A contranormal subgroup is a subgroup whose normal closure in the group is the whole group. Hence a subgroup H of a group G is said to be totally contranormal if HK = K for each subgroup K of G. The purpose of this article is to study the influence of contranormal (totally contranormal) subgroup on groups whose maximal subgroups are smooth groups.
Triangle inequality is regarded as the most prominent and important inequality in the theory of normed spaces and therefore it has been a major topic of interest treated by numerous mathematicians. However, the above inequality, as well as its generalizations are also very important in the theory of quasi-normed spaces. Therefore, that one is a subject of additional research in both quasi-normed and generalized quasi-normed space.
Rumor routing protocol in wireless sensor networks (WSNs), is based on query system. It selects the next hop randomly, but the resultant path from source to destination is not optimal. Most of the work reported on energy efficient and bandwidth estimation in the literature are based on hierarchical protocol. However in this work we have considered data centric protocol and used optimization scheme. We have used ant colony optimization (ACO) in rumor routing protocol. This approach optimizes the route search and helps in establishing a complete route by minimizing the probability of the loop route generated by routing scheme. Energy of the nodes has been calculated and compared for normal routing process with optimizing route searching using ACO. Results are compared with non-optimized route of rumor routing protocol. Further the bandwidth of non-optimal route has been calculated and compared with optimize route.
Minimizing true error of the classification process under uncertainty is one of the difficult issues in the field of machine learning. Researchers do not address this topic until this time despite its importance in practical life. This paper can be considered as a development of the concept of social learning presented the intellectual leap in the machine learning area as given before by the authors. Novelty in this paper is to present a new approach that can deal with the conditions of uncertainty resulting from multiple sources. This paper also presents a new method of social learning based on benefits offered by the Dempster-Shafer theory (DST) of evidence. The paper provides experimental results on six benchmarks. The results attained from the comparison using six benchmarking problems illustrate a superior performance of the proposed method compared with the best results attained in the literature of machine learning domain till now.
Human Computer Interaction Semantic filtering techniques are used in learning environment to track problems in collaborative systems. However, as noted in Adigun et al. , when sharing and dynamism are promoted, a problem of redundancy and integrity appeared not to have been well addressed. An improved ASF-based method of evaluating semantic filtering for social network systems in collaborative learning environment is developed, which assisted participants to achieve greater levels of performance with information sharing from other collaborators, as well as in reusing ideas across the period of collaboration.
In paper  Ahmad et al. investigated the use of sharp function, known from functional analysis, in image processing. The sharp function gives a measure of variations of a function and can be used as an edge detector . We extend the classical notion of sharp function to prove the classical Lebesgue differentiation theorem and Marcinkiewicz theorem for the sublinear operator T(x, y).
The Internet of Things is expected to bring a revolution in the way objects around us communicate with one another and human beings and the way this information will be gathered and distributed. This also means a resultant increase in internet usage and the challenges of securing information over the internet. This paper looks at what components make up the internet of things and its business viability in our ever changing world. Despite security challenges of communicating over the internet, it still remains the leading means of communication and our dependence on the internet and mobile technology is only expected to increase.