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  • 101.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University.
    Leibov, Mikhail
    Horton Point LLC.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Rademacher functions in BMO2011Inngår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 205, nr 1, s. 83-100Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Rademacher sums are investigated in the BMO space on [0, 1]. They span an uncomplemented subspace, in contrast to the dyadic BMOd space on [0, 1], where they span a complemented subspace isomorphic to l2. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec-Pelczyński type alternative with l2 and c0 spaces is proved

  • 102.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Interpolation of Cesaro and Copson spaces2014Inngår i: Proceedings of the Fourth International Symposium on Banach and Function Spaces IV (ISBFS 2012): Kyushu Institute of Technology, Kitakyushu, Japan, 12-15 September 2012 / [ed] Mikio Kato; Lech Maligranda; Tomonari Suzuki, Yokohama: Yokohama Publishers, 2014, s. 123-133Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Summary. Interpolation properties of Cesàro and Copson spaces are investigated. It is shown that the Cesàro function space Ces_p(I), where I = [0, 1] or [0, \infty), is an interpolation space between Ces_{p_0}(I) and Ces_{p_1}(I) for 1 < p_0 < p_1 \leq \infty and 1/p = (1 - \theta)/p_0 + \theta /p_1 with 0 < \theta < 1. The same result is true for Cesàro sequence spaces. For Copson function and sequence spaces a similar result holds even in the case when 1 \leq p_0 < p_1 \leq \infty. At the same time, $Ces_p[0, 1]$ is not an interpolation space between Ces_1[0, 1] and Ces_{\infty}[0, 1] for any 1

  • 103.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Interpolation of cesàro sequence and function spaces2013Inngår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 215, nr 1, s. 39-69Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that Cesp(I) is an interpolation space between Cesp0 (I) and Cesp1 (I) for 1 < p0 < p1 ≤ ∞ and 1/p = (1 - θ)/p0 + θ/p1 with 0 < θ < 1, where I = [0,∞) or [0, 1]. The same result is true for Cesàro sequence spaces. On the other hand, Cesp[0; 1] is not an interpolation space between Ces 1[0; 1] and Ces∞[0; 1].

  • 104.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia .
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lp + L and Lp n L are not Isomorphic for all 1 ≤ p < ∞, p ≠ 22018Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, nr 5, s. 2181-2194Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove the result stated in the title. It comes as a consequence of the fact that the space Lp n L∞, 1 = p < ∞, p ≠ 2, does not contain a complemented subspace isomorphic to Lp. In particular, as a subproduct, we show that Lp nL∞ contains a complemented subspace isomorphic to l2 if and only if p = 2.

  • 105.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia .
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q2018Inngår i: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 356, nr 6, s. 661-665Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+LL2+L∞ and L2∩LL2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].

  • 106.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Rademacher functions in Morrey spaces2016Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 444, nr 2, s. 1133-1154Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Rademacher sums are investigated in the Morrey spaces Mp,wMp,w on [0,1][0,1] for 1≤p<∞1≤p<∞ and weight w being a quasi-concave function. They span l2l2 space in Mp,wMp,w if and only if the weight w is smaller than View the MathML sourcelog2−1/2⁡2t on (0,1)(0,1). Moreover, if 1<p<∞1<p<∞ the Rademacher subspace Rp,wRp,w is complemented in Mp,wMp,w if and only if it is isomorphic to l2l2. However, the Rademacher subspace R1,wR1,w is not complemented in M1,wM1,w for any quasi-concave weight w . In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces Mp,wMp,w is described. It turns out that for any infinite-dimensional subspace X of Rp,wRp,w the following alternative holds: either X is isomorphic to l2l2 or X contains a subspace which is isomorphic to c0c0 and is complemented in Rp,wRp,w.

  • 107.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Structure of Cesaro function spaces: a survey2014Inngår i: Banach Center Publications, ISSN 0137-6934, E-ISSN 1730-6299, Vol. 102, s. 13-40Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Summary. Geometric structure of Cesàro function spaces Ces_p(I), where I = [0, 1] and [0,\infty), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q such that Ces_p[0, 1] contains isomorphic and complemented copies of lq-spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces Ces_p[0, 1].

