Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

Increased risk of malignant mesothelioma of the pleura after residential or domestic exposure to asbestos: a case-control study in Casale Monferrato, Italy.

The association of malignant mesothelioma (MM) and nonoccupational asbestos exposure is currently debated. Our study investigates environmental and domestic asbestos exposure in the city where the largest Italian asbestos cement (AC) factory was located. This population-based case-control study included pleural MM (histologically diagnosed) incidents in the area in 1987-1993, matched by age and sex to two controls (four if younger than 60). Diagnoses were confirmed by a panel of five pathologists. We interviewed 102 cases and 273 controls in 1993-1995, out of 116 and 330 eligible subjects. Information was checked and completed on the basis of factory and Town Office files. We adjusted analyses for occupational exposure in the AC industry. In the town there were no other relevant industrial sources of asbestos exposure. Twenty-three cases and 20 controls lived with an AC worker [odds ratio (OR) = 4.5; 95% confidence interval (CI), 1.8-11.1)]. The risk was higher for the offspring of AC workers (OR = 7.4; 95% CI, 1.9-28.1). Subjects attending grammar school in Casale also showed an increased risk (OR = 3.3; 95% CI, 1.4-7.7). Living in Casale was associated with a very high risk (after selecting out AC workers: OR = 20.6; 95% CI, 6.2-68.6), with spatial trend with increasing distance from the AC factory. The present work confirms the association of environmental asbestos exposure and pleural MM, controlling for other sources of asbestos exposure, and suggests that environmental exposure caused a greater risk than domestic exposure

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte

Multicentric study on malignant pleural mesothelioma and non-occupational exposure to asbestos

Insufficient evidence exists on the risk of pleural mesothelioma from non-occupational exposure to asbestos. A population-based case–control study was carried out in six areas from Italy, Spain and Switzerland. Information was collected for 215 new histologically confirmed cases and 448 controls. A panel of industrial hygienists assessed asbestos exposure separately for occupational, domestic and environmental sources. Classification of domestic and environmental exposure was based on a complete residential history, presence and use of asbestos at home, asbestos industrial activities in the surrounding area, and their distance from the dwelling. In 53 cases and 232 controls without evidence of occupational exposure to asbestos, moderate or high probability of domestic exposure was associated with an increased risk adjusted by age and sex: odds ratio (OR) 4.81, 95% confidence interval (CI) 1.8–13.1. This corresponds to three situations: cleaning asbestos-contaminated clothes, handling asbestos material and presence of asbestos material susceptible to damage. The estimated OR for high probability of environmental exposure (living within 2000 m of asbestos mines, asbestos cement plants, asbestos textiles, shipyards, or brakes factories) was 11.5 (95% CI 3.5–38.2). Living between 2000 and 5000 m from asbestos industries or within 500 m of industries using asbestos could also be associated with an increased risk. A dose–response pattern appeared with intensity of both sources of exposure. It is suggested that low-dose exposure to asbestos at home or in the general environment carries a measurable risk of malignant pleural mesothelioma. © 2000 Cancer Research Campaig

Multipulse phases in k-mixtures of Bose-Einstein condensates

For a competitive system of k coupled nonlinear Schroedinger equations we prove the existence, when the competition parameter is large, of positive radial solutions on R^N. We show that, when the competition parameter goes to infinity, the profile of each component separates, in many pulses, from the others. Moreover, we can prescribe the location of such pulses in terms of the oscillations of the changing-sign solutions of the scalar nonlinear Schroedinger equation. Within an Hartree-Fock approximation, this provides a theoretical indication of phase separation into many nodal domains for the k-mixtures of Bose-Einstein condensates.Comment: 21 page

Spatial clustering of childhood leukaemia: summary results from the EUROCLUS project.

The interpretation of reports of clusters of childhood leukaemia is difficult, first because little is known about the causes of the disease, and second because there is insufficient information on whether cases show a generalized tendency to cluster geographically. The EUROCLUS project is a European collaborative study whose primary objective is to determine whether the residence locations of cases at diagnosis show a general tendency towards spatial clustering. The second objective is to interpret any patterns observed and, in particular, to see if clustering can be explained in terms of either infectious agents or environmental hazards as aetiological agents. The spatial distribution of 13351 cases of childhood leukaemia diagnosed in 17 countries between 1980 and 1989 has been analysed using the Potthoff-Whittinghill method. The overall results show statistically significant evidence of clustering of total childhood leukaemia within small census areas (P=0.03) but the magnitude of the clustering is small (extra-Poisson component of variance (%) = 1.7 with 90% confidence interval 0.2-3.1). The clustering is most marked in areas that have intermediate population density (150-499 persons km[-2]). It cannot be attributed to any specific age group at diagnosis or cell type and involves spatial aggregation of cases of different ages and cell types. The results indicate that intense clusters are a rare phenomenon that merit careful investigation, although aetiological insights are more likely to come from investigation of large numbers of cases. We present a method for detecting clustering that is simple and readily available to cancer registries and similar groups