Strong laws of large numbers for the mth-order asymptotic odd–even Markov chains indexed by an m-rooted Cayley tree

In this article, we will study the strong laws of large numbers and asymptotic equipartition property (AEP) for mth-order asymptotic odd–even Markov chains indexed by an m-rooted Cayley tree. First, the definition of mth-order asymptotic odd–even Markov chains indexed by an m-rooted Cayley tree is introduced, then the strong limit theorem for this Markov chains is established. Next, the strong laws of large numbers for the frequencies of ordered couple of states for mth-order asymptotic odd–even Markov chains indexed by an m-rooted Cayley tree are obtained. Finally, we prove the AEP for this Markov chains.     

Fuzzy process capability indices for simple linear profile

Process capability indices are numerical tools that quantify how well a process can meet customer requirements, specifications or engineering tolerances. Fuzzy logic is incorporated to deal imprecise, incomplete data along with uncertainty. This paper develops two fuzzy methods for measuring the process capability in simple linear profiles for the circumstances in which lower and upper specification limits are imprecise. To guide practitioners, numerical example is provided.     

Population Marginal Means in the Linear Model: An Alternative to Least Squares Means

The parameter concept in the term least squares mean is defined and given the more meaningful name population marginal mean; and its estimation is discussed.     

中外数字文化象征片论

数字并不只限于计数方面 ,而是承载着许多的文化信息。通过对比研究揭示数字在中外不同文化中的象征意义 ,有助于从一个侧面了解中外文化之异同     

On moments of the supremum of normed weighted averages

Let {X, X_n; n ≥ 1} be a sequence of real-valued iid random variables, 0 < r < 2 and p > 0. Let D = { A = (a_nk; 1 ≤ k ≤ n, n ≥ 1); a_nk, ? R and sup_{n, k} |a_n,k| < ∞}. Set S_n( A ) = ∑ⁿ_k=1a_{n, k}X_k for A ? D and n ≥ 1. This paper is devoted to determining conditions whereby E{sup_{n ≥ 1}, |S_n( A )|/n^1/r}^p < ∞ or E{sup_{n ≥ 2} |S_n( A )|/2n log n)^1/2}^p < ∞ for every A ? D. This generalizes some earlier results, including those of Burkholder (1962), Choi and Sung (1987), Davis (1971), Gut (1979), Klass (1974), Siegmund (1969) and Teicher (1971).     

数码列{a_i}_0~m的G-S系数

本文引入数码列的G-S系数的概念,给出了一般数码列的G-S系数N_(k-1),单调数码列的G-S系数N_(K~2-1)等结果.     

Trends in intercountry adoption: Analysis of data from 20 receiving countries, 1998–2004

The implications of developments in intercountry adoption worldwide in the early years of the twenty-first century are explored, based on analysis of data from 20 receiving countries. Between 1998 and 2004, intercountry adoption increased by 42 per cent. Problems in data collection and analysis are examined, as is the reliability of estimates of numbers of children sent by countries of origin when derived from data provided by receiving countries. Also considered are various measures of standardization which can be used to facilitate comparison between countries and show trends over time. The potential for more detailed comparative analysis is explored.     

关于实数理论八条定理的注记

在这篇文章里,我们简要分析实数理论八条定理的内在联系,并指出它们所提供的数学方法的特色.