The Mathematics of Lars Valerian Ahlfors

Some Geometric Aspects of the Work of

Let me begin with a personal reminiscence of Lars Ahlfors. My rst contact with him came when he was my undergraduate advisor at Harvard. It was the advisor's job to review and approve the courses that the student had selected. When I entered his ooce and handed him my study card, he looked it over quickly, said \You seem to know what you are doing," and signed the card. This was the only advice...

The Length-area Method and Discrete Riemann Mappings

J.R.R. Tolkien, author of The Hobbit and The Lord of the Rings, despaired of interruptions that took him away from his work. It’s not so much the interruptions alone, he said, as the fear of interruptions. We all have our tricks to find uninterrupted hours for mathematics. When I was in Wisconsin it got really cold during the winter and it stayed really cold. The way I found uninterrupted time ...

Generation of the Ahlfors Five Islands Theorem

Ahlfors’ contribution to the theory of meromorphic functions

This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. This article is an exposition for non-specialists of Ahlfors’ work in the theory of meromorphic functions. When the domain is not specified we mean meromorphic functions in the complex plane C. The theory of meromorphic functions probably begins with t...

Effect of Valerian on Sleep Disorder in Postmenopausal Women: A Systematic Review

Introduction: Menopause-related sleep problems do not necessarily affect the amount of sleep but also the quality of sleep. The most likely mechanism of action of valerian on sleep is its effect on GABA receptors. The aim of this study was to summarize the results of clinical trials on the effect of valerian on sleep disorders in postmenopausal women by systematic review. Materials and Methods...