Classroom note: Corrections to a well-known proposition concerning the two-dimensional density function

The purpose of this article is to bring attention to an error in a well-known proposition concerning the two-dimensional density function, which appears in several intermediate textbooks on probability and statistics. A counterexample is presented, and two corrected versions of the proposition are suggested.     

关于一个数论函数的导数及应用

Kanemitsu教授给出了欧拉求和函数的推广公式Lu(x,a)=0n相似文献   

邻接树图是哈密尔顿图猜想的一个等价命题

本文给出了简单图的邻接树图是哈密尔顿图”猜想的等价命题,阐明只需证明该猜想对2－连通图成立即可,另外,我们给出了该猜想一种特殊情形的构造性证明。     

关于二元函数极值的一个错误命题

本文举出反例,说明文[1]中一个关于二元函数极值的命题是错误的,并结合反例,详尽的剖析了错误产生的原因,以及命题作者所给证明中的疏漏.     

A value-adding approach to reliability under preventive maintenance costs and its applications

No equipment (system) can be perfectly reliable in spite of the utmost care and best efforts on the part of the designer, decision-maker and manufacturer. The two sides of maintenance are corrective and preventive maintenance. It is generally assumed that a preventive maintenance action is less costly than a repair maintenance action. We examine this proposition in detail on the basis of a failure-time model that relates conformance quality to reliability. Illustratively, we present reliability in the context of contracts with asymmetric information. The model shows how to overcome information rents through price distortions and quantity rationing. The paper ends with a conclusion and an outlook to future studies.     

用可分命题简化证明实数系中定理

修改了连续归纳法,利用修改后的连续归纳法证明了一个关于可分命题的重要定理,利用该定理简化证明实数系中若干定理.     

基于DEA-博弈论模型的铁路电子车票实名制查验评价分析

将基于数据包络分析(DEA)模型和纳什讨价还价博弈论结合, 作为一种合作博弈方法, 对铁路电子车票实名制的查验进行了综合评价, 为准确评估铁路电子车票实名制查验的效率, 加强铁路客运服务水平提供决策判断。本文以20个不同等级的铁路车站为研究对象, 分人工和机器两大类, 选取身份证购票比例、通勤员工购票比例、临时身份证购票比例, 以及人工查验旅客数/小时/通道、机器查验的通过人数/闸机/小时、闸机人脸自动识别比例和延误比例等7个指标作为投入指标, 选取人、证、票三证合一的实名制查验比例作为产出指标, 基于数据包络分析(DEA)和纳什讨价还价博弈论结合的合作博弈模型, 从人工查验和机器查验两个角度对铁路电子车票实名制查验进行统一综合评价。案例结果表明, 铁路电子车票实名制查验效率呈现出人工查验和机器查验效率不均衡的态势; 车站人脸识别闸机的数量投入与所需闸机数量的不匹配是造成实名制查验效率下降的主要原因。根据评价结果, 从人工和机器查验两个角度提出了可行建议, 促进了铁路电子车票实名制查验效率的进一步提升。     

命題演算的公理系統

<正> §1. 問題的提出 對於傳統的二值邏輯系統(以後叫做系統M)所作的公理系統,優點最多的可說是Hilbert-Bernays[1]Ⅰ册66頁上所载的(一名Munster派公理,以後即用此名).這個公理系統共有兩個模式(又名原則)及五组公理,模式即代入原則     

一个三角形几何不等式的推广

首先从第3届国际数学奥林匹克IMO竞赛命题中一个三角形几何不等式出发,将问题推广到对更一般的三角几何不等式及多边形几何不等式的研究.然后利用凸函数的Jensen不等式,得到更一般的三角形几何不等式及圆外切多边形几何不等式,推广了原命题.     

A multi-objective approach to supply chain visibility and risk

This paper investigates the twin effects of supply chain visibility (SCV) and supply chain risk (SCR) on supply chain performance. Operationally, SCV has been linked to the capability of sharing timely and accurate information on exogenous demand, quantity and location of inventory, transport related cost, and other logistics activities throughout an entire supply chain. Similarly, SCR can be viewed as the likelihood that an adverse event has occurred during a certain epoch within a supply chain and the associated consequences of that event which affects supply chain performance. Given the multi-faceted attributes of the decision making process which involves many stages, objectives, and stakeholders, it beckons research into this aspect of the supply chain to utilize a fuzzy multi-objective decision making approach to model SCV and SCR from an operational perspective. Hence, our model incorporates the objectives of SCV maximization, SCR minimization, and cost minimization under the constraints of budget, customer demand, production capacity, and supply availability. A numerical example is used to demonstrate the applicability of the model. Our results suggest that decision makers tend to mitigate SCR first then enhance SCV.     

