图论中若干重要定理的历史注记

考察了图论中若干重要定理的历史背景,这些定理包括图论基本定理,矩阵-树定理,门格尔定理,霍尔定理,柯尼希定理,塔特定理,彼得森定理,库拉托夫斯基定理,布鲁克斯定理和维津定理.     

A weak variant of Hindman’s Theorem stronger than Hilbert’s Theorem

Hirst investigated a natural restriction of Hindman’s Finite Sums Theorem—called Hilbert’s Theorem—and proved it equivalent over \(\mathbf {RCA}_0\) to the Infinite Pigeonhole Principle for all colors. This gave the first example of a natural restriction of Hindman’s Theorem provably much weaker than Hindman’s Theorem itself. We here introduce another natural restriction of Hindman’s Theorem—which we name the Adjacent Hindman’s Theorem with apartness—and prove it to be provable from Ramsey’s Theorem for pairs and strictly stronger than Hirst’s Hilbert’s Theorem. The lower bound is obtained by a direct combinatorial implication from the Adjacent Hindman’s Theorem with apartness to the Increasing Polarized Ramsey’s Theorem for pairs introduced by Dzhafarov and Hirst. In the Adjacent Hindman’s Theorem homogeneity is required only for finite sums of adjacent elements.     

零对称BZ-代数的充要条件

重新证明文[10]中几个重要结论并修正文[10]中的定理1(11)和定理2．在此基础上，利用这些重新证明过的结论及修正过的定理可以按照文[10]中引理3，定理4，定理6，定理7，定理10的证明过程原样证明文[10]中的相应结果．因而在文[10]中，除性质11是结合BZ一代数的等价性质(见文[15])，定理1(11)及定理2需要进行修正外，其余结论及证明过程均成立．     

一类高阶微分方程第二特征值的上界

本文研究形如（１．１）的第二特征上界问题,得到了定理１ 和定理２,其中定理１ 的估计系数与［ａ,ｂ］无关,定理２ 的结果在一定条件下比定理１ 好．     

Ferrers digraphs and threshold graphs

We deduce a set of known characterizations of threshold graphs (Theorem 3) from a set of characterizations of Ferrers digraphs (Theorem 1) by investigating the connection between symmetric Ferrers digraphs and threshold graphs. A direct proof of Theorem 3 is easier than the one provided in here, but the purpose of this paper is to view Theorem 1 as an extension of Theorem 3 to the directed case (this extension point of view still holds on an algorithmic ground).     

混合序列加权和的强收敛性

本文给出混合序列加权和的强收敛性的一些充分条件，这些结论推广和改进了文［１］定理３，文［２］定理３；文［３］定理４．１５以及文［４］定理４．     

线性锥系统的Tucker型相容性定理

为了将线性规划中的基础理论之一的Tucker定理推广到一般线性锥系统上,应用对偶锥的概念和线性锥系统的Farkas引理,给出了一般线性系统的Tucker定理,所得结果显示含齐次线性不等式组的线性锥系统和它的对偶系统都存在Tucker定理,且Tucker定理结论的表达式基本相同,这为进一步研究锥规划提供了便利.     

The Hahn-Vitali-Saks and the Uniform Boundedeess Theorem in topological groups

It is shown in this paper that the Theorem of Hahn-Vitali-Saks (Theorem 4) and the Uniform Boundedness Theorem (Theorem 5) hold true for measures with values in a topological group. The proofs given here for these theorems seem to the authors to be more direct than the usual proofs for real valued measures.     

半群环的右Artin性

本文研究了一般半群环的右Artin性的刻划问题，改进了JanOkniski在[3]中的结果，并给出了半群环是右Artin环的刻划．最后进一步指出在一定条件下，R[S1]和R[S1]的链条件是等价的．     

Hindman’s Theorem is only a Countable Phenomenon

We pursue the idea of generalizing Hindman’s Theorem to uncountable cardinalities, by analogy with the way in which Ramsey’s Theorem can be generalized to weakly compact cardinals. But unlike Ramsey’s Theorem, the outcome of this paper is that the natural generalizations of Hindman’s Theorem proposed here tend to fail at all uncountable cardinals.     

