Graphical solutions for structural regression assist errors-in-variables modelling

Structural regression attempts to reveal an underlying relationship by compensating for errors in the variables. Ordinary least-squares regression has an entirely different purpose and provides a relationship between error-included variables. Structural model solutions, also known as the errors-in-variables and measurement-error solutions, use various inputs such as the error-variance ratio and x-error variance. This paper proposes that more accurate structural line gradient (coefficient) solutions will result from using the several solutions together as a system of equations. The known data scatter, as measured by the correlation coefficient, should always be used in choosing legitimate combinations of x- and y-error terms. However, this is difficult using equations. Chart solutions are presented to assist users to understand the structural regression process, to observe the correlation coefficient constraint, to assess the impact of their error estimates and, therefore, to provide better quality estimates of the structural regression gradient.     

Abel分部求和公式与排序定理

Ａｂｅｌ分部求和公式与排序定理王慧兴众所周知，排序定理在不等式的证明和最优化设计方面发挥着出奇制胜的作用。本文运用Ａｂｅｌ分部求和公式给出排序定理一个新证明，因而排序定理可作为Ａｂｅｌ分部求和公式的一个推论，进而开拓Ａｂｅｌ分部求和公式在中等数学中的...     

浅议数学分析教学的几个问题

浅议数学分析教学的几个问题王保全１关于极限运算问题极限概念、极限方法是数学分析最基本最重要的概念和方法。它既是教学的重点又是教学的难点。明析极限运算的特性，对教好极限十分有益。１．１极限运算的非初等性初等数学主要以数作为研究对象，讨论数与数之间的联系...     

A lower bound for the transition density function of a stochastic differential equation

Let W_t be a one-dimensional Brownian motion on the probability space (Ω,F,P), and let dx_t = a(x_t)dt + b(x_t)dw_t, b²(x) > 0, be a one-dimensional Ito stochastic differential equation. For a(x) = a₀ + a₁x + … + a_nxⁿ on a bounded interval we obtain a lower bound for p(t,x,y), the transition density function of the homogeneous Markov process x_t, depending directly on the coefficients a₀,a₁, …, a_n, and b(x).     

A note on the joint distribution of correlated quadratic forms

In the present paper, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal.     

Two Variations of the Minimum Steiner Problem

Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s S and t T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}–2,min {|S|,|T|}–1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|–2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.An extended abstract of part of this paper appears in Hsu et al. (1996).Supported in part by the National Science Foundation under Grants CCR-9309743 and INT-9207212, and by the Office of Naval Research under Grant No. N00014-93-1-0272.Supported in part by the National Science Council, Taiwan, ROC, under Grant No. NSC-83-0408-E-001-021.     

蒋介石与九一八事变后的地方军事冲突

面对九一八事变后的地方军事冲突,下野再起的蒋介石固守低调调解,羁縻默认,不用武力解决的政策,集中精力巩固基本区域、发展基本势力,建立有力之中央.这既是蒋介石处理地方军事冲突的基本逻辑,也是对整个地方实力派问题的基本判断.此种逻辑与判断,一方面,在千头万绪、错综复杂的情境下,实不失为解决问题的路径之一,且取得相当成功;另一方面,仍是武力解决问题逻辑之延续,以至未能彻底消除地方实力派的地方主义和派系主义.     

当代台湾乡土文学发展异变探析

1980年代以来,传承中国新文学传统的台湾乡土文学因受“本土论”思潮的影响而被“台湾文学论”取代.当代台湾乡土文学的发展异变既是全球化语境中台湾本土文化的自觉应对,也和它与生俱来的政治意识形态因素息息相关.当代台湾乡土文学的发展异变并没有隔断中国新文学传统,所谓的“台湾文学”并不是独立于中国文学之外的文学形态,而是“文化台独”在文学上的反映,并非台湾文学自身运动的发展.     

地方文化如何融入幼儿园区域游戏——以淄博市为例

以淄博市为例,探讨地方文化与幼儿园教育活动的融合路径,认为应根植地方文化,开发具有地方特色的幼儿园区域游戏,特别是大力彰显地方传统游戏的历史文化精神,并通过区域游戏架起幼儿与地方文化双向创生的桥梁,一方面积极推进地方文化精神的永续传承,另一方面积极促进幼儿精神世界的健康成长。     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.