The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.

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

abstract:

The aim of this study is to clarify the relationship between the concept of  inconsistency and the measurement of the inverse relationship of overlap and contrast. The study will address the following points:

1. Explaining the true nature of inconsistency and contrast, as understanding their relationship is essential for determining them.
2. Examining the view of the scholars regarding their significance as approaches to understanding the relationship.

• Identifying the relationship between inconsistency and contrast in terms of overlap and contrast.

The study aims to reach a common point that achieves a balance between two interests, which are generally in conflict with the public interest and the interest of the individual owner of private property, by extrapolating the provisions of the constitutional judiciary that include the protection of private property, and this protection extends to every right of financial value and is not limited to a specific type, but It included everything that can be estimated with money, as ownership is no longer an advantage for the owner, but rather has become a right for him and a social function. The tax is imposed on what is derived from it, but if there is a need to prejudice it, the conditions, limits and restrictions expressly stipulated in the

In this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data  sets