  • 108.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Structure of Rademacher subspaces in Cesàro type spaces2015Inngår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 226, nr 3, s. 259-279Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The structure of the closed linear span R of the Rademacher functions in the Cesàro space Ces∞ is investigated. It is shown that every infinite-dimensional subspace of R either is isomorphic to l2 and uncomplemented in Ces∞, or contains a subspace isomorphic to c0 and complemented in R. The situation is rather different in the p-convexification of Ces∞ if 1 < p < ∞.

  • 109. Astashkin, Sergey V.
    et al.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Semenov, E. M.
    Department of Mathematics, Voronezh State University.
    Multiplicator space and complemented subspaces of rearrangement invariant space2003Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 202, nr 1, s. 247-276Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the multiplicator space M(X) of an rearrangement invariant (r.i.) space X on [0, 1] and the nice part N0 (X) of X, that is, the set of all a ∈ X for which the subspaces generated by sequences of dilations and translations of a are uniformly complemented, coincide when the space X is separable. In the general case, the nice part is larger than the multiplicator space. Several examples of descriptions of M(X) and N0(X) for concrete X are presented

  • 110.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tikhomirov, Konstantin E.
    Department of Mathematical and Statistical Sciences, University of Alberta.
    New examples of K-monotone weighted Banach couples2013Inngår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 218, nr 1, s. 55-88Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Some new examples of K-monotone couples of the type (X;X(ω)), where X is a symmetric space on [0; 1] and ω is a weight on [0; 1], are presented. Based on the property of ω-decomposability of a symmetric space we show that, if a weight ω changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X;X(ω)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t1/p for some p ⋯ [1;∞], then X = Lp. At the same time a Banach couple (X;X(ω)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space, we find conditions which guarantee that (X;X(ω)) is K-monotone

  • 111.
    Astashkin, S.V.
    et al.
    Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Semenov, E.M.
    Department of Mathematics, Voronezh State University.
    On complementability of subspaces generated by contractions and shifts of functions2002Inngår i: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 66, nr 3, s. 390-392Artikkel i tidsskrift (Fagfellevurdert)
  • 112.
    Atumi, M.K.
    et al.
    Newcastle University.
    Goss, J.P.
    Newcastle University.
    Briddon, P.R.
    Newcastle University.
    Shirf, F.E.
    Newcastle University.
    Rayson, Mark
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Hyperfine interactions at nitrogen interstitial defects in diamond2013Inngår i: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 25, nr 6Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Diamond has many extreme physical properties and it can be used in a wide range of applications. In particular it is a highly effective particle detection material, where radiation damage is an important consideration. The WAR9 and WAR10 are electron paramagnetic resonance centres seen in irradiated, nitrogen-containing diamond. These S = 1/2 defects have C2v and C1h symmetry, respectively, and the experimental spectra have been interpreted as arising from nitrogen split-interstitial centres. Based upon the experimental and theoretical understanding of interstitial nitrogen defect structures, the AIMPRO density functional code has been used to assess the assignments for the structures of WAR9 and WAR10. Although the calculated hyperfine interaction tensors are consistent with the measured values for WAR9, the thermal stability renders the assignment problematic. The model for the WAR10 centre yields principal directions of the hyperfine tensor at variance with observation. Alternative models for both centres are discussed in this paper, but no convincing structures have been found.

  • 113.
    Axelsson, B.O.M.
    et al.
    Luleå tekniska universitet.
    Lundberg, Staffan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Grönlund, Anders
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Träteknologi.
    Studies of the main cutting force at and near a cutting edge1993Inngår i: European Journal of Wood and Wood Products, ISSN 0018-3768, E-ISSN 1436-736X, Vol. 51, nr 1, s. 43-48Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present work is a study of how various parameters affect the cutting forces at, and near a cutting edge when cutting wood at full speed and with all cutting edges of the tool. Statistical methods from experimental results are used to develop a model

