Stefan; Wall, Peter (Journal article; Tidsskriftartikkel; Peer reviewed, 2013)
      We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. ...
    • Design of water shock tube for testing shell materials 

      Ji, Hongjuan; Mustafa, Mohamad; Khawaja, Hassan Abbas; Ewan, Bruce C.; Moatamedi, Mojtaba (Journal article; Tidsskriftartikkel; Peer reviewed, 2014-04-15)
      This paper presents design considerations for a shock tube experimental rig used to investigate the dynamic failure mechanisms of shell geometries subjected to water shock impact loading. In such setup, it is desirable that the drive pressure used within the tube can provide a wide range of impulsive loads on the test structures and some flexibility can be achieved on the applied pulse durations. ...
    • 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 ...
    • 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 ...
    • Time scale Hardy-type inequalities with ‘broken’ exponent p 

      Oguntuase, James A; Fabelurin, Olanrewaju O; Adeagbo-Sheikh, Abdulaziz G; Persson, Lars Erik (Peer reviewed, 2015-01-16)
      In this paper, some new Hardy-type inequalities involving ?broken? exponents are derived on arbitrary time scales. Our approach uses both convexity and superquadracity arguments, and the results obtained generalize, complement and provide refinements of some known results in literature
    • 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 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.
    • 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.
    • Asymptotics of a spectral-sieve problem 

      Amirat, Youcef; Bodart, Olivier; Chechkin, Gregory; Piatnitski, Andrey (Peer reviewed, 2015-11-18)
      In a bounded domain with a thin periodically punctured interface we study the limit behavior of the bottom of spectrum for a Steklov type spectral problem, the Steklov boundary condition being imposed on the perforation surface. For a certain range of parameters we construct the effective spectral problem and justify the convergence of eigenpairs.
    • Homogenization of random Navier–Stokes-type system for electrorheological fluid 

      Piatnitski, Andrey; Zhikov, Vasily (Peer reviewed, 2015-11-19)
      The paper deals with homogenization of Navier–Stokes-type system describing electrorheological fluid with random characteristics. Under non-standard growth conditions we construct the homogenized model and prove the convergence result. The structure of the limit equations is also studied.
    • 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 ...
    • Some new estimates of the ‘Jensen gap’ 

      Abramovich, Shoshana; Persson, Lars Erik (Peer reviewed, 2016-02-01)
    • Fremtidens fleksible distribusjonsnett : fleksibel nettdrift, forbrukerfleksibilitet, plusskunder og forretningsmodeller 

      Sæle, Hanne; Bremdal, Bernt Arild; Tøndel, Inger Anne; Istad, Maren Kristine; Foosnæs, Jan Andor; Nordbø, Per Erik; Kirkeby, Henrik; Høverstad, Boye Annfelt; Mathisen, Geir (Research report; Forskningsrapport, 2016-02-15)
      Denne rapporten er utarbeidet i WP1 og WP2 i prosjektet "Fleksibilitet i fremtidens smarte distribusjonsnett - FlexNett" (2015-2017). FlexNett-prosjektet har som målsetting å bidra til økt fleksibilitet i fremtidens smarte distribusjonsnett gjennom å demonstrere og verifisere tekniske og markedsmessige løsninger for fleksibilitet på ulike nivå i nettet til nytte for ulike aktører. <br> Målsettingen ...
    • Some sharp inequalities for integral operators with homogeneous kernel 

      Lukkassen, Dag; Persson, Lars Erik; Samko, Stefan G. (Peer reviewed, 2016-04-09)
      One goal of this paper is to show that a big number of inequalities for functions in Lp(R+), p ≥ 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and ...