Fuzzy集的退化锥和关于闭性的几个充分条件

本文对Fuzzy集引进退化锥、后退锥、投影锥等概念,并利用它们建立了关于Fuzzy集闭性的几个充分性条件。这些结果对于讨论具有控制锥的Fuzzy多目标规划是有用的。     

Machine Learning Models and Statistical Complexity to Analyze the Effects of Posture on Cerebral Hemodynamics

The mechanism of cerebral blood flow autoregulation can be of great importance in diagnosing and controlling a diversity of cerebrovascular pathologies such as vascular dementia, brain injury, and neurodegenerative diseases. To assess it, there are several methods that use changing postures, such as sit-stand or squat-stand maneuvers. However, the evaluation of the dynamic cerebral blood flow autoregulation (dCA) in these postures has not been adequately studied using more complex models, such as non-linear ones. Moreover, dCA can be considered part of a more complex mechanism called cerebral hemodynamics, where others (CO₂ reactivity and neurovascular-coupling) that affect cerebral blood flow (BF) are included. In this work, we analyzed postural influences using non-linear machine learning models of dCA and studied characteristics of cerebral hemodynamics under statistical complexity using eighteen young adult subjects, aged 27 ± 6.29 years, who took the systemic or arterial blood pressure (BP) and cerebral blood flow velocity (BFV) for five minutes in three different postures: stand, sit, and lay. With models of a Support Vector Machine (SVM) through time, we used an AutoRegulatory Index (ARI) to compare the dCA in different postures. Using wavelet entropy, we estimated the statistical complexity of BFV for three postures. Repeated measures ANOVA showed that only the complexity of lay-sit had significant differences.     

On the anomalous behaviour of a class of locality statistics

A scan statistic methodology for detecting anomalies has been developed for application to graphs, where “anomalies” are equated with vertices that exhibit distinctive local connectivity properties. We present an “anomaly graph” construction that illustrates the capabilities of these scan statistics via the behaviour of their associated locality statistics on our anomaly graphs.     

A note on self-normalized Dickey-Fuller test for unit root in autoregressive time series with GARCH errors

In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.     

Testing for the equality of two binomial proportions

There are two statistics one might choose when testing whether two binomial probabilities are the same. This note provides a large sample answer to Robbins' question of which is preferable.     

A simple model for automatically measuring radon exhalation rate from medium surface

A simple model to measure radon exhalation rate from medium surface is developed in this paper. This model is based on a combination of the “accumulation chamber” technique and a radon monitor. The radon monitor is used to perform measurement of radon concentration evolution inside the accumulation chamber, and radon exhalation rate is evaluated via nonlinear least-square fitting of the measured data. If the flow rate of the pump is high enough, radon concentration in the detector's internal cell becomes to be equal to that in the accumulation chamber quickly, and the simple model for measuring the radon exhalation rate can be generated analytically. Generally, the pump flow rate of radon monitor is low, not satisfying the condition. We find other sufficient conditions of this simplified model. On these conditions, the radon exhalation rate can be calculated accurately through this model even the flow rate of the pump is not so high. This method can be applied to develop and improve the instruments for measuring the radon exhalation rate.     

一类总体参数的统计推断方法

根据一类总体分布函数的特性,对其应用适当的变换,进而给出了这类总体参数的统计推断方法．     

城市蔬菜产品品种污染监控系统的研究及其应用

蔬菜产品中的农药残留问题一直为市民所关心,为了让市民了解日常消费的蔬菜产品品种的质量状况和污染水平,本文结合深圳市布吉、福田两大农产品批发市场2003年1~4月份的监测抽样数据,应用主成分分析及Hotelling统计量等多元统计方法,结合SAS系统与Delphi系统建立城市蔬菜产品品种污染监控系统。该监控系统不仅可以为市场提供及时的蔬菜产品品种质量状况和污染水平的信息,而且对于及时监控流入市场的蔬菜质量、保障市民身体健康、引导市场消费等都具有重要意义。     

Sufficient conditions for variational problems with variable endpoints: Coupled points

In this paper we demonstrate that the notion of coupled points developed in [29] for the variable endpoints variational problems is the analog of that of conjugate points when the endpoints are fixed. We provide weak and strong local optimality criteria using the strengthening of necessary conditions involving both the coupled points and the regularity concepts.This research was supported by a grant from NSERC Canada and a summer support from Michigan State University.     

均值已知的条件下方差的统计推断

充分利用总体的信息，讨论了正态总体均值μ已知的条件下，方差σ^2的统计推断问题．