结构的延拓及三斜结构系统的代数弹性运动的数学性质

本文的目的并非简单地评述弹性静力学。著名的Cauchy六方程,其命题是由位移函数(u_i, u_j, u_k)=u(xi, xj, xk)的九个偏导数线性表达的,但其逆命题是该六个方程不可能表达阵(?(u_i, u_j, u_k)/?(xi, xj, xk))的九个元素,这是由于在给定点上的变形的几何表示至今尚不完全[1]。用几何语言来说,其逆命题的含意就是:在空间中任意三角形(正交除外)边的“平方长”运算用Pythogora's定理的结论是不真的[2]。本文将叙述代数弹性运动的某些数学规律及其与上述问题的关系。     

Zpk+1环上的循环码的Gray像

定义了Znpk+1到Znpkp的Gray映射,给出该映射的一个性质,证明了Zpk+1环上码长为n的码为循环码的充要条件是它的Gray像是Zp上长度为npk指数为pk的准循环码.     

关于Ponomarev-系统的一些注记(英文)

本文给出一个反例,证明了在一个Ponomarev-系统(f,M,X,P)中,P是点有限不蕴涵f是紧有限.这纠正了有关Ponomarev-系统的一个错误命题.作为Ponomarev-系统(f,M,X,P)的进一步结果,本文分别给出了f是紧映射以及P是点有限的充分必要条件.此外,本文还给出了Ponomarev-系统中映射与网络的一些其他关系.     

关于三角模的直觉模糊群及其同态像

本文在K．Atanassov引进的直觉模糊集概念的基础上,利用T模和S模,定义了两个直觉模糊集的乘积．给出了关于三角模的直觉模糊群的概念及其等价命题,最后在两个经典群同态与同构意义下,研究了这种直觉模糊群的同态像及原像等问题。     

A note on “Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality” [Positivity. 18, 449–473(2014)]

The note points out that the sufficiency of proposition 2.1 in Anh (Positivity 18:449–473, 2014) is erroneous and we provide an example to illustrate it. Also the proof of proposition 2.2 in Anh (Positivity 18:449–473, 2014) is incorrect and we give a new proof.     

A nonlinear analytic approach to the splitting theorem of Jacobs–de Leeuw–Glicksberg

In this paper, we study nonlinear analytic methods for linear contractive semigroups in Banach spaces and apply them to the splitting theorem of Jacobs–de Leeuw–Glicksberg. Using these results, we obtain the extension of Lin’s proposition for a group of linear operators to a semigroup.     

An approach to evolving novel organizational forms

A key problem in organization theory is to suggest new organizational forms. In this paper, I suggest the use of genetic algorithms to search for novel organizational forms by reproducing some of the mechanics of organizational evolution. Issues in using genetic algorithms include identification of the unit of selection, development of a representation and determination of a method for calculating organizational fitness. As an example of the approach, I test a proposition of Thompson's about how interdependent positions should be assigned to groups. Representing an organization as a collection of routines might be more general and still amenable to evolution with a genetic algorithm. I conclude by discussing possible objections to the application of this technique.Syracuse University School of Information Studies     

基于公式真度的公式集约简

基于经典命题逻辑的真度理论,讨论了经典命题逻辑系统当中公式集的约简问题。提出了真度约简及α-真度约简的概念,为公式集的约简提供了一种可行的操作方法。     

Newton's solution to the equiangular spiral problem and a new solution using only the equiangular property

This paper is a study of Proposition IX of Book I of Newton's Principia, the problem of determining the centripetal force for an equiangular spiral. In Newton's main proof of this proposition there is an error concerning his reason for the figure SPRQT being “given in kind,” and a very interesting technique of varying things in the neighborhood of a limit. This main proof utilized Newton's formula for the limit of SP²QT²/QR given in Corollary I to Proposition VI of the Principia. Newton also gave an alternate proof which utilized his formula for SY²PV given in Corollary III to Proposition VI. The “given” of Proposition IX was “a spiral PQS, cutting all the radii SP, SQ, &c., in a given angle.” Both the main proof and the alternate proof implicitly depend on the property of the equiangular spiral that the radius of curvature at any point is proportional to the pole distance SP. We here offer a new proof of Newton's proposition which does not depend on this implicit assumption.     

On statistical inference in sample surveys and the underlying role of randomization

Summary Assuming only the existence of a universe and a frame that identifies its members (ultimate sampling units), and a minimum number of necessary but nonrestrictive assumptions, the writer derives a basic proposition which shows that for sample surveys any form of inference about any universe characteristic must depend on the sampling distribution of estimates generated by randomization, and, by direct implication, the sampling design. Unbiasedness is validated by this proposition, but likelihood appears to be in conflict with it, and by implication with randomization. The relation between high or low variance and correspondingly low or high probability for an estimator is also investigated in the paper. Finally it is argued that restrictions on randomization may be injurious to normality.