A local homology theory for linearly compact modules

We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local homology modules of linearly compact modules are proved. A duality theory between local homology and local cohomology modules of linearly compact modules is developed by using Matlis duality and Macdonald duality. As consequences of the duality theorem we obtain some generalizations of well-known results in the theory of local cohomology for semi-discrete linearly compact modules.Comment: 24 page

An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures

This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement

Genetic diversity of black soldier flies in Vietnam

The Black Soldier Fly (BSF), Hermetia illucens (Linnaeus, 1758), is found in temperate and tropical regions of the world. In recent years, BSF has been cultivated as fodder in some areas of Vietnam. The genetic diversity of BSF in Vietnam has not yet been assessed. This study aimed to investigate the nucleotide diversity in COI sequences of BSF in Vietnam. We examined the COI nucleotide sequences of 22 BSFs using flies or larval tissue samples for DNA extraction and subsequent sequencing. Our analysis showed that the nucleotide composition of BSF consisted of 25.36% A, 36.04% T, 21.25% C, and 17.35% G, with a significant prevalence of A+T nucleotides of 61.40% compared to 38.60% for G+C nucleotides. Among 22 individual BSFs samples collected from ten provinces and cities, spanning seven agro-ecological regions in Vietnam, we identified 9 different haplotypes, which were distributed in five clades but mainly clustered in two main clades: E and F. Clade E, prominently represented by branch E, showed a higher abundance in Asia, while Clade F has been identified in Europe, Uganda, South Korea, Oceania and North America. Our results highlight the relatively high genetic diversity of the Vietnamese BSF population. In addition, the COI nucleotide sequences of these Vietnamese BSF samples were similar to those of Asian and Australian countries, showing significant similarities to the Palearctic and Oriental regions. These results provide valuable insights to inform BSF breeding and development in Vietnam