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 Trio Neural Model for Dynamic Entity Relatedness Ranking

Measuring entity relatedness is a fundamental task for many natural language processing and information retrieval applications. Prior work often studies entity relatedness in static settings and an unsupervised manner. However, entities in real-world are often involved in many different relationships, consequently entity-relations are very dynamic over time. In this work, we propose a neural networkbased approach for dynamic entity relatedness, leveraging the collective attention as supervision. Our model is capable of learning rich and different entity representations in a joint framework. Through extensive experiments on large-scale datasets, we demonstrate that our method achieves better results than competitive baselines.Comment: In Proceedings of CoNLL 201

SOLUTIONS TO IMPROVE THE EFFECTIVENESS OF PHYSICAL EDUCATION FOR STUDENTS AT CHU VAN AN HIGH SCHOOL, THAI NGUYEN PROVINCE, VIETNAM

Introduction: Physical education is a part of Physical Education and Sports, which is one of the basic activities with a clear orientation of Physical Education and Sports in society, which is an organizational process to transmit and absorb the values of physical education and sports in the education system, or general education of the school. Materials: The article considers the results of the author's research in the article assessing the status of physical education work of students at Chu Van An High School, Thai Nguyen Province to serve as a basis for the development of measures. improve the effectiveness of physical education in schools. Research methods: Using basic scientific research methods such as pedagogical observation, survey, interview, and statistical mathematics, the paper has developed solutions to improve the effectiveness of physical education for students at Chu Van An High School, Thai Nguyen Province, Vietnam. Results: As a result, on the basis of theoretical and practical research, the article has selected 6 measures to improve the effectiveness of the physical education work of the school. These six measures received the agreement and approval of school officials and teachers (over 90%) while ensuring practicality, feasibility, uniformity and scientificity. Conclusion: The solutions developed by the project will serve as a foundation for practical application to improve the effectiveness of physical education at Chu Van An High School, Thai Nguyen Province, Vietnam.  Article visualizations

The role of the material fracture properties in the size-effect law of concrete structures

The size effect of the nominal stress at failure in concrete structures is dealt within general. An existence of a rather large fracture process zone in front of crack tip is proved to be the main reason leading to the size effect of the nominal strength. On the basis of the new general size-effect law and numerical results of fracture propagation, a particularly proposed size effect law for beams in bending is developed, in which the role of each material fracture characteristic, especially the shape of the stress - crack opening curve, is elaborated clearly