## Search

Now showing items 1-7 of 7

#### 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 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Rescue of stranded persons. C18. Rescue of stranded passengers in the Arctic

(Forskningsrapport; Research report, 2018-12)

Since we (the authors) could not be a part of the whole SARex 3 exercise this year, we joined the
expedition later than the rest of the participants. We gladly accepted the invitation from the Governor
of Svalbard, Kjerstin Askholt, and her staff in Longyearbyen to join their service vessel, MS Polarsyssel,
to meet The Norwegian Coast Guard’s vessel, (NOCGV) Svalbard, at the location where the ...

#### 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.