ON PROPERTIES OF DIFFERENCE POLYNOMIALS

We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f（z）f（z ＋ c）.

RITT-WU'S CHARACTERISTIC SET METHOD FOR ORDINARY DIFFERENCE POLYNOMIAL SYSTEMS WITH ARBITRARY ORDERING

In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.

Some results on zeros and uniqueness of difference-differential polynomials

We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.

UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

The Zeros of a Certain Homogeneous Difference Polynomials of Meromorphic Functions

Let f(z) be a function transcendental and meromorphic in the plane of growth order less than 1. This paper focuses on discuss and estimate the number of the zeros of a certain homogeneous difference polynomials of degree k in f(z), and obtains that this certain homogeneous difference polynomials has infinitely many zeros.

Some Uniqueness Results of Q-Shift Difference Polynomials Involving Sharing Functions

In this paper, we mainly study the uniqueness of specific q-shift difference polynomials and of meromorphic functions, which share a common small function and get the corresponding results. In addition, we also investigate the problem of value distribution on q-shift difference polynomials of entire functions.

Zero distribution of some difference polynomials

In this paper,suppose that a,c∈C{0},c_(j)∈C(j=1,2,···,n) are not all zeros and n≥2,and f (z) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely many multiple zeros,the zero distribution of difference polynomials of f (z+c)-af^(n)(z) and f (z)f (z+c_1)···f (z+c_n) are investigated.A number of examples are also presented to show that our results are best possible in a certain sense.

Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities

In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.

Polynomial Quasisolutions Method for Some Linear Differential Difference Equations of Mixed Type

The paper considers a scalar linear differential difference equation （LDDE） of mixed type x（t） = （a0 ＋ a1t）X（t） ＋ （b0 ＋ b1t）x（t - 1） ＋ （d0 ＋ d1tx（t ＋ 1） ＋ f（t）, t ∈ R, （＊） where f（t） = ∑n=0^F fn^tn. This equation is investigated with the use of the method of polynomial quasisolutions based on the representation of an unknown function in the form of polynomial x（t） = ∑n=0^N xn^tn. As a result of substitution of this function into equation （＊）, there appears a residual △（t） = 0（t^N）, for which an exact analytical representation has been obtained. In turn, this allows one to find the unknown coefficients xn and consequently the polynomial quasisolution x（t）. Several examples are considered.

ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

In this article, the existence of finite order entire solutions of nonlinear difference equations fn＋ Pd（z, f） = p1 eα1 z＋ p2 eα2 z are studied, where n ≥ 2 is an integer, Pd（z, f） is a difference polynomial in f of degree d（≤ n-2）, p1, p2 are small meromorphic functions of ez, and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.

AN ACCURATE SOLUTION OF THE POISSON EQUATION BY THE FINITE DIFFERENCE-CHEBYSHEV-TAU METHOD

A new finite difference-Chebyshev-Tau method for the solution of the two-dimensional Poisson equation is presented. Some of the numerical results are also presented which indicate that the method is satisfactory and compatible to other methods.

Numerical Solution for the Fractional Wave Equation Using Pseudo-Spectral Method Based on the Generalized Laguerre Polynomials

In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. The properties of Laguerre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which is solved by the finite difference method. An approximate formula of the fractional derivative is given. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. Numerical solutions of FWE are given and the results are compared with the exact solution.

The Method of Finite Difference Regression

In this paper I present a novel polynomial regression method called Finite Difference Regression for a uniformly sampled sequence of noisy data points that determines the order of the best fitting polynomial and provides estimates of its coefficients. Unlike classical least-squares polynomial regression methods in the case where the order of the best fitting polynomial is unknown and must be determined from the R2 value of the fit, I show how the t-test from statistics can be combined with the method of finite differences to yield a more sensitive and objective measure of the order of the best fitting polynomial. Furthermore, it is shown how these finite differences used in the determination of the order, can be reemployed to produce excellent estimates of the coefficients of the best fitting polynomial. I show that not only are these coefficients unbiased and consistent, but also that the asymptotic properties of the fit get better with increasing degrees of the fitting polynomial.

The factorial structure of self-reported androgen-promoted physiological traits

Androgens make major contributions to average sex differences in anatomy, physiology, and behavior. Despite having established their crucial role in sexual differentiation, much remains to be learned about how androgens coordinate their influences. The present study was undertaken to shed light on androgenic effects on the body using self-reported survey data. We analyzed the ratings provided by over 11,000 college students on the magnitude of eleven traits that previous research has shown to be influenced by testosterone or other androgens. Predictably, the average values for all eleven traits were significantly greater in males than in females. Nevertheless, when data were analyzed separately according to sex of the respondents, some of the traits failed to positively correlate with one another, suggesting that not all an-drogen-influenced traits differentiate in a simple fashion. Factor analysis of these eleven traits by sex reinforced this view by identifying four factors. In men, the primary factor loaded most heavily on: masculine body build, masculine mannerisms, overall physical strength, upper body strength, and lower body strength. The primary factor for women was limited to: upper body strength, lower body strength, and overall physical strength. In both sexes, the primary factor was interpreted as reflecting the influence of perinatal and post-pubertal testosterone exposure. The other three factors may reflect the effects of other androgens (e.g., androstenediol), or the influence of female hormones such as estradiol. Findings were discussed in terms of future use of self-reported physiological measures for assessing androgenic effects on the human body.

