数学命题在珠算硬、软件建设中的作用（上）——兼谈中进制理论的一项应用

运用珠算解决高等数学问题的关键所在，即珠算的硬软件建设。本文摒弃千年古制、万国常法，借助数学命题揭示珠算硬件、软件的内部机制，为应用数学和珠算开拓了广阔而崭新的研究领域。     

广义Lucas数列的一些求和公式

由二次线性递推公式所定义的Lucas数列ΣLnΣ在数学的理论研究中有重要的作用.本文在已有的有关广义Lucas数列相关定理的基础上进一步推广,给出了更为广泛的广义Lucas数列的求和公式,采用了递推归纳的方法证明。     

Consistency and asymptotic normality of least squares estimators in generalized STAR models

Space–time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkova et al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.     

第二类stirling数S（n，n-L）中n、M、L之间关系的探讨

摘要：第二类stirling数5（n，n-L）是分配问题中实用价值很高的分配数，计算起来均较为繁琐，在限制条件n≥M下，对于n与L的取值不同目前已出现一些不同的计算公式，但对于n、M、L之间的内在联系还缺乏较深的认识，通过对n、M、L之间关系的讨论，揭示了它们的内在规律，并给出了S（n,n-L）的一个计算公式．     

Household Expenditure Patterns for Tourism Products and Services

The growing importance of the tourism industry, coupled with demographic, social and economic changes, highlights the need to study consumersÆ expenditure patterns for tourism products. Using 1990 Consumer Expenditure Survey data, this study examined leisure travel expenditure patterns of households, especially food, lodging, transportation, and sightseeing/entertainment expenditures. The results show that demographic and socioeconomic and cultural factors have a varying effect on each of the four expenditure categories. The research findings bear implications for marketing segmentation in various components of tourism industry, and suggest an effective research approach to develop pragmatic segmentation strategies.     

The double exponential jump diffusion model for pricing European options under fuzzy environments

The interest rate and volatility may have different values in the different commercial banks and financial institutions. Moreover, the fluctuations of the underlying assets are rare events, and there are not enough historical data to estimate the jump intensity in a precise sense. This paper considers European option pricing problems with the fuzzy interest rate, fuzzy drift, fuzzy volatility and fuzzy jump intensity. We present the fuzzy pricing formula of European options based on the Kou's double exponential jump diffusion model. We also obtain the crisp possibilistic mean option pricing formula in fuzzy double exponential jump diffusion model by using the crisp possibilistic mean values of the fuzzy numbers. Comparing with B-S formula, numerical analysis and empirical results show that the fuzzy double exponential jump diffusion formula and the crisp possibilistic mean option pricing formula are reasonable and can be taken as reference pricing tools for the financial investors.     

Exact arbitrage, well-diversified portfolios and asset pricing in large markets

For a market with an atomless continuum of assets, we formulate the intuitive idea of a “well-diversified” portfolio, and present a notion of “exact arbitrage”, strictly weaker than the more conventional notion of “asymptotic arbitrage”, and necessary and sufficient for the validity of an APT pricing formula. Our formula involves “essential” risk, one based on a specific index portfolio constructed from factors and factor loadings that are endogenously extracted to satisfy an optimality property involving a finite number of factors. We illustrate how our results can be translated to markets with a large but finite number of assets.     

GDP growth,terms-of-trade effects,and total factor productivity

The purpose of this paper is to assess the contribution of each one of the major factors explaining Australian nominal GDP growth: technological change, movements in the terms of trade, increases in the endowments of labour and capital, and changes in domestic output prices. We use an index number technique as well as an econometric approach. Moreover, we look at several methods to decompose total factor productivity growth into secular and unexpected components. All our empirical results have a tight theoretical foundation, being based on the GDP function approach to modelling the production sector of an open economy.     

Generation and distribution of the total factor productivity gains in US industries

This study estimates productivity gains and their distribution among inputs and outputs for 63 American industries over the period 1987–2012. Using the traditional surplus accounting method, the Total Factor Productivity (TFP) growth rates are divided into their price change components in order to determine the stakeholders who do or do not receive price advantages.

An initial analysis showed that TFP of US industries increased at an average trend of 0.8% and established that remunerations to employees and firms’ profitability constituted 49% and 39%, respectively, of the accumulated economic surplus from the productivity gains. Suppliers of intermediate inputs retained 12.1% of the surplus. Finally, customers, equipment and structure providers were the losers in the distribution of economic surplus via, respectively, a significant growth of relative final demand prices and a substantial price decrease of these assets.

A second step analysis underlined that industries with high TFP growth rates mainly benefited customers and firms via output price decreases and profitability improvements while industries with low or negative TFP changes hurt customers through significant output price increases. The sectoral level analysis also showed that employees’ remunerations depend only slightly on productivity gains produced within their industrial sectors.     

Testing hypotheses with fuzzy data: The fuzzy <Emphasis Type="Bold">p</Emphasis>-value

Statistical hypothesis testing is very important for finding decisions in practical problems. Usually, the underlying data are assumed to be precise numbers, but it is much more realistic in general to consider fuzzy values which are non-precise numbers. In this case the test statistic will also yield a non-precise number. This article presents an approach for statistical testing at the basis of fuzzy values by introducing the fuzzy p-value. It turns out that clear decisions can be made outside a certain interval which is determined by the characterizing function of the fuzzy p-values.