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

The reduction number and degree bound of projective subschemes

In this paper, we prove the degree upper bound of projective subschemes in terms of the reduction number and show that the maximal cases are only arithmetically Cohen-Macaulay subschemes with linear resolution. Furthermore, it can be shown that there are only two types of reduced, irreducible projective varieties with almost maximal degree. We also give explicit Betti tables for almost maximal cases. Interesting examples are provided to understand our main results

Impact assessment of a local seventeen-year initiative on cassava-based soil conservation measure on sloping land as a climate-smart agriculture practice in Van Yen District, Yen Bai Province, Vietnam

Van Yen District in Yen Bai Province represents the general terrain conditions and farming systems of the northern mountainous region of Vietnam. It has suffered land degradation due to soil erosion and nutrient depletion, which in turn led to declined crop yield, and food insecurity. The district experienced these impacts due to unsustainable upland agricultural practices. The Department of Agriculture and Rural Development realized that their previous practices would not leave anything behind for the next generations. This prompted them to launch an agricultural conservation program in 2003 to restore degraded soils, which would improve the production in the farms, and diversify incomes and the household economy of local farmers. Over the 17 years of implementation, the program has introduced six conservation measures that have been well-received and implemented by the farmers of Van Yen. This report assesses the impacts of the 17-year program using the economic, environmental, and social lenses with a focus on the cassava crop, considering the traditional cassava monocrop system (or non-adoption group) and the six conservation measures (or adoption group). The study applied a mixed-methods approach, using semi-questionnaire to collect qualitative information from 488 farmers across six communes and surveys to collect soil samples to assess the levels of soil restoration among certain measures. The study also used the quantitative research findings from two other research studies conducted in Mau Dong Commune to help discuss its findings