△_(h)-GOULD-HOPPER APPELL POLYNOMIALS

In this paper,we introduce the △_(h)-Gould-Hopper Appell polynomials An(x,y;h)via h-Gould-Hopper polynomials G_(n)^(h)(x,y).These polynomials reduces to △_(h)-Appell polynomials in the case y=0,△-Appell polynomials in the case y=0 and h=2D-Appell polynomials in the case h→0,2D △-Appell polynomials in the case h=1 and Appell polynomials in the case h→0 and y=0.We obtain some well known main properties and an explicit form,determinant representation,recurrence relation,shift operators,difference equation,integro-difFerence equation and partial difference equation satisfied by them.Determinants satisfied by △_(h)-Gould-Hopper Appell polynomials reduce to determinant of all subclass of the usual polynomials.Recurrence,shift operators and difference equation satisfied by these polynomials reduce to recurrence,shift operators and difference equation of △_(h)-Appell polynomials,△-Appell polynomials;recurrence,shift operators,differential and integro-differential equation of 2D-Appell polynomials,recurrence,shift operators,integrodifference equation of 2D △-Appell polynomials,recurrence,shift operators,differential equation of Appell polynomials in the corresponding cases.In the special cases of the determining functions,we present the explicit forms,determinants,recurrences,difference equations satisfied by the degenerate Gould-Hopper Carlitz Bernoulli polynomials,degenerate Gould-Hopper Carlitz Euler polynomials,degenerate Gould-Hopper Genocchi polynomials,△_(h)-Gould-Hopper Boole polynomials and △_(h)-Gould-Hopper Bernoulli polynomials of the second kind.In particular cases of the degenerate Gould-Hopper Carlitz Bernoulli polynomials,degenerate Gould-Hopper Genocchi polynomials,△_(h)-Gould-Hopper Boole polynomials and △_(h)-Gould-Hopper Bernoulli polynomials of the second kind,corresponding determinants,recurrences,shift operators and difference equations reduce to all subclass of degenerate so-called families except for Genocchi polynomials recurrence,shift operators,and differential equation.Degenerate Gould-Hopper Carlitz Euler polynomials do not satisfy the recurrences and differential equations of 2D-Euler and Euler polynomials.

A Fundamental Relationship of Polynomials and Its Proof

A fundamental algebraic relationship for a general polynomial of degree n is given and proven by mathematical induction. The stated relationship is based on the well-known property of polynomials that the nth-differences of the subsequent values of an nth-order polynomial are constant.

基于多项式代理模型的车顶绝缘子背风侧沿面压力优化研究

高速气流下,车顶绝缘子背风侧出现低气压会使得闪络电压降低,影响列车安全运行,为了改善车顶绝缘子背风侧的低气压现象,使用代理模型对车顶绝缘子结构参数进行优化。在车顶绝缘子结构参数上选取了伞裙上、下倾角以及伞裙间距作为因子,以绝缘子背风侧沿面压力的最小值作为响应,采用全因子试验设计方法获取样本数据,并对因子的主效应和交互效应进行分析,在此基础上建立多项式代理模型,进一步得到最佳的结构参数,最后进行闪络试验验证其有效性。结果表明:伞裙上、下倾角的主效应与伞裙间距相比更加显著,各因子之间没有显著的交互效应;最佳参数:伞裙上、下倾角分别为8°和0°,伞裙间距为45mm,背风侧沿面压力最小值提高了25.62%,同时压力平均值提高了42.47%;在100m/s的风速条件下,车顶绝缘子的闪络电压提高了16.80%。研究结果可以为车顶绝缘子结构设计提供参考。

融合T-分布小波变异的混沌鲸鱼优化算法

针对鲸鱼优化算法难以跳出局部最优导致收敛精度不足的问题,提出一种融合了T-分布小波变异和多项式差分学习策略的鲸鱼优化算法.该算法首先引入Circle混沌扩大搜索范围,提高收敛速度;然后采用T-分布小波变异策略平衡全局和局部搜索能力;最后采用多项式差分学习策略改进算法的优化精度.对3种改进策略作单一引入的仿真对比分析,并将改进的鲸鱼优化算法在12个可变维度的基准测试函数上进行仿真,对本文改进的鲸鱼优化算法与其他改进策略的鲸鱼优化算法以及其他几种智能算法进行比较.结果表明,基于T-分布小波变异和多项式差分学习策略的改进鲸鱼优化算法具有较好的稳定性,收敛速度和精度更好.

一类微分-差分多项式的值分布及分担有理函数的唯一性

本文利用Nevanlinna值分布理论,研究了零级超越亚纯函数条件下的一类微分-差分多项式的值分布问题,以及两个零级超越亚纯的微分-差分多项式在极点相同(不计重数)的条件下CM分担一个有理函数的唯一性问题,得到了两个定理及三个推论,所得结果改进或推广了陈文杰等人以及赵秋霞等人的相关结果.