代数构造及在Ramsey理论中的应用

这篇文章在伽罗瓦域上的代数构造和关于一些特定类型图的Ramsey数之间建立了一个关系. 研究了关于伽罗瓦域上的代数构造的方程及方程组的解. 我们得到了一些关于二部图的Ramsey数的新的下界和上界.     

Multifold factorizations of cyclic groups into subsets

Let $(G,+)$ be an abelian group. A finite multiset A over G is said to give a λ-fold factorization of G if there exists a multiset B over G such that each element of G occurs λ times in the multiset $A+B:=\{a+b:a\in A,b\in B\}$. In this article, restricting G to a cyclic group, we will provide sufficient conditions on a given multiset A under which the exact value or an upper bound of the minimum multiplicity λ of a factorization of G can be given by introducing a concept of ‘lcm-closure’. Furthermore, a couple of properties on a given factor A will be shown when A has a prime or prime power order (cardinality). A relation to multifold factorizations of the set of integers will be also glanced at a general perspective.     

红黑排序混合算法收敛速度分析

The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.     

Carbon nanotubes-assisted polyacrylamide gel electrophoresis for enhanced separation of human serum proteins and application in liverish diagnosis

The application of pore-gradient polyacrylamide gel electrophoresis (PG-PAGE) incorporated with carbon nanotube modified by Triton X-100 and carboxylation so as to improve the separation of human serum proteins is reported. The novel PG-PAGE was made by adding water-soluble single-walled carbon nanotubes (CNTs) when preparing the polyacrylamide gel. Significant improvements in separation of complement C3 protein and haptoglobin (Hp) in human serum were achieved. It was estimated that the interactions between the hydrophilic groups on the proteins and the surface of the CNTs result in different adsorption kinetics of complement C3 and Hp subtype on the nanoparticles incorporated in the gel, thus enhancing the separation of the two proteins in serum. This new CNT matrix-assisted PG-PAGE method for enhanced separation of complement C3 and Hp in human serum was successfully applied to distinguish the samples from liverish patients and healthy people.     

Computational efficiency analysis of Wu et al.’s fast modular multi-exponentiation algorithm

Very recently, for speeding up the computation of modular multi-exponentiation, Wu et al. presented a fast algorithm combining the complement recoding method and the minimal weight binary signed-digit representation technique. They claimed that the proposed algorithm reduced the number of modular multiplications from 1.503k to 1.306k on average, where the value k is the maximum bit-length of two exponents. However, in this paper, we show that their claim is unwarranted. We analyze the computational efficiency of Wu et al.’s algorithm by modeling it as a Markov chain. Our main result is that Wu et al.’s algorithm requires 1.471k modular multiplications on average.     

Graphs G for which both G and G¯ are Contraction Critically k-Connected

 An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is called contraction critically k-connected. For k≥4, we prove that if both G and its complement Gˉ are contraction critically k-connected, then |V(G)|<k ^5/3+4k ^3/2. Received: October, 2001 Final version received: September 18, 2002 AMS Classification: 05C40     

The Ihara zeta function of the complement of a semiregular bipartite graph

We study the Ihara zeta function of the complement of a semiregular bipartite graph. A factorization formula for the Ihara zeta function is derived via which the number of spanning trees is computed. For a class of complements of semiregular bipartite graphs, it is shown that they have the same Ihara zeta function if and only if they are cospectral.     

基于溶胶-凝胶技术可更新的安培分析免疫传感器用于人血清中补体3的测定

在低温下，通过混合石墨粉，补体3抗血清，溶胶－凝胶而制备了一种基于啼－凝胶技术的可更新的安培分析免疫传感器。该传感器坚固，多孔，拥有一个更新的表面，在辣根过氧化物酶标记的补体3的协助下，通过竞争性的免疫分析来确定人血清中补体3的含量。以邻－氨酚作为底物，－150mV作为工作电位，响应电流与补体3的浓度在1．17－35．1μg/mL范围内呈线性关系，检出限为0．56μg/mL。分析血清样本结果表明所制备的传感器在临床分析中是可行的。     

Complements to Projective Almost Complete Tilting Modules

ABSTRACT

An equivalent version of the Generalized Nakayama Conjecture states that any projective almost complete tilting module admits a finite number of non-isomorphic indecomposable complements. Motivated by this connection, we investigate the number of possible complements of projective almost complete tilting modules for some particular classes of Artin algebras, namely monomial algebras and algebras with exactly two simple modules.