A Note on Semilocal Reciprocity Laws on Curves

The aim of this work is to offer a definition of the Contou-Carrère symbol associated with a closed point of an algebraic curve and with a local ring of dimension zero, first, and then with a semilocal ring of dimension zero, from the commutator of a certain central extension. When the curve is complete, we deduce the reciprocity law in both cases. Moreover, we give some applications to the residues, and obtain explicit relations between the classic residue and the Witt residue.

Communicated by C. Pedrini.     

A note on node packing polytopes on hypergraphs

A facial structure of the node packing polytope, i.e., of the convex hull of integer solutions of the node packing problem, on hypergraphs is studied. First, the results extracted by Chvàtal and by Balas and Zemel on canonical facets of the node packing polytopes on graphs are generalized to derive some specific hypergraphs having canonical facets. Second, it is shown that the facial structure of the node packing polytope on a hypergraph, named a fat graph, has a very close relationship to the facial structures of the node packing polytope and also of the convex hull of integer solutions of an integer linear program, which are defined on a specific graph corresponding to the fat graph.     

A note on upper bounds on the cp-rank

Hanna and Laffey gave an upper bound on the cp-rank of a completely positive matrix, in terms of its rank and the number of zeros in a full rank principal submatrix. This bound, for the case that the matrix is positive, was improved by Barioli and Berman. In this paper a new straightforward proof of both results is given, and the same approach is used to improve Hanna and Laffey’s bound in the case that the matrix has a zero entry.     

On certain conjectures on invariant measures on semigroups

A conjecture stating that a locally compact semigroup admits a twosided semi-invariant measure iff it contains a kernel which is a unimodular group, is proven. Also a conjecture stating that the support of an r^*-invariant measure is a left group, is proven under the condition that for some a ε F (=support of the measure), aF is right cancellative. Moreover four types of invariance for regular probability measures are shown to be equivalent. Also a new proof of the equivalence of a two-sided semi-invariant probability measure and the existence of a kernel which is a compact group, is given.     

A note on submodular set cover on matroids

We consider a problem related to the submodular set cover on polymatroids, when the ground set is the family of independent sets of a matroid. The achievement here is getting a strongly polynomial running time with respect to the ground set of the matroid even though the family of independent sets has exponential size. We also address the optimization problem of the maximization of submodular set functions on the independent sets of a matroid.     

基于偏好锥的DEA-DA模型研究

扩展的DEA-DA模型是一种结合数据包络分析(DEA)和判别分析(DA)的非参数判别分析方法。一种锥比率DEA模型C^2WH可以利用锥比率体现决策对样本指标和决策单元的偏好。因此，本将C^2WH模型和DA模型结合，建立了基于偏好锥的DEA-DA模型与方法，并就偏好锥为多面凸锥的情况给出了实例分析。结果表明，所建模型可以在判别分析过程中体现决策的偏好，从而形成主观与客观的集成评价。     

Remarks on contact relations on Boolean algebras

The paradigmatic example for a contact relation is that of having nondisjoint closures for regions in n-dimensional space. Generally, a contact relation is a binary relation on a Boolean algebra reflecting some of the properties of this example. We prove in this paper a topological and an algebraic representation theorem for contact algebras and solve two problems due to Düntsch and Winter and to Dimov and Vakarelov, respectively.     

A Note on vector bundles on Hirzebruch surfaces

In literature, two basic construction methods have been used to study vector bundles on a Hirzebruch surface. On the one hand, we have Serre?s method and elementary modifications, describing rank-2 bundles as extensions in a canonical way (Brînz?nescu and Stoia, 1984 [4], [5], Brînz?nescu, 1996 [6], Brosius, 1983 [7], Friedman, 1998 [9]), and on the other hand, we have a Beilinson-type spectral sequence (Buchdahl, 1987 [8]). Morally, the Beilinson spectral sequence indicates how to recover a bundle from the cohomology of its twists and from some sheaf morphisms (the differentials of the sequence). The aim of this Note is to show that the canonical extension of a rank-2 bundle can be deduced from the Beilinson spectral sequence of a suitable twist, called the normalization. In the final part we give a cohomological criterion for a topologically trivial vector bundle on a Hirzebruch surface to be trivial. To emphasize the relations and the differences between these two construction methods mentioned above, two different proofs are given.     

关于非紧流形上的Ricci流的一个注记

设（M^3,90）是非紧三维Riemann流形,其Ricci曲率非负,单射半径有正的下界,且当x→∞时数量曲率R（x）→0。则以（M^3,go）为初始值的Ricci流在M^3×[0,∞）上有长期解。这推广了马和朱最近的一个结果．在高维情形我们也有相应的结果,并且我们给Chau,Tam和Yu在Ktihler情形的类似定理一个新的证明。     

基于传导变换的客户价值研究

以企业为价值感受主体、客户为价值感受客体的客户价值,衡量了客户对企业的相对重要性.首先基于传导变换理论,给出传导知识的定义,然后建立传导度以度量主动变换导致客户价值发生传导变换的效果,探讨了客户价值传导信息元集和传导知识的获取.研究可以为企业提供制定客户关系管理策略的依据,为客户价值研究提供新的思路.     

