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On the present work it is presented a new category of continued fraction functions (CFF) of a real variable $$\lambda$$ , named “the $$\epsilon$$ class”, such that $$\lambda$$ enters in the CFF through small or infinitesimal contributions in the partial quotients. These CFF emerge on the secular equation of the Sturm–Liouville equation (SLE) by a finite difference treatment. Also, it was obtained the eigenvalues of the one-dimensional Schrodinger equation (a particular case of SLE) from the CFF secular equation. The case of the two-dimensional Schrodinger equation was partially studied.

Essential oils are complex mixtures of organic substances with large commercial importance in the pharmaceutical, food, fragrance, and cosmetic industries due to their organoleptic and biological properties. Also, these materials are also luminescent what has taken several studies about its potential uses for the detection and quality control of essential oils, imaging, and for the investigation of the synergies of their constituents. Concerning this, the present work is dedicated to studying the optical properties of selected essential oils: citronella ( Cymbopogon winterianus), Japanese mint ( Mentha arvensis), clove bud ( Syzygium aromaticum), and bergamot ( Citrus bergamia). We carried out a comparative study of the photoluminescence and the ultraviolet–visible optical absorption (abs-UV–Vis) of these essential oils with their typical constituents. To inspect the effects of the intermolecular interactions on the optical response of these systems, mixtures between the essential oils constituents following the expected average percent mass fraction were also studied. From these experiments, the main results were bathochromic effects in the abs-UV–Vis spectra; excimer formation in citral, isopulegol, isomenthone, eugenol, and eugenyl acetate; excimer emission enhancing and specific solvent effect in the essential oils photoluminescence spectra. These results contribute to the knowledge of essential oils’ applications, especially in the evaluation of components’ interactions through a simple abs-UV–Vis assay.

As is well known, the heat exchange between bodies at different temperatures enclosured at vacuum without thermal contact can be described by the Stefan–Boltzmann law of radiation, where each body receives a fraction of radiant heat from the others depending on their distances and individual temperatures, geometrical shapes, emissivities, and absorptivities. However, when these bodies are surrounded by a gaseous atmosphere conductive and convective phenomena enter on the scenario, leading to a complex mechanism of heat exchange. Here, we study an experimental realization of such situation for two bodies employing a kind of vacuum gauge, on a range of surrounding air pressure between 26 and 1035 mbar, and analyze the heat exchange on the framework of Stefan–Boltzmann law. It is verified empirically that the ratio between the thermal power irradiated by the bodies is independent on their individual heat radiances, and depends only on the surrounding gas pressure.

Here we study the convergence of numeric solutions for the one-dimensional Schrodinger–Poisson problem for electrons confined into a semiconductor quantum well structure. One kind of algorithm that is largely used is based on a simple iterative procedure that is finished when the solution is achieved when particular parameter (for example, an energy) converges. There is also the possibility of the employ of a mixing parameter to control the variation of a particular parameter of the system, or to fix the number of iterations while a particular parameter of the system is gradually increased (for example, the electron density). We show that the two latter algorithms are capable of solving the problem for a wider class of situations if compared to the former iterative without mixing, without significant loss of precision.

Here we present the results of magneto resistance measurements in tilted magnetic field and compare them with calculations. The comparison between calculated and measured spectra for the case of perpendicular fields enable us to estimate the dependence of the valley splitting as a function of the magnetic field and the total Landé g -factor (which is assumed to be independent of the magnetic field). Since both the exchange contribution to the Zeeman splitting as well as the valley splitting are properties associated with the 2D quantum confinement, they depend only on the perpendicular component of the magnetic field, while the bare Zeeman splitting depends on the total magnetic field. This information aided by the comparison between experimental and calculated gray scale maps permits to obtain separately the values of the exchange and the bare contribution to the g -factor.

Parabolic quantum wells (PQWs) have been studied by temperature dependent photoluminescence (PL). Two kind of samples have been studied. Concerning the undoped sample, the dominant luminescences were the bulk GaAs and the fundamental transition of the PQW. The evolution on temperature of the energy position of both PL emissions follows the well known Varshing formula. For the doped samples strong radiative recombination of the electron gas with photogenerated holes was observed. At low temperature strong Fermi level enhancement occurs in the luminescence as a result of the multi-electron-hole scattering, which is smear out increasing the temperature. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this article we investigated structural and vibrational properties of an amorphous alloy of the In-Se system. The amorphous InSe9 alloy was produced by mechanical alloying and it was studied using Raman spectroscopy and extended X-ray absorption fine structure spectroscopy techniques, and from them several properties, such as vibrational modes, average coordination numbers and interatomic distances, structural and thermal disorders, assymetry of the partial distribution functions g ij (r), thermal expansions and Einstein temperatures were determined and compared to the values found in other alloys of the In-Se system. This comparison indicated some important differences among our alloy produced by mechanical alloying and alloys produced by other techniques, which is a clear indication of the influence of the fabrication technique in their physical properties. The main differences occur in the vibrational spectrum, with the presence of new vibrational modes, and in the structure, since Se-Se pairs are found in a higher quantity than in other In-Se alloys.

Mn ions were implanted in p-type cubic GaN at doses from 0.6 to 2.4×1016cm−2 at 200 keV energy. A 200-nm-thick epitaxial layer, grown by molecular beam epitaxy on GaAs(001) substrate, is used for the Mn implantation. The Mn implanted samples were subjected to an annealing at 950 °C for 1–5 min. The structural quality of the samples was investigated by high resolution x-ray diffraction and Raman spectroscopy. The annealing procedure leads to a significant increasing of the crystalline quality of the samples. Hysteresis loops were observed for all cubic GaMnN annealed samples and ferromagnetism was detected up to room temperature.

Photoluminescence measurements at different temperatures have been performed to investigate the optical response of a two-dimensional electron gas in n-type wide parabolic quantum wells. A series of samples with different well widths in the range of 1000–3000A was analyzed. Many-body effects, usually observed in the recombination process of a two-dimensional electron gas, appear as a strong enhancement in the photoluminescence spectra at the Fermi level at low temperature only in the thinnest parabolic quantum wells. The suppression of the many-body effect in the thicker quantum wells was attributed to the decrease of the overlap between the wavefunctions of the photocreated holes and the two-dimensional electrons belonging to the highest occupied electron subband.