The ESA mission BepiColombo will explore the planet Mercury with equipment allowing an extremely accurate tracking. While determining its orbit around Mercury, it will be possible to indirectly observe the motion of its center of mass, with an accuracy several orders of magnitude better than what is possible by radar ranging to the planet's surface. This is an opportunity to conduct a relativity experiment which will be a modern version of the traditional tests of general relativity, based upon Mercury's perihelion advance and the relativistic light propagation near the Sun. We define the mathematical methods to be used to extract from the data of the BepiColombo mission, as presently designed, the best constraints on the main post-Newtonian parameters, especially ,␥ and the Nordtvedt parameter , but also the dynamic oblateness of the Sun J 2᭪ and the preferred frame parameters ␣ 1 ,␣ 2 . We have performed a full cycle simulation of the BepiColombo radio science experiments, including this relativity experiment, with the purpose of assessing in a realistic ͑as opposed to formal͒ way the accuracy achievable on each parameter of interest. For ␥ the best constraint can be obtained by means of a dedicated superior conjunction experiment, with a realistic accuracy Ӎ2ϫ10 Ϫ6 . For  the main problem is the very strong correlation with J 2᭪ ; if the Nordtvedt relationship ϭ4Ϫ␥Ϫ3 is used, as it is legitimate in the metric theories of gravitation, a realistic accuracy of Ӎ2ϫ10 Ϫ6 for  and Ӎ2ϫ10 Ϫ9 for J 2᭪ can be achieved, while itself is constrained within Ӎ10 Ϫ5 . If the preferred frame parameters ␣ 1 ,␣ 2 are included in the analysis, they can be constrained within Ӎ8ϫ10 Ϫ6 and Ӎ10 Ϫ6 , respectively, at the price of some degradation in , J 2᭪ and . It is also possible to test the change with time of the gravitational constant G, but the results are severely limited because of the problems of absolute calibration of the ranging transponder, to the point that the improvement as compared with other techniques ͑such as lunar laser ranging͒ is not so important.
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.
We show that the number of solutions of a nonlinear elliptic problem on a Riemannian manifold depends on the topological properties of the manifold. In particular we consider the Lustemik-Schnirelmann category and the Pomcare polynomial of the manifold
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the $\alpha$-continued fraction transformations $T_\alpha$ and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results about the real slice of the Mandelbrot set, and the set of univoque numbers
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.