Fractional programming approach to fuzzy weighted average

This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the -cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the -cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the optimal solution can be found analytically. Consequently, the exact form of the membership function can be derived by taking the inverse function of the -cut. For other cases, a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method. Examples are given for illustration.     

Approximation Algorithms for Dispersion Problems

Given a collection of weighted sets, each containing at most k elements drawn from a finite base set, the k-set packing problem is to find a maximum weight sub-collection of disjoint sets. A greedy algorithm for this problem approximates it to within a factor of k, and a natural local search has been shown to approximate it to within a factor of roughly k − 1. However, neither paradigm can yield approximations that improve on this.We present an approximation algorithm for the weighted k-set packing problem that combines the two paradigms by starting with an initial greedy solution and then repeatedly choosing the best possible local improvement. The algorithm has a performance ratio of 2(k + 1)/3, which we show is asymptotically tight. This is the first asymptotic improvement over the straightforward ratio of k.     

Weighted Solution of Small-Deflection Buckling Equation of Thin Shell

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Lattice Paths,q-Multinomials and Two Variants of the Andrews-Gordon Identities

A few years ago Foda, Quano, Kirillov and Warnaar proposed and proved various finite analogs of the celebrated Andrews-Gordon identities. In this paper we use these polynomial identities along with the combinatorial techniques introduced in our recent paper to derive Garrett, Ismail, Stanton type formulas for two variants of the Andrews-Gordon identities.     

双参数广义加权平均值及其单调性

本文定义了双参数广义加权平均值,研究了它的基本性质和单调性,推广了加权平均值的概念,给出它的一些应用.     

加权支持向量机在证券指数预测中的研究

支持向量机是基于统计学习理论的新一代学习机器.它使用结构风险最小化原则,运用核技巧,较好地解决了学习问题.本文提出了一种基于支持向量机的加权算法,并将其应用于证券,指数预测.与径向基神经网络相比较,加权支持向量机表现出了良好的性能.     

线性模型中M估计分布的随机加权方法逼近

在线性模型中,M估计的渐近分布通常都涉及到不易估计的未知误差分布的某些量,如果要估计渐近方差,就需对这些冗余参数进行估计.利用随机加权方法可以避免先对误差分布中的冗余参数进行估计.给出了当自变量是随机变量时,M估计分布的随机加权逼近,证明了M估计分布的随机加权逼近是一致相合的.当取不同的凸函数,样本大小和随机权时,进一步利用蒙特卡洛方法研究估计分布.研究表明随机权取泊松权时,不仅达到同样的效果而且可以减小计算量.     

高次有限元外推的进一步研究

对高次矩形元,我们给出了一个外推算法.利用离散格林函数权模估计和渐进不等式展开,证明了外推算法可以提高泊松方程有限元逼近解的精度.     

The Serre duality theorem for a non-compact weighted CR manifold

It is proved that the Hodge decomposition and Serre duality hold on a non-compact weighted CR manifold with negligible boundary. A complete CR manifold has negligible boundary. Some examples of complete CR manifolds are presented.

     

Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions ...