INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

The Effects of Prenatal Exposure to Altered Melatonin Levels on Hippocampal Gene Expression in the Male Rat

The stability of the circadian rhythm for mammals depends on the levels of serotonin and melatonin, neurohormones that signal for lightness and darkness, respectively. Disruption in the stability of neurohormones has been shown to be a critical factor in psychopathological disorders in humans. For example, altering levels of melatonin in utero through administration of melatonin or the melatonin receptor antagonist, luzindole, has been shown to cause changes in developmental growth and adult behavior in the male rat. Analysis of relative adult hippocampal gene expression with RT-PCR revealed differences in ARNTL expression that suggested abnormality in clock gene expression of the rats that were prenatally exposed to altered levels of melatonin. Differences in the degree of plasticity as suggested by previous behavior testing did not result in differences in gene expression for GABA receptors or NMDA receptors. Morevoer, growth associated protein 43, GAP-43, a protein that is necessary for neuronal growth cones as well as long term learning has been found to be critical for axon and presynaptic terminal formation and retention in other studies, but hippocampal gene expression in our study showed no significant alteration after exposure to various maternal melatonin levels. However, ARNTL is a key regulatory component of clock genes and the circadian cycle so that alterations in the expression of thi critical gene may lead to critical changes in neuronal growth and plasticity. Our data support the conclusion that the manipulation of maternal melatonin levels alters the brain development and the circadian cycles that may lead to physiological and behavioral abnormalities in adult offspring.