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

     Various document types play an influential role in a lot of our lives activities today; hence preserving their integrity is an important matter. Such documents have various forms, including texts, videos, sounds, and images.  The latter types' authentication will be our concern here in this paper. Images can be handled spatially by doing the proper modification directly on their pixel values or spectrally through conducting some adjustments to some of the addressed coefficients. Due to spectral (frequency) domain flexibility in handling data, the domain coefficients are utilized for the watermark embedding purpose. The integer wavelet transform (IWT), which is a wavelet transform based on the lifting scheme,

      Recently, digital communication has become a critical necessity and so the Internet has become the most used medium and most efficient for digital communication. At the same time, data transmitted through the Internet are becoming more vulnerable. Therefore, the issue of maintaining secrecy of data is very important, especially if the data is personal or confidential. Steganography has provided a reliable method for solving such problems. Steganography is an effective technique in secret communication in digital worlds where data sharing and transfer is increasing through the Internet, emails and other ways. The main challenges of steganography methods are the undetectability and the imperceptibility of con

The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

the digital public relations aim at make the workers getting the necessary information about the governmental institutions where they work and the enveronment surrounding them. it also tries to let the workers get the special knowlege of tthe publich relations and their jobs like the works of planning , arranging the active communication and executive skills needed in their writing , editing , special art skills for designing , production and technological skills to deal with the computer.
the problem of the research includes some questions as :
1- what are the uses achieved by degetal public relations workers at Iraqi universities (Baghdad, Mustansiriya, and Iraqi)
2- what are the tools used to apply digital public relations

ABSTRACT

The research aims to clarify the role of electronic marketing and what it can achieve in promoting the products of the national industry in Iraq. Marketing channel depends on modern communication and information technology that industrial and metal companies can use in promoting and selling their products along with traditional marketing outlets. To achieve the objectives of the research, a questionnaire was used, which consists of three axes, the first includes the personal data of the sample (gender, age, educational attainment, place of residence, marital status, income level), while the second axis includes various questions about the products of the national industry. Third axis includes que

   This paper presents an investigation of peristaltic flow of Bingham plastic fluid in an inclined tapered asymmetric channel with variable viscosity. Taken into consideration Hall current, velocity, thermal slip conditions, Energy equation is modeled by taking Joule heating effect into consideration and by holding assumption of long wavelength and low Reynolds number approximation these equations simplified into couple of non-linear ordinary differential equations that solved using perturbation technique. Graphical analysis has been involved for various flow parameters emerging in the problem. We observed two opposite behaviors for Hall parameter and Hartman number on velocity axial and temperature curves.

Background: Dental implants act as infrastructure for fixed restoration to look like as a natural tooth. Osseointegration is a biological events and considered as a base for success of dental implant. The aim of this study is to evaluate the bond strength between bone and Ti implant coated with mixture of nano hydroxyapatite-chitosan-collagen compared with Ti implants coated with nano hydroxyapatite implanted in rabbit tibia, after different period of implantation time (two and six weeks) by torque removal test. Material and methods: 36 screws of commercially pure titanium; 8mm in length and 3mm diameter , 18 screws coated with mixture of nano hydroxyapatite-chitosan-collagen and18 screws coated with nano hydroxyapatite by dip coating. St

This study presents the debonding propagation in single NiTi wire shape memory alloy into linear low-density polyethylene matrix composite the study of using the pull-out test. The aim of this study is to investigate the pull-out tests to check the interfacial strength of the polymer composite in two cases, with activation NiTinol wire and without activation. In this study, shape memory alloy NiTinol wire 2 mm diameter and linear fully annealed straight shape were used. The study involved experimental and finite element analysis and eventually comparison between them. This pull-out test is considered a substantial test because its results have a relation with behavior of smart composite materials. The pull-out test was carried out by a u