  • 114.
    Bagge, Niklas
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Nilimaa, Jonny
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Enochsson, Ola
    Sabourova, Natalia
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Emborg, Mats
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Elfgren, Lennart
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Lundmark, Tore
    Ramböll Sverige AB, Luleå.
    Tu, Yongming
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Protecting a five span prestressed bridge against ground deformations2015Inngår i: IABSE Conference Geneva 2015: Structural Engineering: Providing Solutions to Global Challenges, Geneva: International Association for Bridge and Structural Engineering, 2015, s. 255-262Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    A 55 year-old, 121.5 m long, five span prestressed bridge was situated in the deformation zone close to a mine in Kiruna in northern Sweden. There was a risk for uneven ground deformations so the bridge was analyzed and monitored. Results and measures taken to ascertain the robustness of the bridge are presented.The analysis resulted in an estimate that the bridge could sustain 24 mm in uneven horizontal and 83 mm in uneven vertical displacement of the two supports of a span. To be able to sustain larger deformations, the columns of the bridge were provided with joints, where shims could be inserted to counteract the settlements. To accomplish this, each one of the 18 columns of the bridge was unloaded by help of provisional steel supports. The column was then cut and a new foot was mounted to it. This made it possible to lift each individual column with two jacks, when needed, and to adjust its height by inserting or taking away shim plates.The deformations of the bridge and the surrounding ground were monitored. The eigenmodes of the bridge were studied with accelerometers and by analysis with finite elements (FE) models. Comparison indicated good agreement between the model and the actual bridge, with calculated eigenfrequencies of 2.17, 4.15 and 4.67 Hz, for the first transversal, vertical and torsional modes, respectively. Measurements during winter resulted in higher values due to increased stiffness caused by frozen materials.

  • 115.
    Bangert, U.
    et al.
    School of Physics, University of Exeter.
    Barnes, R.
    Lunar & Planetary Lab., Arizona University, Tucson.
    Hounsome, L.S.
    School of Physics, University of Exeter.
    Jones, R.
    School of Physics, University of Exeter.
    Blumenau, A.T.
    Max-Planck-Institut für Eisenforschung GmbH.
    Briddon, P.R.
    School of Natural Science, University of Newcastle upon Tyne.
    Shaw, M.J.
    School of Natural Science, University of Newcastle upon Tyne.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Electron energy loss spectroscopic studies of brown diamonds2006Inngår i: Philosophical Magazine, ISSN 1478-6435, E-ISSN 1478-6443, Vol. 86, nr 29-31, s. 4757-4779Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate both experimentally and theoretically, low-loss electron energy losses in brown type IIa monocrystalline diamonds both before and after high-temperature, high-pressure anneals which remove the brown colouration. We find additional losses within and near the band edge for brown diamond which are significantly reduced after treatment. The additional losses are not associated with dislocations. Graphitic inclusions are detected by EELS as well as TEM studies for some brown diamonds before treatment. These lead to pronounced subgap absorption. However, all brown diamonds exhibit additional losses which are due to point defects lying in the regions between dislocations. First principles theoretical modelling shows that common dislocations are not responsible for the brown colouration but a -bonded vacancy disk lying on {111} planes gives broad bands lying in the diamond band gap, possesses an optical absorption spectrum similar to that of brown diamond, and leads to additional electron energy losses in the band edge region. These and similar defects are suggested to be responsible for the brown colouration. Mechanisms are proposed for their formation and removal.

  • 116.
    Baramidze, Lasha
    et al.
    Department of Mathematics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications2016Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikkel-id 242Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove and discuss some new Hp-Lptype 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

  • 117.
    Barza, S.
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Marcoci, A.N.
    Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Best constants between equivalent norms in Lorentz sequence spaces2012Inngår i: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 2012Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.

  • 118.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Burenkov, Victor
    School of Mathematics, University College Cardiff.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights1998Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, nr 1, s. 53-67Artikkel i tidsskrift (Fagfellevurdert)
  • 119.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Heinig, Hans P.
    Department of Mathematics and Statistics, McMaster University, Hamilton.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Duality theorem over the cone of monotone functions and sequences in higher dimensions2002Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 7, nr 1, s. 79-108Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let f be a non-negative function defined on ℝ+n which is monotone in each variable separately. If 1 < p < ∞, g ≥ 0 and v a product weight function, then equivalent expressions for sup ∫ℝ(+)(n) fg/(ℝ+nfpv)1/p are given, where the supremum is taken over all such functions f. Variants of such duality results involving sequences are also given. Applications involving weight characterizations for which operators defined on such functions (sequences) are bounded in weighted Lebesgue (sequence) spaces are also pointed out.

