对合Quantale范畴的极限

构造出了对合Quantale范畴的极限结构，得到对合Quantale范畴是连通的、点化的、完备的范畴，并给出了若干特殊的极限结构。     

单纯Quantale及其Quantale商

讨论Quantale上的同余与Quantale商之间的关系,研究单纯Quantale的性质,给出一类Quantale是单纯Quantale的等价刻画。最后从Quantale商的角度对单纯Quantale进行了研究,得到单纯Quantale的若干特征定理。     

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。     

对合Quantale范畴的逆系统

本文得到了对合Quantale范畴逆系统及逆极限的结构,引入了两个逆系统之间映射的概念,给出了逆极限之间的极限映射,并研究了它们的若干性质.     

幂等余 Quantale

讨论了幂等余Quantale与左纯元、子余Quantale的一些相关性质,发现幂等余Quantale的左纯元构成的集合是对应的子余Quantale;每个幂等余Quantale都可有一个核映射与子余Quantale保持对应关系;并且幂等余Quantale与核映射,左右纯元,Frame等都有一定关系.     

幂等左侧余Quantale的特征

更好地讨论Quantale这一崭新数学分支的各种性质;给出幂等余Quantale及幂等左侧余Quantale的定义;幂等左侧余Quantale既是子余Quantale又是商余Quantale;且其补集是简单余Quantale;幂等余Quantale具有和其他Quantale类似的一些性质,并且与简单余Quantale也...     

余Quantale及其性质

讨论余Quantale的一些性质,引入预余Quantale的概念并给出预余Quantale成为余Quantale的充要条件,构造了一些子余Quantale结构。     

模糊集Quantale与Quantale的嵌入

给出模糊集Quantale的定义,在此基础上对Quantale与它对应的模糊集Quantale二者之间的关系进行比较,得到如果一个Quantale是可换的、单位的,则它的模糊集Quantale也是可换的、单位的结论。然后给出Quantale的一种嵌入方式。     

Quantale的若干新的性质

讨论Quantale的若干性质，给出Prequantale构成Quantale的两个充要条件，论证在严格双侧Quantale上逆序对合对应的惟一性并给出了Quantale是分配格的一个条件。     

对偶Quantale上的Par运算及其性质

在对偶Quantale上定义了Par运算凵,并研究了其性质.给出了单位Quantale是对偶Quantale的充要条件,在此基础上得出对偶Quantale的等价刻画.证明了在一定条件下对偶Quantale的子Quantale亦是对偶Quantale.     

一个Bargmann系统与耦合Burgers族解的对合表示

本文给出耦合Burgers族的换位表示，并通过对耦合Burgers族Lax系统的非线性化得到一个Bargmann系统，证明该系统为Liouville完全可积的，还给出耦合Burgers族解的对合表示.     

Quantale中理想的扩张

讨论理想Quantale的性质,给出了当Q是可换Quantale时,Q中理想都是半素理想的一个条件.引入了理想的扩张的概念,证明了与序半群中的一些经典结论相一致的命题.通过理想的扩张构造了一个Quantale上的同余,得到了当原理想是素理想时,这个同余所确定的Quantale商是Frame且找到了它的具体结构.     

Fixed points of involutive interval-valued negations

Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained.     

C. Neumann System Associated with the Levi Hierarchy

51.Intr0ductionUsuallyasolitonequationcanbeexpressedasthecompatibleconditionofanover-determinedsystem,theso-calledLaxpair-Wehavea1readyknownthatthetwol1nearequationsintheLaxpaircanben0nlinearizedtobetw0c0mpatible,comp1etelyintegrableHamilt0niansystemsintheLioll"i1lesenseundersomecertainc0nstraintconditionsbetweentheeigenfunctionsandthepotentials(seeL1J).Am0ngtheseconstraintconditionsaretheretheBargmannconstraint{see[1,2,4j),theC.Neumannconstraint(see[l,4J),andthesymmetryconstra1nt(see[5,6j…     

An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System

In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division,Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package.     

On a logic of involutive quantales

The logic just corresponding to (non‐commutative) involutive quantales, which was introduced by Wendy MacCaull, is reconsidered in order to obtain a cut‐free sequent calculus formulation, and the completeness theorem (with respect to the involutive quantale model ) for this logic is proved using a new admissible rule. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Girard Quantale中的模糊关联滤子

在Girard Quantale中引入了模糊滤子和模糊关联滤子的概念,研究了Girard Quantale中模糊滤子和模糊关联滤子的一些性质,给出了Girard Quantale中模糊关联滤子的若干等价刻画,探讨了模糊关联滤子与模糊布尔滤子之间的关系.     

Duality for multimodules

Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and involutions; tensor products and contractions; inner products; first-order differential operators. A construction of an (involutive) colored properad of multimodules is suggested.     

一个有限维完全可积系统和MDWW方程解的对合表示

本文讨论高阶ＭＤＷＷ方程的Ｌａｘ对，在位势与特征函数之间的约束条件下，Ｌａｘ系统被非线性化成为有限维Ｌｉｏｕｖｉｌｌｅ完全可积系统．并且获得了高阶ＭＤＷＷ方程解的对合表示．