An infinite-dimensional Evans function theory is developed for the elliptic eigenvalue problem associated with the stability of travelling solitary waves in a channel. Also, a bundle is constructed over the complex domain, so that its first Chern number gives the number of eigenvalues inside the domain.

In order to assess the involvement of aromatase CYP19 isoforms and endogenous sex steroids in gonadal sex differentiation and development of the Japanese fugu (Takifugu rubripes), an aromatase inhibitor (AI, fadrozole) was administered to developing fishes from the ‘first feeding’ till the 100th day after hatching. It was observed that ovarian cavity formation was inhibited by fadrozole at doses of 500 and 1000 µg/g diet, which was followed by testicular differentiation in all treated fugu. In the non-treated fugu, CYP19A was predominantly expressed in the ovary and CYP19B in the brain (in both sexes), although both were expressed interchangeably at low levels. An exceptionally high expression of CYP19B was also evident in testis throughout the study period. Both forms of CYP19 mRNA showed low levels of expression in brain and gonad with no significant differences between the two AI treatments. AI treatment inhibited CYP19A mRNA in trunk during the crucial period of ovarian cavity formation and CYP19B in gonad and brain by the end of gonadal sex differentiation. An elevation of testosterone and 11-ketotestosterone was observed which can be associated with the down-regulation of the circulating 17β-estradiol production during the AI treatment period. After stopping AI treatment, both circulating estrogen and androgen were normalized. The current results suggest that suppression of CYP19A before and during morphological sex differentiation inhibits ovarian cavity formation in fugu. Furthermore, non-detectable limits of 17β-estradiol and high testosterone levels by the end of the gonadal differentiation period can be ascribed to inhibition of CYP19B, suggesting that conversion of 17β-estradiol from testosterone is plausibly regulated by CYP19B, and that this factor (CYP19B) may play an important role in AI-induced testicular development after gonadal sex differentiation through regulation of the testosterone–17β-estradiol balance in fugu.

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