一类多项式零点问题的证明

多项式零点问题的证明,已见于若干学报或教材．其方法可谓多种多样,但显复杂．本文先将Rolle定理加以推广,称之为“广义Rolle定理”,然后借助于该定理,证明一类著名的多项式零点值问题．     

行政诉讼履行法定职责实体判决论——以“尹荷玲案”为核心

“司法审查有限原则”是行政诉讼法的基本原则,这导致了“履行法定职责实体判决”存在争议。“尹荷玲案”不但证成了履行法定职责实体判决存在的正当性,而且明确了该判决适用的“双阶要件”,即“理由具备、事实清楚、法律规定明确”的一般要件,与“法效果唯一性”的特别要件。其中“法效果唯一性”分为两种情况:一是羁束行政行为,二是行政裁量收缩为零,这恰与《行政诉讼法》修改后“给付判决”与“履行判决”的规定相契合。纵观司法实践,重做判决、履行判决、给付判决形成了“程序性判决—提示性判决—履行法定职责实体判决”3种判决方式,体现了三者功能的相似性。作为实质化解争议的履行法定职责实体判决,也彰显了司法推动制度发展的功能。     

Marginal zero-inflated regression models for count data

Data sets with excess zeroes are frequently analyzed in many disciplines. A common framework used to analyze such data is the zero-inflated (ZI) regression model. It mixes a degenerate distribution with point mass at zero with a non-degenerate distribution. The estimates from ZI models quantify the effects of covariates on the means of latent random variables, which are often not the quantities of primary interest. Recently, marginal zero-inflated Poisson (MZIP; Long et al. [A marginalized zero-inflated Poisson regression model with overall exposure effects. Stat. Med. 33 (2014), pp. 5151–5165]) and negative binomial (MZINB; Preisser et al., 2016) models have been introduced that model the mean response directly. These models yield covariate effects that have simple interpretations that are, for many applications, more appealing than those available from ZI regression. This paper outlines a general framework for marginal zero-inflated models where the latent distribution is a member of the exponential dispersion family, focusing on common distributions for count data. In particular, our discussion includes the marginal zero-inflated binomial (MZIB) model, which has not been discussed previously. The details of maximum likelihood estimation via the EM algorithm are presented and the properties of the estimators as well as Wald and likelihood ratio-based inference are examined via simulation. Two examples presented illustrate the advantages of MZIP, MZINB, and MZIB models for practical data analysis.     

Analysis of dependently truncated data in Cox framework

Truncation is a known feature of bone marrow transplant (BMT) registry data, for which the survival time of a leukemia patient is left truncated by the waiting time to transplant. It was recently noted that a longer waiting time was linked to poorer survival. A straightforward solution is a Cox model on the survival time with the waiting time as both truncation variable and covariate. The Cox model should also include other recognized risk factors as covariates. In this article, we focus on estimating the distribution function of waiting time and the probability of selection under the aforementioned Cox model.     

Hypothesis Tests for Neyman's Bias in Case–Control Studies

Survival bias is a long recognized problem in case–control studies, and many varieties of bias can come under this umbrella term. We focus on one of them, termed Neyman's bias or ‘prevalence–incidence bias’. It occurs in case–control studies when exposure affects both disease and disease-induced mortality, and we give a formula for the observed, biased odds ratio under such conditions. We compare our result with previous investigations into this phenomenon and consider models under which this bias may or may not be important. Finally, we propose three hypothesis tests to identify when Neyman's bias may be present in case–control studies. We apply these tests to three data sets, one of stroke mortality, another of brain tumors, and the last of atrial fibrillation, and find some evidence of Neyman's bias in the former two cases, but not the last case.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

Truncation invariant copulas and a testing procedure

ABSTRACT

The class of bivariate copulas that are invariant under truncation with respect to one variable is considered. A simulation algorithm for the members of the class and a novel construction method are presented. Moreover, inspired by a stochastic interpretation of the members of such a class, a procedure is suggested to check whether the dependence structure of a given data set is truncation invariant. The overall performance of the procedure has been illustrated on both simulated and real data.     

文艺学美学方法论视角下的电视新闻节目研究

从1958 年北京电视台开播,我国电视新闻正式诞生到现在,已经过去了57 年的时间。在这57 年的时间中,中国的电视 新闻事业得到了跨越性的发展。从最初的黑白电视到彩色画面;从只能节目录播到全程直播;从只有几个单独的电视台到现 在的电视新闻传输的全覆盖。尤其是90 年代后,随着现代科技的发展、新兴的数字技术给电视新闻传播带来了巨大的影响。 人们对于新闻节目的制作质量要求越来越高,但是电视新闻节目的质量却良莠不齐,所以如何吸收借鉴各行各业的优秀精华, 不断提升电视新闻节目的质量,带给观众美的享受,则是新闻工作者的不懈追求。而文艺学美学方法论中的诸多内容,都对电 视新闻节目的研究大有裨益     

稳压电源的自适应去火弧技术

针对传统基于继电器控制的稳压电源在带负载工作时,档位切换常常伴随火弧现象的问题,设计了一种可广泛 应用于此类稳压电源上的自适应去火弧技术：使用光耦和多级运放完成对零点和电压电流的采样;基于单片机的10量, 实现对继电器的驱动和控制;基于RCC自激震荡原理为系统提供稳定电源;设计了稳压器的完整软件系统程序,并在软 件中应用自适应去火弧算法。实验结果表明：自适应去火弧技术,能够有效地规避火弧现象的产生,并能够根据条件作 出调整。采用自适应去火弧技术的稳压系统达到了设计目标,延长了系统工作寿命。     

微言天算,零记号以及瞿昙历对中国古代数学的推进

本文论述我国古代天文历法的修定以及零记号的使用对数学计算的推进。