<p style='text-indent:20px;'>We present a generalization of the most usual symmetries in differential equations known as time-reversibility and equivariance ones. We check that typical properties are also valid for new definition unifies both. With it, we able to families planar polynomial vector fields having equilibrium points center type. Moreover, provide highest lower bound local cyc...

The oxygen-deficient layered perovskite YBaCuFeO5 (YBCFO) is a rare type-II multiferroic material where ferroelectricity, driven by incommensurate spiral magnetic order, believed to be achievable up temperatures higher than room temperature. A cycloidal order rather helical an essential ingredient for the existence of ferroelectricity in this material. Motivated recent experimental study on Mn-...

In this paper orbital stability of solutions of weakly coupled nonlinear Schrödinger equations is studied. It is proved that ground state solutions-scalar or vector ones-are orbitally stable, while bound states with Morse index strictly greater than one are not stable. Moreover, an instability result for large exponent in the nonlinearity is presented.

[1] The accuracy of geologic chronologies can, in principle, be improved through orbital tuning, the systematic adjustment of a chronology to bring the associated record into greater alignment with an orbitally derived signal. It would be useful to have a general test for the success of orbital tuning, and one proposal has been that eccentricity ought to covary with the amplitude envelope assoc...