Approximately 20% of familial amyotrophic lateral sclerosis (FALS) arises from germ-line mutations in the superoxide dismutase-1 (SOD1) gene. However, the molecular mechanisms underlying the process have been elusive. Here, we show that a neuronal homologous to E6AP carboxyl terminus (HECT)-type ubiquitin-protein isopeptide ligase (NEDL1) physically binds… (More)
— This paper focuses on the nematode C. elegans, which has a relatively simple structure, and is one of the most analyzed organisms among multicellular ones. We aim to develop a mathematical model of this organism to analyze control mechanisms with respect to locomotion. First, a new motor control model of the C. elegans is proposed, which includes both of… (More)
A positive integer is called a (Ore's) harmonic number if its positive divisors have integral harmonic mean. Ore conjectured that every harmonic number greater than 1 is even. If Ore's conjecture is true, there exist no odd perfect numbers. In this paper, we prove that every odd harmonic number greater than 1 must be divisible by a prime greater than 10 5 .
It is proved that every odd perfect number is divisible by a prime greater than 10 7 .