顾客满意与忠诚的非线性关系研究:展望理论的解释

在营销领域,虽然顾客满意一般被视为忠诚的关键决定因素,但是将这两个概念联系起来的确切函数形式仍然是一个研究不足并且存在争议的课题。通过对三个产品类别的调查数据进行正交多项式回归分析,作者考察了顾客满意对忠诚的非线性作用。研究发现支持了S形的函数形式,即曲线在中部陡峭、两端平坦。这一发现符合展望理论的一般性预测。本研究的发现增进了顾客满意与忠诚之间非线性关系在理论基础方面的理解。     

高阶等差数列的函数解法

高阶等差数列的函数解法王坛，王曜如果一个数列｛ａｎ｝，从第二项起，每一项与它前一项的差所得的新数列｛ａｎ＋１－ａ．ｎ｝为等差数列，我们称此数列｛ａｎ｝为二阶等差数列。如果数列｛ａｎ｝中由｛ａｎ＋１－ａｎ｝组成的数列为一个二阶等差数列，则称原数列｛ａｎ...     

关于推广的Bernstein多项式的同时逼近

研究推广的Bernstein多项式Cn（f,Sn；x）对函数及其导数的同时逼近；对于f∈C（0,1）^n＋1,p≥1，给出了Cn^（p）（f,Sn；x）的渐进展开式．     

一类工艺控制问题的求解方法

给出了一类工艺控制问题的数学模型、求解方法，对其水库大坝振动辗辗压砂砾料施工工艺的质量指标－相对密度进行了预报与控制，研究了工程的经济性及赶进度模型。     

用最小多项式求线性微分方程组的基解矩阵

给出了最小多项式的两个性质；从理论上阐述了最小多项式与任何由矩阵级数定义的矩阵函数间的关系，并给出了用最小多项式代替特征多项式计算矩阵函数的方法；最后通过实例验证了该方法在简化计算方面的有效性．     

Efficient Bandwidth Selection in Non-parametric Regression

In this paper we use non-parametric local polynomial methods to estimate the regression function, m ( x ). Y may be a binary or continuous response variable, and X is continuous with non-uniform density. The main contributions of this paper are the weak convergence of a bandwidth process for kernels of order (0, k ), k =2 ^j , j ≥1 and the proposal of a local data-driven bandwidth selection method which is particularly beneficial for the case when X is not distributed uniformly. This selection method minimizes estimates of the asymptotic MSE and estimates the bias portion in an innovative way which relies on the order of the kernel and not estimation of m ²( x ) directly. We show that utilization of this method results in the achievement of the optimal asymptotic MSE by the estimator, i.e. the method is efficient. Simulation studies are provided which illustrate the method for both binary and continuous response cases.     

求sum from k=1 to n(k~m)之和的一种新方法

本文提出了一种以多项式函数为主要工具去求前n个正整数的方幂之和的新方法。     

EXPECTATIONS OF RATIOS OF QUADRATIC FORMS IN NORMAL VARIABLES: EVALUATING SOME TOP-ORDER INVARIANT POLYNOMIALS

Chikuse's (1987) algorithm constructs top-order invariant polynomials with multiple matrix arguments. Underlying it is a set of simultaneous equations for which all integer solutions must be found. Each solution represents a component of the sum of terms which comprise the polynomial. The system of equations has a specialised structure which may be exploited to obtain a polynomial with r matrix arguments in terms of a polynomial with r-1 matrix arguments. This is demonstrated for two particular polynomials that have two matrix arguments. These results are applied to problems involving expectations of ratios of quadratic forme in normal variables; analytic as well as computable formulae are derived.     

n元二次式极值的矩阵求法

本文利用Ｔｉｊ（ｋ）（ｊ＜ｉ）型行初等变换，给出了ｎ元二次式的极值判定及求法．     

收入因素与人口因素建模的实证分析

就收入因素与人口因素关系模型的构建作了探讨,找到了GDP与总人口的无约束的二阶二次多项式分布滞后正负反馈模型.从模型的各项综合评价指标看,无论是GDP关于总人口的正反馈模型,还是其负反馈模型,均是与预测效果拟合相当良好的经济计量模型.