English
norskBlar i forfatter Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag) "Lukkassen, Dag"
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Generalized Chessboard Structures Whose Effective Conductivities Are Integer Valued
(Journal article; Tidsskriftartikkel; Peer reviewed, 2012-03-06)We consider generalized chessboard structures where the local conductivity takes two values 𝑎 and 𝑏 . All integer combinations of 𝑎 and 𝑏 which make the components of effective conductivity matrix integer valued are found. Moreover, we discuss the problem of estimating the effective conductivity matrix by using the finite-element method. -
Geometric Construction of Some Lehmer Means
(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 ... -
A New Development of the Classical Single Ladder Problem via Converting the Ladder to a Staircase
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-02-08)Our purpose is to shed some new light on problems arising from a study of the classical Single Ladder Problem (SLP). The basic idea is to convert the SLP to a corresponding Single Staircase Problem. The main result (Theorem 1) shows that this idea works fine and new results can be obtained by just calculating rational solutions of an algebraic equation. Some examples of such concrete calculations ... -
On geometric construction of some power means
(Journal article; Peer reviewed, 2018-11-27)In the homogenization theory, there are many examples where the effective conductivities of composite structures are power means of the local conductivities. The main aim of this paper is to initiate research concerning geometric construction of some power means of three or more variables. We contribute by giving methods for the geometric construction of the harmonic mean $ P_{-1} $ and the arithmetic ... -
On heat conduction in domains containing noncoaxial cylinders
(Journal article; Peer reviewed; Tidsskriftartikkel, 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
(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 ... -
Reiterated homogenization of nonlinear monotone operators in a general deterministic setting
(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 ... -
Some inequalities related to strong convergence of Riesz logarithmic means
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-23)In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series. -
Some new Fourier inequalities for unbounded orthogonal systems in Lorentz-Zygmund spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-20)In this paper we prove some essential complements of the paper (J. Inequal. Appl. 2019:171, 2019) on the same theme. We prove some new Fourier inequalities in the case of the Lorentz–Zygmund function spaces L q,r (logL ) α Lq,r(logL)α involved and in the case with an unbounded orthonormal system. More exactly, in this paper we prove and discuss some new Fourier inequalities of this type for ... -
Some sharp inequalities for integral operators with homogeneous kernel
(Peer reviewed; Journal article; Tidsskriftsartikkel, 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 ... -
Weighted Hardy Operators in Complementary Morrey Spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2012) -
Weighted Hardy Operators in Complementary Morrey Spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2012-11-11)We study the weighted -boundedness of the multidimensional weighted Hardy-type operators and with radial type weight , in the generalized complementary Morrey spaces defined by an almost increasing function . We prove a theorem which provides conditions, in terms of some integral inequalities imposed on and , for such a boundedness. These conditions are sufficient in the general case, but we ... -
Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces
(Journal article; Peer reviewed; Tidsskriftartikkel, 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. ...
