Some homoclinic phenomena in the three-body problem

We prove the existence of transversal homoclinic points in the collinear three-body problem, restricted and general, and in the planar circular restricted three-body problem. As a consequence the shift of Bernoulli is proved to be included as a subsystem of a suitable section of the flow for the three cases studied. Then the existence of all the possible types of final evolution follows.     

A Set of Methods in Transportation Network Synthesis and Analysis

This paper deals with the problem of modifying a transportation network so as to fit it with existing demand. A set of procedures were applied to the replanning of medium-sized town bus routes in several case-studies; the chosen approach, which is the result of five years research applied in about 10 towns in France, is described and results are presented and discussed for two cases.     

Quadratic systems with a rational first integral of degree 2: A complete classification in the coefficient space $$\mathbb{R}^{12} $$

A quadratic polynomial differential system can be identified with a single point of through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of having a rational first integral of degree 2. We show that there are only 24 topologically different phase portraits in the Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide a unique representative of every class modulo an affine change of variables and a rescalling of the time variable. Moreover, each one of these 24 representatives is determined by a set of invariant conditions and each respective first integral is given in invariant form directly in The authors are partially supported by a MEC/FEDER grant MTM2005-06098-C02-01, and a CONACIT grant number 2005SGR-00550. Partially supported by CRDF-MRDA CERIM-1006-06     

Solvent effect in the Walden inversion reactions

The solvent effect on the fluoride exchange reaction has been studied by means of ab initio calculations using the 3-21G basis set. It is shown that the motion of the solvent molecules is an important part of the reaction coordinate.     

Mixed fluoroamine complexes of chromium(III)

Summary Mixed difluoro(diamine)(diamme)chromium(III) complexes have been synthesized with ethylenediamine (en), 1,3 propanediamine(tn) and 1,2-cyclohexanediamine(chxn):trans-[CrF₂(aa)(bb)]Br (aa=en, bb=tn; aa=tn, bb= chxn) andcis-[CrF₂(aa)(bb)]Br (aa=en, bb=chxn). The corresponding fluoroaqua(diamine) (diamine)chromium(III) complexes have been prepared by acid hydrolysis as perchlorate or iodide salts. All have been characterized by chemical analysis, electronic and i.r. spectra and conductivity measurements.