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 .

Value Engineering is an analytical study on projects or services using a specific procedure and a multidisciplinary working group, works for the identification and classification of the project functions; either for a better perfuming of these functions or to lessen the total project cost or the two together. Value Engineering main aim is on finding innovative alternatives, without effecting the basic requirements of the project, its methodology based on the functional balancing between the three elements of production "performance, quality and cost". This methodology based on the "functional analysis", had shown high possibilities in solving any problem facing the production procedure , achieve better investment for available re

Early detection of eye diseases can forestall visual deficiency and vision loss. There are several types of human eye diseases, for example, diabetic retinopathy, glaucoma, arteriosclerosis, and hypertension. Diabetic retinopathy (DR) which is brought about by diabetes causes the retinal vessels harmed and blood leakage in the retina. Retinal blood vessels have a huge job in the detection and treatment of different retinal diseases. Thus, retinal vasculature extraction is significant to help experts for the finding and treatment of systematic diseases. Accordingly, early detection and consequent treatment are fundamental for influenced patients to protect their vision. The aim of this paper is to detect blood vessels from

This article presents a polynomial-based image compression scheme, which consists of using the color model (YUV) to represent color contents and using two-dimensional polynomial coding (first-order) with variable block size according to correlation between neighbor pixels. The residual part of the polynomial for all bands is analyzed into two parts, most important (big) part, and least important (small) parts. Due to the significant subjective importance of the big group; lossless compression (based on Run-Length spatial coding) is used to represent it. Furthermore, a lossy compression system scheme is utilized to approximately represent the small group; it is based on an error-limited adaptive coding system and using the transform codin

    Natural Language Processing (NLP) deals with analysing, understanding and generating languages likes human. One of the challenges of NLP is training computers to understand the way of learning and using a language as human.  Every training session consists of several types of sentences with different context and linguistic structures. Meaning of a sentence depends on actual meaning of main words with their correct positions. Same word can be used as a noun or adjective or others based on their position. In NLP, Word Embedding is a powerful method which is trained on large collection of texts and encoded general semantic and syntactic information of words. Choosing a right word embedding generates more efficient result than others

The purpose of this article is to introduce reverse engineering procedure (REP). It can achieved by developing an industrial mechanical product that had no design schemes throughout the 3D-Scanners. The aim of getting a geometric CAD model from 3D scanner is to present physical model. Generally, this used in specific applications, like commercial plan and manufacturing tasks. Having a digital data as stereolithography (STL) format. Converting the point cloud be can developed as a work in programming by producing triangles between focuses, a procedure known as triangulation. Then it could be easy to manufacture parts unknown documentation and transferred the information to CNC-machines. In this work, modification was proposed and used in RE

Optical Mark Recognition (OMR) is the technology of electronically extracting intended data from marked fields, such as squareand bubbles fields, on printed forms. OMR technology is particularly useful for applications in which large numbers of hand-filled forms need to be processed quickly and with a great degree of accuracy. The technique is particularly popular with schools and universities for the reading in of multiple choice exam papers. This paper proposed OMRbased on Modify Multi-Connect Architecture (MMCA) associative memory, its work in two phases: training phase and recognition phase. The proposed method was also able to detect more than one or no selected choice. Among 800 test samples with 8 types of grid answer sheets and tota

Image classification takes a large area in computer vision in term of quality or type or data sharing and so on Iraqi Anber Rice in they need this kind of work, where few in the field of computer science that deal with the types of Iraqi Anber rice, and because of the Anber Rice are grown and produced in Iraq only, and because of the importance of rice around the world and especially in Iraq. In this paper a proposed system distinguishes between the classes of Iraqi Anber Rice that Grown in different parts of Iraq, and have their own specifications for each class by using moment invariant and KNN algorithm. Iraqi Anber Rice that is more than Fiftieth class Cultivated and irrigated in different parts of Iraq, and because of the different