Repetitive cluster-tilted algebras

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C_Fm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in C_Fm and the structure of repetitive cluster-tilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of C_Fm, and prove that the tilting graph KC_Fm of C_Fm is connected.     

关于γ—可重排列方面的一个计数公式

本文给也了规格为２＾ｍ的２ｍ个元的γ－可重排列的个数的一个计算公式。     

经济问题的模糊聚类

应用模糊聚类的正交方法，解决经济领域中的一个聚类问题。     

A quantum analogue of generic bases for affine cluster algebras

We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster algebras.     

基于投入产出表的区域价值链集群识别研究——以上海为例

区域价值链集群分析是集群分析作为区域经济创新性和竞争优势分析工具的重要表现形式。而区域价值链集群识别是进行区域价值链集群分析的第一步。为了实现区域价值链集群依据经济系统各部门间网络互动联系来确定其核心主导产业及其前后向密切关联产业的识别目标,本文选取了以最大值法和投入产出分析法相结合的区域价值链识别方法。由此进行的识别研究表明,上海共有通信、化工、通专、金属、石油核燃料五类价值链集群,它们通过内部和彼此间的互动交织构成了密切关联的网络,并在很大程度上反映了上海经济系统的核心组成。而相应的经济技术分析表明,通专价值链集群将很有可能在上海大力发展先进制造业的产业结构升级大背景下赶超通信价值链集群而成为新一轮发展的亮点。     

Periodicities in Cluster Algebras and Cluster Automorphism Groups

We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among (strict) direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A) for a cluster algebra A and the group AutMn(S) for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.     

LOB中基于工期决定因素分析的资源均衡算法研究

资源均衡是重复性项目中的经典调度问题,本文提出一种新的基于平衡线法(line of balance,LOB)的资源均衡方法。首先,本文提出LOB中关键路线的确定方法,确定关键路线及关键工序类型。而后,本文分析项目总工期的决定因素,对不同类型关键工序的特性及其与总工期、资源调整之间的关系进行了研究,论证了在LOB的资源均衡问题中,由于逆关键工序、点关键工序这些特殊工序的存在,可以在保证项目总工期不变的前提下,通过同时调整关键工序和非关键工序实现资源优化。按照这一思路,论文设计了LOB中资源均衡的遗传算法。算例分析表明该资源均衡算法的优化性能。本文提出的资源均衡思路和算法能帮助项目计划人员拓展资源优化空间,达到更好的资源均衡效果。     

The Cluster Function of Single-Valued Functions

Given a single-valued function f between topological spaces X and Y, we interpret the cluster set C(f;x) as a multivalued function F=C(f;⋅) associated to f – the cluster function of f. For appropriate metrizable spaces X and Y, we characterize cluster functions C(f;⋅) among arbitrary set-valued functions F and show that every cluster function F=C(f;⋅) admits a selection h of Baire class 2 such that F=C(h;⋅). Mathematics Subject Classifications (2000) Primary: 54C50, 54C60; secondary: 26A21, 54C65.This research was partially supported by DFG Grant RI 1087/2.     

Frobenius morphisms and stable module categories of repetitive algebras

Let k be the algebraic closure of a finite field F_q and A be a finite dimensional k-algebra with a Frobenius morphism F.In the present paper we establish a relation between the stable module category of the repetitive algebra  of A and that of the repetitive algebra of the fixed-point algebra A~F.As an application,it is shown that the derived category of A~F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.     

重复结构振动控制的降维方法

提出了对称结构、旋转周期结构和链式结构的振动控制的降维方法．以某种对称的方式设置广义坐标的凝聚、传感器、驱动器的位置以及输入与控制力的关系,即可使控制系统具有和结构同样的重复性．对凝聚了的广义坐标和系统输入采用适当的变换,即可通过执行一些子结构的控制问题实现整体系统的振动控制,从而使控制问题的维度显著降低．     

连续调查的整群抽样

本文讨论了连续调查中应用普查方法时的整群抽样和分层整群抽样。     

Applications of BGP-reflection functors: isomorphisms of cluster algebras

Given a symmetrizable generalized Cartan matrix A, for any index k, one can define an automorphism associated with A, of the field Q(u1,…, un) of rational functions of n independent indeterminates u1,…,un.It is an isomorphism between two cluster algebras associated to the matrix A (see sec. 4 for the precise meaning). When A is of finite type, these isomorphisms behave nicely; they are compatible with the BGP-reflection functors of cluster categories defined in a previous work if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the "truncated simple reflections" defined by Fomin-Zelevinsky. Using the construction of preprojective or preinjective modules of hereditary algebras by DIab-Ringel and the Coxeter automorphisms (i.e. a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.     

