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。     

关于高等数学中的逻辑证明

逻辑证明在高等数学及其教学中占有重要地位 .本文着重从间接证明尤其是反证法的逻辑结构入手 ,剖析了高等数学中的范例 .反证法离不开充分条件假言推理的否定后件式 ,其中的后件“q”可以是直言命题或关系命题 ,也可以是联言命题、选言命题、假言命题和负命题     

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.     

一个命题的多种证明

在解答某文献中的一个问题的过程中,得到了一个命题.用不同的方法给出了该名题的多种证明.     

一道高等数学题条件的减弱

针对一道关于连续导函数性质的习题，指出其命题条件过强，并在减弱后的条件下，分别运用达布定理和泰勒公式，证明了相应结论．     

Correction to “Properties of pseudoholomorphic curves in symplectisations I: Asymptotics”

In our paper [1] we derived the proposition 2.1 from Lemma 2.2 which is clearly false and our aim is to give a proof of the proposition. We take the opportunity to remove also a flaw in the proof of Lemma 3.3. The results of [1] remain unaffected.     

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.     

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。     

一个关于函数单调性命题的推广

文[1],[2]给出一个关于函数单调性的命题,但条件较为苛刻,应用范围非常有限。本文对其进行了推广,使其更具有一般性.     

Correction to a proposition related to ergodicity of Markov chains

Proposition 5.5.6 (ii) in the book Markov Chains and Stochastic Stability (2nd ed, Cambridge Univ. Press, 2009) has been used in the proof of a theorem about ergodicity of Markov chains. Unfortunately, an example in this paper shows that this proposition is not always true. Thus, a correction of this proposition is provided.     

关于“GM(1,1)模型的适用范围”一文的一个注记

本文扩展了刘思峰和邓聚龙的一个命题的适用范围 ,最后给出了一个相应新命题     

A Note on Semiconcave Function

This article gives a simple proof of an equivalent proposition on semiconcave function (see [L.C. Evans (1998). Partial Differential Equations. American Mathematical Society; p. 130]). The proof of sufficiency of the proposition can be easily obtained. We prove its necessity by three steps: First, we prove that the equivalent proposition holds for discrete points <artwork name="GAPA31045ei1">; Secondly, we obtain continuity of semiconcave function; Finally, by using the fact that the sequences λ_m ^k are dense in the interval (0, 1), we prove that the equivalent proposition holds for each λ ∈ (0, 1).     

Russellian Propositions and Properties

This paper discusses a problem for Russellian propositions. According to Russellianism, each word in a sentence contributes its referent to the proposition expressed by the sentence. Russellian propositions have normally been conceived of as problematic for two reasons, viz. they cannot account for the unity of the proposition and they have problems with non-referring singular names. In this paper, I argue that Russellianism also faces a problem with respect to properties. It is inconsistent with both traditional realism and trope-theories. The only theory of properties which is consistent with Russellianism is Platonism. Moreover, it is argued that Russellianism needs a particularly implausible version of Platonism.     

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   

A Partial Order on Uncertainty and Information

Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the uncertainty on a given random subject. Consider the uncertainty measure as the variance of a random variable. Given the information that its outcome is in an interval, the uncertainty is expected to reduce when the interval shrinks. This proposition is not generally true. In this paper, we provide a necessary and sufficient condition for this proposition when the random variable is absolutely continuous or integer valued. We also give a similar result on Shannon information.     

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.     

Completing Diophantus, De polygonis numeris, prop. 5

The last proposition of Diophantus’ De polygonis numeris, inquiring the number of ways that a number can be polygonal and apparently aiming at “simplifying” the definitory relation established by Diophantus himself, is incomplete. Past completions of this proposition are reported in detail and discussed, and a new route to a “simplified” relation is proposed, simpler, more transparent and more “Greek looking” than the others. The issue of the application of such a simplified relation to solving the problem set out by Diophantus is also discussed in full detail.     

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.     

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     

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.