Borelli’s edition of books V–VII of Apollonius’s Conics,and Lemma 12 in Newton’s Principia

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia.

     

Pasquale del Pezzo, Duke of Caianello, Neapolitan mathematician

This article is dedicated to a reconstruction of some events and achievements, both personal and scientific, in the life of the Neapolitan mathematician Pasquale del Pezzo, Duke of Caianello.     

A class of periodic trend models for seasonal time series

Trend and seasonality are the most prominent features of economic time series that are observed at the subannual frequency. Modeling these components serves a variety of analytical purposes, including seasonal adjustment and forecasting. In this paper we introduce unobserved components models for which both the trend and seasonal components arise from systematically sampling a multivariate transition equation, according to which each season evolves as a random walk with a drift. By modeling the disturbance covariance matrix we can encompass traditional models for seasonal time series, like the basic structural model, and can formulate more elaborate ones, dealing with season specific features, such as seasonal heterogeneity and correlation, along with the different role of the nonstationary cycles defined at the fundamental and the harmonic frequencies in determining the shape of the seasonal pattern.     

Effect of liver damage by thioacetamide on microsomal aromatization of testosterone in rats (author's transl)]

Rat liver microsomes, NADPH-regenerating system, and 1beta, 2beta-3H-testosterone have been incubated in vitro. The loss of tritium from the steroid, associated with aromatization of testosterone, was linear with time for 20 min and required NADPH. Pre-treatment of the rats with thioacetamide raised the liberation of tritium from 1beta, 2beta-3H-testosterone. The results suggest that liver damage by thioacetamide in rats may give rise to increased aromatization of testosterone.     

Chicken genomics: feather-pecking and victim pigmentation

Feather-pecking in domestic birds is associated with cannibalism and severe welfare problems. It is a dramatic example of a spiteful behaviour in which the victim's fitness is reduced for no immediate direct benefit to the perpetrator and its evolution is unexplained. Here we show that the plumage pigmentation of a chicken may predispose it to become a victim: birds suffer more drastic feather-pecking when the colour of their plumage is due to the expression of a wild recessive allele at PMEL17, a gene that controls plumage melanization, and when these birds are relatively common in a flock. These findings, obtained using an intercross between a domestic fowl and its wild ancestor, have implications for the welfare of domestic species and offer insight into the genetic changes associated with the evolution of feather-pecking during the early stages of domestication.     

Compact sources as the origin of the soft gamma-ray emission of the Milky Way

The Milky Way is known to be an abundant source of gamma-ray photons, now determined to be mainly diffuse in nature and resulting from interstellar processes. In the soft gamma-ray domain, point sources are expected to dominate, but the lack of sensitive high-resolution observations did not allow for a clear estimate of the contribution from such sources. Even the best imaging experiment revealed only a few point sources, accounting for about 50% of the total Galactic flux. Theoretical studies were unable to explain the remaining intense diffuse emission. Investigating the origin of the soft gamma-rays is therefore necessary to determine the dominant particle acceleration processes and to gain insights into the physical and chemical equilibrium of the interstellar medium. Here we report observations in the soft gamma-ray domain that reveal numerous compact sources. We show that these sources account for the entirety of the Milky Way's emission in soft gamma-rays, leaving at most a minor role for diffuse processes.     

Metabolism of amphibian spermatozoa in relation to their motility

Summary Bufo arenarum spermatozoa were able to sustain motility both under aerobic and anaerobic conditions. In aerobiosis, the oxygen consumption varies between 2.6 and 4.2 l O₂/10⁸ cells/h at 30°C. The synthesis of lactic acid by anaerobic spermatozoa demonstrated the existence of an active glycolytic pathway.This work was supported by the Consejo Nacional de Investigaciones Científicas y Técnicas and the Latinoamerican Program of Human Reproduction (PLAMIRH), grant 34-95-2-75.     

Seasonal heteroscedasticity and trends

This paper discusses the possibility of accommodating features such as seasonal heteroscedasticity and trends in a seasonal model. The former takes place when one or more seasonal effects are more variable than others and it is quite pervasive in hydrology, although interesting examples are found in economics, where it has recently been shown to characterize the output of the manufacturing series; seasonal trends occur when the seasonal effect shows a systematic tendency to increase or decrease its amplitude over the years. We consider different models of seasonality available in the literature and we argue that the Harrison and Stevens seasonal model enhances the flexibility that is necessary to capture effects associated to particular seasons. The resulting seasonally heteroscedastic model provides an explanation for the periodicity in the series alternative to that provided by the literature on periodic integration. © 1998 John Wiley & Sons, Ltd.