Wakamatsu-silting complexes

We introduce Wakamatsu-silting complexes (resp., Wakamatsu-tilting complexes) as a common generalization of both silting complexes (resp., tilting complexes) and Wakamatsu-tilting modules. Characterizations of Wakamatsu-silting complexes are given. In particular, we show that a complex T is Wakamatsu-silting if and only if its dual DT is Wakamatsu-silting. It is conjectured that compact Wakamatsu-silting complexes are just silting complexes. We prove that the conjecture lies under the finitistic dimension conjecture.     

INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are sta...     

Facial non‐repetitive edge‐coloring of plane graphs

A sequence r₁, r₂, …, r_2n such that r_i=r_{n+ i} for all 1≤i≤n is called a repetition. A sequence S is called non‐repetitive if no block (i.e. subsequence of consecutive terms of S) is a repetition. Let G be a graph whose edges are colored. A trail is called non‐repetitive if the sequence of colors of its edges is non‐repetitive. If G is a plane graph, a facial non‐repetitive edge‐coloring of G is an edge‐coloring such that any facial trail (i.e. a trail of consecutive edges on the boundary walk of a face) is non‐repetitive. We denote π′_f(G) the minimum number of colors of a facial non‐repetitive edge‐coloring of G. In this article, we show that π′_f(G)≤8 for any plane graph G. We also get better upper bounds for π′_f(G) in the cases when G is a tree, a plane triangulation, a simple 3‐connected plane graph, a hamiltonian plane graph, an outerplanar graph or a Halin graph. The bound 4 for trees is tight. © 2010 Wiley Periodicals, Inc. J Graph Theory 66: 38–48, 2010     

Preprojective Cluster Variables of Acyclic Cluster Algebras

It is proved that any cluster-tilted algebra defined in the cluster category 𝒞(H) has the same representation type as the initial hereditary algebra H. For any valued quiver (Γ, Ω), an injection from the subset 𝒫?(Ω) of the cluster category 𝒞(Ω) consisting of indecomposable preprojective objects, preinjective objects, and the first shifts of indecomposable projective modules to the set of cluster variables of the corresponding cluster algebra 𝒜_Ω is given. The images are called “preprojective cluster variables”. It is proved that all preprojective cluster variables other than u_i have denominators u ^dim M in their irreducible fractions of integral polynomials, where M is the corresponding preprojective module or preinjective module. In case the valued quiver (Γ, Ω) is of finite type, the denominator theorem holds with respect to any cluster. Namely, let x = (x₁,…, x_n) be a cluster of the cluster algebra 𝒜_Ω, and V the cluster tilting object in 𝒞(Ω) corresponding to x, whose endomorphism algebra is denoted by Λ. Then the denominator of any cluster variable y other than x_i is x ^dim M, where M is the indecomposable Λ-module corresponding to y. This result is a generalization of the corresponding result of Caldero–Chapoton–Schiffler to the non-simply-laced case.     

聚类分析在虎骨代用品研究中的应用

本文通过聚类分析的方法利用虎和某些动物的腿骨和椎骨骨胶中１７种氨基酸含量的数据，对虎骨和这些动物骨进行分类，以研究虎骨与其它动物骨的相似性，为挑选虎骨的代用品提供科学的依据。文中的分析依赖《多元统计分析实用程序》软件包，并同时采用了程序中动态聚类分析和系统聚类分析中最短距离和类平均几种聚类方法进行。由这些方法得到的大体相近的一些结论，达到了本文分析的目的。     

平移不变的随机串测度

利用围道估计的方法，刻划在相变点处的平移不变随机串测度，证明了：对二维以上情况，当口充分大时，在临界点处，平移不变随机串测度有且只有两个极点，也即任一平移不变随机串测度都是这两个极点的凸组合．     

非脆弱离散重复控制的二维模型方法

针对一类线性离散系统,提出一种基于二维模型的非脆弱离散重复控制设计方法.通过独立地考虑重复控制系统的控制与学习行为,建立离散重复控制系统的二维模型. 在此基础上,针对重复控制器和反馈控制器具有不确定性的离散重复控制系统,给出了基于线性矩阵不等式的系统稳定性条件和重复控制律. 最后,数值仿真实例验证了所提方法的有效性.