ASYMPTOTIC APPROXIMATIONS OF R-STIRLING NUMBERS

Using a modified saddle-point method we obtained asymptotic approximation of the r-Stirling numbers of the first and second kind. Here we used a nontrivial trans formation of the same type as that discussed by N.M. Temme[13], to put the integral representations in volved into a form on which we can apply the saddle point

Asymptotic Approximations of Apostol-Tangent Polynomials in Terms of Hyperbolic Functions

The tangent polynomials Tn(z)are generalization of tangent numbers or the Euler zigzag numbers Tn.In particular,Tn(0)=Tn.These polynomials are closely related to Bernoulli,Euler and Genocchi polynomials.One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostol-type polynomials.One of these Apostol-type polynomials is the Apostol-tangent polynomials Tn(z,λ).Whenλ=1,Tn(z,1)=Tn(z).The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and Temme.The same method was applied to the Genocchi polynomials by Corcino et al.The essential steps in applying the method are(1)to obtain the integral representation of the polynomials under study using their exponential generating functions and the Cauchy integral formula,and(2)to apply the saddle point method.It is found out that the method is applicable to Apostol-tangent polynomials.As a result,asymptotic approximation of Apostol-tangent polynomials in terms of hyperbolic functions are derived for large values of the parameter n and uniform approximation with enlarged region of validity are also obtained.Moreover,higher-order Apostol-tangent polynomials are introduced.Using the same method,asymptotic approximation of higherorder Apostol-tangent polynomials in terms of hyperbolic functions are derived and uniform approximation with enlarged region of validity are also obtained.It is important to note that the consideration of Apostol-type polynomials and higher order Apostol-type polynomials were not done by Lopez and Temme.This part is first done in this paper.The accuracy of the approximations are illustrated by plotting the graphs of the exact values of the Apostol-tangent and higher-order Apostol-tangent polynomials and their corresponding approximate values for specific values of the parameters n,λand m.

Asymptotic Approximations of Jacobi Polynomials and Their Zeros with Error Bounds

Many fields require the zeros of orthogonal polynomials. In this paper, the middle variable was improved to give a new asymptotic approximation, with error bounds, for the Jacobi polynomials P (α,β) n(cosθ) (0≤θ≤π/2,α,β>-1), as n→+∞. An accurate approximation with error bounds is also constructed for the zero θ n,s of P (α,β) n(cosθ)(α≥0,β>-1).

Asymptotic Approximations of Jacobi Functions and Their Zeros with Error Bounds

The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable x（t）, we＇ve got a new form of asymptotic approximation, completed with error bounds, it is constructed for the Jacobi functions φu^（α,β）（t）（α 〉 -1） as μ→∞. Besides, an accurate approximation with error bounds is also constructed correspondingly for the zeros tμ,s of φu^（α,β）（t）（α≥ 0） as μ→∞, uniformly with respect to s = 1, 2,....

Asymptotic Analysis Methods for Structural Reliability

Applying Laplace asymptotic approximation of integral, asymptotic analysis methods of structural reliability are proposed in generalized and orthogonal random space. Analytic results show that the proposed methods are simple in calculation and accurate enough for problems of continuous random variables.

ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

Hydrodynamics and Sensitivity Analysis of a Williamson Fluid in Porous-Walled Wavy Channel

In this work,a steady,incompressible Williamson fluid model is investigated in a porous wavy channel.This situation arises in the reabsorption of useful substances from the glomerular filtrate in the kidney.After 80%reabsorption,urine is left,which behaves like a thinning fluid.The laws of conservation of mass and momentum are used to model the physical problem.The analytical solution of the problem in terms of stream function is obtained by a regular perturbation expansion method.The asymptotic integration method for small wave amplitudes and the RK-Fehlberg method for pressure distribution has been used inside the channel.It is demonstrated that the forward flow becomes fast in the narrow region(at x=0.75),which dominates the upward flow inside the channel.To study the impact of model parameters on outputs,we applied normalized local sensitivity analysis and noticed that the most influential parameter for the longitudinal velocity profile is the dimensionless wave amplitude.The reabsorption parameter is sensitive for transverse velocity in the narrow region,and the Weissenberg number has a strong effect on the pressure inside the channel.Further,the least sensitive parameters for the velocity components and pressure have been identified.

On the helical pipe flow with a pressure-dependent viscosity

We address the flow of incompressible fluid with a pressure-dependent viscosity through a pipe with helical shape. The viscosity-pressure relation is defined by the Barus law. The thickness of the pipe and the helix step are assumed to be of the same order and considered as the small parameter. After transforming the starting problem, we compute the asymptotic solution using curvilinear coordinates and standard perturbation technique. The solution is provided in the explicit form clearly showing the influence of viscosity-pressure dependence and pipe＇s geometry on the effective flow.

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poeschl-Teller （tPT） potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ（κ± i 1）r^-2. In view of spin and pseudo-spin （p-spin） symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method （AIM）. We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.

A class of epidemic virus transmission population dynamic system

A class of epidemic virus transmission population dynamic system is considered. Firstly, using the functional homotopic analysis method, an initial approximate function is selected. Then, the arbitrary order approximate analytic solutions are obtained successively. Finally, the accuracy of the obtained approximate analytic solutions is described. The influence of the various physical parameters for the epidemic virus transmission population dynamic system is discussed.

Comparison Properties for Asymptotically Tracially Approximation C^(*)-algebras

We show that the following properties of the C*-algebras in a class P are inherited by simple unital C*-algebras in the class of asymptotically tracially in P :(1) n-comparison,(2) α-comparison(1 ≤ α < ∞).

Accidental Degeneracies in N dimensions for Potential Class αr^(2d-2)-βr^(d-2) via Asymptotic Iteration Method(AIM)

In mathematical physics the main goal of quantum mechanics is to obtain the energy spectrum of an atomic system.In many practices,Schrodinger equation which is a second order and linear differential equation is solved to do this analysis.There are many theoretic mathematical methods serving this purpose.We use Asymptotic Iteration Method(AIM) to obtain the energy eigenvalues of Schrodinger equation in N-dimensional euclidean space for a potential class given as αr^(2d-2)-βr^(d-2).We also obtain a restriction on the eigenvalues that gives degeneracies.Besides,we crosscheck the eigenvalues and degeneracies using the perturbation theory in the view of the AIM.

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type

In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions.The numerical method combines boundary value technique,asymptotic expansion approximation,shooting method and finite difference scheme.In order to get a numerical solution for the derivative of the solution,the domain is divided into two regions namely inner region and outer region.The shooting method is applied to the inner region while standard finite difference scheme(FD)is applied for the outer region.Necessary error estimates are derived for the method.Computational efficiency and accuracy are verified through numerical examples.The method is easy to implement and suitable for parallel computing.