多项式数值逼近法在黑体辐射问题反演中的应用

本文提出求解黑体辐射问题的新方法,即采用多项式数值反演法——拉盖尔、勒让德、切比雪夫多项式数值逼近法等求解黑体辐射中的反演问题,数值计算结果显示采用勒让德、切比雪夫多项式数值逼近法的比Laplace反演法以及Tikhonov正则化方法等要精确,并且程序简单、算法高效。

位数随机的有效数字自动运算算法

针对物理实验数据的自动处理,提出一种位数随机的有效数字自动运算算法,包括有效数字运算结果的科学记数表示算法、有效位数的取舍算法、数据表示形式的转换算法以及不同位数有效数字的运算算法。对有效数字多项式的自动运算实验结果表明,该算法符合运算优先级的要求,运算结果符合有效数字的取舍原则,算法运算的结果与人工运算的结果完全相同,算法满足位数随机的物理实验数据的自动处理要求。

ON VALUE DISTRIBUTIONS OF GENERAL DIFFERENTIAL MONOMIALS

Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0】2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0.

Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.

A Discussion about Reducing the Amount of Calculation of Direct Method

The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolation is not only reliable but also can save the amount of calculation by nearly 36%. Large amount of calculation and lacking strict theoretical bas is has been th e two disadvantage of direct method by new. If this defect is not overcome, they will not only s eriously affect the application of this method, but also hinder its further rese arch. Based on sufficient calculation practice, this article has made a primary discussion about the theory and method of reducing the amount of calculation, an d has achieved some satisfactory results.

A New Third S.N.Bernstein Interpolation Polynomial

In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x) . The convergence order is the best order if \{f(x)∈C j[-1,1],\}0jr, where r is an odd natural number.

Value Distribution of Differential Polynomials in Meromorphic Functions

Let f（z） be a meromorphic function and ψ be the differential polynomial of f which satisfies the condition of -↑N（r, f）＋-↑N （r, 1/f） = S（r, f）. We obtain several results about the zero point of the ψ and those results extend and improve the results of Yang and Yi in this paper.

C^1 C^2INTERPOLATION OF SCATTERED DATA POINTS

In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.

Heron Triangle and Diophantine Equation

In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.

On the Pal's Problem

The correct answer of Pal's interpolation polynomial problem has been given in this paper ,especially, the explict form of this polynomial has been obtained.

Train crossing modeling based on measurements and best numerical approximation in subway tunnels

Communication based train control systems （CBTC） must work even in the worst situation-- train crossing. This paper models the propagation characteristics in one of the most common and piv- otal scenarios--train crossing in subway tunnels which is rarely mentioned in previous publications. Firstly, measurements for train crossing scenario at 2.4 GHz in a real subway line in Madrid have been made. The field measurement is the most reliable way to reveal the propagation characteristics involving shadowing effect and fast fading. Moreover, to precisely describe the fast fading distribu- tion and eliminate the inevitable weak points of traditional fitting way, a best numerical approxima- tion method using Legendre orthogonal polynomials has been proposed. Comparisons show that this method works better and is of greater physical significance. Finally, a complete statistical model is given and all the coefficients can be applied by system designers for the link and system level simu- lations.

Effect of Polynomial Expressed Distribution Dust Particles for Unmagnetized Two-Ion-Temperature Dusty Plasma

Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinearwave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species.The numerical results of variations of linear dispersion with respect to the different dust size distribution are given.Moreover,how the amplitude,width,and propagation velocity of solitary wave vary vs different dust size distribution isalso studied numerically in this paper.

A polynomial smooth epsilon-support vector regression based on cubic spline interpolation

Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models, this study takes cubic spline interpolation to generate a new polynomial smooth function ｜×｜ε^ 2, in g-insensitive support vector regression. Theoretical analysis shows that Sε^2 -function is better than pε^2 -function in properties, and the approximation accuracy of the proposed smoothing function is two order higher than that of classical pε^2 -function. The experimental data shows the efficiency of the new approach.

ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED L^p SPACES

In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.

Efficiently Counting Affine Roots of Mixed Trigonometric Polynomial Systems

Estimating the number of isolated roots of a polynomial system is not only a fundamental study theme in algebraic geometry but also an important subproblem of homotopy methods for solving polynomial systems. For the mixed trigonometric polynomial systems, which are more general than polynomial systems and rather frequently occur in many applications, the classical B6zout number and the multihomogeneous Bezout number are the best known upper bounds on the number of isolated roots. However, for the deficient mixed trigonometric polynomial systems, these two upper bounds are far greater than the actual number of isolated roots. The BKK bound is known as the most accurate upper bound on the number of isolated roots of a polynomial system. However, the extension of the definition of the BKK bound allowing it to treat mixed trigonometric polynomial systems is very difficult due to the existence of sine and cosine functions. In this paper, two new upper bounds on the number of isolated roots of a mixed trigonometric polynomial system are defined and the corresponding efficient algorithms for calculating them are presented. Numerical tests are also given to show the accuracy of these two definitions, and numerically prove they can provide tighter upper bounds on the number of isolated roots of a mixed trigonometric polynomial system than the existing upper bounds, and also the authors compare the computational time for calculating these two upper bounds.

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ＋ exp （λτ）） ＋ V1（ d ＋ exp （ λτ） ） / （b ＋ exp （λτ））. We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.

Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor's Theorem

Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated using the operator form of Taylor＇s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e.l＇ ≠ k＇ and m＇≠ n＇ .Their selection rules are a/so given. We also verify the correctness of those integral formulas numerically.

SEMI-ALGEBRAICALLY CONNECTED COMPONENTS OF MINIMUM POINTS OF A POLYNOMIAL FUNCTION

In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.

Numerical Algorithm Based on Quintic Nonpolynomial Spline for Solving Third-Order Boundary Value Problems Associated with Draining and Coating Flows

A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows. The authors show that the approximate so- lutions obtained by the numerical algorithm developed by using uonpolynomial quintic spline functions ave better than those produced by other spline and domain decomposition methods. The algorithm is tested on two problems associated with draining and coating flows to demonstrate the practical usefulness of the approach.