Some Problems on the Classical N-Body Problem

Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects such as central configurations, stability of relative equilibrium, singularities, integral manifolds, etc. Following Steve Smale in his list, the criteria for our selection are: (1) Simple statement. Also preferably mathematically precise, and best even with a yes or no answer. (2) Personal acquaintance with the problem, having found it not easy. (3) A belief that the question, its solution, partial results or even attempts at its solution are likely to have great importance for the development of the mathematical aspects of Celestial Mechanics.Comment: 10 pages, list of mathematical problem

Spectroscopic binaries in the Solar Twin Planet Search program: from substellar-mass to M dwarf companions

Previous studies on the rotation of Sun-like stars revealed that the rotational rates of young stars converge towards a well-defined evolution that follows a power-law decay. It seems, however, that some binary stars do not obey this relation, often by displaying enhanced rotational rates and activity. In the Solar Twin Planet Search program we observed several solar twin binaries, and found a multiplicity fraction of $42\% \pm 6\%$ in the whole sample; moreover, at least three of these binaries (HIP 19911, HIP 67620 and HIP 103983) clearly exhibit the aforementioned anomalies. We investigated the configuration of the binaries in the program, and discovered new companions for HIP 6407, HIP 54582, HIP 62039 and HIP 30037, of which the latter is orbited by a $0.06$ M$_\odot$ brown dwarf in a 1-month long orbit. We report the orbital parameters of the systems with well-sampled orbits and, in addition, the lower limits of parameters for the companions that only display a curvature in their radial velocities. For the linear trend binaries, we report an estimate of the masses of their companions when their observed separation is available, and a minimum mass otherwise. We conclude that solar twin binaries with low-mass stellar companions at moderate orbital periods do not display signs of a distinct rotational evolution when compared to single stars. We confirm that the three peculiar stars are double-lined binaries, and that their companions are polluting their spectra, which explains the observed anomalies.Comment: 13 pages, 7 figures, accepted for publication in MNRA

Beneficial effects of the ethanol extract of Caesalpinia pyramidalis on the inflammatory response and abdominal hyperalgesia in rats with acute pancreatitis

AbstractEthnopharmacological relevanceCaesalpinia pyramidalis Tul. (Fabaceae) is a plant found in the Northeast of Brazil that is popularly used to treat inflammation. Acute pancreatitis (AP) is an inflammatory disease for which abdominal pain is a relevant symptom. As there is no specific therapy for AP, we investigated the effect of the ethanol extract from the inner bark of C. pyramidalis (EECp) on the AP induced by common bile duct obstruction (CBDO) in rats.Material and methodsAP was induced in male Wistar rats (200–250g, n=6–8) through laparotomy and subsequent CBDO. Animals were euthanized after 6 (G6h) or 24h (G24h) of induction. In the G6h protocol, animals were pretreated with EECp (100–400mg/kg, p.o.) or vehicle (Tween 80; 0.2%) 1h before CBDO or sham surgery. For the G24h protocol, rats were pretreated with EECp (400mg/kg, 1h before CBDO or 1h before and 12h after CBDO) or vehicle. The following parameters were measured: inflammatory/oxidative (myeloperoxidase activity and malondialdehyde formation in the pancreas and lung, leukocyte counts in the blood and serum nitrate/nitrite), enzymatic (serum amylase and lipase levels) and nociceptive (abdominal hyperalgesia).ResultsInduction of AP by CBDO significantly increased all the parameters evaluated in both G6h and G24h protocols when compared with the respective sham group. In the G6h protocol, the EECp pretreatment (400mg/kg) significantly reduced all these parameters, besides completely inhibiting abdominal hyperalgesia. The same profile of reduction was observed from two administrations of EECp in the G24h protocol, while one single dose of EECp was able to significantly reduce pancreatic MDA, serum lipase levels, leukocyte counts in the blood and abdominal hyperalgesia without affecting the other parameters in the G24h protocol. Furthermore, rutin was found in the EECp.ConclusionsOur results demonstrated that EECp decreases inflammation, lipoperoxidation and hyperalgesia in CBDO-induced AP, making it of interest in future approaches to treat this condition

On the Double Planet System Around HD 83443

The Geneva group has reported two Saturn-mass planets orbiting HD 83443 (K0V) with periods of 2.98 and 29.8 d. The two planets have raised interest in their dynamics because of the possible 10:1 orbital resonance and the strong gravitational interactions. We report precise Doppler measurements of HD 83443 obtained with the Keck/HIRES and the AAT/UCLES spectrometers. These measurements strongly confirm the inner planet with period of 2.985 d, with orbital parameters in very good agreement with those of the Geneva group. However these Doppler measurements show no evidence of the outer planet, at thresholds of 1/4 (3 m/s) of the reported velocity amplitude of 13.8 m/s. Thus, the existence of the outer planet is in question. Indeed, the current Doppler measurements reveal no evidence of any second planet with periods less than a year.Comment: 26 pages incl. 3 tables and 8 figures; uses AASTE

A Keck/HIRES Doppler Search for Planets Orbiting Metal-Poor Dwarfs. I. Testing Giant Planet Formation and Migration Scenarios

We describe a high-precision Doppler search for giant planets orbiting a well-defined sample of metal-poor dwarfs in the field. This experiment constitutes a fundamental test of theoretical predictions which will help discriminate between proposed giant planet formation and migration models. We present here details on the survey as well as an overall assessment of the quality of our measurements, making use of the results for the stars that show no significant velocity variation.Comment: 25 pages, 7 figures, accepted for publication in the Astrophysical Journa

Pressure-induced collapsed-tetragonal phase in SrCo2As2

We present high-energy x-ray diffraction data under applied pressures up to p = 29 GPa, neutron diffraction measurements up to p = 1.1 GPa, and electrical resistance measurements up to p = 5.9 GPa, on SrCo2As2. Our x-ray diffraction data demonstrate that there is a first-order transition between the tetragonal (T) and collapsed-tetragonal (cT) phases, with an onset above approximately 6 GPa at T = 7 K. The pressure for the onset of the cT phase and the range of coexistence between the T and cT phases appears to be nearly temperature independent. The compressibility along the a-axis is the same for the T and cT phases whereas, along the c-axis, the cT phase is significantly stiffer, which may be due to the formation of an As-As bond in the cT phase. Our resistivity measurements found no evidence of superconductivity in SrCo2As2 for p <= 5.9 GPa and T >= 1.8 K. The resistivity data also show signatures consistent with a pressure-induced phase transition for p >= 5.5 GPa. Single-crystal neutron diffraction measurements performed up to 1.1 GPa in the T phase found no evidence of stripe-type or A-type antiferromagnetic ordering down to 10 K. Spin-polarized total-energy calculations demonstrate that the cT phase is the stable phase at high pressure with a c/a ratio of 2.54. Furthermore, these calculations indicate that the cT phase of SrCo2As2 should manifest either A-type antiferromagnetic or ferromagnetic order.Comment: 6 pages, 5 figure