96 Normat 55:1, 96 (2007)

Summary in English

Helge Tverberg, Ernst S.Selmer in

memoriam (Norwegian).

E.Selmer who was chief editor of Nor-

mat for a quarter of a century is chieﬂy

known for the so called Selmer groups in

connection with diophantie cubic equa-

tions, playing a crucial rôle in Wiles

work on the Fermat Conjecture (see

the article by L.Olson below). This is

a short review of his life and work, an

elabouration of a talk given at a memo-

rial conference earlier this year.

Loren D.Olson, Selmergroups - a his-

torical review (Norwegian).

This is an overview of diﬀerent groups

that occur in connection with the diop-

hantine study of ellipt curves. Examples

are of course not only the Mordell-Weil

group and the Tate-Shafarevich groups

but also of course the groups called Sel-

mer groups which ﬁt into the compu-

tation of the previous in a well-known

short exact sequence.

Dan Laksov, Linear maps and linear

recursion (Norwegian).

This paper studies the solutions to li-

near recursions as special linear maps

of rings of polynomials in one variab-

le. This is so to speak the dual point of

view to what is to be found in the li-

terature and gives a natural connection

to the general theory of linear recursion.

In this way the results appear in a clea-

rer light, the proofs become simpler, and

one is naturally led to generalizations

of the theory. In particular it transpi-

res that the restriction to ﬁnite ﬁelds,

or more generally to periodic sequences,

which are predominant in the literature,

is unnecessary for most considerations.

This is illustrated by a detailed presen-

tation of the theory of multigrams.

Jan-Erik Björk och Jan Boman,

The wrench of Fuglesang and encoun-

ters in space (Swedish) .

Fuglesang is the ﬁrst Swedish astronaut

and his space-walk attracted a lot of at-

tention in Swedish media. In particular-

ly it was rumoured that he dropped his

wrench during the walk, and specula-

tion was rife whether it would return

to the space ship after having circled

the Earth. In the article this question

is investigated in detail through celes-

tial mechanics with pertubation theory.

Furthermore it discusses how marginal

the inﬂuence of distant bodies such as

the Moon and the Sun would be on the

problem. The conclusion is that it is

highly unlikely that the tool would pass

suﬃciently close to the space ship after

completing an orbit for it to be possible

to retrieve it.

Bengt Ulin, Triangles of the same cir-

cumference and area (Swedish).

Triangles up to congruence form a 3-

dimensional space, and specifying cir-

cumference and area means ﬁxing two

parameters. One hence expects to ﬁnd a

1-dimensional family. In the article this

is approached from a classical perspec-

tive with explicit calculations of examp-

les. One also notes that for right-angled

triangles the conditions uniquely deter-

mine the triangle, while there will be

two isocles triangles with speciﬁed cir-

cumference and area, one of which has

an angle in excess of sixty degrees. In

the degenerate case, the speciﬁcations

determine the equilateral triangle.