半群环的右Noether性

研究了一般半群的右Noetber性，得到了几个刻划定理．     

微分中值定理的另类证明与推广

通常教科书中,微分中值定理的证明建立在罗尔(Rolle)定理之上.本文以实数连续性中的重要定理———区间套定理为依据,给出了拉格朗日微分中值定理的另类证明.此外,还给出了中值定理的若干推广形式.     

Graph factors

This exposition is concerned with the main theorems of graph-factor theory, Hall’s and Ore’s Theorems in the bipartite case, and in the general case Petersen’s Theorem, the 1-Factor Theorem and thef-Factor Theorem. Some published extensions of these theorems are discussed and are shown to be consequences rather than generalizations of thef-Factor Theorem. The bipartite case is dealt with in Section 2. For the proper presentation of the general case a preliminary theory of “G-triples” and “f-barriers” is needed, and this is set out in the next three Sections. Thef-Factor Theorem is then proved by an argument of T. Gallai in a generalized form. Gallai’s original proof derives the 1-Factor Theorem from Hall’s Theorem. The generalization proceeds analogously from Ore’s Theorem to thef-Factor Theorem.     

集合函数多目标规划的拉格朗日型对偶定理

本文在［１］的基础上．给出了集合函数多目标规划的拉格朗日型弱对偶定理，严格对偶定理和逆对偶定理．     

Corrigendum to: “Fractional Functional Differential Inclusions with Finite Delay” [Nonlinear Anal. 70(5) (2009) 2091–2105]

We correct an error made in the paper (J. Henderson and A. Ouahab, Fractional Functional Differential Inclusions with Finite Delay [Nonlinear Anal. 70(5) (2009) 2091–2015]), in an application of Theorem 4.1 in the proof of Theorem 4.2. We have revised the statement of Theorem 4.2 so that Theorem 4.1 is now applicable in its proof.     

Ein semialgebraischer Beweis der topologischen Form des Hauptsatzes von Zariski

We give a semialgebraic proof of the topological form of Zariski's Main Theorem. As an application we deduce the Riemann Extension Theorem for isoalgebraic functions from Zariski's Main Theorem.     

Notes on Embedding Theorems for Local Hardy spaces

In this note we establish an embedding theorem (Theorem 2.4) for local Hardy spaces in the sense of GOLDBERG [G]. This result is a non-homogeneous version of the theorem of BAERNSTEIN and SAWYER (Theorem BS). Also applying this theorem we establish embedding theorem and Fourier embedding theorem (Theorem 4.2, Theorem 4.3 and Corollary 4.4) for local Hardy spaces.     

Technical Note Discontinuous Implicit Quasivariational Inequalities in Normed Spaces

In this paper, we consider an implicit quasivariational inequality without continuity assumptions in normed spaces. The main result (Theorem 2.1) provides an infinite-dimensional version of Theorem 3.2 in Ref. 1. To achieve such a goal, we employ Theorem 3.2 in Ref. 1 and the technique of Cubiotti in Ref. 2. In particular, Theorem 3.1 covers a recent result of Cubiotti (Theorem 3.1 of Ref. 2) as a special case. Communicated by F. Giannessi This research was partially supported by the National Science Council of Taiwan, ROC.     

The canonical Ramsey theorem and computability theory

Using the tools of computability theory and reverse mathematics, we study the complexity of two partition theorems, the Canonical Ramsey Theorem of Erdös and Rado, and the Regressive Function Theorem of Kanamori and McAloon. Our main aim is to analyze the complexity of the solutions to computable instances of these problems in terms of the Turing degrees and the arithmetical hierarchy. We succeed in giving a sharp characterization for the Canonical Ramsey Theorem for exponent 2 and for the Regressive Function Theorem for all exponents. These results rely heavily on a new, purely inductive, proof of the Canonical Ramsey Theorem. This study also unearths some interesting relationships between these two partition theorems, Ramsey's Theorem, and König's Lemma.

     

罗尔中值定理的一些新证法(英文)

给出了罗尔微分中值定理的三种新的证明方法,其中第二种很简便的方法仅依赖于大家熟知的Heine-Borel有限覆盖定理.由此可见罗尔微分中值定理可以是实数的完备性的直接推论.