On the Structure of Sequentially Generalized Cohen-Macaulay Modules

A finitely generated module $M$ over a local ring is called a sequentially generalized Cohen-Macaulay module if there is a filtration of submodules of $M$: $M_0\subset M_1\subset ... \subset M_t=M$ such that $\dim M_0<\dim M_1< >... <\dim M_t$ and each $M_i/M_{i-1}$ is generalized Cohen-Macaulay. The aim of this paper is to study the structure of this class of modules. Many basic properties of these modules are presented and various characterizations of sequentially generalized Cohen-Macaulay property by using local cohomology modules, theory of multiplicity and in terms of systems of parameters are given. We also show that the notion of dd-sequences defined in \cite{cc} is an important tool for studying this class of modules.Comment: 28 page

H\"older continuous solutions to complex Hessian equations

We prove the H\"older continuity of the solution to complex Hessian equation with the right hand side in $L^p$, $p>\frac{n}{m}$, $1< m< n$, in a $m$-strongly pseudoconvex domain in $\mathbb{C}^n$ under some additional conditions on the density near the boundary and on the boundary data.Comment: 19 pages. Added Theorem 3.7: when the boundary is Holder continuous, there exists a Holder continuous $m$-sh extension to the domai

Impact Evaluation of Multiple Overlapping Programs using Difference-in-differences with Matching

Difference-in-differences with matching is a popular method in impact evaluation. Traditional impact evaluation methods including difference-in-differences with matching often deal with impact measurement of a single binary program. Imbens (1999) and Lechner (2001) extend the matching method to the case of multiple mutually exclusive programs. Frölich (2002) discusses different impact evaluation methods in the similar context. In reality, one can participate in several programs simultaneously and the programs may be overlapping. This paper discusses the method of difference-in-differences with matching in a general context of multiple overlapping programs. The method is applied to measure impacts of formal and informal credit in Vietnam using panel data from two Vietnam Household Living Standard Surveys in 2002 and 2004