  • 120.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Johansson, Maria
    Luleå tekniska universitet, Institutionen för konst, kommunikation och lärande, Pedagogik språk och Ämnesdidaktik.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    A Sawyer duality principle for radially monotone functions in Rn2005Inngår i: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 6, nr 2, artikkel-id 44Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let f be a non-negative function on ℝn, which is radially monotone (0 < f↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup ∫ℝ fg/f↓r(∫ℝn fp v)1/p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given. © 2005 Victoria University

  • 121.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Kaminska, Anna
    Department of Mathematical Sciences, University of Memphis.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sori, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona.
    Mixed norm and multidimensional Lorentz spaces2005Rapport (Annet vitenskapelig)
  • 122.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Kaminska, Anna
    Department of Mathematical Sciences, University of Memphis.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona.
    Mixed norm and multidimensional Lorentz spaces2006Inngår i: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 10, nr 3, s. 539-554Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces.

  • 123.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Marcoci, Anca
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Optimal estimates between equivalent norms in Lorentz sequence spaces2009Rapport (Annet vitenskapelig)
  • 124.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Marcoci, Anca-Nicoleta
    Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science.
    Marcoci, Liviu-Gabriel
    Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Optimal estimates in Lorentz spaces of swquences with an increasing weight2013Inngår i: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 14, nr 1, s. 20-27Artikkel i tidsskrift (Fagfellevurdert)
  • 125.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Carlson type inequalities1998Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2, nr 2, s. 121-135Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A scale of Carlson type inequalities are proved and the best constants are found. Some multidimensional versions of these inequalities are also proved and it is pointed out that also a well-known inequality by Beurling-Kjellberg is included as an endpoint case.

  • 126.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Reversed Hölder type inequalities for monotone functions of several variables1997Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 186, nr 67-80, s. 67-80Artikkel i tidsskrift (Fagfellevurdert)
  • 127.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Weighted multidimensional inequalities for monotone functions1999Inngår i: Mathematica Bohemica, ISSN 0862-7959, Vol. 124, nr 2-3, s. 329-335Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We discuss the characterization of the inequality $$ \biggl(\int_{{\Bbb R}^N_+} f^q u\biggr)^{1/q} \leq C \biggl(\int_{{\Bbb R}^N_+} f^p v \biggr)^{1/p},\quad0

  • 128.
    Barza, Sorina
    et al.
    Karlstads Universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Popa, Emil C.
    Lucian Blaga University of Sibiu.
    Some multiplicative inequalities for inner products and of the Carlson type2008Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242XArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.

  • 129.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Popa, Nicolae
    Institute of Mathematics of Romanian Academy.
    A matriceal analogue of Fejer's theory2003Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 260, nr 1, s. 14-20Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    J. Arazy [1] pointed out that there is a similarity between functions defined on the torus and infinite matrices. In this paper we discuss and develop in the framework of matrices Fejer's theory for Fourier series.

  • 130. Barza, Sorina
    et al.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Rakotondratsiba, Yves
    On weighted multidimensional integral inequalities for mixed monotone functions2000Inngår i: Societe des Sciences Mathematiques de Roumanie. Bulletin Mathematique, ISSN 1220-3874, Vol. 43(91), nr 1, s. 39-45Artikkel i tidsskrift (Fagfellevurdert)
  • 131.
    Barza, Sorina
    et al.
    Karlstads Universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new sharp limit Hardy-type inequalities via convexity2014Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2014, artikkel-id 6Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Some new limit cases of Hardy-type inequalities are proved, discussed and compared. In particular, some new refinements of Bennett's inequalities are proved. Each of these refined inequalities contain two constants, and both constants are in fact sharp. The technique in the proofs is new and based on some convexity arguments of independent interest.

  • 132.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona.
    Multidimensional rearrangement and Lorentz spaces2004Inngår i: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 104, nr 3, s. 203-224Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.

  • 133.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Soria, Javier
    Departamento de Matemàtica, Aplicada i Anàlisi, Universitat de Barcelona.
    Sharp weighted multidimensional integral inequalities of Chebyshev type1999Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 236, nr 2, s. 243-253Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove a general Chebyshev inequality for monotone functions in higher dimensions. This result generalizes the classical one-dimensional inequality and recovers some extensions already known for product weights. In all cases we find the best constant in the inequality. We also consider the case of more general operators.

  • 134. Barza, Sorina
    et al.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Stepanov, Vladimir D.
    Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk.
    On weighted multidimensional embeddings for monotone functions2001Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 88, nr 2, s. 303-319Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We characterize the inequality (∫RN+ fqu)1/q ≤ C(∫RN+fpv)1/p, 0 < q, p < ∞, for monotone functions f ≥ 0 and nonnegative weights u and v. The case q < p is new and the case 0 < p ≤ q < ∞ is extended to a modular inequality with N-functions. A remarkable fact concerning the calculation of C is pointed out

  • 135.
    Baǐarystanov, Askar O.
    et al.
    Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. The Artic University of Norway.
    Shaimardan, Serikbol
    Eurasian National University.
    Temirkhanova, Ainur
    Eurasian National University.
    Some new hardy-type inequalities in q-analysis2016Inngår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 10, nr 3, s. 761-781Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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

  • 136.
    Beeri, Guy
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some mathematical, numerical and engineering aspects of composite structures and perforated solids2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In this doctoral thesis in engineering mathematics we present some new modeling, numerical and engineering aspects and results concerning composite structures and perforated solids.The thesis consists of five papers, which are divided into three parts. Part A functions as an introduction where we look into some of the mathematical, numerical and engineering aspects of the effective in-plane elastic properties of periodic structures. We focus on one- and two-component composites and, in particular, we discuss locally anisotropic perforated structures. Moreover, we describe how the elastic properties of such and more general structures can be calculated. Finally, we present bounds and relations between different effective moduli.In Part B we study twelve of the simplest structures belonging to the class of one-component structures with holes and which, in addition, are three-fold rotational symmetric. We look into the effective elastic in-plane properties such as effective bulk and shear moduli and the so-called Vigdergauz constants. A comparative overview of all of these properties is given. Furthermore, we derive low-density asymptotics and present numerical data from finite element calculations. We also show that several of the studied structures have optimal elastic properties in the limit when the volume fraction of the connected material goes to zero. Finally, some remarks on the manufacturability of the structures are made.In Part C, which is divided into three papers, we continue to explore the effective properties of periodic structures. In paper [C1] we introduce a new model for estimating the elastic effective properties of regular hexagonal honeycombs. In contrast to previous cases, with this model we introduce a new formula, which match and complement the results obtained by Vigdergauz in 1999 in an essential way. Furthermore, by comparing some of the results with numerical finite element computations we find an improved formulae which enable us to estimate the effective properties with an accuracy better than one percent. In paper [C2] we study the effective elastic properties of regular triangular honeycombs. In particular, we obtain some simple approximate formulae for the corresponding Vigdergauz constants with accuracy better than one percent for all densities. In paper [C3] we study a scale of two-component composite structures of equal proportions with infinitely many microlevels. The structures are obtained recursively and we find that their effective conductivities are power means of the local conductivities.

  • 137. Bengtsson, Daniel
    et al.
    Deutgren, Petra
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Isaksson, Mikael
    Olsson, Lennart
    Luleå tekniska universitet.
    Sjöberg, Frank
    Luleå tekniska universitet.
    Öhman, Hans
    Zipper performance when mixing ADSL and VDSL in terms of reach and capacity1997Rapport (Annet vitenskapelig)
    Abstract [en]

    In this contribution we have examined how the maximum reach vary at different bit rates on a VDSL system, when different numbers of ADSL and VDSL systems share the same binder. In this context it is concluded that when using the Zipper duplex scheme, VDSL can coexist with ADSL in the same binder without a significant degradation in reach. Further, it is shown that the Zipper duplex scheme secure that ADSL is not disturbed by NEXT from VDSL The Zipper performance has also been compared with both a TDD proposal and a FDD proposal. The results from this comparison shows that Zipper outperforms FDD and TDD in terms of extended reach at all studied mixes of ADSL and VDSL sharing the same binder. For example with a moderate number (5) of ADSL disturbers, the Zipper reach is 150 meters longer than for TDD, and is 350 meters longer than for FDD when studying the medium range asymmetrical bit rate (26:3.2 Mbps).

