This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

        In our research, we introduced new concepts, namely ^*and **-light mappings, after we knew ^*and **-totally disconnected mappings through the use of -open sets.

Many examples, facts, relationships and results have been given to support our work.

      In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get  of the strengths  and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered

In 2020 one of the researchers in this paper, in his first research, tried to find out the Modified Weighted Pareto Distribution of Type I by using the Azzalini method for weighted distributions, which contain three parameters, two of them for scale while the third for shape.This research compared the distribution with two other distributions from the same family; the Standard Pareto Distribution of Type I and the Generalized Pareto Distribution by using the Maximum likelihood estimator which was derived by the researchers for Modified Weighted Pareto Distribution of Type I, then the Mont Carlo method was used–that is one of the simulation manners for generating random samples data in different sizes ( n= 10,30,50), and in di

   The main aim of this paper is to use the notion  which was introduced in [1], to offered new classes of separation axioms in ideal spaces. So, we offered new type of notions of convergence in ideal spaces via the set. Relations among several types of separation axioms that offered were explained.

Many of the key stream generators which are used in practice are LFSR-based in the sense that they produce the key stream according to a rule y = C(L(x)), where L(x) denotes an internal linear bit stream, produced by small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. In this paper we combine between the output sequences from the linear feedback shift registers with the sequences out from non linear key generator to get the final very strong key sequence

 Abstract

An experimental study was conducted for measuring the quality of surface finishing roughness using magnetic abrasive finishing technique (MAF) on brass plate which is very difficult to be polish by a conventional machining process where the cost is high and much more susceptible to surface damage as compared to other materials. Four operation parameters were studied, the gap between the work piece and the electromagnetic inductor, the current that generate the flux, the rotational Spindale speed and amount of abrasive powder size considering constant linear feed movement between machine head and workpiece. Adaptive Neuro fuzzy inference system  (ANFIS) was implemented for evaluation of a serie

The comparison of double informative priors which are assumed for the reliability function of Pareto type I distribution. To estimate the reliability function of Pareto type I distribution by using Bayes estimation, will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of Pareto  type I distribution . Assuming distribution of three double prior’s chi- gamma squared distribution, gamma - erlang distribution, and erlang- exponential distribution as double priors. The results of the derivaties of these estimators under the squared error loss function with two different double priors. Using the simulation technique, to compare the performance for