Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model

We show that the asymptotic iteration method converges and yields accurate energies for a perturbed Coulomb model. We also discuss alternative perturbation approaches to that model.Comment: 9 pages, 2 figures, 1 tabl

Polymorphisme de l’apolipoprotéine E dans la population du nord du Maroc: fréquence et influence sur les paramètres lipidiques

Introduction: L'objectif de ce travail est de déterminer les fréquences alléliques et génotypiques des sites polymorphes situés dans le gène de l'apolipoprotéine E (apo E) ainsi que leur impact sur les paramètres cliniques et lipidiques dans un échantillon de la population du nord du Maroc cliniquement diagnostiqué ADH. Méthodes: Le génotype de l'apo E a été analysé par séquençage direct chez 46 patients cliniquement diagnostiqués ADH selon les critères standards. Résultats: Les fréquences des allèles epsilon 3, epsilon 2 et epsilon 4 ont été respectivement 78.3%, 2.2% et 19.6%. La fréquence de l'allèle epsilon 4 est très élevée chez la population du nord du Maroc en comparaison avec les populations des autres régions marocaines. Elle est similaire à celle rapportée dans les pays de l'Europe du nord. Les taux du cholestérol total, du cholestérol LDL ainsi que la présence des xanthomes et les maladies cardiovasculaires ne différent pas entre les génotypes de l'apoE. En revanche, les résultats ont montré une influence de l'allèle epsilon4 sur le taux des triglycérides chez les sujets obèses. Conclusion: Le génotype de l'apoE ne peut expliquer le phénotype clinique et biochimique présenté par des patients du Nord du Maroc cliniquement diagnostiqués ADH.Key words: Paramètres lipidiques, Maladies cardiovasculaires, Polymorphisme génétique, Gène APO

Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method

Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before. Without any loss of generality, other states and molecules could be treated in a similar way

Any ll-state solutions of the Hulth\'en potential by the asymptotic iteration method

In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any $l$ states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different $\delta$ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.Comment: 14 pages and 1 figur

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

Structural and optical behaviors of 2D-layered molybdenum disulfide thin film:Experimental and ab-initio insights

The two-dimensional (2D) layered molybdenum disulfide (MoS2) material represents a nominee potent for optoelectronic devices application. In this research work, the experimental characterizations of 2D- MoS2 thin films are reported in terms of various microscopic and spectroscopic techniques. The synthesized MoS2 thin films are grown by employing the pulsed laser deposition (PLD) procedure on SiO2/Si substrates. In order to monitor the deposition rates of ablated films, the buffer argon-gas pressures are varied during the pulsed laser deposition at substrate temperature of 700 °C. The field emission scanning electron microscopy and atomic force microscopy analyzes revealed a change in the surface morphology of MoS2 films when the buffer Ar-gas pressure is varied between 0 and 100 mTorr. For all samples, a 2H-phase is revealed from X-ray diffraction patterns, indicating a reflection (2θ) around 14.85°. By varying the deposition pressure of laser-ablated MoS2 films, the X-ray photoelectron spectroscopy divulged the chemical compositional elements and valence states of Mo and S on the surface of MS2 films with low density of defects. Analysis of the photoluminescence spectroscopy illustrated emission bands spanning from the visible (Vis) to near-infrared (NIR) regimes in the deposition pressures range ~ 0–100 mTorr. This is mainly owing to the change in the recombination of electron–hole pairs and charge transfer between the deposited MoS2 films and SiO2 substrate surface under various buffer gas pressures. Additionally, first-principles electronic structure calculations are performed to qualitatively examine the effect of native point-defect species (sulfur-monovacancy and sulfur-divacancy defects) on the electronic structure and optical properties of 2D- MoS2 sheets. It is unveiled that the variation of compositional sulfur-vacancy defect in MoS2 monolayer creates an in–gap defect levels above the valence states, leading to an acceptor character. Importantly, the enhancement in the optical absorption spectra divulged a shift in the optical gap from Vis-NIR window with the increase of sulfur vacancy contents in MoS2 single-layer. The identification of intrinsic point defects may be beneficial for photovoltaic energy conversion at higher wavelengths by designing next generation 2D-semiconductors, which could be of vital significance for growing 2D layers and multilayers into practical technologies

Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure

Telerobotics: A simulation facility for university research

An experimental telerobotics (TR) simulation suitable for studying human operator (H.O.) performance is described. Simple manipulator pick-and-place and tracking tasks allowed quantitative comparison of a number of calligraphic display viewing conditions. A number of control modes could be compared in this TR simulation, including displacement, rate and acceleratory control using position and force joysticks. A homeomorphic controller turned out to be no better than joysticks; the adaptive properties of the H.O. can apparently permit quite good control over a variety of controller configurations and control modes. Training by optimal control example seemed helpful in preliminary experiments. An introduced communication delay was found to produce decrease in performance. In considerable part, this difficulty could be compensated for by preview control information. That neurological control of normal human movement contains a data period of 0.2 second may relate to this robustness of H.O. control to delay. The Ames-Berkeley enhanced perspective display was utilized in conjunction with an experimental helmet mounted display system (HMD) that provided stereoscopic enhanced views

Genetic Algorithm Optimization Model for Determining the Probability of Failure on Demand of the Safety Instrumented System

A more accurate determination for the Probability of Failure on Demand (PFD) of the Safety Instrumented System (SIS) contributes to more SIS realiability, thereby ensuring more safety and lower cost. IEC 61508 and ISA TR.84.02 provide the PFD detemination formulas. However, these formulas suffer from an uncertaity issue due to the inclusion of uncertainty sources, which, including high redundant systems architectures, cannot be assessed, have perfect proof test assumption, and are neglegted in partial stroke testing (PST) of impact on the system PFD. On the other hand, determining the values of PFD variables to achieve the target risk reduction involves daunting efforts and consumes time. This paper proposes a new approach for system PFD determination and PFD variables optimization that contributes to reduce the uncertainty problem. A higher redundant system can be assessed by generalizing the PFD formula into KooN architecture without neglecting the diagnostic coverage factor (DC) and common cause failures (CCF). In order to simulate the proof test effectiveness, the Proof Test Coverage (PTC) factor has been incorporated into the formula. Additionally, the system PFD value has been improved by incorporating PST for the final control element into the formula. The new developed formula is modelled using the Genetic Algorithm (GA) artificial technique. The GA model saves time and effort to examine system PFD and estimate near optimal values for PFD variables. The proposed model has been applicated on SIS design for crude oil test separator using MATLAB. The comparison between the proposed model and PFD formulas provided by IEC 61508 and ISA TR.84.02 showed that the proposed GA model can assess any system structure and simulate industrial reality. Furthermore, the cost and associated implementation testing activities are reduced

Vertex Operator Superalgebras and Odd Trace Functions

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we call `odd trace functions'. We examine the case of the N=1 superconformal algebra. In particular we compute an odd trace function in two different ways, and thereby obtain a new representation theoretic interpretation of a well known classical identity due to Jacobi concerning the Dedekind eta function.Comment: 13 pages, 0 figures. To appear in Conference Proceedings `Advances in Lie Superalgebras