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1.
We study quadrilateralsQ which are given by two intervals on {:Im = 0} and {:Im = 1}, and two Jordan arcs
1,
2, in {:0 Im 1} connecting these two intervals. Many practical problems require the determination of the modulem(Q) ofQ, but ifQ is long, i.e., if
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2.
A 2-periodic continuous real functionf is said to beperiodically monotone if it has the following property: there exist numbert
1t
2t
3t
1+2 such thatf is nonincreasing fort
1t
2 and nondecreasing int
2tt
3. For any 2-periodic, integrable real functiong with
0
2
|g(t|dt) we define
|