一类神经网络模型的解及其渐近性态

通过对简单一维微分方程的求解,得出了一类人工神经网络模型的解解析表达式。它是由对称阵的特征值与特征向量表达。根据此解析表达式推出了该神经网络模型在特殊情况下的解析表达式。在特殊情况下,特征值与特征向量的神经网络计算已有很多论文论及。最后利用解析表达式分析了该神经网络解的渐近稳定性态。     

A unified view on skewed distributions arising from selections

Parametric families of multivariate nonnormal distributions have received considerable attention in the past few decades. The authors propose a new definition of a selection distribution that encompasses many existing families of multivariate skewed distributions. Their work is motivated by examples that involve various forms of selection mechanisms and lead to skewed distributions. They give the main properties of selection distributions and show how various families of multivariate skewed distributions, such as the skew‐normal and skew‐elliptical distributions, arise as special cases. The authors further introduce several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.     

Contributions to two-sample statistics

When testing the equality of the means from two independent normally distributed populations given that the variances of the two populations are unknown but assumed equal, the classical Student's two-sample t-test is recommended. If the underlying population distributions are normal with unequal and unknown variances, either Welch's t-statistic or Satterthwaite's approximate F test is suggested. However, Welch's procedure is non-robust under most non-normal distributions. There is a variable tolerance level around the strict assumptions of data independence, homogeneity of variances, and identical and normal distributions. Few textbooks offer alternatives when one or more of the underlying assumptions are not defensible. While there are more than a few non-parametric (rank) procedures that provide alternatives to Student's t-test, we restrict this review to the promising alternatives to Student's two-sample t-test in non-normal models.     

加群上的NEAR环

本文讨论了加群上保持零元的映射集合对映射的加法和乘法作成的Near环,证明了它是具有可换加法和单位元的零对称Near环,讨论了它的理想特点,并构造了几类特殊的左、右理想。     

On some robust estimation procedures for quantiles based on data

This paper introduces some robust estimation procedures to estimate quantiles of a continuous random variable based on data, without any other assumptions of probability distribution. We construct a reasonable linear regression model to connect the relationship between a suitable symmetric data transformation and the approximate standard normal statistics. Statistical properties of this linear regression model and its applications are studied, including estimators of quantiles, quartile mean, quartile deviation, correlation coefficient of quantiles and standard errors of these estimators. We give some empirical examples to illustrate the statistical properties and apply our estimators to grouping data.     

表达对称性关系的句法手段

本文主要根据从功能认知角度提出的对称象似原理,探讨了表达对称语义关系的两种句法手段--"融合"手段和"穿插"手段,初步建立了汉语对称关系句法表达手段的框架."融合"手段主要通过添加相互标记和协同标记来实现,该部分主要讨论了"相互、互相、彼此"以及"一起、一齐、一同、一块儿、同时、共同"等融合标记;"穿插"手段主要通过添加穿插标记来实现,该部分主要讨论了"分别、分头、各自"等穿插标记.同时,文中还比较了用法相近的标记的异同.     

改进运动规律凸轮基圆半径的确定

本文针对凸轮机构推杆作改进梯形加速度、改进正弦加速度和３－４－５次多项式运动规律的情况，研究对心式盘形凸轮机构凸轮基圆半径的确定方法，并利用数值计算方法绘制了基圆半径系数β（ｒ＿０／ｈ）的线图．本文是对已有的用于四种基本运动规律确定基圆半径的诺模图￣［３］和补充诺模图［６］的进一步的发展．     

On D-optimal robust second order slope-rotatable designs

Das and Park (2006) introduced slope-rotatable designs overall directions for correlated observations which is known as A-optimal robust slope-rotatable designs. This article focuses D-optimal slope-rotatable designs for second-order response surface model with correlated observations. It has been established that robust second-order rotatable designs are also D-optimal robust slope-rotatable designs. A class of D-optimal robust second-order slope-rotatable designs has been derived for special correlation structures of errors.     

An Efficient Algorithm for the Least-Squares Cross-Validation with Symmetric and Polynomial Kernels

The least-squares cross-validation is a completely automatic method for choosing the smoothing parameter in probability density estimation but this method consume large amounts of computer time. This article concerns an efficient computational algorithm for this method when the kernel is symmetric and polynomial functions.     

Multi-response permutation procedures for a priori classifications

An exact permutation test for analyzing and/or dredging multi-response data at the ordinal or higher levels is presented. The associated test statistic is based on the average distance (or any specified norm) between points within a priori disjoint subgroups of a finite population of points in an r-dimensional space (corresponding to r measured responses from each object in a finite population of objects). Alternative approximate tests based on the beta and normal distributions are provided. Two detailed examples utilizing actual social science data are considered, including comparisons of the approximate tests. An additional example describes the behavior of these tests under a variety of conditions, including extreme data configurations