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.     

稀土元素Ce对Al－Mg－Si变形铝合金铸态组织的影响及机理探讨

改变Ａｌ－Ｍｇ－ｓｉ合金中稀土Ｃｅ的含量，采用金相显微观察，电镜分析等方法，研究稀土元素Ｃｅ对Ａ１－Ｍｇ－Ｓｉ合金铸态组织的影响。结果表明：稀土元素Ｃｅ使晶粒细化，并有效地减小铸态组织的二次枝晶间距。其作用机理是凝固时Ｃｅ与某些元素反应产物可以作为ａ相结晶的晶核，使晶粒细化，并且Ｃｅ与Ｆｅ、Ｓｉ等元素富集在结晶前沿的液相中，造成成份过冷，促进分枝。     

皇家宫苑赏石文化流变研究

中国赏石文化内容丰富且历史悠久。赏石文化就是积淀在赏石中的文化现象 ,是人与自然相互协调、和谐统一的系统。自汉代在宫苑中已有赏石叠置 ,到南朝山水文化繁荣 ,经隋唐尤其是宋代以来赏石经历代王朝收藏、搬运、配置 ,至清乾隆时期 ,皇家赏石文化随宫苑变迁而消长流变 ,达到极高水平。这一流变脉络值得梳理研究。     

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]).     

Number of observations near the maximum in an F α-scheme

Let K _n (a) be the number of observations in the interval (M _n ,?a, M _n ), where M _n is the maximum value in a sequence of size n. We study the asymptotic properties of K _n (a) under the F ^α-scheme and discuss the influence of the associated sequence α _n on the limit behaviour of this random variable.     

Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model

A pivotal characteristic of credit defaults that is ignored by most credit scoring models is the rarity of the event. The most widely used model to estimate the probability of default is the logistic regression model. Since the dependent variable represents a rare event, the logistic regression model shows relevant drawbacks, for example, underestimation of the default probability, which could be very risky for banks. In order to overcome these drawbacks, we propose the generalized extreme value regression model. In particular, in a generalized linear model (GLM) with the binary-dependent variable we suggest the quantile function of the GEV distribution as link function, so our attention is focused on the tail of the response curve for values close to one. The estimation procedure used is the maximum-likelihood method. This model accommodates skewness and it presents a generalisation of GLMs with complementary log–log link function. We analyse its performance by simulation studies. Finally, we apply the proposed model to empirical data on Italian small and medium enterprises.