Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

In this paper we describe several different training algorithms for feed forward neural networks(FFNN). In all of these algorithms we use the gradient of the performance function, energy function, to determine how to adjust the weights such that the performance function is minimized, where the back propagation algorithm has been used to increase the speed of training. The above algorithms have a variety of different computation and thus different type of form of search direction and storage requirements, however non of the above algorithms has a global properties which suited to all problems.

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

In this study the adsorption of cefixime on to selected Iraqi clay bentonite. The aim of this study is to search for selective active surface in adsorption of the drug and to act as physical antidotes in treatment of poisoning if the drug is taken in quantities higher than the recommended dosages. Quantitative estimation of the drug adsorption has been done by utilizing the technique of UV spectrophotometry in λmax (273) nm at different conditions of temperature (25, 37, 45) ˚C found the adsorption decrease with increase the temperature. Study of clay weight of bentonite (0.1-1.5) gm found the adsorption increase with increase of clay weight, study effect of pH (1.2, 3, 5, 7) on adsorption of bentonite found the optimum adsorption

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .