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 .

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 .

This study examines postgraduate students’ awareness of pragmatic aspects, including Grice Maxims, Politeness, and Direct and Indirect forms of speech. According to Paul Grice’s theory of implicature, which is considered one of the most important contributions to pragmatics, this paper discusses how postgraduate students can meet the cooperative principle when communicating effectively. It also outlines how does politeness principles influence obeying or violating the maxims and how is the use of direct or indirect forms of utterances prompted by politeness. Sixteen master’s students of Linguistics and Literature were asked to take a multiple-choice test. The test will be represented along with the interpretation of each optio

Foreign direct investment (FDI) is one of the most practical types of foreign investment. FDI contributes to job creation, foreign exchange earnings and national income escalation, improving semi-skill and skilled labor. Based on our knowledge, this paper is the first study attempting to investigate the effect of political stability on the FDI in Turkey using an econometric approach. Achieving this objective, a co-integration analysis was conducted between the FDI and its determinants in the short-run and long-run including “macroeconomic indicators” and “Political Stability (PS)” in Turkey. Using annual data from 1974 to 2017 via Auto-Regressive Distributed Lag (ARDL) model. The results confirm the positive correlation betwe

Direct contact membrane distillation is an effective method for production of fresh water from saline water. In this study two samples were used as feed solutions; the first one was RO waste from Al-Hilla Coca-Cola Factory (TDS= 2382 mg/l) and the other was Haji Ali drainage water (TDS= 4127 mg/l). Polytetrafluoroethylene (PTFE) hydrophobic membrane supported with polypropylene (PP) was used as flat sheet form with plate and frame cell. Results proved that membrane distillation is an effective technique to produce fresh water with high quality from brine with low salinity content. With membrane area of 8x8 cm², the volume of treated water decreased from 34.97 ml at first half hour to 33.02 ml after 180 min of

The paper uses the Direct Synthesis (DS) method for tuning the Proportional Integral Derivative (PID) controller for controlling the DC servo motor. Two algorithms are presented for enhancing the performance of the suggested PID controller. These algorithms are Back-Propagation Neural Network and Particle Swarm Optimization (PSO). The performance and characteristics of DC servo motor are explained. The simulation results that obtained by using Matlab program show that the steady state error is eliminated with shorter adjusted time when using these algorithms with PID controller. A comparative between the two algorithms are described in this paper to show their effectiveness, which is found that the PSO algorithm gives be

In this study, iron was coupled with copper to form a bimetallic compound through a biosynthetic method, which was then used as a catalyst in the Fenton-like processes for removing direct Blue 15 dye (DB15) from aqueous solution. Characterization techniques were applied on the resultant nanoparticles such as SEM, BET, EDAX, FT-IR, XRD, and zeta potential. Specifically, the rounded and shaped as spherical nanoparticles were found for green synthesized iron/copper nanoparticles (G-Fe/Cu NPs) with the size ranging from 32-59 nm, and the surface area was 4.452 m2/g. The effect of different experimental factors was studied in both batch and continuous experiments. These factors were H2O2 concentration, G-Fe/CuNPs amount, pH, initial DB15

The study presents the test results of Completely Decomposed Granite (CDG) soil tested under drained triaxial compression, direct shear and simple shear tests. Special attention was focused on the modification of the upper halve of conventional Direct Shear Test (DST) to behave as free
head in movement along with vertical strain control during shear stage by using Geotechnical Digital System (GDS). The results show that Free Direct Shear Test (FDST) has clear effect on the measured shear stress and vertical strain during the test. It has been found that shear strength
parameters measured from FDST were closer to those measured from simple shear and drained triaxial compression test. This study also provides an independent check on