The implicit midpoint rules are employed as a powerful numerical technique, and in this article we attend class of viscosity iteration approximations on hierarchical problems for the double rules. We prove strong convergence theorem to unique solution problem technique is established under some favorable conditions imposed control parameters Hilbert spaces. Furthermore, propose applications con...

Key establishment is the basic necessary tool in the network security, by which pairs in the network can establish shared keys for protecting their pairwise communications. There have been some key agreement or predistribution schemes with the property that the key can be established without the interaction ([3], [4], [19]). Recently the hierarchical cryptography and the key management for hier...

Graphs visualizations can become difficult to interpret when they fail to highlight patterns. Additionally, the data to be visualized may be hierarchical in nature. Therefore, graphs with hierarchical data need to offer means of telescoping that collapse or expand subgraphs while aggregating their data. In this paper, we demonstrate an interactive hierarchical edge graph on book prerequisite da...

In this paper, we consider the stability property of class generalized subexponential distributions with respect to product-convolution. Assuming that primary distribution is in distributions, find conditions for second order their product-convolution belongs as well. The similar problem positively decreasing-tailed considered.