自然数幂方和的一个巧妙猜想

文章将利用已知的几种特殊的自然数的幂方和,研究其算法特征,进而给出并证明了自然数幂方和的一个巧妙猜想,希望这一猜想能给自然数的幂方求和寻求更简单的方法提供一些新思路.     

Extreme statistics from the cosine distribution

The cosine distribution serves as a very good teaching example for which exact moment properties of extreme order statistics can be expressed in terms of elementary functions. This article presents the limiting joint distribution of the extreme order statistics for the cosine distribution. It is shown that burrows'(1986) result is a special case of the result presented in this article.     

Lattice path combinatorics for multiple product identities

Lattice paths are enumerated as walks on a lattice under the Delannoy criterion of vertical, horizontal and upward diagonal steps. Delannoy recursions are generalized for arbitrary weights in each of these directions, where the row elements of the Delannoy triangles correspond to lattice paths for all walks at a given length.     

The mean of linear signed rank statistics under alternatives

An expression is presented for the mean of a linear signed rank statistic for the one sample location model. Several examples are given to illustrate its application.     

从解一个古典概率问题所想到的

文章给出一个古典概率问题的两个解法，从而导出几个有趣的等式。     

Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

Given an undirected multigraph G = (V, E) and two positive integers and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an -edge-connected and k-vertex-connected multigraph. In this paper, we show that the problem can be solved in Õ(mn²) time for any fixed and k = 3 if an input multigraph G is 2-vertex-connected, where n = |V| and m is the number of pairs of adjacent vertices in G.     

On Inverse Problems of Optimum Perfect Matching

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l ₁ or l norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l ₁ and l norms. It has been proved that the inverse maximum-weight perfect matching under l norm can be formulated as a maximum-mean alternating cycle problem of an undirected network, and can be solved in polynomial time by a binary search algorithm and in strongly polynomial time by an ascending algorithm, and under l ₁ norm it can be solved by the ellipsoid method. Therefore, inverse problems of maximum-weight perfect matching under l ₁ and l norms are solvable in polynomial time.     

Landau多项式算子与无界函数逼近

利用扩展乘数法构造了 Landau型多项式算子逼近全空间或有界集上无界函数的若干收敛定理 ,给出了具有一般性的结论 ,从而推广了已有文献的若干结果 .     

Admissible minimum bias estimation of response surfaces

The minimum bias estimator was introduced as an alternative to the least squares estimator for approximating response functions by low-order polynomials. Here we show how to obtain an admissible estimator with smaller squared bias.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.