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 was conducted to investigate the relationship between corticosterone hormone in the blood of local Iraqi white chicken mothers and the sexual ratio of the hatching chicks. A field experiment located at the Poultry Research Station, Livestock Department, Agricultural Research Department, Ministry of Agriculture for the period from 16 of September 2018 to 25 of December 2018. One hundred and forty birds of Iraqi local chicken mothers (100 females+ 40 males) at the age of 28 weeks were provided from the poultry research station. The birds were raised in individual cages and distributed sequentially to the cages after the numbering of the females. Data were recorded in three periods, each period was of 28 days, and then the general a

The letters are exposed in some texts of the classical Arabic language (poetry or prose), or in some of the Qur’anic texts, which are the main sources that were adopted on the day when provisions, rules and linguistic controls were established. I say that some of these letters are exposed in some contexts to deletion, mention, or change in the structure and shape of the letter. As for the omission, it is one of the aspects that distinguished Arabic, as well as other languages, for many purposes that differ among their user.

The aim of this study was to know the inhibition activity of squeezed grape waste extract on Bacillus stearpthermophilus by using three different tempretures degree 40, 60 and 80c, in order to reduce the time exposure of food for preservation. This study include two branchs: First: isolation and identification of Bacillus stearothermophilus from soil, 5 sample were collected from the soil of the college agriculture/Baghdad university. Samples were cultured on nutrient agar, microscopic and culturing tests were conducted and many biochemical tests were done. The isolates were cultivated at 55 c and 65 c for differentiate it from Bacillus coagulans which is can^'t grow at 65 c^o. The c

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

In this work, the effect of variation of semi-angle of the conical part on the vibration characteristics of cylindrical-conical coupled structure is investigated. The shell is made of polyester resin reinforced by continuous E-glass fibers. The case is analyzed experimentally and numerically for orthotropic shell structures. The experimental program is conducted by exciting the fabricated structure by an impact hammer and monitoring the response using an attached accelerometer for different semi-angles of the conical part.
Software named SIGVIEW is used to perform the signal processing on the acquired signal in order to measure the natural frequencies and the corresponding mode shapes. The numerical investigation is achieved using ANS

Leishmania is auxotroph to folic acid,antifolates drug inhibit the synthesis and conversion of folate derivatives. In this study, cytotoxic effect of methotrexate was investigated on the procyclic promastigotes proliferation of L. donovani. The results showed a significant (p ≥ 0.05) difference in growth of treated groups at high concentrations (1000, 500, 250, 125.5) μM after 24, 48 hrs., while at 72 hrs. significant difference was observed at all concentration. The IC50 values was measurable after 24, 48 and 72 hrs. and it was 174.238, 52.283 and 109.175 μM, respectively. The present study showed the cytotoxic effect of methotrexate on the proliferation of promastigotes of the visceral type of Leishmania.

Laser beam has been widely used to improve the mechanical properties of the metals. It used for cutting, drilling, hardening, welding……etc. The use of Laser beam has many features in accuracy and speeding in work, also in the treatment of metals locally, and in the places that is hard to reach by traditional ways. In this research a surface treatment was done to medium carbon steel (0.4%C) which is common kind of steel that is used in industry. Pulsing Neodymium -YAG Laser has been used and 1.06 micrometer wave length and 5 msec and the distance is about 30 centimeter between the exit area of the Laser beam from the system and the piece that treated . We are going to check the fatigue resistance for samples that is