  • 138.
    Bennitz, Anders
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Schmidt, Jacob W.
    Technical University of Denmark.
    Thick-walled cylinder theory applied on a conical wedge anchorage2011Inngår i: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648, Vol. 46, nr 5, s. 959-977Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we derive and examine an analytical model for the internal stresses and strains within the anchorage for a prescribed presetting distance. This model is derived from the theory of thick walled cylinders under the assumptions regarding plane stress and axial symmetry. We simplify the resulting system of ten nonlinear equations and derive a method for solving them numerically. A comparison of plotted results for three different angles on the wedge's outer surface and six different presetting distances follows. These results are also compared to both axi-symmetric and 3D FE (Finite Element) models. Analytical and FE axi-symmetric models show good correspondence, though compared to the 3D FE model, they show a clear difference in the predicted radial stress distribution on the FRP. Thus, the derived analytical model can be a useful and faster alternative to FE modeling of axi-symmetric anchorages. However, the model is of more restricted value and should be complemented by, for example, 3D FE models for other designs.

  • 139.
    Bennitz, Anders
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Byggkonstruktion och -produktion.
    Grip, Niklas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Schmidt, Jacob W.
    Department of Civil Engineering, Technical University of Denmark.
    Thick-walled cylinder theory applied on a conical wedge anchorage: Research report with Matlab implementation documentation2010Rapport (Annet vitenskapelig)
    Abstract [en]

    Conical wedge anchorages are frequently used to anchor steel tendons in prestressing applications within the construction industry. To replace the steel tendons with non-corrosive and low weight FRPs (Fiber Reinforced Polymers), the different mechanical interactions between the steel and FRPs call for further development of the anchorage.In this paper, we derive and examine an analytical model for the internal stresses and strains within the anchorage for a prescribed presetting distance. This model is derived from the theory of thick walled cylinders under the assumptions regarding plane stress and axial symmetry. We simplify the resulting system of ten nonlinear equations and derive a method for solving them numerically. A comparison of plotted results for three different angles on the wedge's outer surface and six different presetting distances follows.These results are also compared to both axi-symmetric and 3D FE (Finite Element) models. Analytical and FE axi-symmetric models show good correspondence, though compared to the 3D FE model, they show a clear difference in the predicted radial stress distribution on the FRP. Thus, the derived analytical model can be a useful and fasteralternative to FE modeling of axi-symmetric anchorages. However, the model is of more restricted value and should be complemented by, for example, 3D FE models for other designs.

  • 140.
    Berezhnoi, E. I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Extrapolation of operators and the limits of applicability of Schur's test2003Inngår i: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 393, nr 5, s. 583-586Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Generalizations of the Schur test for integral operators are studied. The authors look at the test from the point of the modern theory of extrapolation of operators. The generalizations are of two types. First of all, instead of operators with positive kernel, a more general class of positive operators is considered. Moreover, instead of Lp spaces, Orlicz, Lorentz and Marcinkiewicz spaces are taken as underlying spaces. In particular it is stated that the Schur extrapolation theorem holds for the class of positive operators. Several negative results are formulated. For instance, the authors show that the Schur extrapolation theorem does not hold for the sublinear Hardy operator in the Lp scale and for the classical Hardy operator in some reflective Orlicz spaces. Moreover, it is claimed that for a certain class of operators one can use Lorentz and Marcinkiewicz spaces instead of L1.and L∞ Proofs are not given.

  • 141.
    Berezhnoi, E. I.
    et al.
    Yaroslavl State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Representability of cones in weighted Lebesgue spaces and extrapolation operators on cones2006Inngår i: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 73, nr 1, s. 59-62Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Representability of cones in weighted Lebesgue spaces and extrapolation operators on cones are discussed. Estimates of operators on some cones in spaces rather than on the entire spaces have become very popular. A reduction of estimating operators on cones to estimating them on new spaces is suggested. such reduction makes it possible to apply the whole apparatus developed for obtaining exact estimates on weith Lebesgue spaces to obtain exact estimates of operators on cones. Using the reduction, it is proved that a new extrapolation theorem for a certain class of operator defined on cones in Lebesgue spaces.

