## Preprints (rote Reihe) des Fachbereich Mathematik

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- average density (3)
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- lacunarity distribution (2)
- occupation measure (2)
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In this paper we show that for each prime p=7 there exists a translation plane of order p^2 of Mason-Ostrom type. These planes occur as 6-dimensional ovoids being projections of the 8-dimensional binary ovoids of Conway, Kleidman and Wilson. In order to verify the existence of such projections we prove certain properties of two particular quadratic forms using classical methods form number theory.

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An a posteriori stopping rule connected with monitoringthe norm of second residual is introduced forBrakhage's implicit nonstationary iteration method, applied to ill-posed problems involving linear operatorswith closed range. It is also shown that for someclasses of equations with such operators the algorithmconsisting in combination of Brakhage's method withsome new discretization scheme is order optimal in the sense of Information Complexity.

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Caloric Restriction (CR) is the only intervention proven to retard aging and extend maximum lifespan in mammalians. A possible mechanism for the beneficial effects of CR is that the mild metabolic stress associated with CR induces cells to express stress proteins that increase their resistance to disease processes. In this article we therefore model the retardation of aging by dietary restriction within a mathematical framework. The resulting model comprises food intake, stress proteins, body growth and survival. We successfully applied our model to growth and survival data of mice exposed to different food levels.

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It is proved that if a finite non-trivial quasi-order is nota linear order then there exist continuum many clones, whichconsist of functions preserving the quasi-order and containall unary functions with this property. It is shown that, fora linear order on a three-element set, there are only 7 suchclones