Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.     

严格循环与强不可约分解

Let W be an injective unilateral weighted shift, and let W(n) be the orthogonal direct sum of n copies of W. In this paper, we prove that, if the commutant of W is strictly cyclic, then W(n) has a unique (SI) decomposition with respect to similarity for every natural number n.     

加权原子空间上Fourier级数的（C，α）算子

对[0,2π]年的区间I,对它的左右两个半区间L,R,定义一种加权原子形如b(t)=1/(p(t))[X1-XR(t)],其中ρ为满足某些性质的非负函数,加权原子b(t)的线性组合构成加权原子空间B（ρ）,本证明了如果f∈B(ρ),则f的Fourier级数的Cesaro平均几乎处处收敛。     

Heteroscedasticity checks for regression models

For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach may readily be extended to handle partial linear, and linear autoregressive models.     

Inference for the Mean Difference in the Two-Sample Random Censorship Model

Inference for the mean difference in the two-sample random censorship model is an important problem in comparative survival and reliability test studies. This paper develops an adjusted empirical likelihood inference and a martingale-based bootstrap inference for the mean difference. A nonparametric version of Wilks' theorem for the adjusted empirical likelihood is derived, and the corresponding empirical likelihood confidence interval of the mean difference is constructed. Also, it is shown that the martingale-based bootstrap gives a correct first order asymptotic approximation of the corresponding estimator of the mean difference, which ensures that the martingale-based bootstrap confidence interval has asymptotically correct coverage probability. A simulation study is conducted to compare the adjusted empirical likelihood, the martingale-based bootstrap, and Efron's bootstrap in terms of coverage accuracies and average lengths of the confidence intervals. The simulation indicates that the proposed adjusted empirical likelihood and the martingale-based bootstrap confidence procedures are comparable, and both seem to outperform Efron's bootstrap procedure.     

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.