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 .

Internal control is system,defined and implemented under its responsibility , which aims to ensure that; laws and regulations are complied with; the instructions and directional guidelines fixed by Executive Management or the Management Borad are applied; the company internal processes are functioning correctlly , particularly those implicating the security of its assets; Financial Information is reliable; and generally contributes to the control over its activities , to the efficiency of its operation and to the efficient utilisation of its Resources. By helping to anticipate and control the risks involved in not meeting the objectives the company has set for itself, the internal control system plays akey role in conducting & monito

This paper presents a new design of a nonlinear multi-input multi-output PID neural controller of the active brake steering force and the active front steering angle for a 2-DOF vehicle model based on modified Elman recurrent neural. The goal of this work is to achieve the stability and to improve the vehicle dynamic’s performance through achieving the desired yaw rate and reducing the lateral velocity of the vehicle in a minimum time period for preventing the vehicle from slipping out the road curvature by using two active control actions: the front steering angle and the brake steering force. Bacterial forging optimization algorithm is used to adjust the parameters weights of the proposed controller. Simulation resul

For businesses that provide delivery services, the efficiency of the delivery process in terms of punctuality is very important. In addition to increasing customer trust, efficient route management, and selection are required to reduce vehicle fuel costs and expedite delivery. Some small and medium businesses still use conventional methods to manage delivery routes. Decisions to manage delivery schedules and routes do not use any specific methods to expedite the delivery settlement process. This process is inefficient, takes a long time, increases costs and is prone to errors. Therefore, the Dijkstra algorithm has been used to improve the delivery management process. A delivery management system was developed to help managers and drivers

          This study deals with the role of compensation system in improving the quality of educational services (University of Halabja as a Model) also our problem was the following question ; What is the role of compensation system in its different dimensions in improving the quality of educational services? And what is the relationship and impact of using the dimensions of the compensation system to improve the quality of educational services? The hypothesis of the research included the correlation and the impacts between the compensation system and its combined variables in the quality of educational services. This was proved through a field study and the distribution of questionn

paid recent developments in the information and communications technology and the accompanying developments in the global market to pay particular accounting information users to demand more sophistication in terms of corporate financial reporting systems, which led to the emergence of a new type of reporting (financial reporting in real time). where is the information and communications technology mainstay Nations for the development and progress, thanks to the development of technology that have made the transmission of information easily conducted and high speed to all who need it, communication is instantaneous and the flow of information via the internet dramatically exceeded the border temporal and spatial anywhere in the w

This research involves design and simulation of GaussianFSK transmitter in UHF band using direct modulation of ΣΔ  fractional-N synthesizer with the following specifications:

Frequency range (869.9– 900.4) MHz, data rate 150kbps, channel spacing (500 kHz), Switching time 1 µs, & phase noise @10 kHz = -85dBc.

New circuit techniques have been sought to allow increased integration of radio transmitters and receivers, along with new radio architectures that take advantage of such techniques. Characteristics such as low power operation, small size, and low cost have become the dominant design criteria by which these systems are judged.

A direct modulation by ΣΔ  fractional-N synthesizer is proposed

NH₃ gas sensor was fabricated based on deposited of Functionalized Multi-Walled Carbon Nanotubes (MWCNTs-OH) suspension on filter paper substrates using suspension filtration method. The structural, morphological and optical properties of the MWCNTs film were characterized by XRD, AFM and FTIR techniques. XRD measurement confirmed that the structure of MWCNTs is not affected by the preparation method. The AFM images reflected highly ordered network in the form of a mat. The functional groups and types of bonding have appeared in the FTIR spectra. The fingerprint (C-C stretch) of MWCNTs appears in 1365 cm^-1, and the backbone of CNTs observed at 1645 cm^-1. A homemade sensi

A security system can be defined as a method of providing a form of protection to any type of data. A sequential process must be performed in most of the security systems in order to achieve good protection. Authentication can be defined as a part of such sequential processes, which is utilized in order to verify the user permission to entree and utilize the system. There are several kinds of methods utilized, including knowledge, and biometric features. The electroencephalograph (EEG) signal is one of the most widely signal used in the bioinformatics field. EEG has five major wave patterns, which are Delta, Theta, Alpha, Beta and Gamma. Every wave has five features which are amplitude, wavelength, period, speed and frequency. The linear