关于格蕴涵代数公理的一个注记

设在一个非空集合L上有一个二元运算→和两个零元运算O与I，除此之外没有其它已知的代数结构，利用这三个运算可以在L上定义一个一元运算′和两个二元运算∨和∧（定义2．1）。本文证明了只要这些运算满足格蕴涵代数的公理（不包括有余格的公理），（L，∨，∧，′）就是一个有泛界O，I的有余格（定理2．2）。因此在定义格蕴涵代数时可以在一个没有任何代数结构的非空集合上定义蕴含运算而不必在一个有泛界的有余格上定义蕴含运算，而且在这两种定义方式中蕴含运算所满足的条件是相同的。     

一类非结合泛代数的次直积分解

本文引入一类非结合泛代数，即零积结合近环，研究其次直积分解，得到两个结构定理。设Ｎ是零积结合分配生成近环，本文证明了：（ｉ）如果Ｎ是次直不可约的且无非零的二次幂零元，则Ｎ是整的；（ｉｉ）Ｎ是零积结合分配生成整近环的次直积当且仅当Ｎ不含非零的二次幂零元。这些结果在这一类泛代数中加强了著名的Ｂｉｒｋｈｏｆｆ定理。     

零级泛与运算模型的单调性

泛逻辑的零级泛与运算模型是一个三角范数谱系, 本文讨论泛逻辑的零级泛与运算模型的单调性, 证明了T(x,y,h)(h∈[0,1])关于h单调递增. 进一步讨论Hamacher三角范数谱系的单调性, 证明了Hamacher三角范数谱系THamacher(λ)(x,y)关于λ单调递减, 且TL(x,y)≤TEinstein(x,y)≤THamacher(λ)(x,y)≤TP(x, y).     

格蕴涵代数定义的简化

证明定义有二元运算→和零元运算(固定元)0的非空集合L(即:L是(2,0)型代数)只要满足四条算律就可成为格蕴涵代数.因此,在定义格蕴涵代数时,我们不必要求L是有界有余格,从L是(2,0)型代数出发即可,这样大大简化了格蕴涵代数的定义.     

关于格的极小生成元集

本文证明了格的极小生成元集一定是最小生成元集且只能是非零完全并既约元全体，证明了分配格具有最小生成元集的必要条件是它满足并无限分配律．本文还证明了完全Ｈｅｙｔｉｎｇ代数具有最小生成元集当且仅当它是强代数格，证明了完备格是强代数格当且仅当它和它的对偶格均是具有最小生成元集的分配格．     

具有Heyting结构的Ockham代数

引入一个具有Heyting结构Ockham代数,简称HO-代数．所谓HO-代数,是指具有（2,2,2,1,0,0）类型的代数（L;∧,∨,→,f,0,1）．其中（L;f）是Ockham代数,（L;→）是Heyting代数,且运算f和→由恒等式f（x→y）=f^2（x）∧f（y）与f（x）→y=f^2（x）∨y所连结．主要讨论了HO-代数的同余关系的性质．并刻画了其次直不可约代数的某些性质．     

带有不等式约束的生长曲线模型中回归系数线性估计的泛容许性

对于带有不等式约束的生长曲线模型：Y=XBZ＋ε，ε^→～（0，σ^2V×I），tr（NB）≥0，本文在矩阵损失函数（d—KBL）（d—KBL）＇下，给出了可估函数KBL的线性估计的泛（西）容许性定义，分别得到了DYF和DYF＋C在齐次估计类LH和非齐次估计类LI中是KBL的泛容许性估计的充要条件．     

一族Hida广义泛函的构造及其性质

本文证明了当一族可微单参数子群｛g0｝0∈R ∪→GL（E），其生成元T被看成是H稠定算子时是自其轭时，有一族可微单参数子群｛L0｝0∈R∪→GL（（E））∪→Y（E，（E））与此相对应。由此我们可得到一族正广义泛函Φx^θ，其相应的测试是一簇转移概率，特别地，当T＝－I时，它们是一簇Ornstein-Unlenbeck转移概率。     