  • 142.
    Berezhnoi, Evgeni
    et al.
    Yaroslav State Univerity, Yaroslavl, Russia.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On the representability of cones of monotone functions in weighted Lebesgue spaces and the extrapolation of operators on these cones2017Inngår i: Algebra i Analiz, ISSN 0234-0852, Vol. 29, nr 4, s. 1-44Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We have proved that boundedness of a sublinear operator on the cone of monotone functions is equivalent to boundedness of the involved operator with it on a new space, which is constructively built. Using this construction we were able to prove a new extrapolation theorems on this cone in weighted Lebesgue spaces.

  • 143.
    Berezhnoǐ, Eugenii I.
    et al.
    P. G. Demidov Yaroslavl, State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones2018Inngår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 29, nr 4, s. 545-574Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is shown that a sublinear operator is bounded on the cone of monotone functions if and only if a certain new operator related to the one mentioned above is bounded on a certain ideal space defined constructively. This construction is used to provide new extrapolation theorems for operators on the cone in weighted Lebesgue spaces.

  • 144.
    Berezhoi, E.I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Representability of some cones in weighted Lebesgue spaces and the extrapolation of operators on cones2006Inngår i: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 406, nr 4, s. 439-442Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, for the most important cones in Lebesgue spaces, we propose reducing the problem of an estimate for an operator on a cone to the problem of an estimate for an operator on a new space, which is obtained constructively from the cone and the original space. Such a reduction makes it possible to apply the entire apparatus developed for obtaining sharp estimates on weighted Lebesgue spaces to obtain sharp estimates for operators on cones. Using this reduction, we also state, for a certain class of operators, a new theorem on the extrapolation of operators defined on cones in Lebesgue spaces.

  • 145.
    Berezhoi, Evgenii I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Representation of Banach ideal spaces and factorization of operators2003Rapport (Annet vitenskapelig)
  • 146.
    Berezhoi, Evgenii I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Representation of Banach ideal spaces and factorization of operators2005Inngår i: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 57, nr 5, s. 897-940Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón-Lozanovskiǐ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lp spaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far from Lp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón-Lozanovskiǐ construction are involved in the proofs

  • 147.
    Berezovsky, Vladimir
    et al.
    Pomorskii State University, Arkhangelsk.
    Men'shikov, Leonid
    Russian Research Centre, Kurchatov Institute, Moscow.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Latham, Chris
    Effect of dipole-dipole interactions between atoms in an active medium2008Inngår i: Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, E-ISSN 1520-8540, Vol. 25, nr 3, s. 458-462Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    On the basis of the results of numerical modeling, it is shown that dipole-dipole interactions among atoms in the active medium strongly influences the character of the associated superradiation. The main effect is to make the nuclear subsystem behave chaotically. Its strength increases with the atom density and leads to the suppression of distant collective correlations and superradiation. Near correlations between the atoms are established, causing a confinement effect: a shielding of radiation in the active medium.

  • 148.
    Berezovsky, V.V.
    et al.
    Lomonosov Pomor State University, Arkhangelsk.
    Men'shikov, L.I.
    Russian Research Centre, Kurchatov Institute, Moscow.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Latham, Chris
    Effect of the dipole-dipole interaction of particles in an active medium on the character of superradiation2008Inngår i: Plasma physics reports (Print), ISSN 1063-780X, E-ISSN 1562-6938, Vol. 34, nr 7, s. 555-561Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The motion of a system of interacting nonlinear charged oscillators is investigated numerically. Because of nonlinearity, the total collective electric field gives rise to a phasing effect-correlations in the phases of the oscillators. The consequence is superradiation-the enhanced spontaneous short-term emission of the energy stored in the oscillators. It is shown that the oscillations of the oscillators become stochastic because of the dipole-dipole interaction between them and their nearest neighbors. As a result, as the density of the oscillators increases, distant collective correlations are suppressed, superradiation ceases to be generated, and radiation is shielded in the medium. The phenomena considered in the present paper can play an important role in cyclotron emission from a plasma and thus should be taken into account in emission calculations. The process whereby the energy of the transverse electron motion in electron cooling devices decreases is analyzed as an example. This process occurs as a result of the development of cyclotron maser instability and has the nature of superradiation. The onset of correlations between individual electrons moving in their Larmor circles is the initial, linear stage of instability developing in the plasma. Superradiation is the final, nonlinear instability stage.

  • 149. 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)
  • 150.
    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)
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