基于Vague集的群决策方法研究

首先介绍了Vague集的基本概念,将直觉模糊集的一些运算规则重新在Vague集上作了定义,提出用Vague值表示的九级语言术语集.接着指出衡量Vague集(值)相似度要考虑的三个因素,提出了新的度量方法.在同时考虑专家决策结果的一致性和专家权重的基础上,提出了汇总各专家Vague意见的方法.最后以一个案例说明了所提出的方法.     

A Note on Hermitian-Einstein Metrics on Parabolic Stable Bundles

Let ${\overline M}Let be a compact complex manifold of complex dimension two with a smooth K?hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on with a stable parabolic structure along D, we prove that there exista a Hermitian-Einstein metric on compatible with the parabolic structure, whose curvature is square integrable. Received February 18, 2000, Accepted September 6, 2000     

受融资影响的项目组合选择研究

本文构建了一个考虑融资的项目组合选择模型,允许企业根据每期的投资计划,合理地调节当期所需要投入的资金预算。如果期初的可用资金量超过了当期的投资额,企业可以尽早将多余的资金释放;反之,若期初的可用资金量不足以支持本期项目的执行,允许企业从外部融资,如银行贷款等,以满足企业实际的需求。融资需要付出一定的代价,且代价与执行项目的风险程度相关。基于此,偿还融资代价对项目组合经济性的影响被引入到项目组合选择模型中。企业需要在全部资金带来的投资收益及融资代价之间进行权衡,以谋求利润最大化。鉴于所构建模型非线性化的特点,本文给出了该模型的等价形式,并进行了理论证明。最后,通过企业实际算例分析,得出结论:1)考虑融资后能够为企业带来更高回报;2)融资相关因素对项目组合的经济性有显著影响。     

Borel on the Questions Versus Borel on the Answers

We consider morphisms (also called Galois-Tukey connections) between binary relations that are used in the theory of cardinal characteristics. In [8] we have shown that there are pairs of relations with no Borel morphism connecting them. The reason was a strong impact of the first of the two functions that constitute a morphism, the so-called function on the questions. In this work we investigate whether the second half, the function on the answers' side, has a similarly strong impact. The main question is: Does the nonexistence of a Borel morphism imply the non-existence of a morphism that is only Borel on the answers' side? We give sufficient conditions for an affirmative answer. The results are applied to the unsplitting relations where it has been open whether there is a morphism that is Borel on the answers' side.     

一类基于分层量化的Domain上的广义Alexander拓扑

文献[8]提出了一类基于分层量化的偏序集结构(以下简称R-偏序集).此结构是sfe[5]的非对称推广,也是拟度量空间(quasi-metric spaces,qms)[3]和广义超度量空间(generalized ultrametric spaces,gums)[4]的一种特殊情形.本文定义了其上的广义Alexande...     

基于学习—遗忘效应的生产率降低损失索赔研究

建设工程项目很多具有重复性施工的特点,本文利用这种特点将学习-遗忘效应应用到平衡作业线(LOB)方法中,分析因为工程中断造成生产率的降低的现象,认为因生产率降低而导致工程工期的延长实际上超过工程实际中断的时间,最后以一个工程案例来说明分析过程.     

Some problems on narrow operators on function spaces

It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L ₁[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i. space exists. Another result establishes sufficient conditions on an r.i. space E under which the orthogonal projection onto the closed linear span of the Rademacher system is a hereditarily narrow operator. This, in particular, answers a question of the first named author and Randrianantoanina (Problem 11.9 in [Popov M., Randrianantoanina B., Narrow Operators on Function Spaces and Vector Lattices, de Gruyter Stud. Math., 45, Walter de Gruyter, Berlin, 2013]).     

Vector fields on smooth threefolds vanishing on complete intersections

A result of J. Wahl shows that the existence of a vector field vanishing on an ample divisor of a projective normal variety X implies that X is a cone over this divisor. If X is smooth, X will be isomorphic to the n-dimensional projective space. This paper is a first attempt to generalize Wahl's theorem to higher codimensions: Given a complex smooth projective threefold X and a vector field on X vanishing on an irreducible and reduced curve which is the scheme theoretic intersection of two ample divisors, X is isomorphic to the 3-dimensional projective space or the 3-dimensional quadric. Received: 24 April 2001     

Some Remarks on Quantum Limits on Zoll Manifolds

We study the concentration of eigenfunctions of the Laplace–Beltrami operator on manifolds all whose geodesics are closed (the so-called Zoll manifolds). Some results on the structure of the set of invariant semiclassical measures associated to sequences of eigenfunctions are given. Among these, we show that any probability measure on the unit tangent bundle of a compact rank-one symmetric space that is invariant by the geodesic flow may be realized as the semiclassical measure of a sequence of eigenfunctions of the Laplacian. This extends a previous result of Jakobson and Zelditch on spheres.     

A note on harmonic forms on complete manifolds

In this note, we will prove that under certain conditions, the space of polynomial growth harmonic functions and harmonic forms with a fixed growth rate on manifolds which are asymptotically nonnegatively curved is finite dimensional. This is a partial generalization of the works of Li and Colding-Minicozzi. We will also give an explicit estimate for the dimension in case the manifold is a complete surface of finite total curvature. This is a generalization to harmonic forms of the work of Li and the author.