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 .

A tunable band pass filter based on fiber Bragg grating sensor using an in-fiber Mach-Zender interferometer with dual micro-cavities is presented. The micro-cavity was formed by splicing together a conventional single-mode fiber and a solid core photonic crystal fiber (SCPCF) with simple arc discharge technique. Different parameters such as arc power, length of the SCPCF and the overlap gap between samples were considered to control the fabrication process. The ellipsoidal air-cavity between the two fibers forms Fabry-Perot cavity. The diffraction loss was very low due to short cavity length. Ellipsoidal shape micro-cavities were experimentally achieved parallel to the propagation axis having dimensions of (24.92 – 62.32) μm of width

<span lang="EN-US">The need for robotics systems has become an urgent necessity in various fields, especially in video surveillance and live broadcasting systems. The main goal of this work is to design and implement a rover robotic monitoring system based on raspberry pi 4 model B to control this overall system and display a live video by using a webcam (USB camera) as well as using you only look once algorithm-version five (YOLOv5) to detect, recognize and display objects in real-time. This deep learning algorithm is highly accurate and fast and is implemented by Python, OpenCV, PyTorch codes and the Context Object Detection Task (COCO) 2020 dataset. This robot can move in all directions and in different places especially in

Abstract

The current research is attempt to test the reflection of the lean management on the human resources management practices of two of the most important communication companies operating in Iraq (`Zain & Asia cell), The research aims to Determine the extent of adoption of the lean management approach in the two researched companies, as it improving human resource management practices. The research problem represented in the existence of lack of in some aspects of the application the lean management approach in service sector and neglecting the impact of its tools on the human resource management practices. For this purpose three principle research hypotheses has been formulated, first there is a correlation rel

The current research aims to know the complementary use of the paper book and the digital book by defining the paper book and the digital book and knowing the methods and methods of obtaining each of them and indicating the extent of their use and for what purpose and knowing the difficulties that researchers face in using each of them and which is better using the paper book or the digital book in preparing research Studies and for no reason. The research relied on the descriptive approach and the questionnaire as a tool for data collection, and it was distributed to professors and students of Iraqi universities. The research sample reached (219) individuals and reached a set of results, the most important of which are: Preference for the

  The purpose of this paper is  to find an arc of degree five in 31 ,29),(2, =qqPG , with stabilizer group of type dihedral group of degree five 5 D and arcs of degree six and ten with stabilizer groups of type alternating group of degree five 5 A ,  then study the effect of  5 D and 5A on the points of projective plane. Also, find a pentastigm which has collinear diagonal points.

In this research two algorithms are applied, the first is Fuzzy C Means (FCM) algorithm and the second is hard K means (HKM) algorithm to know which of them is better than the others these two algorithms are applied on a set of data collected  from the Ministry of Planning on the water turbidity of five areas in Baghdad to know which of these areas are less turbid in clear water to see which months during the year are less turbid in clear water in the specified area.

In this research two algorithms are applied, the first is Fuzzy C Means (FCM) algorithm and the second is hard K means (HKM) algorithm to know which of them is better than the others these two algorithms are applied on a set of data collected  from the Ministry of Planning on the water turbidity of five areas in Baghdad to know which of these areas are less turbid in clear water to see which months during the year are less turbid in clear water in the specified area.

A novel planar type antenna printed on a high permittivity Rogers’ substrate is proposed for early stage microwave breast cancer detection. The design is based on a p-shaped wide-slot structure with microstrip feeding circuit to eliminate losses of transmission. The design parameters are optimized resulting in a good reflection coefficient at −10 dB from 4.5 to 10.9 GHz. Imaging result using inhomogeneous breast phantom indicates that the proposed antenna is capable of detecting a 5 mm size cancerous tumor embedded inside the fibroglandular region with dielectric contrast between the target and the surrounding materials ranging from 1.7 : 1 to 3.6 : 1.

               Microalgae have been used widely in bioremediation processes to degrade or adsorb toxic dyes. Here, we evaluated the decolorization efficiency of Chlorella vulgaris and Nostoc paludosum against two toxic dyes, crystal violet (CV) and malachite green (MG). Furthermore, the effect of CV and MG dyes on the metabolic profiling of the studied algae has been investigated. The data showed that C. vulgaris was most efficient in decolorization of CV and MG: the highest percentage of decolorization was 93.55% in case of MG, while CV decolorization percentage was 62.98%. N. paludosum decolorized MG dye by 77.6%, and the decolorization percentage of CV was 35.1%. Metabolic profiling of