Exact solutions for a class of integrable Henon-Heiles-type systems

We study the exact solutions of a class of integrable Henon-Heiles-type systems (according to the analysis of Bountis et al. (1982)). These solutions are expressed in terms of two-dimensional Kleinian functions. Special periodic solutions are expressed in terms of the well-known Weierstrass function. We extend some of our results to a generalized Henon-Heiles-type system with n+1 degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy

The Cytotoxic Effects of Betulin-Conjugated Gold Nanoparticles as Stable Formulations in Normal and Melanoma Cells

Gold nanoparticles are currently investigated as theranostics tools in cancer therapy due to their proper biocompatibility and increased efficacy related to the ease to customize the surface properties and to conjugate other molecules. Betulin, [lup-20(29)-ene-3β, 28-diol], is a pentacyclic triterpene that has raised scientific interest due to its antiproliferative effect on several cancer types. Herein we described the synthesis of surface modified betulin-conjugated gold nanoparticles using a slightly modified Turkevich method. Transmission electron microscopy (TEM) imaging, dynamic light scattering (DLS), scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) were used for the characterization of obtained gold nanoparticles. Cytotoxic activity and apoptosis assessment were carried out using the MTT and Annexin V/PI apoptosis assays. The results showed that betulin coated gold nanoparticles presented a dose-dependent cytotoxic effect and induced apoptosis in all tested cell lines

Regularization of the circular restricted three-body problem using 'similar' coordinate systems

The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous paper (see \cite{rom11}). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function, we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered in the more massive and the less massive star of the binary system. The 'similar' polar angle's definition is introduced, in order to analyze the regularization's geometrical transformation. The effect of Levi-Civita's transformation is described in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically, for the Earth-Moon binary system.Comment: 24 pages, 7 figures; Accepted for publication in Astrophysics and Space Scienc

The zonal satellite problem. III Symmetries

The two-body problem associated with a force field described by a potential of the form U =Sum(k=1,n) ak/rk (r = distance between particles, ak = real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita’s coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure

Binary collisions in popovici’s photogravitational model

The dynamics of bodies under the combined action of the gravitational attraction and the radiative repelling force has large and deep implications in astronomy. In the 1920s, the Romanian astronomer Constantin Popovici proposed a modified photogravitational law (considered by other scientists too). This paper deals with the collisions of the two-body problem associated with Popovici’s model. Resorting to McGehee-type transformations of the second kind, we obtain regular equations of motion and define the collision manifold. The flow on this boundary manifold is wholly described. This allows to point out some important qualitative features of the collisional motion: existence of the black-hole effect, gradientlikeness of the flow on the collision manifold, regularizability of collisions under certain conditions. Some questions, coming from the comparison of Levi-Civita’s regularizing transformations and McGehee’s ones, are formulated