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 .

     Automated medical diagnosis is an important topic, especially in detection and classification of diseases. Malaria is one of the most widespread diseases, with more than 200 million cases, according to the 2016 WHO report. Malaria is usually diagnosed using thin and thick blood smears under a microscope. However, proper diagnosis is difficult, especially in poor countries where the disease is most widespread. Therefore, automatic diagnostics helps in identifying the disease through images of red blood cells, with the use of machine learning techniques and digital image processing. This paper presents an accurate model using a Deep Convolutional Neural Network build from scratch. The paper also proposed three CNN

DeepFake is a concern for celebrities and everyone because it is simple to create. DeepFake images, especially high-quality ones, are difficult to detect using people, local descriptors, and current approaches. On the other hand, video manipulation detection is more accessible than an image, which many state-of-the-art systems offer. Moreover, the detection of video manipulation depends entirely on its detection through images. Many worked on DeepFake detection in images, but they had complex mathematical calculations in preprocessing steps, and many limitations, including that the face must be in front, the eyes have to be open, and the mouth should be open with the appearance of teeth, etc. Also, the accuracy of their counterfeit detectio

  This paper deals with proposing new lifting scheme (HYBRID Algorithm) that is capable of preventing images and documents which are fraud through decomposing there in to the real colors value arrays (red, blue and green) to create retrieval keys for its properties and store it in the database and then check the document originality by retrieve the query image or document through the decomposition described above and compare the predicted color values (retrieval keys)  of the query document with those stored in the database. The proposed algorithm has been developed from the two known lifting schemes (Haar and D4) by merging them to find out HYBRID lifting scheme. The validity and accuracy of the proposed algorithm have been ev

     Meerkat Clan Algorithm (MCA) is a nature-based metaheuristic algorithm which imitates the intelligent behavior of the meerkat animal. This paper presents an improvement on the MCA based on a chaotic map and crossover strategy (MCA-CC). These two strategies increase the diversification and intensification of the proposed algorithm and boost the searching ability to find more quality solutions. The 0-1 knapsack problem was solved by the basic MCA and the improved version of this algorithm (MCA-CC). The performance of these algorithms was tested on low and high dimensional problems. The experimental results demonstrate that the proposed algorithm had overcome the basic algorithm in terms of solution quality, speed a

Because of vulnerable threats and attacks against database during transmission from sender to receiver, which is one of the most global security concerns of network users, a lightweight cryptosystem using Rivest Cipher 4 (RC4) algorithm is proposed. This cryptosystem maintains data privacy by performing encryption of data in cipher form and transfers it over the network and again performing decryption to original data. Hens, ciphers represent encapsulating system for database tables

         Stream ciphers are an important class of encryption algorithms. There is a vast body of theoretical knowledge on stream ciphers, and various design principles for stream ciphers have been proposed and extensively analyzed. This paper  presents a new method of stream cipher, that by segmenting the plaintext into number of register then any of them combined to any other by using combination logic circuit (And, OR, JK, NOT, XOR), then using variant register in length as a key which provides security enhancement against attacks and then compare the strength of this method with RSA by calculaing the time necessary to get the original text by using the genetic algorithm. And the way that ha

     In this paper, the botnet detection problem is defined as a feature selection problem and the genetic algorithm (GA) is used to search for the best significant combination of features from the entire search space of set of features. Furthermore, the Decision Tree (DT) classifier is used as an objective function to direct the ability of the proposed GA to locate the combination of features that can correctly classify the activities into normal traffics and botnet attacks. Two datasets  namely the UNSW-NB15 and the Canadian Institute for Cybersecurity Intrusion Detection System 2017 (CICIDS2017), are used as evaluation datasets. The results reveal that the proposed DT-aware GA can effectively find the relevant

In this paper, we proposed a hybrid control methodology using improved artificial potential field with modify cat swarm algorithm to path planning of decoupled multi-mobile robot in dynamic environment. The proposed method consists of two phase: in the first phase, Artificial Potential Field method (APF) is used to generate path for each one of robots and avoided static obstacles in environment, and improved this method to solve the local minimum problem by using A* algorithm with B-Spline curve while in the second phase, modify Cat Swarm Algorithm (CSA) is used to control collision that occurs among robots or between robot with movable obstacles by using two behaviour modes: seek mode and track mode. Experimental results show that the p