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non    
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    The development of modern society enriches the methods of reasoning and helps to form the nonformulated logic system, which serves as the necessary tool of thinking for the modern administrative talents.
    现代社会的发展扩展了推理方法,形成了形式逻辑体系,成为现代管理人才必备的思维工具。
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    Non cybernetics,as a new mode of thinking,aims at correctly understanding control and making use of it.
    控理论作为一种新的思维范式,旨归于正确认识和使用控制。
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    The non controlling idea may be considered to be inversely complementary to the controlling thought.
    控思想是对控制思想的逆向补充
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    The main results are:In logic system r,G r, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times;
    主要结果是 :在逻辑系统 Gr,Gr 中 ,重言式不可能由对重言式进行有限次升级算法得到 ;
短句来源
    And congruence partitions about  on F(S) have been given in logic system W,W,W k , respectively by using the concepts of accessible generalized tautology and α contradiction. It is proved that in logic system W,W, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times.
    分别在W ,W ,Wk 中利用可达广义重言式的概念给出F(S)的一个关于 同余的分划 ,并证明了 :在W (W )中 ,重言式不可能由对重言式利用升级算法得到 ;
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  非线性
    This article combines the theories of Lin's Entailment, Dissipation Framework, Cooperation, Non Linearity Mathematics, thus puts forward the principle to carry out Lin's Entailment.
    本文综合制约逻辑、耗散结构论、协同论、非线性数学等理论提出实施制约门的原理 .
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    The main results are:In logic system r,G r, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times;
    主要结果是 :在逻辑系统 Gr,Gr 中 ,重言式可能由对非重言式进行有限次升级算法得到 ;
短句来源
    And congruence partitions about  on F(S) have been given in logic system W,W,W k , respectively by using the concepts of accessible generalized tautology and α contradiction. It is proved that in logic system W,W, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times.
    分别在W ,W ,Wk 中利用可达广义重言式的概念给出F(S)的一个关于 同余的分划 ,并证明了 :在W (W )中 ,重言式可能由对非重言式利用升级算法得到 ;
短句来源
    It is proved that the sets of all exact α tautologies in L n, S n , and G n are all non empty , and the relationship between the sets of all quasi tautologies in these systems and the set of all tautologies in the classical prepositional logic system are considered.
    给出了这些系统子代数的特征性质与计数公式 ,证明了Ln,Sn,Gn 中可达α 重言式类类空 ,并探明了它们与经典逻辑系统重言式的关系 .
短句来源
    The main results are:In logic system ,G,tautologies can not be get by using upgrade algorithm to non tautologies within finite many times;
    主要结果是 :在逻辑系统 G,G中 ,重言式可能由对非重言式进行有限次升级算法得到 ;
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The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the non-arithmetic lattices inSO(n,1) constructed by Gromov and Piatetski-Shapiro [GPS] and to groups generated by reflections.
      
We also show how to distinguish examples of open subsets with a good quotient coming from Mumford's theory and give examples of open subsets with non-quasi-projective quotients.
      
An algebraicG-varietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant divisors having a non void transversal intersection;G has 2r orbits inX.
      
Lichtenstein in the caseu =(n, ?) or(n?), we prove that ?(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S() \ {0}.
      
In [Ka1] its geometric counterpart was applied to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces.
      
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This article gives both an exposition and a critical analysis of some classical concepts concerning infinite aggregates, in particular, the set of natural numbers and the continuum formed by mathematical points. It is pointed out that the complete infinite sequence of natural numbers cannot consist of only finite ordinals, thus a kind of so-called "potential tail" may be defined. Moreover, a kind of non-Cantorian theoy of mathematical continuum with varoius types of ivision is briefly mentioned and discussed....

This article gives both an exposition and a critical analysis of some classical concepts concerning infinite aggregates, in particular, the set of natural numbers and the continuum formed by mathematical points. It is pointed out that the complete infinite sequence of natural numbers cannot consist of only finite ordinals, thus a kind of so-called "potential tail" may be defined. Moreover, a kind of non-Cantorian theoy of mathematical continuum with varoius types of ivision is briefly mentioned and discussed. The essential idea involved is to make a distinction between the division points and the elements of the continuum to be divided.

本文批判地分析了有关无穷集合的某些传统观念,特别是对于自然数集合和由数学点构成的连续统概念。指出了一个完全的自然数无穷序列不可能由且仅由无穷多个有穷序数去组成,如此就引进并定义了叫做“潜尾”的概念。进而简要地陈述并讨论了一组不同类型的数学连续统的非Cantor理论,其实质性的概念在于分辨己被分割了的点与连续统的元素的可分割性之间的区别。

In this artical, two criterions of scientific Discovery are expressed. The principle of incompleteness of knowldge storge is demonstrated, and it is shown that a deductive machine can be both logically non-ampliative and expistemically ampliative. On the basis of principle of unsolvability of Hume's problem, we elucide that it is fesible to establish a inductive machine of discovery.

本文阐述了科学发现的两个判据,在知识存贮有劣性原理的基础上,提出了知识存贮不完全性原理,指出存在一类逻辑上具有非放大性,但认识论上具有放大性的演绎发现机器。在休谟问题逻辑学范围内不可解原理的基础上,论证了不存在通用的归纳发现机器,但建立局部合理的、有效的、完备的归纳发现机器是可行的。最后,本文描述了科学发现机器的结构,并在文献的基础上,描述了一种同时具有发生与评价功能的归纳发现机器并论证了它的合理性。

Paper [1] points out that a fuzzy vector subspaces may have no basis and, even if it has basis, the basis does not have to be a finite set. We refer this kind of a fuzzy vector subspace that has no basis or has only infinite basis as a non-finitely generated fuzzy vector subspaces.The purpose of this paper is to approximate this kind of a non-finitely generated fuzzy vector subspace by a finitely generated one.

文献[1]指出:Fuzzy向量子空间可以没有基底,即使有基底,其基底也不一定是有穷集,我们称这种没有基底、或只有无穷基底的Fuzzy向量子空间为非有限生成的,本文将用有限生成Fuzzy向量子空间来逼近这种非有限生成子空间。

 
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