基础R0-代数的性质及在L*系统中的应用

研究了王国俊教授建立的模糊命题演算的形式演绎系统L^*和与之在语义上相关的R₀-代数,提出了基础R₀-代数的观点并讨论了其中的一些性质,在将L^*系统中的推演证明转化为相应的R₀-代数中的代数运算方面作了一些尝试,作为它的一个应用,证明了L^*系统中的模糊演绎定理。     

关于二元样条空间Sr（3r）（△*）的维数

设△^*任何三角剖分△的ＨＣＴ细分的三角剖分．本文建立了定义于△^*上的二元样条函数空间S^r_（3r）（△^*）的维数公式．我们的证明方法同时给出了S^r_（3r）（△^*）的一组显示的基函数，并阐明基函数具有某种意义的局部最小支集     

分次环，A，Aｅ和Smash积A＃G*是亚直既约环的条件

讨论了分次环Ａ，Ａ_ｅ和Ａ＃Ｇ^*的相关性质，在Ａ是分次忠实时，Ａ＃Ｇ^*是亚直既约环当且仅当Ａ_ｅ是亚直既约环；在Ａ是分次非退化时，Ａ＃Ｇ^*是Ｇ亚直既约环当且仅当Ａ是分次亚直既约环．     

分次环的Smash积A#G*与单位分量Ae理想间的对应

本文对任意群G上的任意分次环A,建立了Smash积A#G^*和单位分量A_e理想间的对应关系,并运用所建立的对应关系研究分次环的Smash积A#G^*和A_e的半素性,素性和单性.     

Hilbert C*模及其有界模映射

设E为C^*代数A上可数生成的Hilbert模,B(E)为E上有界模映射全体,则B(E)保距同构于K(E)的左乘子,其中K(E)为E上“紧”模映射全体。当A为无限维本原C^*代数且E为自对偶模,则E为代数有限生成。     

具有常余维数2k+4不动点集的(Z2)k作用

本文通过构造上协边环MO_*的一组生成元决定了J_*,k^2k+4.     

R3内具给定平均曲率的闭曲面

设H^*是R³内某个开区域内的实值函数,在H^*上加两个条件,在_R³内能找到同胚于给定闭曲面(任意亏格)的曲面,其平均曲率由H^*给出。     

在奇次Legendre多项式零点上的（0，2）*插值

设Ｐ_ｎ表示ｎ次Ｌｅｓｅｎｄｒｅ多项式，本文考虑多项式（１－ｘ²）Ｐ_ｎ．（ｘ）／ｘ（ｎ为奇数）零点上的（０，２）^*插值问题，得到了这种插值的正则性，显式表达式及收敛性．     

C2*d3Πg态的布居反转和弛豫动力学

本文给出了在5—43乇五种不同氩气压力和0.07—1乇钠蒸气压下利用Na+CCl_4反应得到的C₂^*d³Π_g到a³П_u态跃迁的△v=0带序的化学发光光谱。假定C₂^*d³Π_g v=6为优先生成,并然后经碰撞逐渐弛豫到低振动能级,这样就可以计算出C₂^*d³Π_g态的总的脱活速率和振动弛豫速率。计算结果是:在温度为 340℃时,在氩气中其总脱活速率为4.1×10⁶乇^-1秒^-1,振动弛豫速率为2.2×10~6乇^-1秒^-1。在氮气中这两个传能速率则要略高一些。C₂^*d³Π_g态被钠原子猝灭的速率约为10⁷乇^-1秒^-1,约比气动碰撞速率高一个数量级。这是由于发生电荷传递形成了Na⁺C₂^*-中间络合物所引起。     

关于算子方程λA2+μA*2=αA*A+βAA*

本文主要是给出Hilbert空间上满足方程 λA²+μA^*2=αA^*A+βAA^* (λ,μ,α,β都是复数)的有界线性算子A的全部形式,并给出它的应用。     

Groups and C*‐Algebras from a 4‐Dimensional Anzai Flow

The rotation flow on the circle T gives a concrete representation of the irrational rotation algebra, which is an in finite dimensional simple quotient of the group C*‐algebra of the discrete Heisenberg group H₃ analogously certain 2‐ and 3‐dimensional Anzai flows on T ² and T ³are known to give concrete representations of the corresponding quotients of the group C*‐algebras of the groups H₄ and H_5,5. Considered here is the (minimal, effective) 4‐dimensional Anzai flow F = (ℤ, T ⁴) generated by the homeomorphism (y, x, w, v) ↦ (λy, yx, xw, wv); a group H_6,10 is determined by F the faithful in finite dimensional simple quotients of whose group C*‐algebra C*‐(H_6,10 have concrete representations given by F. Furthermore, the rest of the infinite dimensional simple quotients of C*‐(H_6,10 are identified and displayed as C*‐crossed products generated by minimal effective actions and also as matrix algebras over simple C*‐algebras from groups of lower dimension; these lower dimensional groups are H₃ and subgroups of H₄ and H_5,5.     

