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

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

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

Students’ Attitudes Towards Education in Biology-Related Disciplines and the Need for Internationalization : A Survey at a Vietnamese University

This survey examined the attitudes of 538 undergraduate students enrolled at a Vietnamese university towards biology-related disciplines. Employing a structured questionnaire, the study explored several aspects, including students' interests in various biology-related fields, their motivations for pursuing these disciplines, their opinions on teaching methods, their aspirations for internationalization and study abroad experiences, the essential skills they believed were crucial for success, and the areas in teaching that required improvement. The survey results indicated that students acknowledged the significance of fields such as medicine and veterinary sciences, with their motivations largely influenced by job prospects and societal needs. Moreover, the results identified specific areas in teaching that students wanted to have improvement, such as laboratory work, practical skills development, fieldwork experiences, and exchange programs, and their attitude towards internationalization and study abroad opportunities, in relations to the factors such as age, gender, grade, and major. The insights gained from this survey can contribute to the enhancement of educational strategies and the creation of an engaging learning environment for students majoring in biology-related disciplines