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

Biometrics is widely used with security systems nowadays; each biometric modality can be useful and has distinctive properties that provide uniqueness and ambiguity for security systems especially in communication and network technologies. This paper is about using biometric features of fingerprint, which is called (minutiae) to cipher a text message and ensure safe arrival of data at receiver end. The classical cryptosystems (Caesar, Vigenère, etc.) became obsolete methods for encryption because of the high-performance machines which focusing on repetition of the key in their attacks to break the cipher. Several Researchers of cryptography give efforts to modify and develop Vigenère cipher by enhancing its weaknesses.

The cuneiform images need many processes in order to know their contents
and by using image enhancement to clarify the objects (symbols) founded in the
image. The Vector used for classifying the symbol called symbol structural vector
(SSV) it which is build from the information wedges in the symbol.
The experimental tests show insome numbersand various relevancy including
various drawings in online method. The results are high accuracy in this research,
and methods and algorithms programmed using a visual basic 6.0. In this research
more than one method was applied to extract information from the digital images
of cuneiform tablets, in order to identify most of signs of Sumerian cuneiform.

The research deals with the important and modern two subject (career path and the type of training program), and tries to find identify the extent of the impact of the requirements of a career path in determining the type of training program in the Ministry of Oil.

In order to achieve the aim of the research was the formulation of the following hypothesis: the impact of the requirements of the career path a meaningful moral influence in determining the type of training program.

The survey was adopted in the search, and sample consisted of (75) people were a factor in the Oil Ministry of People's managers and officials and staff, and used the questionnaire as an es

Automatic Programming Assessment (APA) has been gaining lots of attention among researchers mainly to support automated grading and marking of students’ programming assignments or exercises systematically. APA is commonly identified as a method that can enhance accuracy, efficiency and consistency as well as providing instant feedback on students’ programming solutions. In achieving APA, test data generation process is very important so as to perform a dynamic testing on students’ assignment. In software testing field, many researches that focus on test data generation have demonstrated the successful of adoption of Meta-Heuristic Search Techniques (MHST) so as to enhance the procedure of deriving adequate test data for efficient t

Some maps of the chaotic firefly algorithm were selected to select variables for data on blood diseases and blood vessels obtained from Nasiriyah General Hospital where the data were tested and tracking the distribution of Gamma and it was concluded that a Chebyshevmap method is more efficient than a Sinusoidal map method through mean square error criterion.

Cipher security is becoming an important step when transmitting important information through networks. The algorithms of cryptography play major roles in providing security and avoiding hacker attacks. In this work two hybrid cryptosystems have been proposed, that combine a modification of the symmetric cryptosystem Playfair cipher called the modified Playfair cipher and two modifications of the asymmetric cryptosystem RSA called the square of RSA technique and the square RSA with Chinese remainder theorem technique. The proposed hybrid cryptosystems have two layers of encryption and decryption. In the first layer the plaintext is encrypted using modified Playfair to get the cipher text, this cipher text will be encrypted using squared

Authors in this work design efficient neural networks, which are based on the modified Levenberg - Marquardt (LM) training algorithms to solve non-linear fourth - order three -dimensional partial differential equations in the two kinds in the periodic and in the non-periodic - Periodic. Software reliability growth models are essential tools for monitoring and evaluating the evolution of software reliability. Software defect detection events that occur during testing and operation are often treated as counting processes in many current models. However, when working with large software systems, the error detection process should be viewed as a random process with a continuous state space, since the number of faults found during testin

This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.