In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Steganography is one of the most popular techniques for data hiding in the different media such as images, audio or video files. This paper introduced the improved technique to hide the secret message using the LSB algorithm inside the RGB true color image by encrypting it using the secret key transformation function. The key is selecting randomly in the GF (2n) with condition it has an inverse value to retrieve the encrypted message. Only two bits are used for the low byte in each pixel (the blue byte) to hide the secret message, since the blue color has a weak effect on human eyes. The message hidden by the suggested algorithm is less vulnerable to be stolen than other similar applications.

Malicious software (malware) performs a malicious function that compromising a computer system’s security. Many methods have been developed to improve the security of the computer system resources, among them the use of firewall, encryption, and Intrusion Detection System (IDS). IDS can detect newly unrecognized attack attempt and raising an early alarm to inform the system about this suspicious intrusion attempt. This paper proposed a hybrid IDS for detection intrusion, especially malware, with considering network packet and host features. The hybrid IDS designed using Data Mining (DM) classification methods that for its ability to detect new, previously unseen intrusions accurately and automatically. It uses both anomaly and misuse dete

The goal of the research is to find the optimization in the test of the appropriate cross-over design for the experiment that the researcher is carrying out (under assumption that there are carry-over effects of the treatments) to posterior periods after the application period (which is often assumed to be the first period). The comparison between the double cross-over design and the cross-over design with extra period. The similarities and differences between the two designs were studied by measuring the Relative Efficiency (RE) of the experiment.

A computational investigation is carried out in the field of charged particle optics with the aid of the numerical analysis methods. The work is concerned with the design of symmetrical double pole piece magnetic lens.  The axial magnetic flux density distribution is determined by using exponential model, from which the paraxial-ray equation is solved to obtain the trajectory of particles that satisfy the suggested exponential model.  From the knowledge of the first and second derivatives of axial potential distribution, the optical properties such as the focal length and aberration coefficients (radial distortion coefficient and spiral distortion coefficient) are determined.  Finally, the pole piece profiles capable of pr