Representation theory of the system quiver

Let A be a three-point algebra with Gabriel quiver the system quiver Q, Then, up to isomorphism and duality, A is tame if and only if A is or degenerates to a factor of a tame algebra in the tame Table T if and only if A/rad5 A is tame, and A is wild if and only if A has a wild algebra in the wild Table W as a factor if and only if A is controlled wild.     

关于严实Hilbert环

在本文中，严实Ｈｉｌｂｅｒｔ环得到了更进一步的刻划．本文的主要结果是：一个环Ａ是严实Ｈｉｌｂｅｒｔ环，当且仅当多项式环Ａ［Ｘ］的每个实极大理想在Ａ上的局限是Ａ的一个极大理想，当且仅当Ａ是实Ｈｉｌｂｅｒｔ环，且Ａ［Ｘ］的每个实极大理想是极大的．     

Digraphs and Inclusion Intervals of Brualdi-type for Singular Values

A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

关于严实Hilbert环

在本文中，严实Ｈｉｌｂｅｒｔ环得到了更进一步的刻划．本文的主要结果是：一个环Ａ是严实Ｈｉｌｂｅｒｔ环，当且仅当多项式环Ａ［Ｘ］的每个实极大理想在Ａ上的局限是Ａ的一个极大理想，当且仅当Ａ是实Ｈｉｌｂｅｒｔ环，且Ａ［Ｘ］的每个实极大理想是极大的．     

Spanning Annuli in 3—manifolds

Al3-manifOldsandsurfacesconsideredinthisPaperareassumedtobecompactandori-entable,andallconcePtsandnotationsnotdefinedinthepaperareStandardfsee,forexample[2,3j.AcompressionbodyHisconstructedbyadding2-handlestoSXIalongacollectionofpairwisdisjointsimpleclosedcurvesonSX{o},andcaPpingoffanyresulting2-spherebound-arycomponentSwith3-balls,whereSisaconnectedclosedorientablesurface.ThecomponentSX{1}Of8Hisdenoted8 Handthesurface8H-8 H,whichmayormaynotbeconnect-ed,isdenoted8H.If8H=gi,Hisahandleb…     

Von Neumann Algebras and Hilbert Quantales

When A is a von Neumann algebra, the set of all weakly closed linear subspaces forms a Gelfand quantale, Max_w A. We prove that Max_w A is a von Neumann quantale for all von Neumann algebras A. The natural morphism from Max_w A to the Hilbert quantale on the lattice of weakly closed right ideals of A is, in general, not an isomorphism. However, when A is a von Neumann factor, its restriction to right-sided elements is an isomorphism and this leads to a new characterization of von Neumann factors.     

Characterizations of Centralizable Mappings on Algebras of Locally Measurable Operators

A linear mapping φ from an algebra A into its bimodule M is called a centralizable mapping at G ∈ A if φ(AB)=φ(A)B=Aφ(B) for each A and B in A with AB=G. In this paper, we prove that if M is a von Neumann algebra without direct summands of type I₁ and type II, A is a *-subalgebra with M ⊆ A ⊆ LS(M) and G is a fixed element in A, then every continuous (with respect to the local measure topology t(M)) centralizable mapping at G from A into M is a centralizer.     

A Characterization of π-Complemented Algebras

π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented.     

On Symmetric Cayley Graphs of Valency Eleven

A Cayley graph Γ=Cay(G,S)is said to be normal if G is normal in Aut Γ.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Γ of finite nonabelian simple groups G,where the vertex stabilizer Av is soluble for A=Aut Γ and v ∈ VΓ.We prove that either Γ is normal or G=A5,A10,A54,A274,A549 or A1099.Further,11-valent symmetric nonnormal Cayley graphs of A5,A54 and A274 are constructed.This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011.     

A stochastic optimal control approach to a class of production and inventory problems

A comprehensible and unified system control approach is presented to solve a class of production/inventory smoothing problems. A nonstationary, non-Gaussian, finite-time linear optimal solution with an attractive computation scheme is obtained for a general quadratic and linear cost structure. A complete solution to a classical production/inventory control problem is given as an example. A general solution to the discrete-time optimal regulator with arbitrary but known disturbance is provided and discussed in detail. A computationally attractive closed-loop suboptimal scheme is presented for problems with constraints or nonquadratic costs. Implementation and interpretation of the results are discussed.     

