Flatness Properties of S-Posets

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomology group vanishes.     

Tensor Products of Approximately Cohen–Macaulay Rings

Our aim in this article is to study a problem originally raised by Grothendieck. We show that the approximately Cohen–Macaulay property is preserved for the tensor product of algebras over a field k. We also discuss the converse problem.     

The Division Relation: Congruence Conditions and Axiomatisability

We examine a universal algebraic abstraction of the semigroup theoretic concept of “divides:” a divides b in an algebra A if for some n ∈ ω, there is a term t(x, y ₁,…, y _n ) involving all of the listed variables, and elements c ₁,…, c _n such that t ^A (a, c ₁,…, c _n ) = b. The first order definability of this relation is shown to be a very broad generalisation of some familiar congruence properties, such as definability of principal congruences. The algorithmic problem of deciding when a finitely generated variety has this relation definable is shown to be equivalent to an open problem concerning flat algebras. We also use the relation as a framework for establishing some results concerning the finite axiomatisability of finitely generated varieties.     

Module-Theoretic Characterizations of Generalized GCD Domains

We give several module-theoretic characterizations of generalized GCD domains. For example, we show that an integral domain R is a generalized GCD domain if and only if semi-divisoriality and flatness are equivalent for torsion-free R-modules if and only if every w-finite w-module is projective if and only if R is w-Prüfer (in the sense of Zafrullah). We also characterize when a pullback R of a certain type is a generalized GCD domain. As an application, we characterize when R = D + XE[X] (here, D ? E is an extension of domains and X is an indeterminate) is a generalized GCD domain.     

On Strongly Copure Flat Modules and Copure Flat Dimensions

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if and only if Ext ⁱ (M, C) = 0 for all flat cotorsion right R-modules C and i ≥ 1. Then we define and investigate copure flat dimensions of left coherent rings. Finally, we give some new characterizations of n-FC rings.     

On Flatness and Completion for Infinitely Generated Modules over Noetherian Rings

Let A be a noetherian commutative ring, and let 𝔞 be an ideal in A. We study questions of flatness and 𝔞-adic completeness for infinitely generated A-modules. This is done using the notions of decaying function and 𝔞-adically free A-module.     

The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel Method

We consider the double layer potential operator W defined on the polyhedral boundary of an infinite cone and prove the invertibility of (I±2W) in the space of continuous functions. To do this we define an operator-valued symbol function for W and show that the spectral radii of its values are less than one half. In the last part of this paper we consider a piecewise constant collocation method for the numerical solution of the double layer potential equation over the boundary of a bounded polyhedron.     

多指标面板数据融合聚类分析

针对多指标面板数据的样品分类和历史时期划分问题,从多元统计分析理论角度提出一个多指标面板数据的融合聚类分析方法。该方法改进了多指标面板数据的因子分析和系统聚类方法,依据Fisher有序聚类理论,构造了Frobenius范数形式的离差平方和函数,提出了多指标面板数据的有序聚类方法。实证结果表明,该方法能够满足系统分析的统一性要求,保证指标之间的不相关;能够克服时间维度上均值处理造成的偏误,信息损失较少;能够解决面板数据有序聚类的问题;弥补了单一分析的片面性和局限性。     

面板数据空间误差分量模型的GMM估计及其应用

本文研究面板数据空间误差分量模型(Spatial Error Components Model,SEC)的估计方法。为克服极大似然法在SEC模型估计中运算的困难,本文提出基于广义矩估计的可行广义最小二乘法(GMM-GLS),证明了估计量的一致性及有限样本下的有效性;并应用此模型,研究2000-2007年中国30个省(西藏除外)的物质资本存量、人力资本存量及能源消耗对实际GDP的影响,结果表明,采用SEC模型所得估计结果更为符合经济现实。     

Differential operators and immersions of a Riemann surface into a Grassmannian

We consider equivariant holomorphic immersions of a universal cover of a compact Riemann surface X into a Grassmannian satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to that takes the natural action of the Galois group on to the action of the Galois group on defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism.