Abstract. We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersymmetries are necessarily (locally) homogeneous.

Abstract. We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sharp and conclude with a remark about the existence of null homogeneous geodesics.Comment: 16 pages, many changes particularly to sections 6 and

Abstract-Recommender systems are software applications that provide or suggest items to intended users. These systems use filtering techniques to provide recommendations. The major ones of these techniques are collaborative-based filtering technique, content-based technique, and hybrid algorithm. The motivation came as a result of the need to integrate recommendation feature in digital libraries in order to reduce information overload. Content-based technique is adopted because of its suitability in domains or situations where items are more than the users. TF-IDF (Term Frequency Inverse Document Frequency) and cosine similarity were used to determine how relevant or similar a research paper is to a user's query or profile of interest. Research papers and user's query were represented as vectors of weights using Keyword-based Vector Space model. The weights indicate the degree of association between a research paper and a user's query. This paper also presents an algorithm to provide or suggest recommendations based on users' query. The algorithm employs both TF-IDF weighing scheme and cosine similarity measure. Based on the result or output of the system, integrating recommendation feature in digital libraries will help library users to find most relevant research papers to their needs.

This is an attempt to investigate the teaching competencies of commerce teacher trainees. The main objectives of the study is find out whether there is any significant difference in the teaching competencies of commerce teacher trainees in respect of their gender, age, and medium studied. Sample of 200 B.Ed. trainees were selected by using purposive sampling technique. It is found that teacher trainees have low teaching competencies. It is revealed that there is significant difference in mean teaching competency scores of male and female, English and Malayalam medium teacher trainees. This study also revealed that there is no significant difference in mean teaching competency scores of trainees who are less than 22 years of age and above 22 years of the age group.