数字的文化承载功能探析

在跨文化交际中,准确运用数字不仅可以表现数字的文化内涵,而且会增强语言的表达能力.     

Automatic clustering algorithm for fuzzy data

Coppi et al. [7 R. Coppi, P. D'Urso, and P. Giordani, Fuzzy and possibilistic clustering for fuzzy data, Comput. Stat. Data Anal. 56 (2012), pp. 915–927. doi: 10.1016/j.csda.2010.09.013[Crossref], [Web of Science ®] , [Google Scholar]] applied Yang and Wu's [20 M.-S. Yang and K.-L. Wu, Unsupervised possibilistic clustering, Pattern Recognit. 30 (2006), pp. 5–21. doi: 10.1016/j.patcog.2005.07.005[Crossref], [Web of Science ®] , [Google Scholar]] idea to propose a possibilistic k-means (PkM) clustering algorithm for LR-type fuzzy numbers. The memberships in the objective function of PkM no longer need to satisfy the constraint in fuzzy k-means that of a data point across classes sum to one. However, the clustering performance of PkM depends on the initializations and weighting exponent. In this paper, we propose a robust clustering method based on a self-updating procedure. The proposed algorithm not only solves the initialization problems but also obtains a good clustering result. Several numerical examples also demonstrate the effectiveness and accuracy of the proposed clustering method, especially the robustness to initial values and noise. Finally, three real fuzzy data sets are used to illustrate the superiority of this proposed algorithm.     

A strong law of large number for negatively dependent and non identical distributed random variables in the framework of sublinear expectation

Abstract

In this article, in the framework of sublinear expectation initiated by Peng, we derive a strong law of large numbers (SLLN) for negatively dependent and non identical distributed random variables. This result includes and extends some existing results. Furthermore, we give two examples of our result for applications.     

永久随机数在多层次调查中的应用

采用永久随机数法抽样技术抽到的样本具有很好地样本兼容的性质。本文讨论了采用序贯srswor抽样技术和Poisson抽样技术这两种永久随机数法抽样技术时,多层次调查的实现问题,希望能为多层次调查的实现提供一点启示。     

Eisenstein判别法的推广

论述了Eisenstein判别法的若干具有实用价值的推广形式,并把Eisenstein判别法推广到了整环上.     

Computational Forecasting of Wavelet-converted Monthly Sunspot Numbers

Monthly average sunspot numbers follow irregular cycles with complex nonlinear dynamics. Statistical linear models constructed to forecast them are therefore inappropriate, while nonlinear models produce solutions sensitive to initial conditions. Two computational techniques - neural networks and genetic programming - that have their advantages are applied instead to the monthly numbers and their wavelet-transformed and wavelet-denoised series. The objective is to determine if modeling wavelet-conversions produces better forecasts than those from modeling series' observed values. Because sunspot numbers are indicators of geomagnetic activity their forecast is important. Geomagnetic storms endanger satellites and disrupt communications and power systems on Earth.     

完全数与梅森素数

完全数与梅森素数是初等数论中所涉及的几个特殊的数，本文简述它们的有关概况，论证了完全数与梅森素数之间的紧密联系．     

Long-range correlation analysis of the Wichmann-Hill random number generator

The distribution of points (r _n,r _n+s), n = 0, 1, 2,...whose coordinates are terms at distance s of the pseudorandom sequence generated by the Wichmann and Hill method is studied. It is known that for many congruential generators critical values of the distance s exist such that these points, far from being uniformly distributed, are concentrated on very few lines. An algorithm is described for computing the critical distances within the Wichmann-Hill sequence and the results obtained are compared with those of other linear congruential generators.     

On the Asymmetric Marcinkiewicz-Zygmund Strong Law of Large Numbers for Linear Random Fields

In this article, the asymmetric Marcinkiewicz-Zygmund strong law of large numbers for linear random field under negative association is obtained. Our result generalizes a result in Gut and Studtmüller (2009 Gut , A. , Studtmüller , U. ( 2009 ) An asymmetric Marcinkiewicz-Zygmund LLN for random fields . Statist. Probab. Lett. 79 : 1016 – 1020 .[Crossref], [Web of Science ®] , [Google Scholar]). An asymmetric Marcinkiewicz-Zygmund LLN for random fields to the linear random field by using the Beverige-Nelson decomposition.     

General results of complete convergence and complete moment convergence for weighted sums of some class of random variables

ABSTRACT

In the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013 Shen, A.T. (2013). On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal.2013, Article ID 216236: 1–7. [Google Scholar]).