ESTIMATING THE ANGLE BETWEEN THE MEAN DIRECTIONS OF TWO SPHERICAL DISTRIBUTIONS

This paper considers the problem of calculating a confidence interval for the angular difference between the mean directions of two spherical random variables with rotationally symmetric unimodal distributions. For large sample sizes, it is shown that the asymptotic distribution of 1 – cos α, where α is the sample angular difference, is approximately exponential if the true difference is zero, and approximately normal for a ‘large’ true difference; a scaled beta approximation is determined for the general case. For small sample sizes, a bootstrap approach is recommended. The results are applied to two sets of palaeomagnetic data.     

基于虚拟现实的球形机构分析

利用虚拟现实的方法来设计球形机构,并把VR作为一种全新的设计接口,可在三维空间中实现球形机构的设计和论证。开发了一种新方法来设计球形机构,该方法可使设计者随意在由固定物体构成的设计环境中放置移动物体的几何模型,固定物体作为机构的基础和可能的运动干涉体,从而在考虑机构与环境干涉问题的同时,实现机构的运动分析。     

中国辩证法论纲

中国古代先哲学家在对自然、社会和人自身的探索中,提出了丰富的辩证法思想,主要内容包括相依相待,天人一理--世界万物普遍联系观察;天地絪縕,万物化醇--永恒运动和变化的发展观;一物两体,中庸和谐--对立统一观.西代哲人对世界的整体的、有机的、系统的、协调的、动态平衡、相关互补和包容并存关系的揭示,展示了中华民族独特的辩证思维智慧.     

ASSESSING AND TESTING FOR THRESHOLD NONLINEARITY IN STOCK RETURNS

This paper proposes a test for threshold nonlinearity in a time series with generalized autore‐gressive conditional heteroscedasticity (GARCH) volatility dynamics. This test is used to examine whether financial returns on market indices exhibit asymmetric mean and volatility around a threshold value, using a double‐threshold GARCH model. The test adopts the reversible‐jump Markov chain Monte Carlo idea of Green, proposed in 1995, to calculate the posterior probabilities for a conventional GARCH model and a double‐threshold GARCH model. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity with asymmetric behaviour of the mean and volatility. Simulation experiments demonstrate that the test works very well in distinguishing between the conventional GARCH and the double‐threshold GARCH models. In an application to eight international financial market indices, including the G‐7 countries, clear evidence supporting the hypothesis of threshold nonlinearity is discovered, simultaneously indicating an uneven mean‐reverting pattern and volatility asymmetry around a threshold return value.     

带有流动性约束的投资组合模型及其应用

在考虑组合投资收益与风险受市场流动性影响等因素的条件下,提出了一种带有模糊流动性约束的投资组合模型,并利用可能性理论将其转化为二次规划模型,得到该模型的解。通过实例证明:在不确定的金融资本市场,投资者可根据此模型来选择自己的投资组合,使有限资源得到最大程度利用。     

Simultaneous determination of the optimal process mean and cutting speed for a manufacturing process

The relationship between machining speed and the process mean for a manufacturing process has received little attention. This paper presents an analytical model and its solution procedure to simultaneously determine the optimal machining speed and process mean when the objective is to minimize the total cost per part. The total cost of the model includes replacement (resetting), production and quality costs. A global optimization algorithm is used to solve the proposed unconstrained model. Numerical examples to demonstrate the effectiveness of the proposed model are given and an extensive sensitivity analysis of the proposed model parameters is also provided. It has been concluded that machining speed and process mean are highly related. Therefore, the machining conditions should be taken into account when solving process mean targeting problems.     

The Use of Different Happiness Rating Scales: Bias and Comparison Problem?

This paper uses data of reported happiness which is measured at 4, 5, 7 and 11 likert-scale points. A group of 137 respondents was selected to study the comparison problem on the estimated mean happiness using direct rescaling. It is found that the 11-point scale’s estimated mean happiness is significantly higher than the 4 and 7-point scale. This paper also proposes an alternate method of rescaling using transition probabilities as weights. This adjusted rescaling resembles the calculation of expected value and provides better mean comparison.     

On the estimation of the distribution of alcohol consumption

The parameters of the distribution of alcohol consumption are estimated from the population mean and the mode of the log-normal distribution, separately for each sex. The lack of representativeness of the sample due to the failure to reach heavy drinkers is overcome. The distributions of alcohol consumption show a tight relationship between mean and standard deviation.     

《读者》之路：一个时代的见证和参与

作为改革开放和思想解放的产物,《读者》以高雅、清新、隽永的真善美的传播与人文关怀、以高品质高品位的价值追求,成就了作为“中国人的心灵读本”和中国期刊第一品牌的美誉。她不但见证了改革开放30年的社会变迁。参与了这一时期国人文化价值观的建构、民族灵魂的重铸、和谐文化的创新传播,还记录了这一时代变革中千万读者的情感和社会风尚。因此,“《读者》之路”就是改革开放之路、思想解放之路、多元文化的传播之路、和谐文化的创新之路、精神甘露的播撒之路、文化品牌的成长之路、文化产业的发展之路。