同调光滑连通上链DG代数的一个注记

本文给出了有关同调光滑连通上链微分分次(简称DG)代数的两个重要结论.具体地说,当A是同调光滑连通上链DG代数且其同调分次代数H(A)是诺特分次代数时,证明D_(fg)(A)中的任意Koszul DG A-模都是紧致的.另外,当A是Kozul连通上链DG代数且其同调分次代数H(A)是有平衡对偶复形的诺特分次代数时,证明A的同调光滑性质等价于D_(fg)(A)=D~c(A).     

On a Plus-Construction for Algebras over an Operad

We prove a analogous to Quillen's plus-construction in the category of algebras over an operad. For that purpose we prove that this category is a closed model category and prove the existence of an obstruction theory. We apply further this plus-construction for the specific cases of Lie algebras and Leibniz algebras which are a noncommutative version of Lie algebras: let sl(A) be the kernel of the trace map gl(A)A/[A,A], where A is an associative algebra with unit and gl(A) is the Lie algebra of matrices over A. Then the homotopy of slA)⁺ in the category of Lie algebras is the cyclic homology of A whereas it is the Hochschild homology of A in the category of Leibniz algebras.     

关于实Hilbert环

通过引进“强实Hilbert环”这一概念,本文证明了,一个环A是强实Hilbert环,当且仅当多项式环A[X]是实Hilbert环,当且仅当A[X]的每个实极大理想在A上的局限是实极大的,从而文献[1]中两个主要结果被否定.此外,本文还研究了所谓的“严格的实Hilbert环”,这类环对于半代数零点定理等方面的探讨更具应用意义.     

ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I

The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.     

不完全信息下考虑效率和规模的多时点并购决策

针对企业并购过程中存在不完全信息和多时点信息的问题,提出了一种考虑效率和规模的企业并购决策方法. 通过证据推理集结并购双方的不完全的、多时点的评价信息,利用\,DEA\,方法判断合并企业规模是否过大,并筛选出可行并购方案,再根据合并企业竞争型并购交叉效率高低决策最佳并购目标. 最后算例分析说明了方法的有效性和实用性.     

关于一类具有相同非负群逆和M-P逆的非负矩阵的进一步研究

1引言设A是n阶非负方阵．设矩阵方程(1)AXA=A,(2)XAX=X,(3)(AX)~T= AX,(4)(XA)~T=XA,(5)AX=XA．A具有非负广义逆是指存在非负方阵X满足方程(1)～(4),并记为A~(?)．A具有非负群逆是指存在非负方阵X满足方程(1),(2),(5),并记为A~#．在A~(?)存在的前提下,两者相同的充分必要条件有(a)AA~(?)=A~(?)A；(b)A~(?)=p(A),其     

3-连通3-正则图中的可序子集

图G的k元点集X={x1,x2,…,xk}被称为G的k-可序子集,如果X的任意排列都按序排在G的某个圈上.称G是k-可序图,如果G的每一个k元子集都是G的k-可序子集.称G为k-可序Hamilton图,如果X的任意排列都位于G的Hamilton圈上.研究了3-连通3-正则图的可序子集的存在性问题.     

广义Schur补的广义逆

对四分块矩阵A=A(︿) A(︿,︿′)A(︿′,︿) A(︿′)来说 ,如果 A和 A(︿)都是非奇异的 ,则A- 1 (︿′) =(A/︿) - 1 ,这里 A/ ︿=A(︿′) -A(︿′,︿) A(︿) - 1 A(︿,︿′)是 A(︿)在 A中的 Schur补 .王伯英教授指出上述等式 ,对半正定的 Hermitian矩阵而言 ,一般也是不能推广到 Moore-Penrose逆上去的 .在某些限制条件下 ,我们证明了广义逆的主子矩阵与广义 Schur补的关系是密切的 ,它使经典结果成为特例     

完全正矩阵的整数分解

n阶矩阵A称为完全正的,如果A有分解:A=BB^T,其中B为元素非负矩阵,B的最小可能列数称为A的分解指数.本文考察低阶双非负矩阵在整数环上的完全正分解及其分解指数.