Relative equilibria of four identical satellites

We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the limit when m/M -> 0. In some cases two small bodies will coalesce at the limit. We call the other equilibria the relative equilibria of four separate identical satellites. We prove rigorously that there are only three such equilibria, all already known after the numerical researches in [SaY]. Our main contribution is to prove that any equilibrium configuration possesses a symmetry, a statement indicated in [CLO2] as the missing key to proving that there is no other equilibrium.Comment: 16 pages, 2 figure

Some remarks about Descartes' rule of signs

What can we deduce about the roots of a real polynomial in one variable by simply considering the signs of its coefficients? On one hand, we give a complete answer concerning the positive roots, by proposing a statement of Descartes' rule of signs which strengthens the available ones while remaining as elementary and concise as the original. On the other hand, we provide new kinds of restrictions on the combined numbers of positive and negative roots.Comment: 10 page

Symmetry of Planar Four-Body Convex Central Configurations

International audienceWe study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles

The Empirical Mass-Luminosity Relation for Low Mass Stars

This work is devoted to improving empirical mass-luminosity relations and mass-metallicity-luminosity relation for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the mass-luminosity relation. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28 to 0.50 solar mass. Three-piecewise continuous improved mass-luminosity relations in K, J, H and V bands, respectively, are obtained. The visual mass-metallicity-luminosity relation is also improved based on our K band mass-luminosity relation and the available observational metallicity data.Comment: 8 pages, 2 figures. Accepted for publication in Astrophysics & Space Scienc

Robust Automatic Target Recognition Algorithm for Large-Scene SAR Images and Its Adaptability Analysis on Speckle

Aiming at the multiple target recognition problems in large-scene SAR image with strong speckle, a robust full-process method from target detection, feature extraction to target recognition is studied in this paper. By introducing a simple 8-neighborhood orthogonal basis, a local multiscale decomposition method from the center of gravity of the target is presented. Using this method, an image can be processed with a multilevel sampling filter and the target’s multiscale features in eight directions and one low frequency filtering feature can be derived directly by the key pixels sampling. At the same time, a recognition algorithm organically integrating the local multiscale features and the multiscale wavelet kernel classifier is studied, which realizes the quick classification with robustness and high accuracy for multiclass image targets. The results of classification and adaptability analysis on speckle show that the robust algorithm is effective not only for the MSTAR (Moving and Stationary Target Automatic Recognition) target chips but also for the automatic target recognition of multiclass/multitarget in large-scene SAR image with strong speckle; meanwhile, the method has good robustness to target’s rotation and scale transformation.</jats:p

Simulation study of asteroid mass determination using CSST asteroid observations

The objective of this study is to explore the potential of the Chinese Space Station Telescope (CSST) in asteroid mass determination with asteroid-asteroid close encounters. The CSST is expected to observe some asteroids with an accuracy of several milliarcseconds and has a limiting magnitude of 26 (AB mag) or higher in the g and r bands. By combining CSST observations with existing ground-based observations, significant improvements in asteroid mass precision can be achieved. To quantify the CSST’s capability in asteroid mass determination, three types of simulations are conducted. In Type A simulation, 58 close encounters with available Gaia DR2 observations were considered, assuming CSST observes asteroids at a frequency similar to Gaia’s. After using the simulated CSST observations, asteroid mass precision is improved substantially. In seven events, the determined precision are better than 5%. Type B simulation is performed based on a tentative optical survey plan of CSST, but the limited opportunities to observe asteroids involved in a close encounter with strong perturbation from to-be-determined masses. As a result, the precision of mass determination is low, though the improvement brought by CSST data is obvious. This implies that the dedicated observations are necessary for CSST to contribute masses with high precision. Type C simulation is performed with a small amount of CSST observing time, to be specific for a strong encounter, 144 observations spanning 3 years centered at the encounter time, totaling about 7.2 observation hours. In this case, CSST can determine a number of asteroid masses, of which 10 asteroid’s precision are expected to be better than 10%

Inflammation-related collagen fibril destruction contributes to temporomandibular joint disc displacement via NF-κB activation

Temporomandibular joint (TMJ) disc displacement is one of the most significant subtypes of temporomandibular joint disorders, but its etiology and mechanism are poorly understood. In this study, we elucidated the mechanisms by which destruction of inflamed collagen fibrils induces alterations in the mechanical properties and positioning of the TMJ disc. By constructing a rat model of TMJ arthritis, we observed anteriorly dislocated TMJ discs with aggravated deformity in vivo from five weeks to six months after a local injection of Freund’s complete adjuvant. By mimicking inflammatory conditions with interleukin-1 beta in vitro, we observed enhanced expression of collagen-synthesis markers in primary TMJ disc cells cultured in a conventional two-dimensional environment. In contrast, three-dimensional (3D)-cultivated disc cell sheets demonstrated the disordered assembly of inflamed collagen fibrils, inappropriate arrangement, and decreased Young’s modulus. Mechanistically, inflammation-related activation of the nuclear factor kappa-B (NF-κB) pathway occurs during the progression of TMJ arthritis. NF-κB inhibition reduced the collagen fibril destruction in the inflamed disc cell sheets in vitro, and early NF-κB blockade alleviated collagen degeneration and dislocation of the TMJ discs in vivo. Therefore, the NF-κB pathway participates in the collagen remodeling in inflamed TMJ discs, offering a potential therapeutic target for disc displacement.</p