对合Quantale中对合运算与特殊元的关系

结合Quantale中的特殊元（如对称元、左（右）准对称元、左（右，双）边元、Locale元、正则元），完备格中的〈〈、△关系，紧元、超紧元以及对舍Quantale中的对合运算＊等概念，讨论了它们之间的关系。     

自反算子代数的环自同构

设Ａ是Ｂａｎａｃｈ空间Ｘ上的自反算子代数，并且Ａ的不变子空间格ＬａｔＡ满足 ０＋≠０和Ｘ_≠Ｘ，ａ：Ａ→Ａ是环自同构．如果Ｘ是实空间，并且ｄｉｍ　Ｘ　＞１；则存在Ｘ上的线性有界可逆算子Ａ，使得ａ（Ｔ）＝ＡＴＡ～（－１）；Ｔ∈Ａ：如果Ｘ是复空间，并且ｄｉｍ Ｘ　＝∞，则ａ（Ｔ）＝ＡＴＡ～（－１），Ｔ∈Ａ．其中Ａ：Ｘ→Ｘ是线性、或者共轭线性有界可逆算子．     

Universal Induction and True Universal Arithmetic

We prove that every finitely generated (as a ring) model for induction for universal formulas without parameters satisfies also all true universal sentences. Mathematics Subject Classification: 03C62.     

基于万有引力定律的数据分类效果评价

针对模糊C-均值聚类算法对初始化分类参数的选择比较敏感而导致分类结果差异性较大的不足，提出基于万有引力定律的分类效果好坏的评价准则。实验结果表明。本文定义的分类效果评价准则是可行的。     

On the Universal Splitting Property

We prove that if an incomplete computably enumerable set has the the universal splitting property then it is low₂. This solves a question from Ambos-Spies and Fejer [1] and Downey and Stob [7]. Some technical improvements are discussed.     

Universal cycles for permutations

A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham.     

Universal arcs in local tournaments

An arc $uv$ of a digraph $D$ is called universal if $uv$ and $w$ are in a common cycle for any vertex $w$ of $D$. In this paper we characterize local tournaments whose every arc is universal.     

Universal Abelian H-spaces

The question of the existence of universal homotopy commutative and homotopy associative H-spaces (called Abelian H-spaces) is studied. Such a space T(X) would prolong a map from X into an Abelian H-space to a unique H-map from T into X. Examples of such pairs (X,T) are given and conditions are discussed which limit the possible spaces X for which such a T can exist. Contrary to published assertions, the Anick spaces are shown not to be universal Abelian H-spaces for the corresponding Moore spaces; however conditions are discussed which could lead to a universal property with respect to a more limited range of targets, and a restricted universal property is proven.     

Buchstaber Invariants of Universal Complexes

Davis and Januszkiewicz introduced (real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes,which now can be seen as "colorings".The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K,then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex.It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3.This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.     

On Universal Equivalence of Partially Commutative Metabelian Lie Algebras

In this paper, we consider partially commutative metabelian Lie algebras whose defining graphs are cycles. We show that such algebras are universally equivalent iff the corresponding cycles have the same length. Moreover, we give an example showing that the class of partially commutative metabelian Lie algebras such that their defining graphs are trees is not separable by universal theory in the class of all partially commutative metabelian Lie algebras.     

Universal quantum semigroupoids

We introduce the concept of a universal quantum linear semigroupoid (UQSGd), which is a weak bialgebra that coacts on a (not necessarily connected) graded algebra A universally while preserving grading. We restrict our attention to algebraic structures with a commutative base so that the UQSGds under investigation are face algebras (due to Hayashi). The UQSGd construction generalizes the universal quantum linear semigroups introduced by Manin in 1988, which are bialgebras that coact on a connected graded algebra universally while preserving grading. Our main result is that when A is the path algebra $\mathbb{k}Q$ of a finite quiver Q, each of the various UQSGds introduced here is isomorphic to the face algebra attached to Q. The UQSGds of preprojective algebras and of other algebras attached to quivers are also investigated.