Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass

The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

A New Class of Exactly Solvable Models within the Schrodinger Equation with Position Dependent Mass

The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.

Relativistic Study of Spinless Particles for Generalized Hylleraas Potential with Position Dependent Mass

The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding wave functions expressed in terms ofa Jacobi polynomial are obtained using the parametric generalization of NU （Nikiforo-Uvarov） method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term （potential barrier）. To test the accuracy of the result, we compared the approximation scheme with the centrifugal term and the result shows a good agreement with the centrifugal term for a short-range potential. The results obtained in this work would have many applications in semiconductor quantum well structures, quantum dots, quantum liquids. Under limiting cases, the results could be used to study the binding energy and interaction of some diatomic molecules which is of great applications in nuclear physics, atomic and molecular physics and other related areas. We have also discussed few special cases of generalized Hylleraas potential such as Rosen-Morse, Woods-Saxon and Hulthen potentials.

Coherent States and Uncertainty Product of the Harmonic Oscillator with Position-Dependent Mass

In this work, we applied the invariant method to calculate the coherent state of the harmonic oscillator with position-dependent mass, which in modern physics has great application. We also obtain the calculation of Heisenberg’s uncertainty principle, and we will show that it is verified.

One Dimensional Conservative System with Quadratic Dissipation and Position Depending Mass

Forl a 1-D conservative system with a position depending mass within a dissipative medium, its effect on the body is to exert a force depending on the squared of its velocity, a constant of motion, Lagrangian, generalized linear momentum, and Hamiltonian are obtained. We apply these new results to the harmonic oscillator and pendulum under the characteristics mentioned about, obtaining their constant of motion, Lagrangian and Hamiltonian for the case when the body is increasing its mass.

Asymptotic Iteration Method for Energies of Inversely Linear Potential with Spatially Dependent Mass

The bound-state solution of the position dependent mass Klein-Gordon equation including inversely linear potential is obtained within the framework of the asymptotic iteration method. The relation between the scalar and vector potentials is considered to S（x） = V（x）（β - 1）. In particular, it is shown that the corresponding method exactly reproduces the spectrum of linearly inversely potentials with spatially dependent mass.

Partial Order and Extremes of Multivariate Extreme Value Distributions

This paper studies the dependence order among multivariate extreme value dis- tributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.

Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

Effect of lumbar angular motion on central canal diameter： positional MRI study in 491 cases

Background Lumbar spinal stenosis is a common problem that is receiving attention with the advent of novel treatment procedures. Prior positional MRI studies demonstrated lumbar canal diameter changes with flexion and extension. There have not been any studies to examine the amount of spinal canal diameter change relative to the amount of angular motion. The purpose of this study was to evaluate the correlation between the lumbar canal diameter change and the angular motion quantitatively. Methods Positional MRI （pMRI） images for 491 patients, including 310 males and 181 females （16 years-85 years of age）, were obtained with the subjects in sitting flexion 40 degree, upright, and with extension of 10 degrees within a 0.6 T Positional MRI scanner. Quantitative measurements of the canal diameter and segmental angle of each level in the sagittal midline plane were obtained for each position. Then the diameter change and angular motion were examined for correlation during flexion and extension with linear regression analysis. Results The lumbar segmental angles were lordotic in all positions except L1-2 in flexion. The changes of canal diameters were statistically correlated with the segmental angular motions during flexion and extension （P 〈0.001）. The amount of canal diameter change correlated with the amount of angular change and was expressed as a ratio. Conclusions Positional MRI demonstrated the amount of spinal canal diameter change that was statistically correlated with the segmental angular motion of the spine during flexion and extension. These results may be used to predict the extent of canal diameter change when interspinous devices or positional changes are used to treat spinal stenosis and the amount of increased canal space may be predicted with the amount of angular or positional change of the spine. This may correlate with symptomatic relief and allow for improved success in the treatment of spinal stenosis.

DEPENDENCE ANALYSIS OF REGRESSION MODELS IN TIME SERIES

In this paper, the relative dependence of a linear regression model is studied. In particular, the dependence of autoregressive models in time series are investigated. It is shown that for the first-order non-stationary autoregressive model and the random walk with trend and drift model, the dependence between two states decreases with lag. Some numerical examples are presented as well.

Optical properties of Al_(x)Ga_(1-x)As/GaAs Woods-Saxon quantum well in the presence of hydrostatic pressure and applied electric field

The third harmonic generation(THG),linear and nonlinear optical absorption coefficients(OACs),and refractive index changes(RICs)are investigated in a Woods-Saxon quantum well(QW)modulated by the hydrostatic pressure and applied electric field.The effect of non-uniform aluminum doping(position-dependent effective mass(PDEM))on the mass of the system is discussed,and further to explore the influence of PDEM on the nonlinear THG,OACs,and RICs of the Woods-Saxon QW.These nonlinear optical properties above are obtained using the compact-density matrix formalism.The electron states in a Woods-Saxon QW under the constant effective mass(CEM)and PDEM are calculated by solving the Schr?dinger equation via the finite difference technique.The contributions from competing effects of the hydrostatic pressure and applied electric field to the nonlinear optical properties with CEM and PDEM are reported,as well as the comparison with each other.The observations reveal that the regulation of external fields and the influence of PDEM play an important role in the photoelectric properties of QW.