Derived representation type and Gorenstein projective modules of an algebra under crossed product

Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.     

Linear Functional Equations in Banach Modules over a C *-Algebra

The paper is a survey on the Hyers–Ulam–Rassias stability of linear functional equations in Banach modules over a C ^*-algebra. Its contents is divided into the following sections: 1. Introduction; 2. Stability of the Cauchy functional equation in Banach modules; 3. Stability of the Jensen functional equation in Banach modules; 4. Stability of the Trif functional equation in Banach modules; 5. Stability of cyclic functional equations in Banach modules over a C ^*-algebra; 6. Stability of cyclic functional equations in Banach algebras and approximate algebra homomorphisms; 7. Stability of algebra *-homomorphisms between Banach *-algebras and applications.     

Azumaya Extensions and Galois Correspondence

For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/A^H separable and A^H Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of separable subalgebras of C_A(A^H), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems.1991 Mathematics Subject Classification: 16W30, 16H05     

The Coherent Cohomology Ring of an Algebraic Group

Let G be a group scheme of finite type over a field, and consider the cohomology ring H ^*(G) with coefficients in the structure sheaf. We show that H ^*(G) is a free module of finite rank over its component of degree 0, and is the exterior algebra of its component of degree 1. When G is connected, we determine the Hopf algebra structure of H ^*(G).     

Homomorphisms and composition operators on algebras of analytic functions of bounded type

Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Fréchet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X^* and Y^*) are isomorphic? We prove that if X^* or Y^* has the approximation property and H_wu(U) and H_wu(V) are topologically algebra isomorphic, then X^* and Y^* are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H_b(U) and H_b(V), giving conditions under which an algebra isomorphism between H_b(X) and H_b(Y) is equivalent to an isomorphism between X^* and Y^*. We also obtain characterizations of different algebra homomorphisms as composition operators, study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on H_b(X) with pathological behaviors.     

EXTENSIONS OF HILBERT MODULES AND HANKEL OPERATORS

1.IntroductionInthepresentpaper,wewillcontinuethestudyofHilbertmodules[1-5].LetHbeaHilbertspaceandAafunctionalgebra.WesaythatHisaHilbertmoduleoverAifthereisamultiplication(a,f)-affromAxHtoH,makingHintoanXmoduleandif,inaddition,theactionisjointlycontinuousinthesup-normonAandtheHilbertspacenormonH.ThecategoryHofallHilbertNmodulesisanaturalsettingfornumerousquestionsinoperatortheory.In[9],DouglasandPaulseninitiatedasystematicstudyofHilbertmodules'theywereabletotranslatemanyconceptsandpro…     

Weak generators of the algebral ∞ and the commutant of a model operator

Let B be a Blaschke product with simple zeros in the unit disk, let Λ be the set of its zeros, and let ϕ∈H^∞. It is known that ϕ+BH^∞ is a weak^* generator of the algebra H^∞/BH^∞ if (for B that satisfy the Carleson condition (C)) and only if the sequence ϕ(Λ) is a weak^* generator of the algebra l^∞. In this paper, we show that for any Blaschke product B with simple zeros that does not satisfy condition (C), there exists B=B₁·…·B_N, where N ∈ℕ, and B₁, …, B_N are Blaschke products satisfying condition (C), there exists a function ϕ∈H^∞ such that ϕ(Λ) is a weak^* generator of the algebra l^∞, and ϕ+BH^∞ is not a weak^* generator of the algebra H^∞/BH^∞. Bibliography: 12 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 73–85. Translated by M. F. Gamal'.     

DOI-KOPPINEN HOPF BIMODULES ARE MODULES

I construct a generalized twisted smash product A ^H B, which gives an abstract structure of Cibils-Rosso's algebra X associated to a finite-dimensional Hopf algebra H, for the H-bimodule algebra A and H-bicomodule algebra B. I show that the Doi-Koppinen Hopf (H, B, D)-bimodules are modules over a certain algebra which is of this type. Moreover, if D is finitely generated projective as a k-module, there exists a k-module-preserving equivalence of categories between the category of Doi-Koppinen (H, B, D)-Hopf bimodules and the category of left (D ^*op ? D ^*) ^{H?H op} (B ? B ^op )-modules.