Theoretical and practical issues in purchasing power parities illustrated with reference to the 1993 Organization for Economic Co-operation and Development data

This paper deals first with some theoretical issues in purchasing power parities, including the definition of a generalized class of additive indices, which includes the standard Geary–Khamis and Iklé indices as special cases, and the definition of indicators of price and quantity structure which are independent of the particular units in which quantities are originally expressed. The paper then provides a comparative analysis of the results of applying these techniques to the 1993 Organization for Economic Co-operation and Development data and relates the results to underlying features of the price and expenditure data.     

汉语古诗词中模糊数字的翻译

古诗词中含有大量的模糊数字，这些数字对诗词的意境刻画起了重要作用。本文从文化角度出发，采用英汉对比的方法，通过对诗词中数字特殊文化内涵的分析，探讨模糊数字的翻译方法——直译法、转移法和归化法。     

论罗马数字的规范化问题

当前，中文电子媒体中作为序号的罗马数字使用很不规范。基于对传媒语言语料库的详细调查，我们分析了这种现象产生的可能原因及不规范使用罗马数字可能带来的问题，并提出了规范化使用罗马数字的建议。     

On the statistical inference of a machine-generated autoregressive AR(1) model

We have obtained the asymptotic bias and the limiting distribution for the Yule–Walker estimator of the autoregressive parameter under a considerably weaker assumption than that of independence in the noise sequence. Among other things, these suggest robustness of the classical results and throw some light on the use of simulations based on pseudorandom numbers in verifying these results.     

A maximum-likelihood estimator with infinite error

The standard error of the maximum-likelihood estimator for 1/μ based on a random sample of size N from the normal distribution N(μ,σ²) is infinite. This could be considered to be a disadvantage.Another disadvantage is that the bias of the estimator is undefined if the integral is interpreted in the usual sense as a Lebesgue integral. It is shown here that the integral expression for the bias can be interpreted in the sense given by the Schwartz theory of generalized functions. Furthermore, an explicit closed form expression in terms of the complex error function is derived. It is also proven that unbiased estimation of 1/μ is impossible.Further results on the maximum-likelihood estimator are investigated, including closed form expressions for the generalized moments and corresponding complete asymptotic expansions. It is observed that the problem can be reduced to a one-parameter problem depending only on , and this holds also for more general location-scale problems. The parameter can be interpreted as a shape parameter for the distribution of the maximum-likelihood estimator.An alternative estimator is suggested motivated by the asymptotic expansion for the bias, and it is argued that the suggested estimator is an improvement. The method used for the construction of the estimator is simple and generalizes to other parametric families.The problem leads to a rediscovery of a generalized mathematical expectation introduced originally by Kolmogorov [1933. Foundations of the Theory of Probability, second ed. Chelsea Publishing Company (1956)]. A brief discussion of this, and some related integrals, is provided. It is in particular argued that the principal value expectation provides a reasonable location parameter in cases where it exists. This does not hold generally for expectations interpreted in the sense given by the Schwartz theory of generalized functions.     

谈中国文化史与文学史中的以四论列现象

中国的文化与文学史上有大量的对各种人物与其他事物以四论列的情况。考察这些实例,能够发现它们有很多不是按照历史事实自然建立的,而是一种独特的文化现象。这种现象不易用数理文化来加以解释,而更多地与汉语与中国诗歌文化的一些特点有关。这种现象从宋代开始大量出现,从一个侧面反映了宋代以来中国经济、文化的繁荣。     

关于限制性手写体汉字预处理探索

就限制性手写体汉字的预处理问题进行了一些讨论，对通过摄像机摄入的限制性手写体汉字提出了一种预处理方法，对汉字采用了位置正规化、大小正规化、平滑处理、细化处理的相结合的方法，通过预处理的汉字，使汉字识别率大大的提高     

初始点任意的摄动梯度投影法

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δｋ取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。     

Modified explicit inversive congruential pseudorandom numbers with power of 2 modulus

A modified version of the explicit inversive congruential method with power of 2 modulus for generating uniform pseudorandom numbers is introduced. The statistical independence behaviour of the generated sequences is studied based on the distribution of all pairs of successive pseudorandom numbers over the entire period. Lower and upper bounds for the discrepancy of the corresponding two-dimensional point sets are established. These results certainly play only a minor part in studying the statistical independence behaviour of the generated sequences, but they show that modified explicit inversive congruential pseudorandom numbers have some attractive properties at least regarding their two-dimensional discrepancy. The method of proof relies heavily on a thorough analysis of certain exponential sums.