Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a Stanley-Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen-Macaulay. In particular, all symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen-Macaulayness can pass from a symbolic power to another symbolic powers in different ways.Comment: The published version of this paper contains a gap in the proofs of Theorem 2.5 and Theorem 3.5. This version corrects the proofs with almost the same arguments. Moreover, we have to modify the definition of tight complexes in Theorem 2.5. These changes don't affect other things in the published version. A corrigendum has been sent to the journa

The Current Adoption of Dry-Direct Seeding Rice (DDSR) in Thailand and Lessons Learned for Mekong River Delta of Vietnam

The paper documents the joint study trip, organized by CCAFS Southeast Asia for Vietnamese rice researchers, extension workers, as well as local decision makers, to visit Thailand in April 2018. The goal of the study trip was to observe and learn the experience of Thai farmers on the large-scale adoption process of dry-direct seeding rice (DDSR), a viable alternative to address regional scarcity of fresh water in irrigation caused by the drought and salinity intrusion in the Mekong River Delta

Folding model study of the elastic α+α\alpha + \alpha scattering at low energies

The folding model analysis of the elastic $\alpha + \alpha$ scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the $^4$He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the $\alpha + \alpha$ optical potential at low energies quite unambiguously and found that the $\alpha + \alpha$ overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic $\alpha + \alpha$ and $\alpha$-nucleus scattering at low energies using the same realistic density dependent M3Y interaction