有界格上t-子模和t-子余模的构造

二元聚合函数的构造方法研究是一个有趣且有意义的研究课题。基于有界格子区间上一个给定的t-子模E,提出了一种在有界格L上构造t-子模Tλ,E的方法。这种构造方法可以通过归纳推广到适用于任何有界格的t-子模的另一种构造;基于有界格子区间上一个给定的t-子余模F,提出了一种在有界格L上构造t-子余模Sλ,F的方法,这种构造方法也可以通过归纳推广到适用于任何有界格的t-子余模的另一种构造。该研究不仅补充了二元聚合函数的构造方法研究中的空白领域,还对进一步研究其他二元函数聚合的构造提供了理论基础。

关于生成子余代数和生成子余模

本文继续文献［１］，［３］中生成子余代数的研究，并加以推广，引入了生成子余模的定义。获得了两者之间的一些基本结果。

π-余模余代数与π-余模余理想

引进了π-H-余模余代数、π-■-模代数的定义,给出了一些相关的性质,然后证明了局部有限维的π-H-余模余代数的对偶是一个π-H*-模代数;接着又引进了π-H-子余模、π-H-余模余理想、π-■-子模以及π-H-模子代数等概念,证明了π-H-余模余理想与π-H*-模子代数间的对应关系.

Hom-余模的若干性质(英文)

根据Hom-结合代数的概念来新定义子Hom-余模、Hom-模同态、Hom-余模同态的概念,并进一步讨论它们的基本性质.

Duality theorem for smash coproduct over quantum groupoids

The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.

Effects of welding parameters on weld shape and residual stresses in electron beam welded Ti_2AlNb alloy joints

In order to estimate the residual stresses in Ti2AlNb alloy jointed by electron beam welding (EBW), a computational approach based on finite element method was developed. Meanwhile, experiments were carried out to verify the numerical results. The comparison between the simulation results and measurements suggests that the developed computational approach has sufficient accuracy to predict the welding residual stress distributions. The results show that the central area of the fusion zone suffers tensile stresses in three directions. When the other parameters remain unchanged, the focus current has great impact on the weld shape and size, and then affects the residual stress level significantly. Moreover, the thick plate full-penetrated EBW weld suffers near 1000 MPa tensile stress of Z-direction in the center of the fusion zone. The wider weld has lower tensile stress in Z-direction, resulting in lower risk for cracking.

Sweedler's dual of Hopf algebras in HHYDQCM

Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoidal category HHYDQCM is introduced and the specific structure maps are given.Thirdly,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is discussed.It proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.

余模分解与余代数分解的关系

设M是C_-余模,C和M分别能被分解成不可分的子余代数和子余模的直和.给出这两个分解式之间的关系,从而给出了C的可约性和可分性与M的相关可约性和可分性之间的关系.

π-代数与π-子模

引进了π-模,π-余模等概念,研究了π-代数A上的π-模和π-子模的一些性质,把代数上的相关性质推广到了π-代数上;给出了π-代数A上的π-模和π-子模的一些充分必要条件.

Solution to the Yang-Baxter Equation and QuantumYang-Baxter H-comodules

Let H be an arbitrary Hopf algebra over a field k. In this paper, at first wedeal with the relationship between solutions to the Yang-Baxter equation and quantumYang-Baxter H-comodules; then we use the results to give a solution to the Yang-Baxterequation over H.

Homomorphisms between Two Sets of Fuzzy Subsemigroups *

Let S and T be semigroups. F(S) and F,(S) denote the sets of all fuzzy subsets and all fuzzy subsemigroups of 5, respectively. In this paper, we discuss the homomorphisms between F(S)(Fs(S)) and F(T)(Fs(T)). We introduce the concept of fuzzy quotient subsemigroup and generalize the fundamental theorems of homomorphism of semigroups to fuzzy subsemigroups.

THE CODIMENSION FORMULA ON AF-COSUBMODULES

Let M1, M2 be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2 and dimM1/M2 = k < '. If M2 is an AF-cosubmodule, then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of M2 related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in [14].