关于数论函数方程δ（x^2＋y）＋δ（x＋y^2）=2ψ（x^3＋y^3）

对于正整数k，设δ（k）和ψ（k）分别是k的约数和函数和Dedekind函数．该文证明了：方程仅有正整数解（x,y）=（1，1）．     

The Continuous Run Sum Chart

The run sum chart is an effective two-sided chart that can be used to monitor for process changes. It is known that it is more sensible than the Shewhart chart with runs rules and its performance improves as the number of regions increases. However, as the number of regions increses the resulting chart has more parameters to be defined and its design becomes more involved. In this article, we introduce a one-parameter run sum chart. This chart accumulates scores equal to the subgroup means and signals when the cummulative sum exceeds a limit value. A fast initial response feature is proposed and its run length distribution function is found by a set of recursive relations. We compare this chart with other charts suggested in the literature and find it competitive with the CUSUM, the FIR CUSUM, and the combined Shewhart FIR CUSUM schemes.     

Influence measure for the L1 regression

Because outliers and leverage observations unduly affect the least squares regression, the identification of influential observations is considered an important and integrai part of the analysis. However, very few techniques have been developed for the residual analysis and diagnostics for the minimum sum of absolute errors, L₁ regression. Although the L₁ regression is more resistant to the outliers than the least squares regression, it appears that outliers (leverage) in the predictor variables may affect it. In this paper, our objective is to develop an influence measure for the L₁ regression based on the likelihood displacement function. We illustrate the proposed influence measure with examples.     

多维理论视角下的合作行为探析

合作行为一直是国内外学者们的重要研究课题,不同的学科、不同的理论给出了不同的解释。学者们以"行为体之间的合作行为的发生和维持"作为研究主题,分别从以基因为核心变量下的合作行为、文化影响下的合作行为、博弈互动影响下的合作行为和认知影响下的合作行为等多维理论视角对合作行为做出阐释,这些理论阐释既有共同点,也有不同点,既有相一致的方面,也有相冲突的方面。通过对这些理论阐释的基本内容和关键变量进行系统梳理和逻辑剖析,展现这些理论阐释的各自优缺点,并在此基础上对这些理论观点加以综合比较,最终揭示行为体之间的合作行为是如何发生并维持下去的。     

Sampling inspection for resubmitted lots

Lot resubmissions are allowed in situations where the original inspection results are suspected or when the supplier is allowed to opt for resampling as per the provisions of the contract etc. This paper examines the situation of resampling of lots and derives the performance measures of a resampling scheme having a single sampling plan for inspection. The usefulness and limitations of resampling of resubmitted lots are also discussed     

从《非（国语〉》看柳宗元的历史著作观

柳宗元通过对《国语》一书中所记载的历史事件、历史现象的批驳，阐述了关于历史著作的一些观点和看法。柳宗元认为历史著作应注重内容的真实，写作内容应有所选择，应简洁，前后一致，并具有教育的功能。在一定程度上，柳宗元的历史著作观也是其经学著作观，反映了柳宗元对经学文献的看法，体现了柳宗元的经学研究观念，反映了中唐时期经学、史学的变化。柳宗元的历史著作观与其哲学观、历史观密不可分。     

Asymptotic behaviour of a test statistic for detection of change in mean of vectors

The paper gives an asymptotic distribution of a test statistic for detecting a change in a mean of random vectors with dependent components. The studied test statistic has a form of a maximum of a square Euclidean norms of vectors with components being standardized partial cumulative sums of deviations from means. The limit distribution was obtained using a result of Piterbarg [1994. High deviations for multidimensional stationary Gaussian processes with independent components. In: Zolotarev, V.M. (Ed.), Stability Problems for Stochastic Models, pp. 197–210].     

Optimal non-diagonal-type estimators in linear regression under the prediction error sum of squares criterion

This article considers the notion of the non-diagonal-type estimator (NDTE) under the prediction error sum of squares (PRESS) criterion. First, the optimal NDTE in the PRESS sense is derived theoretically and applied to the cosmetics sales data. Second, we make a further study to extend the NDTE to the general case of the covariance matrix of the model and then give a Bayesian explanation for this extension. Third, two remarks concerned with some potential shortcomings of the NDTE are presented and an alternative solution is provided and illustrated by means of simulations.     

堆垒级数部分和的一般公式

利用阶乘幂差分的重要性质,得到堆垒级数部分和的一般公式.     

中美俄博弈模式分析:决策层级、动机及过程

以中美俄博弈的决策模式为研究对象,并通过列举中美和中俄两个具有合作性质的博弈案例,进而深入分析中美俄博弈的决策角色、决策动机和决策过程,指出决策角色可分为第一层级、第二层级和辅助层级,而国家利益是最重要的决策动机.为了追求决策效率,三国决策者紧密控制决策过程,防止其他权力部门分享决策权.