算术半格的信息系统表示

本文给出了算术信息系统的概念,证明了算术信息系统是算术半格的表示。基于算术信息系统之间的逼近映射,我们得到了算术信息系统范畴和算术半格范畴之间的范畴等价。     

L-模糊自然数的乘法运算和幂运算

在L是完全分配格时,定义了L-模糊自然数的乘法运算和幂运算,研究了乘法运算、幂运算的交换律、结合律以及乘法对加法的分配律等性质。     

基于可拓变换的二维随机变量分布律的研究

建立了随机事元之间的关系事元,研究随机事件之间的关系.利用关系元刻画了两个随机事件之间的关系.运用可拓变换初步研究了二维离散型随机变量的分布律和边缘分布律的传导分布.     

求解模糊数限定运算的一种新方法

针对模糊数限定运算比较困难的问题,提出了一种比较便捷的运算方法.首先,利用模糊结构元理论给出了模糊数一种新的表现定理.在此定理基础上,得到了模糊数运算的解析表达形式.解决了模糊结构元中,非同序模糊数和非单调模糊数不能运算的问题,统一并拓展了模糊数运算的结构元表述形式.     

算术半格的闭包空间表示

本文主要讨论算术半格的闭包空间表示.首先通过在给定的闭包空间中增加适当的条件,提出了算术闭包空间的概念,并且给出了算术半格的闭包空间表示.接着提出了算术闭包空间之间的算术逼近映射的概念,并证明了以算术逼近映射作为态射的算术闭包空间范畴和以Scott连续函数作为态射的算术半格范畴之间的范畴等价性.     

感悟等号意义 提高运算能力

学生在等式的计算中常常容易出错,因此在教学中要引导学生理解运算的算理,寻求合理简洁的解决问题的途径.学生对等号的意义有了深刻的理解和感悟,才能够提高运算能力,培养严谨的学习品质.     

探索运算推理能力的培养

数学运算推理能力是从运算对象不同来说的,要培养学生各种运算推理能力,首先要学生掌握各种运算的有关知识,并且在运算过程中,还有运算的准确程度、快慢程度、合理程度以及简捷程度的不同．这些方面的区别会反映出运算推理能力的大小．要学生具有正确、迅速的运算推理能力,就不能停留在只是了解一些有关运算的知识,还要善于分析运算对象的性质和特点,善于运用运算规律和法则,     

泛逻辑的零级泛运算模型的代数性质

讨论泛逻辑的零级泛运算模型的基本代数性质。证明T（x,y,^）是阿基米德型三角范数;泛与运算模型与泛蕴涵运算模型形成一个伴随对;当h∈（0,0．75）时,有界格（[0,1],∨,∧,,＊,→0,1）做成一个MV-代数;当h∈（0．75,1）时,有界格（[0,1],∨,∧,＊,→0,1）做成一个乘积代数。进一步,给出了零级泛与运算模型与泛或运算模型的加性生成元与乘性生成元。     

算术图一个猜想的证明

Ａｃｈａｒｙａ和Ｈｅｄｇｅ提出猜想：(i)若圈Ｃ_4t＋１( t≥1, t∈N) 是(k, d )－算术图，则Ｋ＝２ｄｔ+ 2r ( r≥0, r∈N ) ; ( ii) 若圈C_4t＋3是(k, d )-算术图, 则k= (2t+ 1) d + 2r ( r≥0, r∈N ). 本文证明了上述猜想为真.     

算术结构的不可判定性

本文证明了两种算术结构Ｎ；＋，ｎ２ｎ，｜２ｎ及Ｎ；＋，ｎ２ｎｌｏｇ２ｎ中可定义乘法运算从而包含算术结构Ｎ；＋，×及，而由于后者的不可判定性推导出前二者的不可判定性。     

Completely Arithmetical Rings

We introduce a type of commutative ring R in which its ideal lattice has a strong form of the distributive property. We show that if R is reduced, then it is a semilocal von Neumann regular ring. In this case, we show that the K ₁ group of this ring has a relatively simple structure.     

Arithmetical Sacks Forcing

We answer a question of Jockusch by constructing a hyperimmune-free minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.The first author was supported in part by the Marsden Fund of New Zealand.The second author was supported by a postdoctoral fellowship from the New Zealand Institute for Mathematics and its Applications, NSF of China No.10471060 and No.10420130638.     

Arithmetical conservation results

In this paper we present a proof of Goodman’s Theorem, a classical result in the metamathematics of constructivism, which states that the addition of the axiom of choice to Heyting arithmetic in finite types does not increase the collection of provable arithmetical sentences. Our proof relies on several ideas from earlier proofs by other authors, but adds some new ones as well. In particular, we show how a recent paper by Jaap van Oosten can be used to simplify a key step in the proof. We have also included an interesting corollary for classical systems pointed out to us by Ulrich Kohlenbach.     

Pullbacks of Arithmetical Rings

We give necessary and sufficient conditions that the pullback of a conductor square be a chain ring (i.e., a ring whose ideals are totally ordered by inclusion). We also give necessary and sufficient conditions that the pullback of a conductor square be an arithmetical ring (i.e., a ring which is locally a chain ring at every maximal ideal). For any integral domain D with field of fractions K, we characterize all Prüfer domains R between D[X] and K[X] such that the conductor C of K[X] into R is nonzero. As an application, we show that for n ≥ 2, such a ring R has the n-generator property (every finitely generated ideal can be generated by n elements) if and only if R/C has the same property.