A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

A family of high algebraic order ten-step methods is obtained in this paper. The new developed methods have vanished phase-lag (the first one) and phase-lag and its first derivative (the second one). We apply the new developed methods to the resonance problem of the radial Schrödinger equation. The efficiency of the new proposed methods is shown via error analysis and numerical applications.     

A new two stages tenth algebraic order symmetric six-step method with vanished phase-lag and its first and second derivatives for the solution of the radial Schrödinger equation and related problems

The presentation, development and analysis of a new two-stages tenth algebraic order symmetric six-step method is introduced, for the first time in the literature, in this paper. More specifically, we present the development of the new method (requesting the highest algebraic order and the elimination of the phase-lag and its first and second derivatives), the analysis (error analysis and stability and interval of periodicity analysis) and the evaluation of the new developed method comparing its efficiency with the efficiency of well known methods and very recently produced methods in the literature on the approximate solution of the resonance problem of the one dimensional (or radial) Schrödinger equation. From the developments achieved and the results presented, we prove that the new obtained method is most more effective than other well known or recently developed methods of the literature.     

New two stages high order symmetric six-step method with vanished phase–lag and its first,second and third derivatives for the numerical solution of the Schrödinger equation

In the present paper, we obtain and analyze, for the first time in the literature, a new two-stages high order symmetric six-step method. The specific characteristics of the new proposed method are the highest possible algebraic order, the elimination of the phase–lag and its first, second and third derivatives. Additionally, for the new method we give the analysis of the method (both error and stability and interval of periodicity analysis) and the comparison of the effectiveness of the new developed method with the effectiveness of well known methods and very recently produced methods in the literature. The comparison is based on the numerical solution of the Schrödinger equation. The theoretical achievements and the numerical results show the effectiveness of the new developed method in comparison with other well known or recently developed numerical methods.     

Vibrational spectroscopy differentiates between multipotent and pluripotent stem cells

Over the last few years, there has been an increased interest in the study of stem cells in biomedicine for therapeutic use and as a source for healing diseased or injured organs/tissues. More recently, vibrational spectroscopy has been applied to study stem cell differentiation. In this study, we have used both synchrotron based FTIR and Raman microspectroscopies to assess possible differences between human pluripotent (embryonic) and multipotent (adult mesenchymal) stem cells, and how O(2) concentration in cell culture could affect the spectral signatures of these cells. Our work shows that infrared spectroscopy of embryonic (pluripotent) and adult mesenchymal (multipotent) stem cells have different spectral signatures based on the amount of lipids in their cytoplasm (confirmed with cytological staining). Furthermore, O(2) concentration in cell culture causes changes in both the FTIR and Raman spectra of embryonic stem cells. These results show that embryonic stem cells might be more sensitive to O(2) concentration when compared to mesenchymal stem cells. While vibrational spectroscopy could therefore be of potential use in identifying different populations of stem cells further work is required to better understand these differences.     

Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation

A tenth algebraic order eight-step method is developed in this paper. For this method  we require the phase-lag and its first and second derivatives to be vanished. A comparative error analysis and a comparative stability analysis are also presented in this paper. The new proposed method is applied for the numerical solution of the one-dimensional Schrödinger equation. The efficiency of the new methodology is proved via the theoretical analysis and the numerical applications. General conclusions about the importance of several properties on the construction of numerical algorithms for the approximate solution of the radial Schrödinger equation are also presented.     

A Note on the Almost Everywhere Convergence to Initial Data for Some Evolution Equations

The weighted Lebesgue spaces of initial data for which almost everywhere convergence of the heat equation holds was only very recently characterized. In this note we show that the same weighted space of initial data is optimal for the heat–diffusion parabolic equations involving the harmonic oscillator and the Ornstein–Uhlenbeck operator.     

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.     

Synthesis of nano-sized zeolite-Y functionalized with 5-amino-3-thiomethyl 1H-pyrazole-4-carbonitrile for effective Fe(III)-chelating strategy

Zeolite crystals having faujasite-type (FAU) topology in the nanometer range were first synthesized from amorphous rice husk ash at a low temperature of 363 K under autogenous pressure. Following this, surface functionalization of the produced zeolite with 5-amino-3-thiomethyl 1H-pyrazole-4-carbonitrile (pyrazole; Py) was carried out by two different methods, namely liquefied-period adsorption of Py (Py/Y_im) and a flexible ligand method (Py/Y_ss). The latter provides a larger amount of Py formed into as-made zeolite-Y. The sorption of Fe(III) onto Py/NaY afforded large meso–macroporosity introduced by the aggregation–assembly between Fe(III)Py complexes and NaY zeolite, which was typically evidenced for Fe(III)Py/Y_ss. The materials were characterized by XRD, FT-IR spectroscopy, thermal analysis (TGA) and porous structure by N₂ adsorption–desorption at 77 K. The XRD evaluation showed that the zeolite structure was managed right after adding Fe(III) to Py/Y, although a change in intensity of the zeolite reflections on complex formation was noticed. The FT-IR spectrum of Fe(III)Py/Y_ss exhibited two bands at 3594 and 3542 cm^?1 assigned to bridging hydroxyl groups associated with a Brönsted site, which did not exist in the spectra of Fe(III)Py/Y_im and Fe(III)-exchanged as-made NaY zeolite. This effect was ascribed to the induced greater electronegativity of the ligand towards Fe(III) species in dissociation of water molecules, producing acidic protons that are potential Brönsted acid sites. It was also evident that the Fe(III) adsorption capacity on Py/Y_ss is greater than on as-made NaY zeolite and Py/Y_im, owing most likely to the increasing concentration of the incorporating Py ligand which leads to an increase in the number of binding sites. The Fe(III) adsorption onto Py/Y_ss was well described by the pseudo-second-order kinetic model. Density functional theory (B3LYP/6-311G*) was performed to understanding the interaction mode of the ligand and complex with zeolite. The QSPR was calculated depending on the optimization geometries, frontier molecular orbitals, thermodynamic parameters, and global chemical reactivates, which were discussed for the studied compounds. The HOMOs, LUMOs and molecular electrostatic potentials were plotted to elucidate the interaction manner of the tested compounds with the zeolite. The nonlinear optical properties were elucidated via 1st and 2nd hyper-polarizabilities. The auto-degradation behavior was predicted for the complex, based on the ionization optional and bond dissociation enthalpy. The interactions between P_y and Fe(III)P_y with the zeolite surface have been described with molecular dynamics using a Monte Carlo simulation.     

A Comprehensive Theoretical Analysis of <Superscript>6,7</Superscript>Li + <Superscript>64</Superscript>Zn Elastic Scattering in a Wide Angular Range Around the Coulomb Barrier

In this paper, the elastic scattering angular distributions of ^6,7Li on ⁶⁴Zn have been investigated by using various nuclear potentials. For this, we use the phenomenological Woods-Saxon potential, the real double folding potential with the density-independent M3Y effective interaction supplemented with an imaginary part in Woods-Saxon form and the double folding potentials multiplied with a normalization factor of the real and imaginary parts via the density-independent and CDM3Y6 density-dependent versions of the M3Y effective interaction have been used. The results have been compared with each other as well as with the experimental data. It has been observed that the agreement between the theoretical results and earlier reported data is perfect. Finally, the change of the total reaction cross sections with energy has been investigated.