A generalized expression for the second hypervirial of an arbitrary hydrogenic radial function is obtained. We illustrate the power of this result showing that a general recurrence relation among hydrogenic matrix elements becomes a simple consequence of it. We also exhibit that a particular case of such a recurrence relation can be rederived employing the hypervirial theorem and the well known mapping between the Morse and the Coulomb problems.

When we talk about steganographic algorithms, it is imperative to study the quality of the image hosting and image retrieval, and is also necessary to consider the robustness of the algorithm. This paper presents the experimental results obtained by applying a steganographic algorithm to RGB images. The measures used are qualitative and quantitative related to the multichannel of Human Vision System. When this algorithm is employed we see that the numerical calculations performed by the computer cause errors and alterations in the images chosen, so we applied a scaling factor depending on the number of bits of the image to adjust these errors.

This article presents a generalization of the standard Darboux transform applied to Sturm–Liouville differential equations. This is achieved with the aid of an ansatz as a particular solution for the Riccati relationship involved, which in turn led us to obtain its generalized Darboux solution that contains, as a particular case, the standard Darboux transform. The proposed generalized Darboux transform (GDT), applied to the quantum mechanical field, gives the opportunity to prove the existence of standard and generalized Darboux potentials that match with the so-called isospectral potentials. This is exemplified by obtaining, through the GDT, a set of standard and generalized Darboux potentials that form the partner of the one-dimensional harmonic oscillator model for any quantum principal number. The worked example indicates how the GDT can be used to obtain the isospectral potentials associated to any known specific potential. We consider also the application of our method as proposed to the theory of solitons in order to show why the GDT will be important in other fields of application where the standard Darboux transform is usually concerned.

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